Paper code basis

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cvoelcker 2025-07-15 19:05:07 -04:00
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outputs/
wandb/
logs/
uv.lock
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type: brax
name:
max_episode_steps: 1000
reward_scaling: 0.1
terminate: true
vmin: 0
vmax: 150

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type: brax
name:
max_episode_steps: 1000
reward_scaling: 0.1
terminate: true
vmin: 0
vmax: 200

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type: isaaclab
name:
action_bounds: [-1, 1]

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type: maniskill
name:
reconfiguration_freq: 1
partial_reset: true
asymmetric_obs: false
max_episode_steps: 50
stochastic_eval: true
has_final_obs: true
env_kwargs:
obs_mode: state
render_mode: rgb_array
sim_backend: physx_cuda
vmin: -15
vmax: 15

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type: mjx
name:
max_episode_steps: 1000
reward_scaling: 1.0
terminate: false
asymmetric_observation: false
vmin: 0
vmax: 150

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type: mjx
name:
max_episode_steps: 1000
reward_scaling: 1.0
terminate: false
push_distractions: false
asymmetric_observation: true
vmin: -10
vmax: 10

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lmbda: 0.95
num_epochs: 4
aux_loss_mult: 1.0

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num_envs: 1024
num_steps: 128
num_mini_batches: 64
num_epochs: 8
kl_bound: 0.1

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num_envs: 1024
num_steps: 64
num_mini_batches: 32
num_epochs: 8
kl_bound: 0.1

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num_envs: 1024
num_steps: 32
num_mini_batches: 16
num_epochs: 8
kl_bound: 0.1

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gamma: 0.97
critic_hidden_dim: 1024
num_envs: 1024
num_steps: 128
num_mini_batches: 16
num_epochs: 8
kl_bound: 0.1

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gamma: 0.97
critic_hidden_dim: 1024
num_envs: 1024
num_steps: 32
num_mini_batches: 4
num_epochs: 8
kl_bound: 0.1

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amp_enabled: false
amp_device: "cuda"
cuda: true
amp_dtype: f32
torch_deterministic: false
device_rank: 0
compile: true

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config/ppo.yaml Normal file
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defaults:
- env: brax
- experiment_overrides: default
- trial_spec: default
- _self_
hyperparameters:
lr: 3e-4
gamma: 0.99
lmbda: 0.95
clip_ratio: 0.2
value_coef: 0.5
entropy_coef: 0.0
total_time_steps: 50_000_000
num_steps: 64
num_mini_batches: 32
num_envs: 2048
num_epochs: 16
max_grad_norm: 0.5
normalize_advantages: True
normalize_env: True
anneal_lr: False
num_eval: 20
max_episode_steps: 1000
name: "ppo"
tags: ["ppo_baseline_retuned"]
seed: 0
num_seeds: 1
tune: false
checkpoint_dir: null
trials: 8
wandb:
mode: "online" # set to online to activate wandb
entity: "viper_svg"
project: "online_sac"

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defaults:
- env: brax
- experiment_overrides: default
- trial_spec: default
- platform: torch
- _self_
hyperparameters:
# env and run settings (mostly don't touch)
total_time_steps: 50_000_000
normalize_env: true
max_episode_steps: 1000
eval_interval: 2
num_eval: 20
# optimization settings (seem very stable)
lr: 3e-4
anneal_lr: false
max_grad_norm: 0.5
polyak: 1.0 # maybe ablate ?
# problem discount settings (need tuning)
gamma: 0.99
lmbda: 0.95
lmbda_min: 0.50 # irrelevant if no exploration noise is added
# batch settings (need tuning for MJX humanoid)
num_steps: 128
num_mini_batches: 128
num_envs: 1024
num_epochs: 4
# exploration settings (currently not touched)
exploration_noise_max: 1.0
exploration_noise_min: 1.0
exploration_base_envs: 0
# critic architecture settings (need to be increased for MJX humanoid)
critic_hidden_dim: 512
actor_hidden_dim: 512
vmin: ${env.vmin}
vmax: ${env.vmax}
num_bins: 151
hl_gauss: true
use_critic_norm: true
num_critic_encoder_layers: 2
num_critic_head_layers: 2
num_critic_pred_layers: 2
use_simplical_embedding: False
# actor architecture settings (seem stable)
use_actor_norm: true
num_actor_layers: 3
actor_min_std: 0.0
# actor & critic loss settings (seem remarkably stable)
## kl settings
kl_start: 0.01
kl_bound: 0.1 # switched to tighter bounds for MJX
reduce_kl: true
reverse_kl: false # previous default "false"
update_kl_lagrangian: true
actor_kl_clip_mode: "clipped" # "full", "clipped", "kl_relu_clipped", "kl_bound_clipped", "value"
## entropy settings
ent_start: 0.01
ent_target_mult: 0.5
update_entropy_lagrangian: true
## auxiliary loss settings
aux_loss_mult: 1.0
measure_burnin: 3
name: "sac"
seed: 0
num_seeds: 1
tune: false
checkpoint_dir: null
num_trials: 10
tags: ["experimental"]
wandb:
mode: "online" # set to online to activate wandb
entity: "viper_svg"
project: "online_sac"
hydra:
job:
chdir: True

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pyproject.toml Normal file
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[project]
name = "Relative Entropy Pathwise Policy Optimization"
version = "0.1.0"
description = "Code release for the REPPO paper"
readme = "README.md"
requires-python = ">=3.12"
dependencies = [
"black>=25.1.0",
"brax>=0.12.1",
"distrax>=0.1.5",
"flax>=0.10.3",
"gymnax>=0.0.8",
"hydra-core>=1.3.2",
"hydra-submitit-launcher>=1.2.0",
"jax-tqdm>=0.3.1",
"jax[cuda12]==0.5.3 ; sys_platform == 'linux'",
"jax==0.5.3 ; sys_platform == 'darwin'",
"mani-skill>=3.0.0b21",
"matplotlib>=3.10.0",
"optax>=0.2.4",
"optuna-integration>=4.3.0",
"optuna>=4.3.0",
"playground",
"plotly>=6.0.1",
"rliable>=1.2.0",
"tensordict>=0.8.3",
"torch>=2.7.1",
"tyro>=0.9.25",
"sapien>=3.0.0b1",
"wandb>=0.20.1",
"torchinfo>=1.8.0",
"debugpy>=1.8.14",
"notebook>=7.4.4",
"inflection>=0.5.1",
"scalene>=1.5.51",
"torchinfo>=1.8.0",
"debugpy>=1.8.14",
]
[build-system]
requires = ["hatchling"]
build-backend = "hatchling.build"
[tool.hatch.build.targets.wheel]
packages = ["onpolicy_sac"]
[tool.ruff]
# Exclude a variety of commonly ignored directories.
exclude = [
".eggs",
".git",
".git-rewrite",
".hg",
".ipynb_checkpoints",
".mypy_cache",
".nox",
".pants.d",
".pyenv",
".pytest_cache",
".pytype",
".ruff_cache",
".svn",
".tox",
".venv",
".vscode",
"__pypackages__",
"_build",
"buck-out",
"build",
"dist",
"node_modules",
"site-packages",
"outputs",
"multirun",
"wandb"
]
# Same as Black.
line-length = 88
indent-width = 4
# Assume Python 3.13
target-version = "py313"
[tool.ruff.lint]
# Enable Pyflakes (`F`) and a subset of the pycodestyle (`E`) codes by default.
# Unlike Flake8, Ruff doesn't enable pycodestyle warnings (`W`) or
# McCabe complexity (`C901`) by default.
select = ["E4", "E7", "E9", "F"]
# ignores not assigning lambda rule for jax compatibility
ignore = ["E731"]
# Allow fix for all enabled rules (when `--fix`) is provided.
fixable = ["ALL"]
unfixable = []
# Allow unused variables when underscore-prefixed.
dummy-variable-rgx = "^(_+|(_+[a-zA-Z0-9_]*[a-zA-Z0-9]+?))$"
[tool.ruff.format]
# Like Black, use double quotes for strings.
quote-style = "double"
# Like Black, indent with spaces, rather than tabs.
indent-style = "space"
# Like Black, respect magic trailing commas.
skip-magic-trailing-comma = false
# Like Black, automatically detect the appropriate line ending.
line-ending = "auto"
# Enable auto-formatting of code examples in docstrings. Markdown,
# reStructuredText code/literal blocks and doctests are all supported.
#
# This is currently disabled by default, but it is planned for this
# to be opt-out in the future.
docstring-code-format = false
# Set the line length limit used when formatting code snippets in
# docstrings.
#
# This only has an effect when the `docstring-code-format` setting is
# enabled.
docstring-code-line-length = "dynamic"
[tool.uv.sources]
playground = { git = "https://github.com/younggyoseo/mujoco_playground" }

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from functools import partial
from typing import Any, Tuple, Union
import chex
import gymnax
import jax
import jax.numpy as jnp
from brax import envs
from brax.envs.wrappers.training import AutoResetWrapper, EpisodeWrapper
from flax import struct
from gymnax.environments import environment, spaces
from gymnax.environments.environment import Environment
from gymnax.environments.spaces import Box
from ml_collections import ConfigDict
from mujoco_playground import MjxEnv, registry
from mujoco_playground._src.wrapper import wrap_for_brax_training, Wrapper
class MjxGymnaxWrapper(Environment):
def __init__(
self,
env_or_name: str | MjxEnv,
episode_length: int = 1000,
action_repeat: int = 1,
reward_scale: float = 1.0,
push_distractions: bool = False,
config: dict = None,
asymmetric_observation: bool = False,
):
if isinstance(env_or_name, str):
if config is None:
config = registry.get_default_config(env_or_name)
is_humanoid_task = env_or_name in [
"G1JoystickRoughTerrain",
"G1JoystickFlatTerrain",
"T1JoystickRoughTerrain",
"T1JoystickFlatTerrain",
]
if is_humanoid_task:
config.push_config.enable = push_distractions
else:
config = ConfigDict(config)
env = registry.load(env_or_name, config=config)
if episode_length is not None:
env = wrap_for_brax_training(
env, episode_length=episode_length, action_repeat=action_repeat
)
self.env = env
else:
self.env = env_or_name
self.reward_scale = reward_scale
if isinstance(self.env.observation_size, int):
self.dict_obs = False
else:
self.dict_obs = True
if asymmetric_observation:
self.dict_obs_key = "privileged_state"
else:
self.dict_obs_key = "state"
print(self.dict_obs_key)
super().__init__()
def action_space(self, params):
return gymnax.environments.spaces.Box(
low=-1.0,
high=1.0,
shape=(self.env.action_size,),
)
def observation_space(self, params):
if self.dict_obs:
return Box(
low=-float("inf"),
high=float("inf"),
shape=self.env.observation_size["state"],
), Box(
low=-float("inf"),
high=float("inf"),
shape=self.env.observation_size[self.dict_obs_key],
)
else:
return Box(
low=-float("inf"),
high=float("inf"),
shape=(self.env.observation_size,),
), Box(
low=-float("inf"),
high=float("inf"),
shape=(self.env.observation_size,),
)
@property
def default_params(self) -> gymnax.EnvParams:
return gymnax.EnvParams()
def reset(self, key):
state = self.env.reset(key)
# state.info["truncation"] = 0.0
obs = state.obs if not self.dict_obs else state.obs["state"]
critic_obs = state.obs if not self.dict_obs else state.obs[self.dict_obs_key]
return obs, critic_obs, state
def step(self, key, state, action):
# action = jnp.nan_to_num(action, 0.0)
state = self.env.step(state, action)
obs = state.obs if not self.dict_obs else state.obs["state"]
critic_obs = state.obs if not self.dict_obs else state.obs[self.dict_obs_key]
return (
obs,
critic_obs,
state,
state.reward * self.reward_scale,
state.done > 0.5,
{},
)
@struct.dataclass
class LogEnvState:
env_state: environment.EnvState
episode_returns: jnp.ndarray
episode_lengths: jnp.ndarray
returned_episode_returns: jnp.ndarray
returned_episode_lengths: jnp.ndarray
timestep: jnp.ndarray
truncated: jnp.ndarray
info: Any = None
def unwrapped(self):
return self.env_state
def set_env_state(self, env_state):
return self.replace(env_state=env_state)
class LogWrapper(Wrapper):
"""Log the episode returns and lengths."""
def __init__(self, env: environment.Environment, num_envs: int):
super().__init__(env)
self.num_envs = num_envs
@partial(jax.jit, static_argnums=(0,))
def reset(self, key) -> Tuple[chex.Array, environment.EnvState]:
obs, critic_obs, env_state = self.env.reset(key)
state = LogEnvState(
env_state=env_state,
episode_returns=jnp.zeros((self.num_envs,)),
episode_lengths=jnp.zeros((self.num_envs,), dtype=jnp.int32),
returned_episode_returns=jnp.zeros((self.num_envs,)),
returned_episode_lengths=jnp.zeros((self.num_envs,), dtype=jnp.int32),
timestep=jnp.zeros((self.num_envs,), dtype=jnp.int32),
truncated=jnp.ones((self.num_envs,), dtype=jnp.float32),
info={
"returned_episode": jnp.zeros((self.num_envs,), dtype=jnp.bool_),
"returned_episode_returns": jnp.zeros((self.num_envs,)),
"timestep": jnp.zeros((self.num_envs,), dtype=jnp.int32),
"returned_episode_lengths": jnp.zeros(
(self.num_envs,), dtype=jnp.int32
),
},
)
return obs, critic_obs, state
@partial(jax.jit, static_argnums=(0,))
def step(
self,
key: chex.PRNGKey,
state: environment.EnvState,
action: Union[int, float],
) -> Tuple[chex.Array, environment.EnvState, float, bool, dict]:
obs, critic_obs, env_state, reward, done, info = self.env.step(
key, state.env_state, action
)
new_episode_return = state.episode_returns + reward
new_episode_length = state.episode_lengths + 1
info["returned_episode_returns"] = (
state.returned_episode_returns * (1 - done) + new_episode_return * done
)
info["returned_episode_lengths"] = (
state.returned_episode_lengths * (1 - done) + new_episode_length * done
)
info["timestep"] = state.timestep
info["returned_episode"] = done
state = LogEnvState(
env_state=env_state,
episode_returns=new_episode_return * (1 - done),
episode_lengths=new_episode_length * (1 - done),
returned_episode_returns=state.returned_episode_returns * (1 - done)
+ new_episode_return * done,
returned_episode_lengths=state.returned_episode_lengths * (1 - done)
+ new_episode_length * done,
timestep=state.timestep + 1,
truncated=env_state.info["truncation"],
info=info,
)
return obs, critic_obs, state, reward, done, info
class BraxGymnaxWrapper:
def __init__(
self,
env_name,
backend="generalized",
episode_length=1000,
reward_scaling=1.0,
terminate=True,
):
env = envs.get_environment(
env_name=env_name, backend=backend, terminate_when_unhealthy=terminate
)
env = EpisodeWrapper(env, episode_length=episode_length, action_repeat=1)
env = AutoResetWrapper(env)
self.env = env
self.action_size = self.env.action_size
self.observation_size = (self.env.observation_size,)
self.default_params = ()
self.reward_scaling = reward_scaling
def reset(self, key):
state = self.env.reset(key)
return state.obs, state
def step(self, key, state, action):
next_state = self.env.step(state, action)
return (
next_state.obs,
next_state.obs,
next_state,
next_state.reward * self.reward_scaling,
next_state.done > 0.5,
{},
)
def observation_space(self):
return spaces.Box(
low=-jnp.inf,
high=jnp.inf,
shape=(self.env.observation_size,),
), spaces.Box(
low=-jnp.inf,
high=jnp.inf,
shape=(self.env.observation_size,),
)
def action_space(self):
return spaces.Box(
low=-1.0,
high=1.0,
shape=(self.env.action_size,),
)
class ClipAction(Wrapper):
def __init__(self, env, low=-0.999, high=0.999):
super().__init__(env)
self.low = low
self.high = high
def step(self, key, state, action):
"""TODO: In theory the below line should be the way to do this."""
# action = jnp.clip(action, self.env.action_space.low, self.env.action_space.high)
action = jnp.clip(action, self.low, self.high)
return self.env.step(key, state, action)
@struct.dataclass
class NormalizeVecObsEnvState:
mean: jnp.ndarray
var: jnp.ndarray
critic_mean: jnp.ndarray
critic_var: jnp.ndarray
count: float
env_state: environment.EnvState
truncated: float
info: Any = None
def unwrapped(self):
return self.env_state.unwrapped()
def set_env_state(self, env_state):
return self.replace(env_state=self.env_state.set_env_state(env_state))
class NormalizeVec(Wrapper):
def __init__(self, env):
super().__init__(env)
def _init_state(self, key):
obs, critic_obs, env_state = self.env.reset(key)
return NormalizeVecObsEnvState(
mean=jnp.mean(obs, axis=0),
var=jnp.var(obs, axis=0),
critic_mean=jnp.mean(critic_obs, axis=0),
critic_var=jnp.var(critic_obs, axis=0),
count=obs.shape[0],
env_state=env_state,
)
def _compute_stats(self, mean, var, count, obs):
batch_mean = jnp.mean(obs, axis=0)
batch_var = jnp.var(obs, axis=0)
batch_count = obs.shape[0]
delta = batch_mean - mean
tot_count = count + batch_count
new_mean = mean + delta * batch_count / tot_count
m_a = var * count
m_b = batch_var * batch_count
M2 = m_a + m_b + jnp.square(delta) * count * batch_count / tot_count
new_var = M2 / tot_count
return new_mean, new_var
def reset(self, key, params=None):
obs, critic_obs, env_state = self.env.reset(key)
if params is not None:
mean = params.mean
var = params.var
critic_mean = params.critic_mean
critic_var = params.critic_var
count = params.count
else:
mean = jnp.mean(obs, axis=0)
var = jnp.var(obs, axis=0)
critic_mean = jnp.mean(critic_obs, axis=0)
critic_var = jnp.var(critic_obs, axis=0)
count = obs.shape[0]
state = NormalizeVecObsEnvState(
mean=mean,
var=var,
critic_mean=critic_mean,
critic_var=critic_var,
count=count,
env_state=env_state,
truncated=env_state.truncated,
info=env_state.info,
)
return (
(obs - state.mean) / jnp.sqrt(state.var + 1e-2),
(critic_obs - state.critic_mean) / jnp.sqrt(state.critic_var + 1e-2),
state,
)
def step(self, key, state, action):
obs, critic_obs, env_state, reward, done, info = self.env.step(
key, state.env_state, action
)
new_mean, new_var = self._compute_stats(state.mean, state.var, state.count, obs)
new_critic_mean, new_critic_var = self._compute_stats(
state.critic_mean, state.critic_var, state.count, critic_obs
)
new_count = state.count + obs.shape[0]
state = NormalizeVecObsEnvState(
mean=new_mean,
var=new_var,
critic_mean=new_critic_mean,
critic_var=new_critic_var,
count=new_count,
env_state=env_state,
truncated=env_state.truncated,
info=env_state.info,
)
return (
(obs - state.mean) / jnp.sqrt(state.var + 1e-2),
(critic_obs - state.critic_mean) / jnp.sqrt(state.critic_var + 1e-2),
state,
reward,
done,
info,
)

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from __future__ import annotations
import gymnasium as gym
import numpy as np
import torch
from gymnasium.wrappers import TimeLimit
from loguru import logger as log
from stable_baselines3.common.vec_env import SubprocVecEnv
# Disable all logging below CRITICAL level
log.remove()
log.add(lambda msg: False, level="CRITICAL")
def make_env(env_name, rank, render_mode=None, seed=0):
"""
Utility function for multiprocessed env.
:param rank: (int) index of the subprocess
:param seed: (int) the inital seed for RNG
"""
if env_name in [
"h1hand-push-v0",
"h1-push-v0",
"h1hand-cube-v0",
"h1cube-v0",
"h1hand-basketball-v0",
"h1-basketball-v0",
"h1hand-kitchen-v0",
"h1-kitchen-v0",
]:
max_episode_steps = 500
else:
max_episode_steps = 1000
def _init():
env = gym.make(env_name, render_mode=render_mode)
env = TimeLimit(env, max_episode_steps=max_episode_steps)
env.unwrapped.seed(seed + rank)
return env
return _init
class HumanoidBenchEnv:
"""Wraps HumanoidBench environment to support parallel environments."""
def __init__(self, env_name, num_envs=1, render_mode=None, device=None):
# NOTE: HumanoidBench action space is already normalized to [-1, 1]
device = device or torch.device("cuda" if torch.cuda.is_available() else "cpu")
self.sim_device = device
self.num_envs = num_envs
# Create the base environment
self.envs = SubprocVecEnv(
[make_env(env_name, i, render_mode=render_mode) for i in range(num_envs)]
)
if env_name in [
"h1hand-push-v0",
"h1-push-v0",
"h1hand-cube-v0",
"h1cube-v0",
"h1hand-basketball-v0",
"h1-basketball-v0",
"h1hand-kitchen-v0",
"h1-kitchen-v0",
]:
self.max_episode_steps = 500
else:
self.max_episode_steps = 1000
# For compatibility with MuJoCo Playground
self.asymmetric_obs = False # For comptatibility with MuJoCo Playground
self.num_obs = self.envs.observation_space.shape[-1]
self.num_actions = self.envs.action_space.shape[-1]
def reset(self):
"""Reset the environment."""
observations = self.envs.reset()
observations = torch.from_numpy(observations).to(
device=self.sim_device, dtype=torch.float
)
return observations
def render(self):
assert self.num_envs == 1, (
"Currently only supports single environment rendering"
)
return self.envs.render()
def step(self, actions):
assert isinstance(actions, torch.Tensor)
actions = actions.cpu().numpy()
observations, rewards, dones, raw_infos = self.envs.step(actions)
# This will be used for getting 'true' next observations
infos = dict()
infos["observations"] = {"raw": {"obs": observations.copy()}}
truncateds = np.zeros_like(dones)
for i in range(self.num_envs):
if raw_infos[i].get("TimeLimit.truncated", False):
truncateds[i] = True
infos["observations"]["raw"]["obs"][i] = raw_infos[i][
"terminal_observation"
]
observations = torch.from_numpy(observations).to(
device=self.sim_device, dtype=torch.float
)
rewards = torch.from_numpy(rewards).to(
device=self.sim_device, dtype=torch.float
)
dones = torch.from_numpy(dones).to(device=self.sim_device)
truncateds = torch.from_numpy(truncateds).to(device=self.sim_device)
infos["observations"]["raw"]["obs"] = torch.from_numpy(
infos["observations"]["raw"]["obs"]
).to(device=self.sim_device, dtype=torch.float)
infos["time_outs"] = truncateds
return observations, rewards, dones, infos

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from typing import Optional
import gymnasium as gym
import torch
from isaaclab.app import AppLauncher
app_launcher = AppLauncher(headless=True)
simulation_app = app_launcher.app
from isaaclab_tasks.utils.parse_cfg import parse_env_cfg
class IsaacLabEnv:
"""Wrapper for IsaacLab environments to be compatible with MuJoCo Playground"""
def __init__(
self,
task_name: str,
device: str,
num_envs: int,
seed: int,
action_bounds: Optional[float] = None,
):
env_cfg = parse_env_cfg(
task_name,
device=device,
num_envs=num_envs,
)
env_cfg.seed = seed
self.seed = seed
self.envs = gym.make(task_name, cfg=env_cfg, render_mode=None)
self.num_envs = self.envs.unwrapped.num_envs
self.max_episode_steps = self.envs.unwrapped.max_episode_length
self.action_bounds = action_bounds
self.num_obs = self.envs.unwrapped.single_observation_space["policy"].shape[0]
self.asymmetric_obs = "critic" in self.envs.unwrapped.single_observation_space
if self.asymmetric_obs:
self.num_privileged_obs = self.envs.unwrapped.single_observation_space[
"critic"
].shape[0]
else:
self.num_privileged_obs = 0
self.num_actions = self.envs.unwrapped.single_action_space.shape[0]
def reset(self, random_start_init: bool = True) -> torch.Tensor:
obs_dict, _ = self.envs.reset()
# NOTE: decorrelate episode horizons like RSLRL
if random_start_init:
self.envs.unwrapped.episode_length_buf = torch.randint_like(
self.envs.unwrapped.episode_length_buf, high=int(self.max_episode_steps)
)
return obs_dict["policy"]
def reset_with_critic_obs(self) -> tuple[torch.Tensor, torch.Tensor]:
obs_dict, _ = self.envs.reset()
return obs_dict["policy"], obs_dict["critic"]
def step(
self, actions: torch.Tensor
) -> tuple[torch.Tensor, torch.Tensor, torch.Tensor, dict]:
if self.action_bounds is not None:
actions = torch.clamp(actions, -1.0, 1.0) * self.action_bounds
obs_dict, rew, terminations, truncations, infos = self.envs.step(actions)
dones = (terminations | truncations).to(dtype=torch.long)
obs = obs_dict["policy"]
critic_obs = obs_dict["critic"] if self.asymmetric_obs else None
info_ret = {"time_outs": truncations, "observations": {"critic": critic_obs}}
# NOTE: There's really no way to get the raw observations from IsaacLab
# We just use the 'reset_obs' as next_obs, unfortunately.
# See https://github.com/isaac-sim/IsaacLab/issues/1362
info_ret["observations"]["raw"] = {
"obs": obs,
"critic_obs": critic_obs,
}
return obs, rew, dones, info_ret
def render(self):
raise NotImplementedError(
"We don't support rendering for IsaacLab environments"
)

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from gymnasium import Wrapper
import torch
class ManiSkillWrapper(Wrapper):
"""
A wrapper for ManiSkill environments to ensure compatibility with the expected API.
This wrapper is used to handle the ManiSkill environments in a way that is consistent
with the other environments in the codebase.
"""
def __init__(self, env, max_episode_steps: int, partial_reset, device: str):
super().__init__(env)
self.action_space = env.action_space
self.observation_space = env.observation_space
self.metadata = env.metadata
self.asymmetric_obs = False
self.max_episode_steps = max_episode_steps
self.partial_reset = partial_reset
self.returns = torch.zeros(env.num_envs, dtype=torch.float32, device=device)
self.episode_len = torch.zeros(env.num_envs, dtype=torch.float32, device=device)
self.success = torch.zeros(env.num_envs, dtype=torch.float32, device=device)
@property
def unwrapped(self):
"""
Returns the underlying environment.
"""
return self.env
@property
def num_actions(self):
"""
Returns the number of actions in the action space.
"""
return self.action_space.shape[1]
@property
def num_obs(self):
"""
Returns the number of observations in the observation space.
"""
return self.observation_space.shape[1]
def reset(self, seed=None, options=dict()):
"""
Resets the environment and returns the initial observation.
"""
return self.env.reset(seed=seed, options=options)
def step(self, action):
"""
Takes a step in the environment with the given action.
Returns the next observation, reward, done, and info.
"""
obs, reward, terminated, truncated, info = self.env.step(action)
if "final_info" in info:
self.returns = (
info["final_info"]["episode"]["return"] * info["_final_info"].float()
+ (1.0 - info["_final_info"].float()) * self.returns
)
self.episode_len = (
info["final_info"]["episode"]["episode_len"]
* info["_final_info"].float()
+ (1.0 - info["_final_info"].float()) * self.episode_len
)
self.success = (
info["final_info"]["episode"]["success_once"]
* info["_final_info"].float()
+ (1.0 - info["_final_info"].float()) * self.success
)
info["log_info"] = {
"return": self.returns,
"episode_len": self.episode_len,
"success": self.success,
}
if self.partial_reset:
# maniskill continues bootstrap on terminated, which playground does on truncated.
# This unifies the interfaces in a very hacky way
done = torch.zeros_like(
terminated, dtype=torch.bool, device=terminated.device
)
truncated = torch.logical_or(terminated, truncated)
else:
done = torch.logical_or(terminated, truncated)
truncated = torch.zeros_like(done, dtype=torch.bool, device=done.device)
return obs, reward, done, truncated, info

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from __future__ import annotations
import isaacgymenvs
import torch
from omegaconf import OmegaConf
class MTBenchEnv:
def __init__(
self,
task_name: str,
device_id: int,
num_envs: int,
seed: int,
):
# NOTE: Currently, we only support Meta-World-v2 MT-10/MT-50 in MTBench
task_config = MTBENCH_MW2_CONFIG.copy()
if task_name == "meta-world-v2-mt10":
# MT-10 Setup
assert num_envs == 4096, "MT-10 only supports 4096 environments (for now)"
self.num_tasks = 10
task_config["env"]["tasks"] = [4, 16, 17, 18, 28, 31, 38, 40, 48, 49]
task_config["env"]["taskEnvCount"] = [410] * 6 + [409] * 4
elif task_name == "meta-world-v2-mt50":
# MT-50 Setup
self.num_tasks = 50
assert num_envs == 8192, "MT-50 only supports 8192 environments (for now)"
task_config["env"]["tasks"] = list(range(50))
task_config["env"]["taskEnvCount"] = [164] * 42 + [163] * 8 # 6888 + 1304
else:
raise ValueError(f"Unsupported task name: {task_name}")
task_config["env"]["numEnvs"] = num_envs
task_config["env"]["numObservations"] = 39 + self.num_tasks
task_config["env"]["seed"] = seed
# Convert dictionary to OmegaConf object
env_cfg = {"task": task_config}
env_cfg = OmegaConf.create(env_cfg)
self.env = isaacgymenvs.make(
task=env_cfg.task.name,
num_envs=num_envs,
sim_device=f"cuda:{device_id}",
rl_device=f"cuda:{device_id}",
seed=seed,
headless=True,
cfg=env_cfg,
)
self.num_envs = num_envs
self.asymmetric_obs = False
self.num_obs = self.env.observation_space.shape[0]
assert self.num_obs == 39 + self.num_tasks, (
"MTBench observation space is 39 + num_tasks (one-hot vector)"
)
self.num_privileged_obs = 0
self.num_actions = self.env.action_space.shape[0]
self.max_episode_steps = self.env.max_episode_length
def reset(self) -> torch.Tensor:
"""Reset the environment."""
# TODO: Check if we need no_grad and detach here
with torch.no_grad(): # do we need this?
self.env.reset_idx(torch.arange(self.num_envs, device=self.env.device))
self.env.cumulatives["rewards"][:] = 0
self.env.cumulatives["success"][:] = 0
obs_dict = self.env.reset()
return obs_dict["obs"].detach()
def step(
self, actions: torch.Tensor
) -> tuple[torch.Tensor, torch.Tensor, torch.Tensor, dict]:
"""Step the environment."""
assert isinstance(actions, torch.Tensor)
# TODO: Check if we need no_grad and detach here
with torch.no_grad():
obs_dict, rew, dones, infos = self.env.step(actions.detach())
truncations = infos["time_outs"]
info_ret = {"time_outs": truncations.detach()}
if "episode" in infos:
info_ret["episode"] = infos["episode"]
# NOTE: There's really no way to get the raw observations from IsaacGym
# We just use the 'reset_obs' as next_obs, unfortunately.
info_ret["observations"] = {"raw": {"obs": obs_dict["obs"].detach()}}
return obs_dict["obs"].detach(), rew.detach(), dones.detach(), info_ret
def render(self):
raise NotImplementedError(
"We don't support rendering for IsaacLab environments"
)
MTBENCH_MW2_CONFIG = {
"name": "meta-world-v2",
"physics_engine": "physx",
"env": {
"numEnvs": 1,
"envSpacing": 1.5,
"episodeLength": 150,
"enableDebugVis": False,
"clipObservations": 5.0,
"clipActions": 1.0,
"aggregateMode": 3,
"actionScale": 0.01,
"resetNoise": 0.15,
"tasks": [0],
"taskEnvCount": [4096],
"init_at_random_progress": True,
"exemptedInitAtRandomProgressTasks": [],
"taskEmbedding": True,
"taskEmbeddingType": "one_hot",
"seed": 42,
"cameraRenderingInterval": 5000,
"cameraWidth": 1024,
"cameraHeight": 1024,
"sparse_reward": False,
"termination_on_success": False,
"reward_scale": 1.0,
"fixed": False,
"numObservations": None,
"numActions": 4,
},
"enableCameraSensors": False,
"sim": {
"dt": 0.01667,
"substeps": 2,
"up_axis": "z",
"use_gpu_pipeline": True,
"gravity": [0.0, 0.0, -9.81],
"physx": {
"num_threads": 4,
"solver_type": 1,
"use_gpu": True,
"num_position_iterations": 8,
"num_velocity_iterations": 1,
"contact_offset": 0.005,
"rest_offset": 0.0,
"bounce_threshold_velocity": 0.2,
"max_depenetration_velocity": 1000.0,
"default_buffer_size_multiplier": 10.0,
"max_gpu_contact_pairs": 1048576,
"num_subscenes": 4,
"contact_collection": 0,
},
},
"task": {"randomize": False},
}

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import jax
from mujoco_playground import registry, wrapper_torch
import torch
jax.config.update("jax_compilation_cache_dir", "/tmp/jax_cache")
jax.config.update("jax_persistent_cache_min_entry_size_bytes", -1)
jax.config.update("jax_persistent_cache_min_compile_time_secs", 0)
class PlaygroundEvalEnvWrapper:
def __init__(self, eval_env, max_episode_steps, env_name, num_eval_envs, seed):
"""
Wrapper used for evaluation / rendering environments.
Note that this is different from training environments that are
wrapped with RSLRLBraxWrapper.
"""
self.env = eval_env
self.env_name = env_name
self.num_envs = num_eval_envs
self.jit_reset = jax.jit(jax.vmap(self.env.reset))
self.jit_step = jax.jit(jax.vmap(self.env.step))
if isinstance(self.env.unwrapped.observation_size, dict):
self.asymmetric_obs = True
else:
self.asymmetric_obs = False
self.key = jax.random.PRNGKey(seed)
self.key_reset = jax.random.split(self.key, num_eval_envs)
self.max_episode_steps = max_episode_steps
def reset(self):
self.state = self.jit_reset(self.key_reset)
if self.asymmetric_obs:
obs = wrapper_torch._jax_to_torch(self.state.obs["state"])
else:
obs = wrapper_torch._jax_to_torch(self.state.obs)
return obs
def step(self, actions):
self.state = self.jit_step(self.state, wrapper_torch._torch_to_jax(actions))
if self.asymmetric_obs:
next_obs = wrapper_torch._jax_to_torch(self.state.obs["state"])
else:
next_obs = wrapper_torch._jax_to_torch(self.state.obs)
rewards = wrapper_torch._jax_to_torch(self.state.reward)
dones = wrapper_torch._jax_to_torch(self.state.done)
return next_obs, rewards, dones, dones, None
class RandomizeInitialWrapper(wrapper_torch.RSLRLBraxWrapper):
"""
Wrapper to randomize the initial state of the environment.
This is useful for domain randomization experiments.
"""
def reset(self):
print("Resetting environment with randomization")
obs = super().reset()
self.env_state.info["steps"] = jax.random.randint(
self.key, self.env_state.info["steps"].shape, 0, 1000
).astype(jax.numpy.float32)
print(obs)
return obs
def reset_with_critic_obs(self):
print("Resetting environment with randomization and critic obs")
obs, critic_obs = super().reset_with_critic_obs()
self.env_state.info["steps"] = jax.random.randint(
self.key, self.env_state.info["steps"].shape, 0, 1000
).astype(jax.numpy.float32)
return obs, critic_obs
def step(self, action):
obs, reward, done, info = super().step(action)
return obs, reward, done, done, info
def make_env(
env_name,
seed,
num_envs,
num_eval_envs,
device_rank,
use_tuned_reward=False,
use_domain_randomization=False,
use_push_randomization=False,
):
# Make training environment
train_env_cfg = registry.get_default_config(env_name)
is_humanoid_task = env_name in [
"G1JoystickRoughTerrain",
"G1JoystickFlatTerrain",
"T1JoystickRoughTerrain",
"T1JoystickFlatTerrain",
]
if use_tuned_reward and is_humanoid_task:
# NOTE: Tuned reward for G1. Used for producing Figure 7 in the paper.
# Somehow it works reasonably for T1 as well.
# However, see `sim2real.md` for sim-to-real RL with Booster T1
train_env_cfg.reward_config.scales.energy = -5e-5
train_env_cfg.reward_config.scales.action_rate = -1e-1
train_env_cfg.reward_config.scales.torques = -1e-3
train_env_cfg.reward_config.scales.pose = -1.0
train_env_cfg.reward_config.scales.tracking_ang_vel = 1.25
train_env_cfg.reward_config.scales.tracking_lin_vel = 1.25
train_env_cfg.reward_config.scales.feet_phase = 1.0
train_env_cfg.reward_config.scales.ang_vel_xy = -0.3
train_env_cfg.reward_config.scales.orientation = -5.0
if is_humanoid_task and not use_push_randomization:
train_env_cfg.push_config.enable = False
train_env_cfg.push_config.magnitude_range = [0.0, 0.0]
randomizer = (
registry.get_domain_randomizer(env_name) if use_domain_randomization else None
)
raw_env = registry.load(env_name, config=train_env_cfg)
train_env = RandomizeInitialWrapper(
raw_env,
num_envs,
seed,
train_env_cfg.episode_length,
train_env_cfg.action_repeat,
randomization_fn=randomizer,
device_rank=device_rank,
)
# Make evaluation environment
eval_env_cfg = registry.get_default_config(env_name)
if is_humanoid_task and not use_push_randomization:
eval_env_cfg.push_config.enable = False
eval_env_cfg.push_config.magnitude_range = [0.0, 0.0]
eval_env = registry.load(env_name, config=eval_env_cfg)
eval_env = PlaygroundEvalEnvWrapper(
eval_env, eval_env_cfg.episode_length, env_name, num_eval_envs, seed
)
return train_env, eval_env

3
reppo/jaxrl/__init__.py Normal file
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import jax
jax.config.update("jax_default_matmul_precision", "highest")

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import functools
import flax.struct as struct
import jax
import jax.numpy as jnp
class NormalizationState(struct.PyTreeNode):
mean: struct.PyTreeNode
var: struct.PyTreeNode
count: int
class Normalizer:
@functools.partial(jax.jit, static_argnums=0)
def init(self, tree: struct.PyTreeNode) -> NormalizationState:
return NormalizationState(
mean=jax.tree.map(lambda x: jnp.zeros(x.shape[1:], dtype=x.dtype), tree),
var=jax.tree.map(lambda x: jnp.ones(x.shape[1:], dtype=x.dtype), tree),
count=0,
)
@functools.partial(jax.jit, static_argnums=0)
def update(
self, state: NormalizationState, tree: struct.PyTreeNode
) -> NormalizationState:
var = jax.tree.map(lambda x: jnp.var(x, axis=0), tree)
mean = jax.tree.map(lambda x: jnp.mean(x, axis=0), tree)
batch_size = jax.tree.reduce(lambda x, y: y.shape[0], tree, 0)
delta = mean - state.mean
count = state.count + batch_size
new_mean = state.mean + delta * batch_size / count
m_a = state.var * state.count
m_b = var * batch_size
M2 = m_a + m_b + jnp.square(delta) * state.count * batch_size / count
return state.replace(mean=new_mean, var=M2 / count, count=count)
@functools.partial(jax.jit, static_argnums=0)
def normalize(
self, state: NormalizationState, tree: struct.PyTreeNode
) -> struct.PyTreeNode:
return jax.tree.map(
lambda x, m, v: (x - m) / jnp.sqrt(v + 1e-8), tree, state.mean, state.var
)

758
reppo/jaxrl/ppo_mjx.py Normal file
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import logging
import math
import time
import typing
from typing import Callable, Optional
import distrax
import hydra
import jax
import optax
import plotly.graph_objs as go
from flax import nnx, struct
from flax.struct import PyTreeNode
from gymnax.environments.environment import Environment, EnvParams, EnvState
from jax import numpy as jnp
from jax.experimental import checkify
from jax.random import PRNGKey
from omegaconf import DictConfig, OmegaConf
import wandb
from reppo.env_utils.jax_wrappers import (
BraxGymnaxWrapper,
ClipAction,
LogWrapper,
MjxGymnaxWrapper,
)
from reppo.jaxrl import utils
from reppo.jaxrl.normalization import NormalizationState, Normalizer
logging.basicConfig(level=logging.INFO)
## INITIALIZE CLASS STRUCTURES (NETWORKS, STATES, ...)
class Policy(typing.Protocol):
def __call__(
self,
key: jax.random.PRNGKey,
obs: PyTreeNode,
state: Optional[PyTreeNode] = None,
) -> tuple[PyTreeNode, PyTreeNode]:
pass
class PPOConfig(struct.PyTreeNode):
lr: float
gamma: float
lmbda: float
clip_ratio: float
value_coef: float
entropy_coef: float
total_time_steps: int
num_steps: int
num_mini_batches: int
num_envs: int
num_epochs: int
max_grad_norm: float | None
normalize_advantages: bool
normalize_env: bool
anneal_lr: bool
num_eval: int = 25
max_episode_steps: int = 1000
class Transition(struct.PyTreeNode):
obs: jax.Array
critic_obs: jax.Array
action: jax.Array
reward: jax.Array
log_prob: jax.Array
value: jax.Array
done: jax.Array
truncated: jax.Array
info: dict[str, jax.Array]
class PPOTrainState(nnx.TrainState):
iteration: int
time_steps: int
last_env_state: EnvState
last_obs: jax.Array
last_critic_obs: jax.Array
normalization_state: NormalizationState | None = None
critic_normalization_state: NormalizationState | None = None
class PPONetworks(nnx.Module):
def __init__(
self,
obs_dim: int,
critic_obs_dim: int,
action_dim: int,
hidden_dim: int = 64,
*,
rngs: nnx.Rngs,
):
def linear_layer(in_features, out_features, scale=jnp.sqrt(2)):
return nnx.Linear(
in_features=in_features,
out_features=out_features,
kernel_init=nnx.initializers.orthogonal(scale=scale),
bias_init=nnx.initializers.zeros_init(),
rngs=rngs,
)
self.actor_module = nnx.Sequential(
linear_layer(obs_dim, hidden_dim),
nnx.tanh,
linear_layer(hidden_dim, hidden_dim),
nnx.tanh,
linear_layer(hidden_dim, action_dim, scale=0.01),
)
self.log_std = nnx.Param(jnp.zeros(action_dim))
self.critic_module = nnx.Sequential(
linear_layer(critic_obs_dim, hidden_dim),
nnx.tanh,
linear_layer(hidden_dim, hidden_dim),
nnx.tanh,
linear_layer(hidden_dim, 1, scale=1.0),
)
def critic(self, obs: jax.Array) -> jax.Array:
return self.critic_module(obs).squeeze()
def actor(self, obs: jax.Array) -> distrax.Distribution:
loc = self.actor_module(obs)
pi = distrax.MultivariateNormalDiag(
loc=loc, scale_diag=jnp.exp(self.log_std.value)
)
return pi
def make_policy(train_state: PPOTrainState) -> Policy:
normalizer = Normalizer()
def policy(
key: PRNGKey, obs: jax.Array, state: struct.PyTreeNode = None
) -> tuple[jax.Array, jax.Array]:
if train_state.normalization_state is not None:
obs = normalizer.normalize(train_state.normalization_state, obs)
model = nnx.merge(train_state.graphdef, train_state.params)
pi = model.actor(obs)
value = model.critic(obs)
action = pi.sample(seed=key)
log_prob = pi.log_prob(action)
return action, dict(log_prob=log_prob, value=value)
return policy
def make_eval_fn(
env: Environment, max_episode_steps: int
) -> Callable[[jax.random.PRNGKey, Policy], dict[str, float]]:
def evaluation_fn(key: jax.random.PRNGKey, policy: Policy):
def step_env(carry, _):
key, env_state, obs = carry
key, act_key, env_key = jax.random.split(key, 3)
action, _ = policy(act_key, obs)
env_key = jax.random.split(env_key, env.num_envs)
obs, _, env_state, reward, done, info = env.step(
env_key, env_state, action.clip(-1.0 + 1e-4, 1.0 - 1e-4)
)
return (key, env_state, obs), info
key, init_key = jax.random.split(key)
init_key = jax.random.split(init_key, env.num_envs)
obs, _, env_state = env.reset(init_key)
_, infos = jax.lax.scan(
f=step_env,
init=(key, env_state, obs),
xs=None,
length=max_episode_steps,
)
return {
"episode_return": infos["returned_episode_returns"].mean(
where=infos["returned_episode"]
),
"episode_return_std": infos["returned_episode_returns"].std(
where=infos["returned_episode"]
),
"episode_length": infos["returned_episode_lengths"].mean(
where=infos["returned_episode"]
),
"episode_length_std": infos["returned_episode_lengths"].std(
where=infos["returned_episode"]
),
"num_episodes": infos["returned_episode"].sum(),
}
return evaluation_fn
def make_init(
cfg: PPOConfig,
env: Environment,
env_params: EnvParams = None,
) -> PPOTrainState:
def init(key: jax.random.PRNGKey) -> PPOTrainState:
# Number of calls to train_step
num_train_steps = cfg.total_time_steps // (cfg.num_steps * cfg.num_envs)
# Number of calls to train_iter, add 1 if not divisible by eval_interval
eval_interval = int(
(cfg.total_time_steps / (cfg.num_steps * cfg.num_envs)) // cfg.num_eval
)
num_iterations = num_train_steps // eval_interval + int(
num_train_steps % eval_interval != 0
)
key, model_key = jax.random.split(key)
# Intialize the model
networks = PPONetworks(
obs_dim=env.observation_space(env_params)[0].shape[0],
critic_obs_dim=env.observation_space(env_params)[1].shape[0],
action_dim=env.action_space(env_params).shape[0],
rngs=nnx.Rngs(model_key),
)
# Set initial learning rate
if not cfg.anneal_lr:
lr = cfg.lr
else:
num_iterations = cfg.total_time_steps // cfg.num_steps // cfg.num_envs
num_updates = num_iterations * cfg.num_epochs * cfg.num_mini_batches
lr = optax.linear_schedule(cfg.lr, 1e-6, num_updates)
# Initialize the optimizer
if cfg.max_grad_norm is not None:
optimizer = optax.chain(
optax.clip_by_global_norm(cfg.max_grad_norm),
optax.adam(lr),
)
else:
optimizer = optax.adam(lr)
# Reset and fully initialize the environment
key, env_key = jax.random.split(key)
env_key = jax.random.split(env_key, cfg.num_envs)
obs, critic_obs, env_state = env.reset(env_key)
# randomize initial time step to prevent all envs stepping in tandem
_env_state = env_state.unwrapped()
key, randomize_steps_key = jax.random.split(key)
_env_state.info["steps"] = jax.random.randint(
randomize_steps_key,
_env_state.info["steps"].shape,
0,
cfg.max_episode_steps,
).astype(jnp.float32)
env_state.set_env_state(_env_state)
if cfg.normalize_env:
normalizer = Normalizer()
norm_state = normalizer.init(obs)
critic_normalizer = Normalizer()
critic_norm_state = critic_normalizer.init(critic_obs)
obs = normalizer.normalize(norm_state, obs)
critic_obs = critic_normalizer.normalize(critic_norm_state, critic_obs)
else:
norm_state = None
critic_norm_state = None
# Initialize the state observations of the environment
return PPOTrainState.create(
iteration=0,
time_steps=0,
graphdef=nnx.graphdef(networks),
params=nnx.state(networks),
tx=optimizer,
last_env_state=env_state,
last_obs=obs,
last_critic_obs=critic_obs,
normalization_state=norm_state,
critic_normalization_state=critic_norm_state,
)
return init
def make_train_fn(
cfg: PPOConfig,
env: Environment,
env_params: EnvParams = None,
log_callback: Callable[[PPOTrainState, dict[str, jax.Array]], None] = None,
num_seeds: int = 1,
):
# Initialize the environment and wrap it to admit vectorized behavior.
env_params = env_params or env.default_params
env = ClipAction(env)
env = LogWrapper(env, cfg.num_envs)
eval_fn = make_eval_fn(env, cfg.max_episode_steps)
normalizer = Normalizer()
eval_interval = int(
(cfg.total_time_steps / (cfg.num_steps * cfg.num_envs)) // cfg.num_eval
)
def collect_rollout(
key: PRNGKey, train_state: PPOTrainState
) -> tuple[Transition, PPOTrainState]:
model = nnx.merge(train_state.graphdef, train_state.params)
# Take a step in the environment
def step_env(carry, _) -> tuple[tuple, Transition]:
key, env_state, train_state, obs, critic_obs = carry
if cfg.normalize_env:
norm_state = normalizer.update(train_state.normalization_state, obs)
obs = normalizer.normalize(norm_state, obs)
train_state = train_state.replace(normalization_state=norm_state)
critic_obs = normalizer.normalize(
train_state.critic_normalization_state, critic_obs
)
# Select action
key, act_key, step_key = jax.random.split(key, 3)
pi = model.actor(obs)
action = pi.sample(seed=act_key)
# Take a step in the environment
step_key = jax.random.split(step_key, cfg.num_envs)
next_obs, next_critic_obs, next_env_state, reward, done, info = env.step(
step_key, env_state, action.clip(-1.0 + 1e-4, 1.0 - 1e-4)
)
# Record the transition
transition = Transition(
obs=obs,
critic_obs=critic_obs,
action=action,
reward=reward,
log_prob=pi.log_prob(action),
value=model.critic(critic_obs),
done=done,
truncated=next_env_state.truncated,
info=info,
)
return (
key,
next_env_state,
train_state,
next_obs,
next_critic_obs,
), transition
# Collect rollout via lax.scan taking steps in the environment
rollout_state, transitions = jax.lax.scan(
f=step_env,
init=(
key,
train_state.last_env_state,
train_state,
train_state.last_obs,
train_state.last_critic_obs,
),
length=cfg.num_steps,
)
# Aggregate the transitions across all the environments to reset for the next iteration
_, last_env_state, train_state, last_obs, last_critic_obs = rollout_state
train_state = train_state.replace(
last_env_state=last_env_state,
last_obs=last_obs,
last_critic_obs=last_critic_obs,
time_steps=train_state.time_steps + cfg.num_steps * cfg.num_envs,
)
return transitions, train_state
def learn_step(
key: PRNGKey, train_state: PPOTrainState, batch: Transition
) -> tuple[PPOTrainState, dict[str, jax.Array]]:
# Compute advantages and target values
model = nnx.merge(train_state.graphdef, train_state.params)
if cfg.normalize_env:
last_critic_obs = normalizer.normalize(
train_state.critic_normalization_state, train_state.last_critic_obs
)
else:
last_critic_obs = train_state.last_critic_obs
last_value = model.critic(last_critic_obs)
def compute_advantage(carry, transition):
gae, next_value = carry
done = transition.done
truncated = transition.truncated
reward = transition.reward
value = transition.value
delta = reward + cfg.gamma * next_value * (1 - done) - value
gae = delta + cfg.gamma * cfg.lmbda * (1 - done) * gae
truncated_gae = reward + cfg.gamma * next_value - value
gae = jnp.where(truncated, truncated_gae, gae)
return (gae, value), gae
# Compute the advantage using GAE
_, advantages = jax.lax.scan(
compute_advantage,
(jnp.zeros_like(last_value), last_value),
batch,
reverse=True,
)
target_values = advantages + batch.value
data = (batch, advantages, target_values)
# Reshape data to (num_steps * num_envs, ...)
data = jax.tree.map(
lambda x: x.reshape(
(math.floor(cfg.num_steps * cfg.num_envs), *x.shape[2:])
),
data,
)
def update(train_state, key) -> tuple[PPOTrainState, dict[str, jax.Array]]:
def minibatch_update(carry, indices):
idx, train_state = carry
# Sample data at indices from the batch
minibatch, advantages, target_values = jax.tree.map(
lambda x: jnp.take(x, indices, axis=0), data
)
if cfg.normalize_advantages:
advantages = (advantages - jnp.mean(advantages)) / (
jnp.std(advantages) + 1e-8
)
# Define the loss function
def loss_fn(params):
model = nnx.merge(train_state.graphdef, params)
pi = model.actor(minibatch.obs)
value = model.critic(minibatch.critic_obs)
log_prob = pi.log_prob(minibatch.action)
value_pred_clipped = minibatch.value + (
value - minibatch.value
).clip(-cfg.clip_ratio, cfg.clip_ratio)
value_error = jnp.square(value - target_values)
value_error_clipped = jnp.square(value_pred_clipped - target_values)
value_loss = 0.5 * jnp.mean(
(1.0 - minibatch.truncated)
* jnp.maximum(value_error, value_error_clipped)
)
ratio = jnp.exp(log_prob - minibatch.log_prob)
checkify.check(
jnp.allclose(ratio, 1.0) | (idx != 1),
debug=True,
msg="Ratio not equal to 1 on first iteration: {r}",
r=ratio,
)
actor_loss1 = ratio * advantages
actor_loss2 = (
jnp.clip(ratio, 1 - cfg.clip_ratio, 1 + cfg.clip_ratio)
* advantages
)
actor_loss = -jnp.mean(
(1.0 - minibatch.truncated)
* jnp.minimum(actor_loss1, actor_loss2)
)
entropy_loss = jnp.mean(pi.entropy())
loss = (
actor_loss
+ cfg.value_coef * value_loss
- cfg.entropy_coef * entropy_loss
)
return loss, dict(
actor_loss=actor_loss,
value_loss=value_loss,
entropy_loss=entropy_loss,
loss=loss,
mean_value=value.mean(),
mean_log_prob=log_prob.mean(),
mean_advantages=advantages.mean(),
mean_action=minibatch.action.mean(),
mean_reward=minibatch.reward.mean(),
)
grad_fn = jax.value_and_grad(loss_fn, has_aux=True)
output, grads = grad_fn(train_state.params)
# Global gradient norm (all parameters combined)
flat_grads, _ = jax.flatten_util.ravel_pytree(grads)
global_grad_norm = jnp.linalg.norm(flat_grads)
metrics = output[1]
metrics["advantages"] = advantages
metrics["global_grad_norm"] = global_grad_norm
train_state = train_state.apply_gradients(grads)
return (idx + 1, train_state), metrics
# Shuffle data and split into mini-batches
key, shuffle_key = jax.random.split(key)
mini_batch_size = (
math.floor(cfg.num_steps * cfg.num_envs) // cfg.num_mini_batches
)
indices = jax.random.permutation(shuffle_key, cfg.num_steps * cfg.num_envs)
minibatch_idxs = jax.tree.map(
lambda x: x.reshape(
(cfg.num_mini_batches, mini_batch_size, *x.shape[1:])
),
indices,
)
# Run model update for each mini-batch
train_state, metrics = jax.lax.scan(
minibatch_update, train_state, minibatch_idxs
)
# Compute mean metrics across mini-batches
metrics = jax.tree.map(lambda x: x.mean(0), metrics)
return train_state, metrics
# Update the model for a number of epochs
key, train_key = jax.random.split(key)
(_, train_state), update_metrics = jax.lax.scan(
f=update,
init=(1, train_state),
xs=jax.random.split(train_key, cfg.num_epochs),
)
# Get metrics from the last epoch
update_metrics = jax.tree.map(lambda x: x[-1], update_metrics)
return train_state, update_metrics
# Define the training loop
def train_fn(key: PRNGKey) -> tuple[PPOTrainState, dict]:
def train_eval_step(key, train_state):
def train_step(
state: PPOTrainState, key: PRNGKey
) -> tuple[PPOTrainState, dict[str, jax.Array]]:
key, rollout_key, learn_key = jax.random.split(key, 3)
# Collect trajectories from `state`
transitions, state = collect_rollout(key=rollout_key, train_state=state)
# Execute an update to the policy with `transitions`
state, update_metrics = learn_step(
key=learn_key, train_state=state, batch=transitions
)
metrics = {**update_metrics, **update_metrics}
state = state.replace(iteration=state.iteration + 1)
return state, metrics
train_key, eval_key = jax.random.split(key)
train_state, train_metrics = jax.lax.scan(
f=train_step,
init=train_state,
xs=jax.random.split(train_key, eval_interval),
)
train_metrics = jax.tree.map(lambda x: x[-1], train_metrics)
policy = make_policy(train_state)
eval_metrics = eval_fn(eval_key, policy)
metrics = {
"time_step": train_state.time_steps,
**utils.prefix_dict("train", train_metrics),
**utils.prefix_dict("eval", eval_metrics),
}
return train_state, metrics
def loop_body(
train_state: PPOTrainState, key: PRNGKey
) -> tuple[PPOTrainState, dict]:
# Map execution of the train+eval step across num_seeds (will be looped using jax.lax.scan)
key, subkey = jax.random.split(key)
train_state, metrics = jax.vmap(train_eval_step)(
jax.random.split(subkey, num_seeds), train_state
)
jax.debug.callback(log_callback, train_state, metrics)
return train_state, metrics
# Initialize the policy, environment and map that across the number of random seeds
num_train_steps = cfg.total_time_steps // (cfg.num_steps * cfg.num_envs)
num_iterations = num_train_steps // eval_interval + int(
num_train_steps % eval_interval != 0
)
key, init_key = jax.random.split(key)
# TWK ??: We retain the same initial state for each of the seeds across all episodes?
train_state = jax.vmap(make_init(cfg, env, env_params))(
jax.random.split(init_key, num_seeds)
)
keys = jax.random.split(key, num_iterations)
# Run the training and evaluation loop from the initialized training state
state, metrics = jax.lax.scan(f=loop_body, init=train_state, xs=keys)
return state, metrics
return train_fn
def plot_history(history: list[dict[str, jax.Array]]):
"""
TODO -- TWK: Possibly remove this...
"""
steps = jnp.array([m["time_step"][0] for m in history])
eval_return = jnp.array([m["eval/episode_return"].mean() for m in history])
eval_return_std = jnp.array([m["eval/episode_return"].std() for m in history])
fig = go.Figure(
[
go.Scatter(
x=steps,
y=eval_return,
name="Mean Episode Return",
mode="lines",
line=dict(color="blue"),
showlegend=False,
),
go.Scatter(
x=steps,
y=eval_return + eval_return_std,
name="Upper Bound",
mode="lines",
line=dict(width=0),
showlegend=False,
),
go.Scatter(
x=steps,
y=eval_return - eval_return_std,
name="Lower Bound",
mode="lines",
line=dict(width=0),
fill="tonexty",
fillcolor="rgba(50, 127, 168, 0.3)",
showlegend=False,
),
]
)
fig.update_layout(
xaxis=dict(title=dict(text="Environment Steps")),
)
return fig
def run(cfg: DictConfig):
metric_history = []
# Define callback to log metrics during training
def log_callback(state, metrics):
metrics["sys_time"] = time.perf_counter()
if len(metric_history) > 0:
num_env_steps = state.time_steps[0] - metric_history[-1]["time_step"][0]
seconds = metrics["sys_time"] - metric_history[-1]["sys_time"]
sps = num_env_steps / seconds
else:
sps = 0
metric_history.append(metrics)
episode_return = metrics["eval/episode_return"].mean()
# Use pop() with a default value of None in case 'advantages' key doesn't exist
advantages = metrics.pop("train/advantages", None)
logging.info(
f"step={state.time_steps[0]} episode_return={episode_return:.3f}, sps={sps:.2f}"
)
log_data = {
"eval/episode_return": episode_return,
"train/advantages": wandb.Histogram(advantages),
**jax.tree.map(jnp.mean, utils.filter_prefix("train", metrics)),
}
# Push log data to WandB
wandb.log(log_data, step=state.time_steps[0])
logging.info(OmegaConf.to_yaml(cfg))
# Set up the experimental environment
if cfg.env.type == "brax":
env = BraxGymnaxWrapper(
cfg.env.name
) # , episode_length=cfg.env.max_episode_steps
elif cfg.env.type == "mjx":
env = MjxGymnaxWrapper(cfg.env.name, episode_length=cfg.env.max_episode_steps)
else:
raise ValueError(f"Unknown environment type: {cfg.env.type}")
key = jax.random.PRNGKey(cfg.seed)
train_fn = make_train_fn(
cfg=PPOConfig(**cfg.hyperparameters),
env=env,
log_callback=log_callback,
num_seeds=cfg.num_seeds,
)
for i in range(cfg.trials):
# Initialize WandB reporting
key, train_key = jax.random.split(key)
wandb.init(
mode=cfg.wandb.mode,
project=cfg.wandb.project,
entity=cfg.wandb.entity,
tags=[cfg.name, cfg.env.name, cfg.env.type, *cfg.tags],
config=OmegaConf.to_container(cfg),
name=f"ppo-{cfg.name}-{cfg.env.name.lower()}",
save_code=True,
)
start = time.perf_counter()
train_state, metrics = jax.jit(train_fn)(train_key)
jax.block_until_ready(metrics)
duration = time.perf_counter() - start
# Save metrics and finish the run
logging.info(f"Training took {duration:.2f} seconds.")
# jnp.savez("metrics.npz", **metrics) # TODO: fix the directory here to save to a unique output directory
wandb.finish()
def tune(cfg: DictConfig):
"""
TODO: Signature + also adjusting to run tuning for Brax environments as well
"""
def log_callback(state, metrics):
episode_return = metrics["eval/episode_return"].mean()
t = state.time_steps[0]
wandb.log(
{
"episode_return": episode_return,
},
step=t,
)
env = MjxGymnaxWrapper(cfg.env.name, episode_length=cfg.env.max_episode_steps)
def train_agent():
wandb.init(project=cfg.wandb.project)
run_cfg = OmegaConf.to_container(cfg)
for k, v in dict(wandb.config).items():
run_cfg["experiment"]["hyperparameters"][k] = v
ppo_cfg = PPOConfig(**run_cfg["experiment"]["hyperparameters"])
train_fn = make_train_fn(
cfg=ppo_cfg,
env=env,
log_callback=log_callback,
num_seeds=cfg.num_seeds,
)
train_fn = jax.jit(train_fn)
logging.info(f"Running experiment with params: \n {run_cfg}")
key = jax.random.PRNGKey(cfg.seed)
train_state, metrics = train_fn(key)
jax.block_until_ready(metrics)
sweep_id = wandb.sweep(
sweep={
"name": f"{cfg.name}-{cfg.env.name}",
"method": "bayes",
"metric": {"name": "episode_return", "goal": "maximize"},
"parameters": {
"lr": {
"values": [1e-4, 3e-4, 1e-3],
},
"normalize_env": {
"values": [True, False],
},
},
},
project=cfg.wandb.project,
entity=cfg.wandb.entity,
)
wandb.agent(sweep_id, function=train_agent, count=cfg.tune.num_runs)
@hydra.main(version_base=None, config_path="../../config", config_name="ppo")
def main(cfg: DictConfig):
if cfg.tune:
tune(cfg)
else:
run(cfg)
if __name__ == "__main__":
main()

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import logging
import time
import typing
from typing import Callable
import hydra
import jax
import numpy as np
import optax
import optuna
import plotly.graph_objs as go
from flax import nnx, struct
from flax.struct import PyTreeNode
from gymnax.environments.environment import Environment, EnvParams, EnvState
from jax import numpy as jnp
from jax.random import PRNGKey
from omegaconf import DictConfig, OmegaConf
import wandb
from reppo.env_utils.jax_wrappers import (
BraxGymnaxWrapper,
ClipAction,
LogWrapper,
MjxGymnaxWrapper,
NormalizeVec,
)
from reppo.jaxrl import utils
from reppo.network_utils.jax_models import (
CategoricalCriticNetwork,
CriticNetwork,
SACActorNetworks,
)
logging.basicConfig(level=logging.INFO)
import mujoco
print(mujoco.__file__)
class Policy(typing.Protocol):
def __call__(
self,
key: jax.random.PRNGKey,
obs: PyTreeNode,
) -> tuple[PyTreeNode, PyTreeNode]:
pass
class Transition(struct.PyTreeNode):
obs: jax.Array
critic_obs: jax.Array
action: jax.Array
reward: jax.Array
next_emb: jax.Array
value: jax.Array
done: jax.Array
truncated: jax.Array
importance_weight: jax.Array
info: dict[str, jax.Array]
class ReppoConfig(struct.PyTreeNode):
lr: float
gamma: float
total_time_steps: int
num_steps: int
lmbda: float
lmbda_min: float
num_mini_batches: int
num_envs: int
num_epochs: int
max_grad_norm: float | None
normalize_env: bool
polyak: float
exploration_noise_min: float
exploration_noise_max: float
exploration_base_envs: int
ent_start: float
ent_target_mult: float
kl_start: float
eval_interval: int = 10
num_eval: int = 25
max_episode_steps: int = 1000
critic_hidden_dim: int = 512
actor_hidden_dim: int = 512
vmin: int = -100
vmax: int = 100
num_bins: int = 250
hl_gauss: bool = False
kl_bound: float = 1.0
aux_loss_mult: float = 0.0
update_kl_lagrangian: bool = True
update_entropy_lagrangian: bool = True
use_critic_norm: bool = True
num_critic_encoder_layers: int = 1
num_critic_head_layers: int = 1
num_critic_pred_layers: int = 1
use_simplical_embedding: bool = False
use_actor_norm: bool = True
num_actor_layers: int = 2
actor_min_std: float = 0.05
reduce_kl: bool = True
reverse_kl: bool = False
anneal_lr: bool = False
actor_kl_clip_mode: str = "clipped"
class SACTrainState(struct.PyTreeNode):
critic: nnx.TrainState
actor: nnx.TrainState
actor_target: nnx.TrainState
iteration: int
time_steps: int
last_env_state: EnvState
last_obs: jax.Array
last_critic_obs: jax.Array
def make_policy(
train_state: SACTrainState,
) -> Callable[[jax.Array, jax.Array], tuple[jax.Array, dict]]:
def policy(key: PRNGKey, obs: jax.Array) -> tuple[jax.Array, dict]:
actor_model = nnx.merge(train_state.actor.graphdef, train_state.actor.params)
action: jax.Array = actor_model.det_action(obs)
return action, {}
return policy
def make_eval_fn(
env: Environment, max_episode_steps: int, reward_scale: float = 1.0
) -> Callable[[jax.random.PRNGKey, Policy, PyTreeNode | None], dict[str, float]]:
def evaluation_fn(
key: jax.random.PRNGKey, policy: Policy, norm_state: PyTreeNode | None
):
def step_env(carry, _):
key, env_state, obs = carry
key, act_key, env_key = jax.random.split(key, 3)
action, _ = policy(act_key, obs)
step_key = jax.random.split(env_key, env.num_envs)
obs, _, env_state, reward, done, info = env.step(
step_key, env_state, action
)
return (key, env_state, obs), info
key, init_key = jax.random.split(key)
init_key = jax.random.split(init_key, env.num_envs)
obs, _, env_state = env.reset(init_key, norm_state)
# randomize initial steps
key, env_key = jax.random.split(key)
_, infos = jax.lax.scan(
f=step_env,
init=(key, env_state, obs),
xs=None,
length=max_episode_steps,
)
return {
"episode_return": infos["returned_episode_returns"].mean(
where=infos["returned_episode"]
)
* reward_scale,
"episode_return_std": infos["returned_episode_returns"].std(
where=infos["returned_episode"]
),
"episode_length": infos["returned_episode_lengths"].mean(
where=infos["returned_episode"]
),
"episode_length_std": infos["returned_episode_lengths"].std(
where=infos["returned_episode"]
),
"num_episodes": infos["returned_episode"].sum(),
}
return evaluation_fn
def make_init(
cfg: ReppoConfig,
env: Environment,
env_params: EnvParams = None,
) -> Callable[[jax.Array], SACTrainState]:
def init(key: jax.random.PRNGKey) -> SACTrainState:
# Number of calls to train_step
key, model_key = jax.random.split(key)
actor_networks = SACActorNetworks(
obs_dim=env.observation_space(env_params)[0].shape[0],
action_dim=env.action_space(env_params).shape[0],
hidden_dim=cfg.actor_hidden_dim,
ent_start=cfg.ent_start,
kl_start=cfg.kl_start,
use_norm=cfg.use_actor_norm,
layers=cfg.num_actor_layers,
rngs=nnx.Rngs(model_key),
)
actor_target_networks = SACActorNetworks(
obs_dim=env.observation_space(env_params)[0].shape[0],
action_dim=env.action_space(env_params).shape[0],
hidden_dim=cfg.actor_hidden_dim,
ent_start=cfg.ent_start,
kl_start=cfg.kl_start,
use_norm=cfg.use_actor_norm,
layers=cfg.num_actor_layers,
rngs=nnx.Rngs(model_key),
)
if cfg.hl_gauss:
critic_networks: nnx.Module = CategoricalCriticNetwork(
obs_dim=env.observation_space(env_params)[1].shape[0],
action_dim=env.action_space(env_params).shape[0],
hidden_dim=cfg.critic_hidden_dim,
num_bins=cfg.num_bins,
vmin=cfg.vmin,
vmax=cfg.vmax,
use_norm=cfg.use_critic_norm,
encoder_layers=cfg.num_critic_encoder_layers,
use_simplical_embedding=cfg.use_simplical_embedding,
head_layers=cfg.num_critic_head_layers,
pred_layers=cfg.num_critic_pred_layers,
rngs=nnx.Rngs(model_key),
)
else:
critic_networks: nnx.Module = CriticNetwork(
obs_dim=env.observation_space(env_params)[1].shape[0],
action_dim=env.action_space(env_params).shape[0],
hidden_dim=cfg.critic_hidden_dim,
use_norm=cfg.use_critic_norm,
encoder_layers=cfg.num_critic_encoder_layers,
use_simplical_embedding=cfg.use_simplical_embedding,
head_layers=cfg.num_critic_head_layers,
pred_layers=cfg.num_critic_pred_layers,
rngs=nnx.Rngs(model_key),
)
if not cfg.anneal_lr:
lr = cfg.lr
else:
num_iterations = cfg.total_time_steps // cfg.num_steps // cfg.num_envs
num_updates = num_iterations * cfg.num_epochs * cfg.num_mini_batches
lr = optax.linear_schedule(cfg.lr, 0, num_updates)
if cfg.max_grad_norm is not None:
actor_optimizer = optax.chain(
optax.clip_by_global_norm(cfg.max_grad_norm), optax.adam(lr)
)
critic_optimizer = optax.chain(
optax.clip_by_global_norm(cfg.max_grad_norm), optax.adam(lr)
)
else:
actor_optimizer = optax.adam(lr)
critic_optimizer = optax.adam(lr)
actor_trainstate = nnx.TrainState.create(
graphdef=nnx.graphdef(actor_networks),
params=nnx.state(actor_networks),
tx=actor_optimizer,
)
actor_target_trainstate = nnx.TrainState.create(
graphdef=nnx.graphdef(actor_target_networks),
params=nnx.state(actor_target_networks),
tx=optax.set_to_zero(),
)
critic_trainstate = nnx.TrainState.create(
graphdef=nnx.graphdef(critic_networks),
params=nnx.state(critic_networks),
tx=critic_optimizer,
)
key, env_key = jax.random.split(key)
env_key = jax.random.split(env_key, cfg.num_envs)
obs, critic_obs, env_state = env.reset(key=env_key, params=env_params)
# randomize initial time step to prevent all envs stepping in tandem
_env_state = env_state.unwrapped()
key, randomize_steps_key = jax.random.split(key)
_env_state.info["steps"] = jax.random.randint(
randomize_steps_key,
_env_state.info["steps"].shape,
0,
cfg.max_episode_steps,
).astype(jnp.float32)
env_state.set_env_state(_env_state)
# mock_action = jnp.zeros(
# (1, 6), dtype=jnp.float32
# )
# print(mock_action.shape)
# print(obs.shape)
# print(nnx.tabulate(critic_networks, obs[:1], mock_action))
# print(nnx.tabulate(actor_networks, obs[:1]))
return SACTrainState(
actor=actor_trainstate,
actor_target=actor_target_trainstate,
critic=critic_trainstate,
iteration=0,
time_steps=0,
last_env_state=env_state,
last_obs=obs,
last_critic_obs=critic_obs,
)
return init
def make_train_fn(
cfg: ReppoConfig,
env: Environment,
env_params: EnvParams = None,
log_callback: Callable[[SACTrainState, dict[str, jax.Array]], None] | None = None,
num_seeds: int = 1,
reward_scale: float = 1.0,
):
env_params = env_params # or env.default_params
env = LogWrapper(env, cfg.num_envs)
env = ClipAction(env)
# env = VecEnv(env, cfg.num_envs)
if cfg.normalize_env:
env = NormalizeVec(env)
print(env)
eval_fn = make_eval_fn(env, cfg.max_episode_steps, reward_scale=reward_scale)
action_size_target = (
jnp.prod(jnp.array(env.action_space(env_params).shape)) * cfg.ent_target_mult
)
def collect_rollout(
key: PRNGKey, train_state: SACTrainState
) -> tuple[Transition, SACTrainState]:
actor_model = nnx.merge(train_state.actor.graphdef, train_state.actor.params)
critic_model = nnx.merge(train_state.critic.graphdef, train_state.critic.params)
offset = (
jnp.arange(cfg.num_envs - cfg.exploration_base_envs)[:, None]
* (cfg.exploration_noise_max - cfg.exploration_noise_min)
/ (cfg.num_envs - cfg.exploration_base_envs)
) + cfg.exploration_noise_min
offset = jnp.concatenate(
[
jnp.ones((cfg.exploration_base_envs, 1)) * cfg.exploration_noise_min,
offset,
],
axis=0,
)
def step_env(carry, _) -> tuple[tuple, Transition]:
key, env_state, train_state, obs, critic_obs = carry
key, act_key, step_key = jax.random.split(key, 3)
step_key = jax.random.split(step_key, cfg.num_envs)
# get policy action
og_pi = actor_model.actor(obs)
pi = actor_model.actor(obs, scale=offset)
action = pi.sample(seed=act_key)
next_obs, next_critic_obs, next_env_state, reward, done, info = env.step(
step_key, env_state, action
)
# compute importance weights
action = jnp.clip(action, -0.999, 0.999)
raw_importance_weight = jnp.nan_to_num(
og_pi.log_prob(action).sum(-1) - pi.log_prob(action).sum(-1),
nan=jnp.log(cfg.lmbda_min),
)
importance_weight = jnp.clip(
raw_importance_weight, min=jnp.log(cfg.lmbda_min), max=jnp.log(1.0)
)
# compute next state embedding and value
next_action, log_prob = actor_model.actor(next_obs).sample_and_log_prob(
seed=act_key
)
next_emb, value = critic_model.forward(next_critic_obs, next_action)
reward = (
reward
- cfg.gamma * log_prob.sum(-1).squeeze() * actor_model.temperature()
)
transition = Transition(
obs=obs,
critic_obs=critic_obs,
action=action,
next_emb=next_emb,
reward=reward,
value=value,
done=done,
truncated=next_env_state.truncated,
info=info,
importance_weight=importance_weight,
)
return (
key,
next_env_state,
train_state,
next_obs,
next_critic_obs,
), transition
rollout_state, transitions = jax.lax.scan(
f=step_env,
init=(
key,
train_state.last_env_state,
train_state,
train_state.last_obs,
train_state.last_critic_obs,
),
length=cfg.num_steps,
)
_, last_env_state, train_state, last_obs, last_critic_obs = rollout_state
train_state = train_state.replace(
last_env_state=last_env_state,
last_obs=last_obs,
last_critic_obs=last_critic_obs,
time_steps=train_state.time_steps + cfg.num_steps * cfg.num_envs,
)
return transitions, train_state
def learn_step(
key: PRNGKey, train_state: SACTrainState, batch: Transition
) -> tuple[SACTrainState, dict[str, jax.Array]]:
# compute n-step lambda estimates
def compute_nstep_lambda(carry, transition):
lambda_return, truncated, importance_weight = carry
# combine importance_weights with TD lambda
done = transition.done
reward = transition.reward
value = transition.value
lambda_sum = (
jnp.exp(importance_weight) * cfg.lmbda * lambda_return
+ (1 - jnp.exp(importance_weight) * cfg.lmbda) * value
)
delta = cfg.gamma * jnp.where(truncated, value, (1.0 - done) * lambda_sum)
lambda_return = reward + delta
truncated = transition.truncated
return (
lambda_return,
truncated,
transition.importance_weight,
), lambda_return
_, target_values = jax.lax.scan(
compute_nstep_lambda,
(
batch.value[-1],
jnp.ones_like(batch.truncated[0]),
jnp.zeros_like(batch.importance_weight[0]),
),
batch,
reverse=True,
)
# Reshape data to (num_steps * num_envs, ...)
jax.debug.print("num trunc {}", batch.truncated.sum(), ordered=True)
data = (batch, target_values)
data = jax.tree.map(
lambda x: x.reshape((cfg.num_steps * cfg.num_envs, *x.shape[2:])), data
)
# jax.debug.print("whole data {}", data[0].truncated.sum(), ordered=True)
train_state = train_state.replace(
actor_target=train_state.actor_target.replace(
params=train_state.actor.params
),
)
actor_target_model = nnx.merge(
train_state.actor_target.graphdef, train_state.actor_target.params
)
def update(train_state, key) -> tuple[SACTrainState, dict[str, jax.Array]]:
def minibatch_update(carry, indices):
idx, train_state = carry
# Sample data at indices from the batch
minibatch, target_values = jax.tree.map(
lambda x: jnp.take(x, indices, axis=0), data
)
def critic_loss_fn(params):
critic_model = nnx.merge(train_state.critic.graphdef, params)
critic_pred = critic_model.critic_cat(
minibatch.critic_obs, minibatch.action
).squeeze()
if cfg.hl_gauss:
target_cat = jax.vmap(
utils.hl_gauss, in_axes=(0, None, None, None)
)(target_values, cfg.num_bins, cfg.vmin, cfg.vmax)
critic_update_loss = optax.softmax_cross_entropy(
critic_pred, target_cat
)
else:
critic_update_loss = optax.squared_error(
critic_pred,
target_values,
)
# Aux loss
pred, value = critic_model.forward(
minibatch.critic_obs, minibatch.action
)
aux_loss = jnp.mean(
(1 - minibatch.done.reshape(-1, 1))
* (pred - minibatch.next_emb) ** 2,
axis=-1,
)
# compute l2 error for logging
critic_loss = optax.squared_error(
value,
target_values,
)
critic_loss = jnp.mean(critic_loss)
loss = jnp.mean(
(1.0 - minibatch.truncated)
* (critic_update_loss + cfg.aux_loss_mult * aux_loss)
)
return loss, dict(
value_loss=critic_loss,
critic_update_loss=critic_update_loss,
loss=loss,
aux_loss=aux_loss,
q=critic_pred.mean(),
abs_batch_action=jnp.abs(minibatch.action).mean(),
reward_mean=minibatch.reward.mean(),
target_values=target_values.mean(),
)
def actor_loss(params):
critic_target_model = nnx.merge(
train_state.critic.graphdef,
train_state.critic.params,
)
actor_model = nnx.merge(train_state.actor.graphdef, params)
# SAC actor loss
pi = actor_model.actor(minibatch.obs)
pred_action, log_prob = pi.sample_and_log_prob(seed=key)
value = critic_target_model.critic(
minibatch.critic_obs, pred_action
)
log_prob = log_prob.sum(-1)
entropy = -log_prob
# policy KL constraint
if cfg.reverse_kl:
pi_action, pi_act_log_prob = pi.sample_and_log_prob(
sample_shape=(16,), seed=key
)
pi_action = jnp.clip(pi_action, -1 + 1e-4, 1 - 1e-4)
old_pi = actor_target_model.actor(minibatch.obs)
old_pi_act_log_prob = old_pi.log_prob(pi_action).sum(-1).mean(0)
pi_act_log_prob = pi_act_log_prob.sum(-1).mean(0)
kl = pi_act_log_prob - old_pi_act_log_prob
else:
old_pi_action, old_pi_act_log_prob = actor_target_model.actor(
minibatch.obs
).sample_and_log_prob(sample_shape=(16,), seed=key)
old_pi_action = jnp.clip(old_pi_action, -1 + 1e-4, 1 - 1e-4)
old_pi_act_log_prob = old_pi_act_log_prob.sum(-1).mean(0)
pi_act_log_prob = pi.log_prob(old_pi_action).sum(-1).mean(0)
kl = old_pi_act_log_prob - pi_act_log_prob
lagrangian = actor_model.lagrangian()
if cfg.actor_kl_clip_mode == "full":
actor_loss = (
log_prob * jax.lax.stop_gradient(actor_model.temperature())
- value
+ kl * jax.lax.stop_gradient(lagrangian) * cfg.reduce_kl
)
elif cfg.actor_kl_clip_mode == "clipped":
actor_loss = jnp.where(
kl < cfg.kl_bound,
log_prob * jax.lax.stop_gradient(actor_model.temperature())
- value,
kl * jax.lax.stop_gradient(lagrangian) * cfg.reduce_kl,
)
elif cfg.actor_kl_clip_mode == "value":
actor_loss = (
log_prob * jax.lax.stop_gradient(actor_model.temperature())
- value
)
else:
raise ValueError(
f"Unknown actor loss mode: {cfg.actor_kl_clip_mode}"
)
# SAC target entropy loss
target_entropy = action_size_target + entropy
target_entropy_loss = (
actor_model.temperature()
* jax.lax.stop_gradient(target_entropy)
)
# Lagrangian constraint (follows temperature update)
lagrangian_loss = -lagrangian * jax.lax.stop_gradient(
kl - cfg.kl_bound
)
# total loss
loss = jnp.mean(actor_loss)
if cfg.update_entropy_lagrangian:
loss += jnp.mean(target_entropy_loss)
if cfg.update_kl_lagrangian:
loss += jnp.mean(lagrangian_loss)
return loss, dict(
actor_loss=actor_loss,
loss=loss,
temp=actor_model.temperature(),
abs_batch_action=jnp.abs(minibatch.action).mean(),
abs_pred_action=jnp.abs(pred_action).mean(),
reward_mean=minibatch.reward.mean(),
kl=kl.mean(),
lagrangian=lagrangian,
lagrangian_loss=lagrangian_loss,
entropy=entropy,
entropy_loss=target_entropy_loss,
target_values=target_values.mean(),
)
critic_grad_fn = jax.value_and_grad(critic_loss_fn, has_aux=True)
output, grads = critic_grad_fn(train_state.critic.params)
critic_train_state = train_state.critic.apply_gradients(grads)
train_state = train_state.replace(
critic=critic_train_state,
)
critic_metrics = output[1]
actor_grad_fn = jax.value_and_grad(actor_loss, has_aux=True)
output, grads = actor_grad_fn(train_state.actor.params)
actor_train_state = train_state.actor.apply_gradients(grads)
train_state = train_state.replace(
actor=actor_train_state,
)
actor_metrics = output[1]
return (idx + 1, train_state), {
**critic_metrics,
**actor_metrics,
}
# Shuffle data and split into mini-batches
key, shuffle_key = jax.random.split(key)
mini_batch_size = (cfg.num_steps * cfg.num_envs) // cfg.num_mini_batches
indices = jax.random.permutation(shuffle_key, cfg.num_steps * cfg.num_envs)
minibatch_idxs = jax.tree.map(
lambda x: x.reshape(
(cfg.num_mini_batches, mini_batch_size, *x.shape[1:])
),
indices,
)
# Run model update for each mini-batch
train_state, metrics = jax.lax.scan(
minibatch_update, train_state, minibatch_idxs
)
# Compute mean metrics across mini-batches
metrics = jax.tree.map(lambda x: x.mean(0), metrics)
return train_state, metrics
# Update the model for a number of epochs
key, train_key = jax.random.split(key)
(_, train_state), update_metrics = jax.lax.scan(
f=update,
init=(1, train_state),
xs=jax.random.split(train_key, cfg.num_epochs),
)
# Get metrics from the last epoch
update_metrics = jax.tree.map(lambda x: x[-1], update_metrics)
return train_state, update_metrics
def train_fn(key: PRNGKey, cfg: ReppoConfig) -> tuple[SACTrainState, dict]:
def train_eval_step(key, train_state):
def train_step(
state: SACTrainState, key: PRNGKey
) -> tuple[SACTrainState, dict[str, jax.Array]]:
key, rollout_key, learn_key = jax.random.split(key, 3)
transitions, state = collect_rollout(key=rollout_key, train_state=state)
state, update_metrics = learn_step(
key=learn_key, train_state=state, batch=transitions
)
metrics = {**update_metrics, **update_metrics}
state = state.replace(iteration=state.iteration + 1)
return state, metrics
train_key, eval_key = jax.random.split(key)
eval_interval = int(
(cfg.total_time_steps / (cfg.num_steps * cfg.num_envs)) // cfg.num_eval
)
train_state, train_metrics = jax.lax.scan(
f=train_step,
init=train_state,
xs=jax.random.split(train_key, eval_interval),
)
train_metrics = jax.tree.map(lambda x: x[-1], train_metrics)
policy = make_policy(train_state)
if cfg.normalize_env:
norm_state = train_state.last_env_state
else:
norm_state = None
eval_metrics = eval_fn(eval_key, policy, norm_state)
train_returns = {
"train/episode_return": train_state.last_env_state.info[
"returned_episode_returns"
].mean(),
"train/episode_length": train_state.last_env_state.info[
"returned_episode_lengths"
].mean(),
}
metrics = {
"time_step": train_state.time_steps,
**utils.prefix_dict("train", train_metrics),
**utils.prefix_dict("eval", eval_metrics),
**train_returns,
}
return train_state, metrics
def loop_body(
train_state: SACTrainState, key: PRNGKey
) -> tuple[SACTrainState, dict]:
key, subkey = jax.random.split(key)
train_state, metrics = jax.vmap(train_eval_step)(
jax.random.split(subkey, num_seeds), train_state
)
jax.debug.callback(log_callback, train_state, metrics)
return train_state, metrics
eval_interval = int(
(cfg.total_time_steps / (cfg.num_steps * cfg.num_envs)) // cfg.num_eval
)
num_train_steps = cfg.total_time_steps // (cfg.num_steps * cfg.num_envs)
num_iterations = num_train_steps // eval_interval + int(
num_train_steps % eval_interval != 0
)
key, init_key = jax.random.split(key)
train_state = jax.vmap(make_init(cfg, env, env_params))(
jax.random.split(init_key, num_seeds)
)
keys = jax.random.split(key, num_iterations)
state, metrics = jax.lax.scan(f=loop_body, init=train_state, xs=keys)
return state, metrics
return train_fn
def plot_history(history: list[dict[str, jax.Array]]):
steps = jnp.array([m["time_step"][0] for m in history])
eval_return = jnp.array([m["eval/episode_return"].mean() for m in history])
eval_return_std = jnp.array([m["eval/episode_return"].std() for m in history])
fig = go.Figure(
[
go.Scatter(
x=steps,
y=eval_return,
name="Mean Episode Return",
mode="lines",
line=dict(color="blue"),
showlegend=False,
),
go.Scatter(
x=steps,
y=eval_return + eval_return_std,
name="Upper Bound",
mode="lines",
line=dict(width=0),
showlegend=False,
),
go.Scatter(
x=steps,
y=eval_return - eval_return_std,
name="Lower Bound",
mode="lines",
line=dict(width=0),
fill="tonexty",
fillcolor="rgba(50, 127, 168, 0.3)",
showlegend=False,
),
]
)
fig.update_layout(
xaxis=dict(title=dict(text="Environment Steps")),
)
return fig
# type object
def _get_optuna_type(trial: optuna.Trial, name, values: list):
if all(isinstance(v, int) for v in values):
return trial.suggest_int(name, low=min(values), high=max(values))
elif all(isinstance(v, float) for v in values):
return trial.suggest_float(name, low=min(values), high=max(values))
elif all(isinstance(v, str) for v in values):
return trial.suggest_categorical(name, values)
elif all(isinstance(v, bool) for v in values):
return trial.suggest_categorical(name, [True, False])
else:
raise ValueError("Values must be of the same type (int, float, or str).")
def run(cfg: DictConfig, trial: optuna.Trial | None) -> float:
"""
Run a single trial of the SAC training process with hyperparameter tuning.
Args:
cfg (DictConfig): Configuration for the SAC training.
trial (optuna.Trial | None): Optuna trial object for hyperparameter tuning.
Returns:
float: The mean episode return from the trial.
"""
sweep_metrics = []
if trial is not None:
# Set hyperparameters from the trial
for name, values in cfg.trial_spec.items():
if name in cfg.hyperparameters:
sampled_value = _get_optuna_type(trial, name, values)
# TODO: Why the fuck is this happening
if isinstance(sampled_value, np.float64):
sampled_value = float(sampled_value)
cfg.hyperparameters[name] = sampled_value
else:
raise ValueError(f"Hyperparameter {name} not found in config.")
try:
with open("completed_trials.txt", "r") as f:
completed_trials = int(f.read())
except FileNotFoundError:
completed_trials = 0
metric_history = []
def log_callback(state, metrics):
metrics["sys_time"] = time.perf_counter()
if len(metric_history) > 0:
num_env_steps = state.time_steps[0] - metric_history[-1]["time_step"][0]
seconds = metrics["sys_time"] - metric_history[-1]["sys_time"]
sps = num_env_steps / seconds
else:
sps = 0
metric_history.append(metrics)
episode_return = metrics["eval/episode_return"].mean()
eval_length = metrics["eval/episode_length"].mean()
logging.info(
f"step={state.time_steps[0]} episode_return={episode_return:.3f}, episode_length={eval_length:.3f} sps={sps:.2f}"
)
log_data = {
"eval/episode_return": episode_return,
"eval/episode_length": eval_length,
**jax.tree.map(jnp.mean, utils.filter_prefix("train", metrics)),
}
wandb.log(log_data, step=state.time_steps[0])
# Set up the experiment
if cfg.env.type == "brax":
env = BraxGymnaxWrapper(
cfg.env.name,
episode_length=cfg.env.max_episode_steps,
reward_scaling=cfg.env.reward_scaling,
terminate=cfg.env.terminate,
)
elif cfg.env.type == "mjx":
env = MjxGymnaxWrapper(
cfg.env.name,
episode_length=cfg.env.max_episode_steps,
reward_scale=cfg.env.reward_scaling,
push_distractions=cfg.env.get("push_distractions", False),
asymmetric_observation=cfg.env.get("asymmetric_observation", False),
)
else:
raise ValueError(f"Unknown environment type: {cfg.env.type}")
# build algo config with overrides
train_fn = make_train_fn(
cfg=ReppoConfig(**cfg.hyperparameters),
env=env,
log_callback=log_callback,
num_seeds=cfg.num_seeds,
reward_scale=1.0 / cfg.env.reward_scaling,
)
for i in range(completed_trials, cfg.num_trials):
cfg.seed = cfg.seed + i
wandb.init(
mode=cfg.wandb.mode,
project=cfg.wandb.project,
entity=cfg.wandb.entity,
tags=[
cfg.name,
cfg.env.name,
cfg.env.type,
"hp_tune" if trial is not None else "val",
*cfg.tags,
],
config=OmegaConf.to_container(cfg),
name=f"resampling-{cfg.name}-{cfg.env.name.lower()}",
save_code=True,
)
logging.info(OmegaConf.to_yaml(cfg))
key = jax.random.PRNGKey(cfg.seed)
start = time.perf_counter()
_, metrics = jax.jit(train_fn, static_argnums=(1,))(
key, ReppoConfig(**cfg.hyperparameters)
)
jax.block_until_ready(metrics)
duration = time.perf_counter() - start
# Save metrics and finish the run
logging.info(f"Training took {duration:.2f} seconds.")
jnp.savez("metrics.npz", **metrics)
wandb.finish()
sweep_metrics.append(metrics["eval/episode_return"])
with open("completed_trials.txt", "w") as f:
f.write(str(i))
sweep_metrics_array = jnp.array(sweep_metrics)
return (0.1 * sweep_metrics_array.mean() + sweep_metrics_array[:, -1].mean()).item()
@hydra.main(version_base=None, config_path="../../config", config_name="sac")
def main(cfg: DictConfig):
cfg.hyperparameters = OmegaConf.merge(cfg.hyperparameters, cfg.experiment_overrides)
run(cfg, trial=None)
if __name__ == "__main__":
main()

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reppo/jaxrl/utils.py Normal file
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import distrax
import flax
import jax
import jax.numpy as jnp
def describe(values: jnp.ndarray, axis: tuple | int = 0) -> dict[str, jnp.ndarray]:
"""Compute basic statistics for a batch of values."""
return {
"mean": jnp.mean(values, axis=axis),
"std": jnp.std(values, axis=axis),
"min": jnp.min(values, axis=axis),
"max": jnp.max(values, axis=axis),
}
def merge_dicts(*prefix_dicts: tuple[str, dict], sep: str = "/") -> dict:
"""Merge metric dictionaries with a prefix for each key."""
return {
f"{prefix if prefix else ''}{sep if prefix else ''}{key}": value
for prefix, metrics in prefix_dicts
for key, value in metrics.items()
}
def prefix_dict(prefix: str, metrics: dict, sep: str = "/") -> dict:
"""Add a prefix to all keys in a dictionary."""
return {f"{prefix}{sep}{key}": value for key, value in metrics.items()}
def postfix_dict(postfix: str, metrics: dict, sep: str = "/") -> dict:
"""Add a postfix to all keys in a dictionary."""
return {f"{key}{sep}{postfix}": value for key, value in metrics.items()}
def filter_prefix(prefix: str, metrics: dict, sep: str = "/") -> dict:
"""Filter keys in a dictionary by a prefix."""
return {
key: value for key, value in metrics.items() if key.startswith(prefix + sep)
}
def hl_gauss(inp, num_bins, vmin, vmax, epsilon=0.0):
"""Converts a batch of scalars to soft two-hot encoded targets for discrete regression."""
x = jnp.clip(inp, vmin, max=vmax).squeeze() / (1 - epsilon)
bin_width = (vmax - vmin) / (num_bins - 1)
sigma_to_final_sigma_ratio = 0.75
support = jnp.linspace(
vmin - bin_width / 2, vmax + bin_width / 2, num_bins + 1, dtype=jnp.float32
)
sigma = bin_width * sigma_to_final_sigma_ratio
cdf_evals = jax.scipy.special.erf((support - x) / (jnp.sqrt(2) * sigma))
z = cdf_evals[-1] - cdf_evals[0]
target_probs = cdf_evals[1:] - cdf_evals[:-1]
target_probs = (target_probs / z).reshape(*inp.shape[:-1], num_bins)
uniform = jnp.ones_like(target_probs) / num_bins
return (1 - epsilon) * target_probs + epsilon * uniform
@flax.struct.dataclass
class MultiSampleLogProb:
policy_action: jax.Array
policy_action_log_prob: jax.Array
action: jax.Array
def fast_multi_log_prob(
key: jax.Array,
loc: jax.Array,
scale: jax.Array,
offset_scale: jax.Array,
) -> MultiSampleLogProb:
"""Computes 3 samples from a tanh squashed function
- transformed loc and log_prob
- sample with base scale
- sample with scaled scale
Args:
key: JAX PRNG key.
loc: Location of the distribution.
scale: Scale parameter of the distribution.
offset_scale: Offset scale for the distribution.
"""
# log det factor
# sample base gaussian noise with log prob
base_noise, base_log_prob = distrax.Normal(
jnp.zeros_like(loc), scale
).sample_and_log_prob(seed=key)
base_log_prob = jnp.sum(base_log_prob, axis=-1)
# sample with base scale
base_sample = loc + base_noise
base_sample_transformed = jnp.tanh(base_sample)
# numerically stable jax tanh det jacobian https://github.com/tensorflow/probability/commit/ef6bb176e0ebd1cf6e25c6b5cecdd2428c22963f#diff-e120f70e92e6741bca649f04fcd907b7
base_log_prob -= jnp.sum(
2.0 * (jnp.log(2.0) - base_sample - jax.nn.softplus(-2.0 * base_sample)),
axis=-1,
)
return MultiSampleLogProb(
policy_action=base_sample_transformed,
policy_action_log_prob=base_log_prob,
action=jnp.tanh(loc + offset_scale * base_noise),
)
def multi_softmax(x, dim=8, get_logits=False):
inp_shape = x.shape
if dim is not None:
x = x.reshape(*x.shape[:-1], -1, dim)
if get_logits:
x = jax.nn.log_softmax(x, axis=-1)
else:
x = jax.nn.softmax(x, axis=-1)
return x.reshape(*inp_shape)
def multi_log_softmax(x, dim=8):
if dim is not None:
x = x.reshape(*x.shape[:-1], -1, dim)
return jax.nn.log_softmax(x).reshape(x.shape)
else:
return jax.nn.log_softmax(x, axis=-1)
def simplical_softmax_cross_entropy(pred, target, dim=8):
"""Computes the cross-entropy loss for simplical softmax."""
shape = pred.shape[-1]
if dim is not None:
pred = pred.reshape(*pred.shape[:-1], -1, dim)
target = target.reshape(*target.shape[:-1], -1, dim)
return jnp.sum(-target * jax.nn.log_softmax(pred, axis=-1), axis=-1).mean() / (
shape / dim
)

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import torch
import torch.nn as nn
import torch.nn.functional as F
class DistributionalQNetwork(nn.Module):
def __init__(
self,
n_obs: int,
n_act: int,
num_atoms: int,
v_min: float,
v_max: float,
hidden_dim: int,
device: torch.device = None,
):
super().__init__()
self.net = nn.Sequential(
nn.Linear(n_obs + n_act, hidden_dim, device=device),
nn.ReLU(),
nn.Linear(hidden_dim, hidden_dim // 2, device=device),
nn.ReLU(),
nn.Linear(hidden_dim // 2, hidden_dim // 4, device=device),
nn.ReLU(),
nn.Linear(hidden_dim // 4, num_atoms, device=device),
)
self.v_min = v_min
self.v_max = v_max
self.num_atoms = num_atoms
def forward(self, obs: torch.Tensor, actions: torch.Tensor) -> torch.Tensor:
x = torch.cat([obs, actions], 1)
x = self.net(x)
return x
def projection(
self,
obs: torch.Tensor,
actions: torch.Tensor,
rewards: torch.Tensor,
bootstrap: torch.Tensor,
discount: float,
q_support: torch.Tensor,
device: torch.device,
) -> torch.Tensor:
delta_z = (self.v_max - self.v_min) / (self.num_atoms - 1)
batch_size = rewards.shape[0]
target_z = (
rewards.unsqueeze(1)
+ bootstrap.unsqueeze(1) * discount.unsqueeze(1) * q_support
)
target_z = target_z.clamp(self.v_min, self.v_max)
b = (target_z - self.v_min) / delta_z
l = torch.floor(b).long()
u = torch.ceil(b).long()
l_mask = torch.logical_and((u > 0), (l == u))
u_mask = torch.logical_and((l < (self.num_atoms - 1)), (l == u))
l = torch.where(l_mask, l - 1, l)
u = torch.where(u_mask, u + 1, u)
next_dist = F.softmax(self.forward(obs, actions), dim=1)
proj_dist = torch.zeros_like(next_dist)
offset = (
torch.linspace(
0, (batch_size - 1) * self.num_atoms, batch_size, device=device
)
.unsqueeze(1)
.expand(batch_size, self.num_atoms)
.long()
)
proj_dist.view(-1).index_add_(
0, (l + offset).view(-1), (next_dist * (u.float() - b)).view(-1)
)
proj_dist.view(-1).index_add_(
0, (u + offset).view(-1), (next_dist * (b - l.float())).view(-1)
)
return proj_dist
class Critic(nn.Module):
def __init__(
self,
n_obs: int,
n_act: int,
num_atoms: int,
v_min: float,
v_max: float,
hidden_dim: int,
device: torch.device = None,
):
super().__init__()
self.qnet1 = DistributionalQNetwork(
n_obs=n_obs,
n_act=n_act,
num_atoms=num_atoms,
v_min=v_min,
v_max=v_max,
hidden_dim=hidden_dim,
device=device,
)
self.qnet2 = DistributionalQNetwork(
n_obs=n_obs,
n_act=n_act,
num_atoms=num_atoms,
v_min=v_min,
v_max=v_max,
hidden_dim=hidden_dim,
device=device,
)
self.register_buffer(
"q_support", torch.linspace(v_min, v_max, num_atoms, device=device)
)
self.device = device
def forward(self, obs: torch.Tensor, actions: torch.Tensor) -> torch.Tensor:
return self.qnet1(obs, actions), self.qnet2(obs, actions)
def projection(
self,
obs: torch.Tensor,
actions: torch.Tensor,
rewards: torch.Tensor,
bootstrap: torch.Tensor,
discount: float,
) -> torch.Tensor:
"""Projection operation that includes q_support directly"""
q1_proj = self.qnet1.projection(
obs,
actions,
rewards,
bootstrap,
discount,
self.q_support,
self.q_support.device,
)
q2_proj = self.qnet2.projection(
obs,
actions,
rewards,
bootstrap,
discount,
self.q_support,
self.q_support.device,
)
return q1_proj, q2_proj
def get_value(self, probs: torch.Tensor) -> torch.Tensor:
"""Calculate value from logits using support"""
return torch.sum(probs * self.q_support, dim=1)
class Actor(nn.Module):
def __init__(
self,
n_obs: int,
n_act: int,
num_envs: int,
init_scale: float,
hidden_dim: int,
std_min: float = 0.05,
std_max: float = 0.8,
device: torch.device = None,
):
super().__init__()
self.n_act = n_act
self.net = nn.Sequential(
nn.Linear(n_obs, hidden_dim, device=device),
nn.ReLU(),
nn.Linear(hidden_dim, hidden_dim // 2, device=device),
nn.ReLU(),
nn.Linear(hidden_dim // 2, hidden_dim // 4, device=device),
nn.ReLU(),
)
self.fc_mu = nn.Sequential(
nn.Linear(hidden_dim // 4, n_act, device=device),
nn.Tanh(),
)
nn.init.normal_(self.fc_mu[0].weight, 0.0, init_scale)
nn.init.constant_(self.fc_mu[0].bias, 0.0)
noise_scales = (
torch.rand(num_envs, 1, device=device) * (std_max - std_min) + std_min
)
self.register_buffer("noise_scales", noise_scales)
self.register_buffer("std_min", torch.as_tensor(std_min, device=device))
self.register_buffer("std_max", torch.as_tensor(std_max, device=device))
self.n_envs = num_envs
self.device = device
def forward(self, obs: torch.Tensor) -> torch.Tensor:
x = obs
x = self.net(x)
action = self.fc_mu(x)
return action
def explore(
self, obs: torch.Tensor, dones: torch.Tensor = None, deterministic: bool = False
) -> torch.Tensor:
# If dones is provided, resample noise for environments that are done
if dones is not None and dones.sum() > 0:
# Generate new noise scales for done environments (one per environment)
new_scales = (
torch.rand(self.n_envs, 1, device=obs.device)
* (self.std_max - self.std_min)
+ self.std_min
)
# Update only the noise scales for environments that are done
dones_view = dones.view(-1, 1) > 0
self.noise_scales = torch.where(dones_view, new_scales, self.noise_scales)
act = self(obs)
if deterministic:
return act
noise = torch.randn_like(act) * self.noise_scales
return act + noise
class MultiTaskActor(Actor):
def __init__(self, num_tasks: int, task_embedding_dim: int, *args, **kwargs):
super().__init__(*args, **kwargs)
self.num_tasks = num_tasks
self.task_embedding_dim = task_embedding_dim
self.task_embedding = nn.Embedding(
num_tasks, task_embedding_dim, max_norm=1.0, device=self.device
)
def forward(self, obs: torch.Tensor) -> torch.Tensor:
task_ids_one_hot = obs[..., -self.num_tasks :]
task_indices = torch.argmax(task_ids_one_hot, dim=1)
task_embeddings = self.task_embedding(task_indices)
obs = torch.cat([obs[..., : -self.num_tasks], task_embeddings], dim=-1)
return super().forward(obs)
class MultiTaskCritic(Critic):
def __init__(self, num_tasks: int, task_embedding_dim: int, *args, **kwargs):
super().__init__(*args, **kwargs)
self.num_tasks = num_tasks
self.task_embedding_dim = task_embedding_dim
self.task_embedding = nn.Embedding(
num_tasks, task_embedding_dim, max_norm=1.0, device=self.device
)
def forward(self, obs: torch.Tensor, actions: torch.Tensor) -> torch.Tensor:
task_ids_one_hot = obs[..., -self.num_tasks :]
task_indices = torch.argmax(task_ids_one_hot, dim=1)
task_embeddings = self.task_embedding(task_indices)
obs = torch.cat([obs[..., : -self.num_tasks], task_embeddings], dim=-1)
return super().forward(obs, actions)
def projection(
self,
obs: torch.Tensor,
actions: torch.Tensor,
rewards: torch.Tensor,
bootstrap: torch.Tensor,
discount: float,
) -> torch.Tensor:
task_ids_one_hot = obs[..., -self.num_tasks :]
task_indices = torch.argmax(task_ids_one_hot, dim=1)
task_embeddings = self.task_embedding(task_indices)
obs = torch.cat([obs[..., : -self.num_tasks], task_embeddings], dim=-1)
return super().projection(obs, actions, rewards, bootstrap, discount)

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import math
from typing import Sequence, Union
import distrax
import jax
import jax.numpy as jnp
from flax import nnx
from reppo.jaxrl import utils
def torch_he_uniform(
in_axis: Union[int, Sequence[int]] = -2,
out_axis: Union[int, Sequence[int]] = -1,
batch_axis: Sequence[int] = (),
dtype=jnp.float_,
):
"TODO: push to jax"
return nnx.initializers.variance_scaling(
0.3333,
"fan_in",
"uniform",
in_axis=in_axis,
out_axis=out_axis,
batch_axis=batch_axis,
dtype=dtype,
)
class UnitBallNorm(nnx.Module):
def __call__(self, x: jax.Array) -> jax.Array:
return x / (jnp.linalg.norm(x, axis=-1, keepdims=True) + 1e-8)
def normed_activation_layer(
rngs, in_features, out_features, use_norm=True, activation=nnx.swish
):
layers = [
nnx.Linear(
in_features=in_features,
out_features=out_features,
kernel_init=torch_he_uniform(),
rngs=rngs,
)
]
if use_norm:
layers.append(nnx.RMSNorm(out_features, rngs=rngs))
if activation is not None:
layers.append(activation)
return nnx.Sequential(*layers)
class Identity(nnx.Module):
def __call__(self, x: jax.Array) -> jax.Array:
return x
class FCNN(nnx.Module):
def __init__(
self,
in_features: int,
out_features: int,
hidden_dim: int = 512,
hidden_activation=nnx.swish,
output_activation=None,
use_norm: bool = True,
use_output_norm: bool = False,
layers: int = 2,
input_activation: bool = False,
*,
rngs: nnx.Rngs,
):
if layers == 1:
self.module = normed_activation_layer(
rngs,
in_features,
out_features,
use_norm=use_output_norm,
activation=output_activation,
)
else:
if input_activation:
input_layer = nnx.Sequential(
# nnx.LayerNorm(in_features, rngs=rngs) if use_norm else Identity(),
hidden_activation,
normed_activation_layer(
rngs,
in_features,
hidden_dim,
use_norm=use_norm,
activation=hidden_activation,
),
)
else:
input_layer = nnx.Sequential(
normed_activation_layer(
rngs,
in_features,
hidden_dim,
use_norm=use_norm,
activation=hidden_activation,
)
)
hidden_layers = [
normed_activation_layer(
rngs,
hidden_dim,
hidden_dim,
use_norm=use_norm,
activation=hidden_activation,
)
for _ in range(layers - 2)
]
output_layer = normed_activation_layer(
rngs,
hidden_dim,
out_features,
use_norm=use_output_norm,
activation=output_activation,
)
self.module = nnx.Sequential(
input_layer,
*hidden_layers,
output_layer,
)
def __call__(self, x: jax.Array) -> jax.Array:
return self.module(x)
class CriticNetwork(nnx.Module):
def __init__(
self,
obs_dim: int,
action_dim: int,
hidden_dim: int = 512,
use_norm: bool = True,
use_encoder_norm: bool = False,
use_simplical_embedding: bool = False,
encoder_layers: int = 1,
head_layers: int = 1,
pred_layers: int = 1,
*,
rngs: nnx.Rngs,
):
self.feature_module = FCNN(
in_features=obs_dim + action_dim,
out_features=hidden_dim,
hidden_dim=hidden_dim,
hidden_activation=nnx.swish,
output_activation=utils.multi_softmax if use_simplical_embedding else None,
use_norm=use_norm,
use_output_norm=use_encoder_norm,
layers=encoder_layers,
rngs=rngs,
)
self.critic_module = FCNN(
in_features=hidden_dim,
out_features=1,
hidden_dim=hidden_dim,
hidden_activation=nnx.swish,
output_activation=None,
use_norm=use_norm,
use_output_norm=False,
layers=head_layers,
rngs=rngs,
)
self.pred_module = FCNN(
in_features=hidden_dim,
out_features=hidden_dim,
hidden_dim=hidden_dim,
hidden_activation=nnx.swish,
output_activation=utils.multi_softmax if use_simplical_embedding else None,
use_norm=use_norm,
use_output_norm=False,
layers=pred_layers,
rngs=rngs,
)
def features(self, obs: jax.Array, action: jax.Array):
state = jnp.concatenate([obs, action], axis=-1)
return self.feature_module(state)
def critic_head(self, features: jax.Array) -> jax.Array:
return self.critic_module(features)
def critic(self, obs: jax.Array, action: jax.Array) -> jax.Array:
features = self.features(obs, action)
return self.critic_head(features)
def critic_cat(self, obs: jax.Array, action: jax.Array) -> jax.Array:
features = self.features(obs, action)
return self.critic_head(features)
def forward(self, obs, action):
features = self.features(obs, action)
value = self.critic_head(features)
return self.pred_module(features), value
class CategoricalCriticNetwork(nnx.Module):
def __init__(
self,
obs_dim: int,
action_dim: int,
hidden_dim: int = 512,
use_norm: bool = True,
use_encoder_norm: bool = False,
use_simplical_embedding: bool = False,
encoder_layers: int = 1,
head_layers: int = 1,
pred_layers: int = 1,
num_bins: int = 51,
vmin: float = -10.0,
vmax: float = 10.0,
*,
rngs: nnx.Rngs,
):
self.num_bins = num_bins
self.vmin = vmin
self.vmax = vmax
self.feature_module = FCNN(
in_features=obs_dim + action_dim,
out_features=hidden_dim,
hidden_dim=hidden_dim,
hidden_activation=nnx.swish,
output_activation=utils.multi_softmax if use_simplical_embedding else None,
use_norm=use_norm,
use_output_norm=use_encoder_norm,
layers=encoder_layers,
rngs=rngs,
)
self.critic_module = FCNN(
in_features=hidden_dim,
out_features=self.num_bins,
hidden_dim=hidden_dim,
hidden_activation=nnx.swish,
output_activation=None,
use_norm=use_norm,
use_output_norm=False,
layers=head_layers,
input_activation=not use_simplical_embedding,
rngs=rngs,
)
self.pred_module = FCNN(
in_features=hidden_dim,
out_features=hidden_dim,
hidden_dim=hidden_dim,
hidden_activation=nnx.swish,
output_activation=None,
use_norm=use_norm,
use_output_norm=False,
layers=pred_layers,
input_activation=not use_simplical_embedding,
rngs=rngs,
)
self.zero_dist = nnx.Param(
utils.hl_gauss(jnp.zeros((1,)), num_bins, vmin, vmax)
)
def features(self, obs: jax.Array, action: jax.Array):
state = jnp.concatenate([obs, action], axis=-1)
return self.feature_module(state)
def critic_head(self, features: jax.Array) -> jax.Array:
cat = self.critic_module(features) # + self.zero_dist.value * 40.0
return cat
def critic_cat(self, obs: jax.Array, action: jax.Array) -> jax.Array:
features = self.features(obs, action)
return self.critic_head(features)
def critic(self, obs: jax.Array, action: jax.Array) -> jax.Array:
value_cat = jax.nn.softmax(self.critic_cat(obs, action), axis=-1)
value = value_cat.dot(
jnp.linspace(self.vmin, self.vmax, self.num_bins, endpoint=True)
)
return value
def forward(self, obs, action):
features = self.features(obs, action)
value_cat = jax.nn.softmax(self.critic_head(features), axis=-1)
value = value_cat.dot(
jnp.linspace(self.vmin, self.vmax, self.num_bins, endpoint=True)
)
return self.pred_module(features), value
def __call__(self, obs: jax.Array, action: jax.Array) -> jax.Array:
features = self.features(obs, action)
value_cat = jax.nn.softmax(self.critic_head(features), axis=-1)
value = value_cat.dot(
jnp.linspace(self.vmin, self.vmax, self.num_bins, endpoint=True)
)
pred = self.pred_module(features)
return value, value_cat, pred
class SACActorNetworks(nnx.Module):
def __init__(
self,
obs_dim: int,
action_dim: int,
hidden_dim: int = 512,
ent_start: float = 0.1,
kl_start: float = 0.1,
use_norm: bool = True,
layers: int = 2,
min_std: float = 0.1,
*,
rngs: nnx.Rngs,
):
self.actor_module = FCNN(
in_features=obs_dim,
out_features=action_dim * 2,
hidden_dim=hidden_dim,
hidden_activation=nnx.swish,
output_activation=None,
use_norm=use_norm,
use_output_norm=False,
layers=layers,
input_activation=False,
rngs=rngs,
)
start_value = math.log(ent_start)
kl_start_value = math.log(kl_start)
self.temperature_log_param = nnx.Param(jnp.ones(1) * start_value)
self.lagrangian_log_param = nnx.Param(jnp.ones(1) * kl_start_value)
self.min_std = min_std
def actor(
self, obs: jax.Array, scale: float | jax.Array = 1.0
) -> distrax.Distribution:
loc = self.actor_module(obs)
loc, log_std = jnp.split(loc, 2, axis=-1)
std = (jnp.exp(log_std) + self.min_std) * scale
pi = distrax.Transformed(distrax.Normal(loc=loc, scale=std), distrax.Tanh())
return pi
def det_action(self, obs: jax.Array) -> jax.Array:
loc = self.actor_module(obs)
loc, _ = jnp.split(loc, 2, axis=-1)
return jnp.tanh(loc)
def temperature(self) -> jax.Array:
return jnp.exp(self.temperature_log_param.value)
def lagrangian(self) -> jax.Array:
return jnp.exp(self.lagrangian_log_param.value)
def __call__(self, obs: jax.Array) -> jax.Array:
loc = self.actor_module(obs)
loc, std = jnp.split(loc, 2, axis=-1)
return jnp.tanh(loc), std, self.temperature(), self.lagrangian()
class TD3ActorNetworks(nnx.Module):
def __init__(
self,
obs_dim: int,
action_dim: int,
hidden_dim: int = 512,
ent_start: float = 0.1,
kl_start: float = 0.1,
use_norm: bool = True,
layers: int = 2,
min_std: float = 0.1,
*,
rngs: nnx.Rngs,
):
self.actor_module = FCNN(
in_features=obs_dim,
out_features=action_dim * 2,
hidden_dim=hidden_dim,
hidden_activation=nnx.swish,
output_activation=None,
use_norm=use_norm,
use_output_norm=False,
layers=layers,
input_activation=False,
rngs=rngs,
)
start_value = math.log(ent_start)
kl_start_value = math.log(kl_start)
self.temperature_log_param = nnx.Param(jnp.ones(1) * start_value)
self.lagrangian_log_param = nnx.Param(jnp.ones(1) * kl_start_value)
self.min_std = min_std
def actor(
self, obs: jax.Array, scale: float | jax.Array = 1.0
) -> distrax.Distribution:
loc = self.actor_module(obs)
loc, log_std = jnp.split(loc, 2, axis=-1)
std = (jnp.exp(log_std) + self.min_std) * scale
pi = distrax.Transformed(distrax.Normal(loc=loc, scale=std), distrax.Tanh())
return pi
def det_action(self, obs: jax.Array) -> jax.Array:
loc = self.actor_module(obs)
loc, _ = jnp.split(loc, 2, axis=-1)
return jnp.tanh(loc)
def temperature(self) -> jax.Array:
return jnp.exp(self.temperature_log_param.value)
def lagrangian(self) -> jax.Array:
return jnp.exp(self.lagrangian_log_param.value)
class TD3DeterministicDist(distrax.Distribution):
def __init__(self, loc: jax.Array, scale: float | jax.Array):
self.loc = loc
self.scale = scale
def sample(self, seed=None):
return self.loc + self.scale * jax.random.normal(seed, self.loc.shape)
def log_prob(self, value: jax.Array) -> jax.Array:
return jnp.zeros_like(value)
def sample_and_log_prob(self, *, seed, sample_shape=...):
sample = self.sample(seed=seed)
log_prob = self.log_prob(sample)
return sample, log_prob

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import torch
from torch import nn
from torch.distributions import constraints
from torch.distributions.transforms import Transform
from torch.distributions.normal import Normal
from reppo.torchrl.reppo import hl_gauss
class TanhTransform(Transform):
r"""
Transform via the mapping :math:`y = \tanh(x)`.
It is equivalent to
.. code-block:: python
ComposeTransform(
[
AffineTransform(0.0, 2.0),
SigmoidTransform(),
AffineTransform(-1.0, 2.0),
]
)
However this might not be numerically stable, thus it is recommended to use `TanhTransform`
instead.
Note that one should use `cache_size=1` when it comes to `NaN/Inf` values.
"""
domain = constraints.real
codomain = constraints.interval(-1.0, 1.0)
bijective = True
sign = +1
log2 = torch.log(torch.tensor(2.0)).to("cuda" if torch.cuda.is_available() else "cpu")
def __eq__(self, other):
return isinstance(other, TanhTransform)
def _call(self, x):
return x.tanh()
def _inverse(self, y):
# We do not clamp to the boundary here as it may degrade the performance of certain algorithms.
# one should use `cache_size=1` instead
return torch.atanh(y)
def log_abs_det_jacobian(self, x, y):
# We use a formula that is more numerically stable, see details in the following link
# https://github.com/tensorflow/probability/blob/master/tensorflow_probability/python/bijectors/tanh.py#L69-L80
return 2.0 * (self.log2 - x - torch.nn.functional.softplus(-2.0 * x))
def get_activation(name):
if name == "gelu":
return nn.GELU()
elif name == "relu":
return nn.ReLU()
elif name == "swish":
return nn.SiLU()
elif name is None:
return nn.Identity()
else:
raise ValueError(f"Unknown activation: {name}")
def normed_activation_layer(
in_features, out_features, use_norm=True, activation="swish", device=None
):
layers = [nn.Linear(in_features, out_features, device=device)]
if use_norm:
layers.append(nn.RMSNorm([out_features], device=device))
if activation is not None:
layers.append(get_activation(activation))
return nn.Sequential(*layers)
class FCNN(nn.Module):
def __init__(
self,
in_features,
out_features,
hidden_dim=256,
hidden_activation="swish",
output_activation=None,
use_norm=True,
use_output_norm=False,
layers=2,
input_activation=False,
device=None,
):
super().__init__()
net = []
if layers == 1:
net.append(
normed_activation_layer(
in_features,
out_features,
use_norm=use_output_norm,
activation=output_activation,
device=device,
)
)
else:
if input_activation:
net.append(get_activation(hidden_activation))
net.append(
normed_activation_layer(
in_features,
hidden_dim,
use_norm=use_norm,
activation=hidden_activation,
device=device,
)
)
for _ in range(layers - 2):
net.append(
normed_activation_layer(
hidden_dim,
hidden_dim,
use_norm=use_norm,
activation=hidden_activation,
device=device,
)
)
net.append(
normed_activation_layer(
hidden_dim,
out_features,
use_norm=use_output_norm,
activation=output_activation,
device=device,
)
)
self.net = nn.Sequential(*net)
def forward(self, x):
return self.net(x)
class CriticNetwork(nn.Module):
def __init__(
self,
n_obs,
n_act,
hidden_dim=256,
use_norm=True,
use_encoder_norm=False,
encoder_layers=1,
head_layers=1,
pred_layers=1,
device=None,
):
super().__init__()
self.feature_module = FCNN(
in_features=n_obs + n_act,
out_features=hidden_dim,
hidden_dim=hidden_dim,
hidden_activation="swish",
output_activation=None,
use_norm=use_norm,
use_output_norm=use_encoder_norm,
layers=encoder_layers,
device=device,
)
self.critic_module = FCNN(
in_features=hidden_dim,
out_features=1,
hidden_dim=hidden_dim,
hidden_activation="swish",
output_activation=None,
use_norm=use_norm,
use_output_norm=False,
layers=head_layers,
device=device,
)
self.pred_module = FCNN(
in_features=hidden_dim,
out_features=hidden_dim,
hidden_dim=hidden_dim,
hidden_activation="swish",
output_activation=None,
use_norm=use_norm,
use_output_norm=False,
layers=pred_layers,
device=device,
)
def features(self, obs, action):
state = torch.cat([obs, action], dim=-1)
return self.feature_module(state)
def critic_head(self, features):
return self.critic_module(features)
def critic(self, obs, action):
features = self.features(obs, action)
return self.critic_head(features)
def forward(self, obs, action):
features = self.features(obs, action)
return self.pred_module(features)
class Critic(nn.Module):
def __init__(
self,
n_obs,
n_act,
num_atoms: int,
vmin: float,
vmax: float,
hidden_dim=256,
use_norm=True,
use_encoder_norm=False,
encoder_layers=1,
head_layers=1,
pred_layers=1,
device=None,
):
super().__init__()
self.num_atoms = num_atoms
self.vmin = vmin
self.vmax = vmax
self.hidden_dim = hidden_dim
self.feature_module = FCNN(
in_features=n_obs + n_act,
out_features=hidden_dim,
hidden_dim=hidden_dim,
hidden_activation="swish",
output_activation=None,
use_norm=use_norm,
use_output_norm=use_encoder_norm,
layers=encoder_layers,
device=device,
)
self.critic_module = FCNN(
in_features=hidden_dim,
out_features=num_atoms,
hidden_dim=hidden_dim,
hidden_activation="swish",
output_activation=None,
use_norm=use_norm,
use_output_norm=False,
input_activation=True,
layers=head_layers,
device=device,
)
self.pred_module = FCNN(
in_features=hidden_dim,
out_features=hidden_dim,
hidden_dim=hidden_dim,
hidden_activation="swish",
output_activation=None,
use_norm=use_norm,
input_activation=True,
use_output_norm=False,
layers=pred_layers,
device=device,
)
self.values = torch.linspace(
vmin, vmax, num_atoms, device=device, dtype=torch.float32
)
zeros = hl_gauss(
torch.zeros(1, device=device), self.vmin, self.vmax, self.num_atoms
)
zeros.requires_grad = True
self.zero_dist = nn.Parameter(
hl_gauss(
torch.zeros(1, device=device), self.vmin, self.vmax, self.num_atoms
)
)
def forward(self, obs, action):
inp = torch.cat([obs, action], dim=-1)
features = self.feature_module(inp)
next_pred = self.pred_module(features)
logits = self.critic_module(features) + 40.9 * self.zero_dist
value_cats = torch.softmax(logits, dim=-1)
value = value_cats @ self.values
return value, logits, next_pred, features
class Actor(nn.Module):
def __init__(
self,
n_obs,
n_act,
ent_start: float,
kl_start: float,
hidden_dim=256,
use_norm=True,
layers=2,
min_std=0.1,
device=None,
):
super().__init__()
self.model = FCNN(
in_features=n_obs,
out_features=2 * n_act,
hidden_dim=hidden_dim,
hidden_activation="swish",
output_activation=None,
use_norm=use_norm,
use_output_norm=False,
layers=layers,
device=device,
)
self.log_temp = nn.Parameter(
torch.log(torch.tensor(ent_start, device=device, dtype=torch.float32))
)
self.log_lagrange = nn.Parameter(
torch.log(torch.tensor(kl_start, device=device, dtype=torch.float32))
)
self.min_std = min_std
def forward(self, obs: torch.Tensor) -> torch.distributions.Distribution:
x = self.model(obs)
mean, log_std = torch.split(x, x.shape[-1] // 2, dim=-1)
std = torch.exp(log_std) + self.min_std
pi = Normal(mean, std, validate_args=False)
transformed_pi = torch.distributions.TransformedDistribution(
pi, [torch.distributions.TanhTransform()]
)
return (
transformed_pi,
torch.tanh(mean),
torch.exp(self.log_temp),
torch.exp(self.log_lagrange),
)
class StochasticPolicy(nn.Module):
def __init__(self, actor: Actor, normalizer: nn.Module = None, *args, **kwargs):
super().__init__(*args, **kwargs)
self.actor = actor
self.normalizer = normalizer
def forward(self, obs: torch.Tensor) -> torch.distributions.Distribution:
if self.normalizer:
obs = self.normalizer(obs)
return self.actor(obs)
class TD3DeterministicPolicy(nn.Module):
def __init__(
self,
n_obs,
n_act,
hidden_dim=256,
use_norm=True,
layers=2,
device=None,
):
super().__init__()
self.model = FCNN(
in_features=n_obs,
out_features=2 * n_act,
hidden_dim=hidden_dim,
hidden_activation="swish",
output_activation=None,
use_norm=use_norm,
use_output_norm=False,
layers=layers,
device=device,
)
def forward(self, obs: torch.Tensor) -> torch.Tensor:
x = self.model(obs)
mean, _ = torch.split(x, x.shape[-1] // 2, dim=-1)
return torch.tanh(mean)

95
reppo/torchrl/envs.py Normal file
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import torch
from omegaconf import DictConfig
def make_envs(cfg: DictConfig, device: torch.device, seed: int = None) -> tuple:
if cfg.env.type == "humanoid_bench":
from reppo.env_utils.torch_wrappers.humanoid_bench_env import (
HumanoidBenchEnv,
)
envs = HumanoidBenchEnv(
cfg.env.name, cfg.hyperparameters.num_envs, device=device
)
return envs, envs
elif cfg.env.type == "isaaclab":
from reppo.env_utils.torch_wrappers.isaaclab_env import IsaacLabEnv
envs = IsaacLabEnv(
cfg.env.name,
device.type,
cfg.hyperparameters.num_envs,
cfg=seed,
action_bounds=cfg.env.action_bounds,
)
return envs, envs
elif cfg.env.type == "mjx":
from reppo.env_utils.torch_wrappers.mujoco_playground_env import make_env
# TODO: Check if re-using same envs for eval could reduce memory usage
envs, eval_envs = make_env(
env_name=cfg.env.name,
seed=seed,
num_envs=cfg.hyperparameters.num_envs,
num_eval_envs=cfg.hyperparameters.num_envs,
device_rank=cfg.platform.device_rank,
use_domain_randomization=False,
use_push_randomization=True,
)
return envs, eval_envs
elif cfg.env.type == "maniskill":
import gymnasium as gym
import mani_skill.envs # noqa: F401
from mani_skill.utils import gym_utils
from mani_skill.utils.wrappers.flatten import FlattenActionSpaceWrapper
from mani_skill.vector.wrappers.gymnasium import ManiSkillVectorEnv
from reppo.env_utils.torch_wrappers.maniskill_wrapper import (
ManiSkillWrapper,
)
envs = gym.make(
cfg.env.name,
num_envs=cfg.hyperparameters.num_envs,
reconfiguration_freq=None,
**cfg.env.env_kwargs,
)
eval_envs = gym.make(
cfg.env.name,
num_envs=cfg.hyperparameters.num_envs,
reconfiguration_freq=1,
**cfg.env.env_kwargs,
)
cfg.env.max_episode_steps = gym_utils.find_max_episode_steps_value(envs)
# heuristic for setting gamma
cfg.hyperparameters.gamma = 1.0 - 10.0 / cfg.env.max_episode_steps
if isinstance(envs.action_space, gym.spaces.Dict):
envs = FlattenActionSpaceWrapper(envs)
eval_envs = FlattenActionSpaceWrapper(eval_envs)
envs = ManiSkillVectorEnv(
envs,
cfg.hyperparameters.num_envs,
ignore_terminations=not cfg.env.partial_reset,
record_metrics=True,
)
eval_envs = ManiSkillVectorEnv(
eval_envs,
cfg.hyperparameters.num_envs,
ignore_terminations=True,
record_metrics=True,
)
return ManiSkillWrapper(
envs,
max_episode_steps=cfg.env.max_episode_steps,
partial_reset=cfg.env.partial_reset,
device=device.type,
), ManiSkillWrapper(
eval_envs,
max_episode_steps=cfg.env.max_episode_steps,
partial_reset=cfg.env.partial_reset,
device=device.type,
)
else:
raise ValueError(
f"Unknown environment type: {cfg.env.type}. Supported types are 'humanoid_bench', 'isaaclab', 'maniskill', and 'mjx'."
)

695
reppo/torchrl/fast_td3.py Normal file
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import os
import sys
os.environ["TORCHDYNAMO_INLINE_INBUILT_NN_MODULES"] = "1"
os.environ["OMP_NUM_THREADS"] = "1"
if sys.platform != "darwin":
os.environ["MUJOCO_GL"] = "egl"
else:
os.environ["MUJOCO_GL"] = "glfw"
os.environ["XLA_PYTHON_CLIENT_PREALLOCATE"] = "false"
os.environ["JAX_DEFAULT_MATMUL_PRECISION"] = "highest"
import math
import random
import time
import numpy as np
import tqdm
import wandb
try:
# Required for avoiding IsaacGym import error
import isaacgym
except ImportError:
pass
import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim
from fast_sac_utils import (
EmpiricalNormalization,
PerTaskRewardNormalizer,
RewardNormalizer,
SimpleReplayBuffer,
save_params,
)
from hyperparams import get_args
from tensordict import TensorDict
from torch.amp import GradScaler, autocast
torch.set_float32_matmul_precision("high")
try:
import jax.numpy as jnp
except ImportError:
pass
def main():
args = get_args()
print(args)
run_name = f"{args.env_name}__{args.exp_name}__{args.seed}"
amp_enabled = args.amp and args.cuda and torch.cuda.is_available()
amp_device_type = (
"cuda"
if args.cuda and torch.cuda.is_available()
else "mps"
if args.cuda and torch.backends.mps.is_available()
else "cpu"
)
amp_dtype = torch.bfloat16 if args.amp_dtype == "bf16" else torch.float16
scaler = GradScaler(enabled=amp_enabled and amp_dtype == torch.float16)
if args.use_wandb:
wandb.init(
project=args.project,
name=run_name,
config=vars(args),
save_code=True,
)
random.seed(args.seed)
np.random.seed(args.seed)
torch.manual_seed(args.seed)
torch.backends.cudnn.deterministic = args.torch_deterministic
if not args.cuda:
device = torch.device("cpu")
else:
if torch.cuda.is_available():
device = torch.device(f"cuda:{args.device_rank}")
elif torch.backends.mps.is_available():
device = torch.device(f"mps:{args.device_rank}")
else:
raise ValueError("No GPU available")
print(f"Using device: {device}")
if args.env_name.startswith("h1hand-") or args.env_name.startswith("h1-"):
from reppo.env_utils.torch_wrappers.humanoid_bench_env import (
HumanoidBenchEnv,
)
env_type = "humanoid_bench"
envs = HumanoidBenchEnv(args.env_name, args.num_envs, device=device)
eval_envs = envs
elif args.env_name.startswith("Isaac-"):
from reppo.env_utils.torch_wrappers.isaaclab_env import IsaacLabEnv
env_type = "isaaclab"
envs = IsaacLabEnv(
args.env_name,
device.type,
args.num_envs,
args.seed,
action_bounds=args.action_bounds,
)
eval_envs = envs
elif args.env_name.startswith("MTBench-"):
from reppo.env_utils.torch_wrappers.mtbench_env import MTBenchEnv
env_name = "-".join(args.env_name.split("-")[1:])
env_type = "mtbench"
envs = MTBenchEnv(env_name, args.device_rank, args.num_envs, args.seed)
eval_envs = envs
else:
from reppo.env_utils.torch_wrappers.mujoco_playground_env import make_env
# TODO: Check if re-using same envs for eval could reduce memory usage
env_type = "mujoco_playground"
envs, eval_envs = make_env(
args.env_name,
args.seed,
args.num_envs,
args.num_eval_envs,
args.device_rank,
use_tuned_reward=args.use_tuned_reward,
use_domain_randomization=args.use_domain_randomization,
use_push_randomization=args.use_push_randomization,
)
n_act = envs.num_actions
n_obs = envs.num_obs if type(envs.num_obs) == int else envs.num_obs[0]
if envs.asymmetric_obs:
n_critic_obs = (
envs.num_privileged_obs
if type(envs.num_privileged_obs) == int
else envs.num_privileged_obs[0]
)
else:
n_critic_obs = n_obs
action_low, action_high = -1.0, 1.0
if args.obs_normalization:
obs_normalizer = EmpiricalNormalization(shape=n_obs, device=device)
critic_obs_normalizer = EmpiricalNormalization(
shape=n_critic_obs, device=device
)
else:
obs_normalizer = nn.Identity()
critic_obs_normalizer = nn.Identity()
if args.reward_normalization:
if env_type in ["mtbench"]:
reward_normalizer = PerTaskRewardNormalizer(
num_tasks=envs.num_tasks,
gamma=args.gamma,
device=device,
g_max=min(abs(args.v_min), abs(args.v_max)),
)
else:
reward_normalizer = RewardNormalizer(
gamma=args.gamma,
device=device,
g_max=min(abs(args.v_min), abs(args.v_max)),
)
else:
reward_normalizer = nn.Identity()
actor_kwargs = {
"n_obs": n_obs,
"n_act": n_act,
"num_envs": args.num_envs,
"device": device,
"init_scale": args.init_scale,
"hidden_dim": args.actor_hidden_dim,
}
critic_kwargs = {
"n_obs": n_critic_obs,
"n_act": n_act,
"num_atoms": args.num_atoms,
"v_min": args.v_min,
"v_max": args.v_max,
"hidden_dim": args.critic_hidden_dim,
"device": device,
}
if env_type == "mtbench":
actor_kwargs["n_obs"] = n_obs - envs.num_tasks + args.task_embedding_dim
critic_kwargs["n_obs"] = n_critic_obs - envs.num_tasks + args.task_embedding_dim
actor_kwargs["num_tasks"] = envs.num_tasks
actor_kwargs["task_embedding_dim"] = args.task_embedding_dim
critic_kwargs["num_tasks"] = envs.num_tasks
critic_kwargs["task_embedding_dim"] = args.task_embedding_dim
if args.agent == "fasttd3":
if env_type in ["mtbench"]:
from reppo.network_utils.fast_td3_nets import (
MultiTaskActor,
MultiTaskCritic,
)
actor_cls = MultiTaskActor
critic_cls = MultiTaskCritic
else:
from reppo.network_utils.fast_td3_nets import Actor, Critic
actor_cls = Actor
critic_cls = Critic
print("Using FastTD3")
elif args.agent == "fasttd3_simbav2":
if env_type in ["mtbench"]:
from reppo.network_utils.fast_td3_nets_simbav2 import (
MultiTaskActor,
MultiTaskCritic,
)
actor_cls = MultiTaskActor
critic_cls = MultiTaskCritic
else:
from reppo.network_utils.fast_td3_nets_simbav2 import Actor, Critic
actor_cls = Actor
critic_cls = Critic
print("Using FastTD3 + SimbaV2")
actor_kwargs.pop("init_scale")
actor_kwargs.update(
{
"scaler_init": math.sqrt(2.0 / args.actor_hidden_dim),
"scaler_scale": math.sqrt(2.0 / args.actor_hidden_dim),
"alpha_init": 1.0 / (args.actor_num_blocks + 1),
"alpha_scale": 1.0 / math.sqrt(args.actor_hidden_dim),
"expansion": 4,
"c_shift": 3.0,
"num_blocks": args.actor_num_blocks,
}
)
critic_kwargs.update(
{
"scaler_init": math.sqrt(2.0 / args.critic_hidden_dim),
"scaler_scale": math.sqrt(2.0 / args.critic_hidden_dim),
"alpha_init": 1.0 / (args.critic_num_blocks + 1),
"alpha_scale": 1.0 / math.sqrt(args.critic_hidden_dim),
"num_blocks": args.critic_num_blocks,
"expansion": 4,
"c_shift": 3.0,
}
)
else:
raise ValueError(f"Agent {args.agent} not supported")
actor = actor_cls(**actor_kwargs)
if env_type in ["mtbench"]:
# Python 3.8 doesn't support 'from_module' in tensordict
policy = actor.explore
else:
from tensordict import from_module
actor_detach = actor_cls(**actor_kwargs)
# Copy params to actor_detach without grad
from_module(actor).data.to_module(actor_detach)
policy = actor_detach.explore
qnet = critic_cls(**critic_kwargs)
qnet_target = critic_cls(**critic_kwargs)
qnet_target.load_state_dict(qnet.state_dict())
q_optimizer = optim.AdamW(
list(qnet.parameters()),
lr=torch.tensor(args.critic_learning_rate, device=device),
weight_decay=args.weight_decay,
)
actor_optimizer = optim.AdamW(
list(actor.parameters()),
lr=torch.tensor(args.actor_learning_rate, device=device),
weight_decay=args.weight_decay,
)
# Add learning rate schedulers
q_scheduler = optim.lr_scheduler.CosineAnnealingLR(
q_optimizer,
T_max=args.total_timesteps,
eta_min=torch.tensor(args.critic_learning_rate_end, device=device),
)
actor_scheduler = optim.lr_scheduler.CosineAnnealingLR(
actor_optimizer,
T_max=args.total_timesteps,
eta_min=torch.tensor(args.actor_learning_rate_end, device=device),
)
rb = SimpleReplayBuffer(
n_env=args.num_envs,
buffer_size=args.buffer_size,
n_obs=n_obs,
n_act=n_act,
n_critic_obs=n_critic_obs,
asymmetric_obs=envs.asymmetric_obs,
playground_mode=env_type == "mujoco_playground",
n_steps=args.num_steps,
gamma=args.gamma,
device=device,
)
policy_noise = args.policy_noise
noise_clip = args.noise_clip
def evaluate():
obs_normalizer.eval()
num_eval_envs = eval_envs.num_envs
episode_returns = torch.zeros(num_eval_envs, device=device)
episode_lengths = torch.zeros(num_eval_envs, device=device)
done_masks = torch.zeros(num_eval_envs, dtype=torch.bool, device=device)
if env_type == "isaaclab":
obs = eval_envs.reset(random_start_init=False)
else:
obs = eval_envs.reset()
# Run for a fixed number of steps
for i in range(eval_envs.max_episode_steps):
with (
torch.no_grad(),
autocast(
device_type=amp_device_type, dtype=amp_dtype, enabled=amp_enabled
),
):
obs = normalize_obs(obs)
actions = actor(obs)
next_obs, rewards, dones, _, infos = eval_envs.step(actions.float())
if env_type == "mtbench":
# We only report success rate in MTBench evaluation
rewards = (
infos["episode"]["success"].float() if "episode" in infos else 0.0
)
episode_returns = torch.where(
~done_masks, episode_returns + rewards, episode_returns
)
episode_lengths = torch.where(
~done_masks, episode_lengths + 1, episode_lengths
)
if env_type == "mtbench" and "episode" in infos:
dones = dones | infos["episode"]["success"]
done_masks = torch.logical_or(done_masks, dones)
if done_masks.all():
break
obs = next_obs
obs_normalizer.train()
return episode_returns.mean().item(), episode_lengths.mean().item()
def update_main(data, logs_dict):
with autocast(
device_type=amp_device_type, dtype=amp_dtype, enabled=amp_enabled
):
observations = data["observations"]
next_observations = data["next"]["observations"]
if envs.asymmetric_obs:
critic_observations = data["critic_observations"]
next_critic_observations = data["next"]["critic_observations"]
else:
critic_observations = observations
next_critic_observations = next_observations
actions = data["actions"]
rewards = data["next"]["rewards"]
dones = data["next"]["dones"].bool()
truncations = data["next"]["truncations"].bool()
if args.disable_bootstrap:
bootstrap = (~dones).float()
else:
bootstrap = (truncations | ~dones).float()
clipped_noise = torch.randn_like(actions)
clipped_noise = clipped_noise.mul(policy_noise).clamp(
-noise_clip, noise_clip
)
next_state_actions = (actor(next_observations) + clipped_noise).clamp(
action_low, action_high
)
discount = args.gamma ** data["next"]["effective_n_steps"]
with torch.no_grad():
qf1_next_target_projected, qf2_next_target_projected = (
qnet_target.projection(
next_critic_observations,
next_state_actions,
rewards,
bootstrap,
discount,
)
)
qf1_next_target_value = qnet_target.get_value(qf1_next_target_projected)
qf2_next_target_value = qnet_target.get_value(qf2_next_target_projected)
if args.use_cdq:
qf_next_target_dist = torch.where(
qf1_next_target_value.unsqueeze(1)
< qf2_next_target_value.unsqueeze(1),
qf1_next_target_projected,
qf2_next_target_projected,
)
qf1_next_target_dist = qf2_next_target_dist = qf_next_target_dist
else:
qf1_next_target_dist, qf2_next_target_dist = (
qf1_next_target_projected,
qf2_next_target_projected,
)
qf1, qf2 = qnet(critic_observations, actions)
qf1_loss = -torch.sum(
qf1_next_target_dist * F.log_softmax(qf1, dim=1), dim=1
).mean()
qf2_loss = -torch.sum(
qf2_next_target_dist * F.log_softmax(qf2, dim=1), dim=1
).mean()
qf_loss = qf1_loss + qf2_loss
q_optimizer.zero_grad(set_to_none=True)
scaler.scale(qf_loss).backward()
scaler.unscale_(q_optimizer)
critic_grad_norm = torch.nn.utils.clip_grad_norm_(
qnet.parameters(),
max_norm=args.max_grad_norm if args.max_grad_norm > 0 else float("inf"),
)
scaler.step(q_optimizer)
scaler.update()
q_scheduler.step()
logs_dict["critic_grad_norm"] = critic_grad_norm.detach()
logs_dict["qf_loss"] = qf_loss.detach()
logs_dict["qf_max"] = qf1_next_target_value.max().detach()
logs_dict["qf_min"] = qf1_next_target_value.min().detach()
return logs_dict
def update_pol(data, logs_dict):
with autocast(
device_type=amp_device_type, dtype=amp_dtype, enabled=amp_enabled
):
critic_observations = (
data["critic_observations"]
if envs.asymmetric_obs
else data["observations"]
)
qf1, qf2 = qnet(critic_observations, actor(data["observations"]))
qf1_value = qnet.get_value(F.softmax(qf1, dim=1))
qf2_value = qnet.get_value(F.softmax(qf2, dim=1))
if args.use_cdq:
qf_value = torch.minimum(qf1_value, qf2_value)
else:
qf_value = (qf1_value + qf2_value) / 2.0
actor_loss = -qf_value.mean()
actor_optimizer.zero_grad(set_to_none=True)
scaler.scale(actor_loss).backward()
scaler.unscale_(actor_optimizer)
actor_grad_norm = torch.nn.utils.clip_grad_norm_(
actor.parameters(),
max_norm=args.max_grad_norm if args.max_grad_norm > 0 else float("inf"),
)
scaler.step(actor_optimizer)
scaler.update()
actor_scheduler.step()
logs_dict["actor_grad_norm"] = actor_grad_norm.detach()
logs_dict["actor_loss"] = actor_loss.detach()
return logs_dict
if args.compile:
mode = None
update_main = torch.compile(update_main, mode=mode)
update_pol = torch.compile(update_pol, mode=mode)
policy = torch.compile(policy, mode=mode)
normalize_obs = torch.compile(obs_normalizer.forward, mode=mode)
normalize_critic_obs = torch.compile(critic_obs_normalizer.forward, mode=mode)
if args.reward_normalization:
update_stats = torch.compile(reward_normalizer.update_stats, mode=mode)
normalize_reward = torch.compile(reward_normalizer.forward, mode=mode)
else:
normalize_obs = obs_normalizer.forward
normalize_critic_obs = critic_obs_normalizer.forward
if args.reward_normalization:
update_stats = reward_normalizer.update_stats
normalize_reward = reward_normalizer.forward
if envs.asymmetric_obs:
obs, critic_obs = envs.reset_with_critic_obs()
critic_obs = torch.as_tensor(critic_obs, device=device, dtype=torch.float)
else:
obs = envs.reset()
if args.checkpoint_path:
# Load checkpoint if specified
torch_checkpoint = torch.load(
f"{args.checkpoint_path}", map_location=device, weights_only=False
)
actor.load_state_dict(torch_checkpoint["actor_state_dict"])
obs_normalizer.load_state_dict(torch_checkpoint["obs_normalizer_state"])
critic_obs_normalizer.load_state_dict(
torch_checkpoint["critic_obs_normalizer_state"]
)
qnet.load_state_dict(torch_checkpoint["qnet_state_dict"])
qnet_target.load_state_dict(torch_checkpoint["qnet_target_state_dict"])
global_step = torch_checkpoint["global_step"]
else:
global_step = 0
dones = None
pbar = tqdm.tqdm(total=args.total_timesteps, initial=global_step)
start_time = None
desc = ""
while global_step < args.total_timesteps:
logs_dict = TensorDict()
if (
start_time is None
and global_step >= args.measure_burnin + args.learning_starts
):
start_time = time.time()
measure_burnin = global_step
with (
torch.no_grad(),
autocast(device_type=amp_device_type, dtype=amp_dtype, enabled=amp_enabled),
):
norm_obs = normalize_obs(obs)
actions = policy(obs=norm_obs, dones=dones)
next_obs, rewards, dones, _, infos = envs.step(actions.float())
print(infos["time_outs"])
truncations = infos["time_outs"]
if args.reward_normalization:
if env_type == "mtbench":
task_ids_one_hot = obs[..., -envs.num_tasks :]
task_indices = torch.argmax(task_ids_one_hot, dim=1)
update_stats(rewards, dones.float(), task_ids=task_indices)
else:
update_stats(rewards, dones.float())
if envs.asymmetric_obs:
next_critic_obs = infos["observations"]["critic"]
# Compute 'true' next_obs and next_critic_obs for saving
true_next_obs = torch.where(
dones[:, None] > 0, infos["observations"]["raw"]["obs"], next_obs
)
if envs.asymmetric_obs:
true_next_critic_obs = torch.where(
dones[:, None] > 0,
infos["observations"]["raw"]["critic_obs"],
next_critic_obs,
)
transition = TensorDict(
{
"observations": obs,
"actions": torch.as_tensor(actions, device=device, dtype=torch.float),
"next": {
"observations": true_next_obs,
"rewards": torch.as_tensor(
rewards, device=device, dtype=torch.float
),
"truncations": truncations.long(),
"dones": dones.long(),
},
},
batch_size=(envs.num_envs,),
device=device,
)
if envs.asymmetric_obs:
transition["critic_observations"] = critic_obs
transition["next"]["critic_observations"] = true_next_critic_obs
obs = next_obs
if envs.asymmetric_obs:
critic_obs = next_critic_obs
rb.extend(transition)
batch_size = args.batch_size // args.num_envs
if global_step > args.learning_starts:
for i in range(args.num_updates):
data = rb.sample(batch_size)
data["observations"] = normalize_obs(data["observations"])
data["next"]["observations"] = normalize_obs(
data["next"]["observations"]
)
raw_rewards = data["next"]["rewards"]
if env_type in ["mtbench"] and args.reward_normalization:
# Multi-task reward normalization
task_ids_one_hot = data["observations"][..., -envs.num_tasks :]
task_indices = torch.argmax(task_ids_one_hot, dim=1)
data["next"]["rewards"] = normalize_reward(
raw_rewards, task_ids=task_indices
)
else:
data["next"]["rewards"] = normalize_reward(raw_rewards)
if envs.asymmetric_obs:
data["critic_observations"] = normalize_critic_obs(
data["critic_observations"]
)
data["next"]["critic_observations"] = normalize_critic_obs(
data["next"]["critic_observations"]
)
logs_dict = update_main(data, logs_dict)
if args.num_updates > 1:
if i % args.policy_frequency == 1:
logs_dict = update_pol(data, logs_dict)
else:
if global_step % args.policy_frequency == 0:
logs_dict = update_pol(data, logs_dict)
for param, target_param in zip(
qnet.parameters(), qnet_target.parameters()
):
target_param.data.copy_(
args.tau * param.data + (1 - args.tau) * target_param.data
)
if global_step % 100 == 0 and start_time is not None:
speed = (global_step - measure_burnin) / (time.time() - start_time)
pbar.set_description(f"{speed: 4.4f} sps, " + desc)
with torch.no_grad():
logs = {
"actor_loss": logs_dict["actor_loss"].mean(),
"qf_loss": logs_dict["qf_loss"].mean(),
"qf_max": logs_dict["qf_max"].mean(),
"qf_min": logs_dict["qf_min"].mean(),
"actor_grad_norm": logs_dict["actor_grad_norm"].mean(),
"critic_grad_norm": logs_dict["critic_grad_norm"].mean(),
"env_rewards": rewards.mean(),
"buffer_rewards": raw_rewards.mean(),
}
if args.eval_interval > 0 and global_step % args.eval_interval == 0:
print(f"Evaluating at global step {global_step}")
eval_avg_return, eval_avg_length = evaluate()
if env_type in ["humanoid_bench", "isaaclab", "mtbench"]:
# NOTE: Hacky way of evaluating performance, but just works
obs = envs.reset()
logs["eval_avg_return"] = eval_avg_return
logs["eval_avg_length"] = eval_avg_length
if args.use_wandb:
wandb.log(
{
"speed": speed,
"frame": global_step * args.num_envs,
"critic_lr": q_scheduler.get_last_lr()[0],
"actor_lr": actor_scheduler.get_last_lr()[0],
**logs,
},
step=global_step,
)
if (
args.save_interval > 0
and global_step > 0
and global_step % args.save_interval == 0
):
print(f"Saving model at global step {global_step}")
save_params(
global_step,
actor,
qnet,
qnet_target,
obs_normalizer,
critic_obs_normalizer,
args,
f"models/{run_name}_{global_step}.pt",
)
global_step += 1
pbar.update(1)
save_params(
global_step,
actor,
qnet,
qnet_target,
obs_normalizer,
critic_obs_normalizer,
args,
f"models/{run_name}_final.pt",
)
if __name__ == "__main__":
main()

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@ -0,0 +1,550 @@
import os
from dataclasses import dataclass
import tyro
@dataclass
class BaseArgs:
# Default hyperparameters -- specifically for HumanoidBench
# See MuJoCoPlaygroundArgs for default hyperparameters for MuJoCo Playground
# See IsaacLabArgs for default hyperparameters for IsaacLab
env_name: str = "HumanoidRun"
"""the id of the environment"""
agent: str = "fasttd3"
"""the agent to use: currently support [fasttd3, fasttd3_simbav2]"""
seed: int = 1
"""seed of the experiment"""
torch_deterministic: bool = True
"""if toggled, `torch.backends.cudnn.deterministic=False`"""
cuda: bool = True
"""if toggled, cuda will be enabled by default"""
device_rank: int = 0
"""the rank of the device"""
exp_name: str = os.path.basename(__file__)[: -len(".py")]
"""the name of this experiment"""
project: str = "FastTD3"
"""the project name"""
use_wandb: bool = True
"""whether to use wandb"""
checkpoint_path: str = None
"""the path to the checkpoint file"""
num_envs: int = 128
"""the number of environments to run in parallel"""
num_eval_envs: int = 128
"""the number of evaluation environments to run in parallel (only valid for MuJoCo Playground)"""
total_timesteps: int = 50000
"""total timesteps of the experiments"""
critic_learning_rate: float = 3e-4
"""the learning rate of the critic"""
actor_learning_rate: float = 3e-4
"""the learning rate for the actor"""
critic_learning_rate_end: float = 3e-4
"""the learning rate of the critic at the end of training"""
actor_learning_rate_end: float = 3e-4
"""the learning rate for the actor at the end of training"""
buffer_size: int = 1024 * 50
"""the replay memory buffer size"""
num_steps: int = 1
"""the number of steps to use for the multi-step return"""
gamma: float = 0.99
"""the discount factor gamma"""
tau: float = 0.1
"""target smoothing coefficient (default: 0.005)"""
batch_size: int = 32768
"""the batch size of sample from the replay memory"""
policy_noise: float = 0.001
"""the scale of policy noise"""
std_min: float = 0.001
"""the minimum scale of noise"""
std_max: float = 0.4
"""the maximum scale of noise"""
learning_starts: int = 10
"""timestep to start learning"""
policy_frequency: int = 2
"""the frequency of training policy (delayed)"""
noise_clip: float = 0.5
"""noise clip parameter of the Target Policy Smoothing Regularization"""
num_updates: int = 2
"""the number of updates to perform per step"""
init_scale: float = 0.01
"""the scale of the initial parameters"""
num_atoms: int = 101
"""the number of atoms"""
v_min: float = -250.0
"""the minimum value of the support"""
v_max: float = 250.0
"""the maximum value of the support"""
critic_hidden_dim: int = 1024
"""the hidden dimension of the critic network"""
actor_hidden_dim: int = 512
"""the hidden dimension of the actor network"""
critic_num_blocks: int = 2
"""(SimbaV2 only) the number of blocks in the critic network"""
actor_num_blocks: int = 1
"""(SimbaV2 only) the number of blocks in the actor network"""
use_cdq: bool = True
"""whether to use Clipped Double Q-learning"""
measure_burnin: int = 3
"""Number of burn-in iterations for speed measure."""
eval_interval: int = 2500
"""the interval to evaluate the model"""
render_interval: int = 500000
"""the interval to render the model"""
compile: bool = True
"""whether to use torch.compile."""
compile_mode: str = "reduce-overhead"
"""the mode of torch.compile."""
obs_normalization: bool = True
"""whether to enable observation normalization"""
reward_normalization: bool = False
"""whether to enable reward normalization"""
use_grad_norm_clipping: bool = False
"""whether to use gradient norm clipping."""
max_grad_norm: float = 0.0
"""the maximum gradient norm"""
amp: bool = True
"""whether to use amp"""
amp_dtype: str = "bf16"
"""the dtype of the amp"""
disable_bootstrap: bool = False
"""Whether to disable bootstrap in the critic learning"""
use_domain_randomization: bool = False
"""(Playground only) whether to use domain randomization"""
use_push_randomization: bool = False
"""(Playground only) whether to use push randomization"""
use_tuned_reward: bool = False
"""(Playground only) Use tuned reward for G1"""
action_bounds: float = 1.0
"""(IsaacLab only) the bounds of the action space (-action_bounds, action_bounds)"""
task_embedding_dim: int = 32
"""the dimension of the task embedding"""
weight_decay: float = 0.1
"""the weight decay of the optimizer"""
save_interval: int = 5000
"""the interval to save the model"""
def get_args():
"""
Parse command-line arguments and return the appropriate Args instance based on env_name.
"""
# First, parse all arguments using the base Args class
base_args = tyro.cli(BaseArgs)
# Map environment names to their specific Args classes
# For tasks not here, default hyperparameters are used
# See below links for available task list
# - HumanoidBench (https://arxiv.org/abs/2403.10506)
# - IsaacLab (https://isaac-sim.github.io/IsaacLab/main/source/overview/environments.html)
# - MuJoCo Playground (https://arxiv.org/abs/2502.08844)
env_to_args_class = {
# HumanoidBench
# NOTE: These tasks are not full list of HumanoidBench tasks
"h1hand-reach-v0": H1HandReachArgs,
"h1hand-balance-simple-v0": H1HandBalanceSimpleArgs,
"h1hand-balance-hard-v0": H1HandBalanceHardArgs,
"h1hand-pole-v0": H1HandPoleArgs,
"h1hand-truck-v0": H1HandTruckArgs,
"h1hand-maze-v0": H1HandMazeArgs,
"h1hand-push-v0": H1HandPushArgs,
"h1hand-basketball-v0": H1HandBasketballArgs,
"h1hand-window-v0": H1HandWindowArgs,
"h1hand-package-v0": H1HandPackageArgs,
"h1hand-truck-v0": H1HandTruckArgs,
# MuJoCo Playground
# NOTE: These tasks are not full list of MuJoCo Playground tasks
"G1JoystickFlatTerrain": G1JoystickFlatTerrainArgs,
"G1JoystickRoughTerrain": G1JoystickRoughTerrainArgs,
"T1JoystickFlatTerrain": T1JoystickFlatTerrainArgs,
"T1JoystickRoughTerrain": T1JoystickRoughTerrainArgs,
"LeapCubeReorient": LeapCubeReorientArgs,
"LeapCubeRotateZAxis": LeapCubeRotateZAxisArgs,
"Go1JoystickFlatTerrain": Go1JoystickFlatTerrainArgs,
"Go1JoystickRoughTerrain": Go1JoystickRoughTerrainArgs,
"Go1Getup": Go1GetupArgs,
"CheetahRun": CheetahRunArgs, # NOTE: Example config for DeepMind Control Suite
# IsaacLab
# NOTE: These tasks are not full list of IsaacLab tasks
"Isaac-Lift-Cube-Franka-v0": IsaacLiftCubeFrankaArgs,
"Isaac-Open-Drawer-Franka-v0": IsaacOpenDrawerFrankaArgs,
"Isaac-Velocity-Flat-H1-v0": IsaacVelocityFlatH1Args,
"Isaac-Velocity-Flat-G1-v0": IsaacVelocityFlatG1Args,
"Isaac-Velocity-Rough-H1-v0": IsaacVelocityRoughH1Args,
"Isaac-Velocity-Rough-G1-v0": IsaacVelocityRoughG1Args,
"Isaac-Repose-Cube-Allegro-Direct-v0": IsaacReposeCubeAllegroDirectArgs,
"Isaac-Repose-Cube-Shadow-Direct-v0": IsaacReposeCubeShadowDirectArgs,
# MTBench
"MTBench-meta-world-v2-mt10": MetaWorldMT10Args,
"MTBench-meta-world-v2-mt50": MetaWorldMT50Args,
}
# If the provided env_name has a specific Args class, use it
if base_args.env_name in env_to_args_class:
specific_args_class = env_to_args_class[base_args.env_name]
# Re-parse with the specific class, maintaining any user overrides
specific_args = tyro.cli(specific_args_class)
return specific_args
if base_args.env_name.startswith("h1hand-") or base_args.env_name.startswith("h1-"):
# HumanoidBench
specific_args = tyro.cli(HumanoidBenchArgs)
elif base_args.env_name.startswith("Isaac-"):
# IsaacLab
specific_args = tyro.cli(IsaacLabArgs)
elif base_args.env_name.startswith("MTBench-"):
# MTBench
specific_args = tyro.cli(MTBenchArgs)
else:
# MuJoCo Playground
specific_args = tyro.cli(MuJoCoPlaygroundArgs)
return specific_args
@dataclass
class HumanoidBenchArgs(BaseArgs):
# See HumanoidBench (https://arxiv.org/abs/2403.10506) for available task list
total_timesteps: int = 100000
@dataclass
class H1HandReachArgs(HumanoidBenchArgs):
env_name: str = "h1hand-reach-v0"
v_min: float = -2000.0
v_max: float = 2000.0
@dataclass
class H1HandBalanceSimpleArgs(HumanoidBenchArgs):
env_name: str = "h1hand-balance-simple-v0"
total_timesteps: int = 200000
@dataclass
class H1HandBalanceHardArgs(HumanoidBenchArgs):
env_name: str = "h1hand-balance-hard-v0"
total_timesteps: int = 1000000
@dataclass
class H1HandPoleArgs(HumanoidBenchArgs):
env_name: str = "h1hand-pole-v0"
total_timesteps: int = 150000
@dataclass
class H1HandTruckArgs(HumanoidBenchArgs):
env_name: str = "h1hand-truck-v0"
total_timesteps: int = 500000
@dataclass
class H1HandMazeArgs(HumanoidBenchArgs):
env_name: str = "h1hand-maze-v0"
v_min: float = -1000.0
v_max: float = 1000.0
@dataclass
class H1HandPushArgs(HumanoidBenchArgs):
env_name: str = "h1hand-push-v0"
v_min: float = -1000.0
v_max: float = 1000.0
total_timesteps: int = 1000000
@dataclass
class H1HandBasketballArgs(HumanoidBenchArgs):
env_name: str = "h1hand-basketball-v0"
v_min: float = -2000.0
v_max: float = 2000.0
total_timesteps: int = 250000
@dataclass
class H1HandWindowArgs(HumanoidBenchArgs):
env_name: str = "h1hand-window-v0"
total_timesteps: int = 250000
@dataclass
class H1HandPackageArgs(HumanoidBenchArgs):
env_name: str = "h1hand-package-v0"
v_min: float = -10000.0
v_max: float = 10000.0
@dataclass
class H1HandTruckArgs(HumanoidBenchArgs):
env_name: str = "h1hand-truck-v0"
v_min: float = -1000.0
v_max: float = 1000.0
@dataclass
class MuJoCoPlaygroundArgs(BaseArgs):
# Default hyperparameters for many of Playground environments
v_min: float = -150.0
v_max: float = 150.0
buffer_size: int = 1024 * 10
num_envs: int = 1024
num_eval_envs: int = 1024
gamma: float = 0.99
@dataclass
class MTBenchArgs(BaseArgs):
# Default hyperparameters for MTBench
reward_normalization: bool = True
v_min: float = -10.0
v_max: float = 10.0
buffer_size: int = 2048 # 2K is usually enough for MTBench
num_envs: int = 4096
num_eval_envs: int = 4096
gamma: float = 0.97
num_steps: int = 8
@dataclass
class MetaWorldMT10Args(MTBenchArgs):
# This config achieves 97 ~ 98% success rate within 10k steps (15-20 mins on A100)
env_name: str = "MTBench-meta-world-v2-mt10"
num_envs: int = 4096
num_eval_envs: int = 4096
num_steps: int = 8
gamma: float = 0.97
@dataclass
class MetaWorldMT50Args(MTBenchArgs):
# FastTD3 + SimbaV2 achieves >90% success rate within 20k steps (80 mins on A100)
# Performance further improves with more training steps, slowly.
env_name: str = "MTBench-meta-world-v2-mt50"
num_envs: int = 8192
num_eval_envs: int = 8192
num_steps: int = 8
gamma: float = 0.99
@dataclass
class G1JoystickFlatTerrainArgs(MuJoCoPlaygroundArgs):
env_name: str = "G1JoystickFlatTerrain"
total_timesteps: int = 100000
v_min: float = -10.0
v_max: float = 10.0
buffer_size: int = 128 # 1024 * 10
num_envs: int = 1024
num_eval_envs: int = 1024
gamma: float = 0.97
critic_hidden_dim: int = 1024
batch_size: int = 8129
@dataclass
class G1JoystickRoughTerrainArgs(MuJoCoPlaygroundArgs):
env_name: str = "G1JoystickRoughTerrain"
total_timesteps: int = 100000
v_min: float = -10.0
v_max: float = 10.0
buffer_size: int = 128 # 1024 * 10
num_envs: int = 1024
num_eval_envs: int = 1024
gamma: float = 0.97
critic_hidden_dim: int = 1024
batch_size: int = 8129
@dataclass
class T1JoystickFlatTerrainArgs(MuJoCoPlaygroundArgs):
env_name: str = "T1JoystickFlatTerrain"
total_timesteps: int = 100000
v_min: float = -10.0
v_max: float = 10.0
buffer_size: int = 128 # 1024 * 10
num_envs: int = 1024
num_eval_envs: int = 1024
gamma: float = 0.97
critic_hidden_dim: int = 1024
batch_size: int = 8129
@dataclass
class T1JoystickRoughTerrainArgs(MuJoCoPlaygroundArgs):
env_name: str = "T1JoystickRoughTerrain"
total_timesteps: int = 100000
v_min: float = -10.0
v_max: float = 10.0
buffer_size: int = 128 # 1024 * 10
num_envs: int = 1024
num_eval_envs: int = 1024
gamma: float = 0.97
critic_hidden_dim: int = 1024
batch_size: int = 8129
@dataclass
class T1LowDofJoystickFlatTerrainArgs(MuJoCoPlaygroundArgs):
env_name: str = "T1LowDofJoystickFlatTerrain"
total_timesteps: int = 1000000
@dataclass
class T1LowDofJoystickRoughTerrainArgs(MuJoCoPlaygroundArgs):
env_name: str = "T1LowDofJoystickRoughTerrain"
total_timesteps: int = 1000000
@dataclass
class CheetahRunArgs(MuJoCoPlaygroundArgs):
# NOTE: This config will work for most DMC tasks, though we haven't tested DMC extensively.
# Future research can consider using LayerNorm as we find it sometimes works better for DMC tasks.
env_name: str = "CheetahRun"
num_steps: int = 3
v_min: float = -500.0
v_max: float = 500.0
std_min: float = 0.1
policy_noise: float = 0.1
@dataclass
class Go1JoystickFlatTerrainArgs(MuJoCoPlaygroundArgs):
env_name: str = "Go1JoystickFlatTerrain"
total_timesteps: int = 50000
std_min: float = 0.2
std_max: float = 0.8
policy_noise: float = 0.2
num_updates: int = 8
@dataclass
class Go1JoystickRoughTerrainArgs(MuJoCoPlaygroundArgs):
env_name: str = "Go1JoystickRoughTerrain"
total_timesteps: int = 50000
std_min: float = 0.2
std_max: float = 0.8
policy_noise: float = 0.2
num_updates: int = 8
@dataclass
class Go1GetupArgs(MuJoCoPlaygroundArgs):
env_name: str = "Go1Getup"
total_timesteps: int = 50000
std_min: float = 0.2
std_max: float = 0.8
policy_noise: float = 0.2
num_updates: int = 8
@dataclass
class LeapCubeReorientArgs(MuJoCoPlaygroundArgs):
env_name: str = "LeapCubeReorient"
num_steps: int = 3
gamma: float = 0.99
policy_noise: float = 0.2
v_min: float = -50.0
v_max: float = 50.0
use_cdq: bool = False
@dataclass
class LeapCubeRotateZAxisArgs(MuJoCoPlaygroundArgs):
env_name: str = "LeapCubeRotateZAxis"
num_steps: int = 1
policy_noise: float = 0.2
gamma: float = 0.99
v_min: float = -10.0
v_max: float = 10.0
use_cdq: bool = False
@dataclass
class IsaacLabArgs(BaseArgs):
v_min: float = -10.0
v_max: float = 10.0
buffer_size: int = 1024 * 10
num_envs: int = 4096
num_eval_envs: int = 4096
action_bounds: float = 1.0
std_max: float = 0.4
num_atoms: int = 251
render_interval: int = 0 # IsaacLab does not support rendering in our codebase
total_timesteps: int = 100000
@dataclass
class IsaacLiftCubeFrankaArgs(IsaacLabArgs):
# Value learning is unstable for Lift Cube task Due to brittle reward shaping
# Therefore, we need to disable bootstrap from 'reset_obs' in IsaacLab
# Higher UTD works better for manipulation tasks
env_name: str = "Isaac-Lift-Cube-Franka-v0"
num_updates: int = 8
v_min: float = -50.0
v_max: float = 50.0
std_max: float = 0.8
num_envs: int = 1024
num_eval_envs: int = 1024
action_bounds: float = 3.0
disable_bootstrap: bool = True
total_timesteps: int = 20000
@dataclass
class IsaacOpenDrawerFrankaArgs(IsaacLabArgs):
# Higher UTD works better for manipulation tasks
env_name: str = "Isaac-Open-Drawer-Franka-v0"
v_min: float = -50.0
v_max: float = 50.0
num_updates: int = 8
action_bounds: float = 3.0
total_timesteps: int = 20000
@dataclass
class IsaacVelocityFlatH1Args(IsaacLabArgs):
env_name: str = "Isaac-Velocity-Flat-H1-v0"
num_steps: int = 8
num_updates: int = 4
total_timesteps: int = 75000
@dataclass
class IsaacVelocityFlatG1Args(IsaacLabArgs):
env_name: str = "Isaac-Velocity-Flat-G1-v0"
num_steps: int = 8
num_updates: int = 4
total_timesteps: int = 50000
@dataclass
class IsaacVelocityRoughH1Args(IsaacLabArgs):
env_name: str = "Isaac-Velocity-Rough-H1-v0"
num_steps: int = 8
num_updates: int = 4
buffer_size: int = 1024 * 5 # To reduce memory usage
total_timesteps: int = 50000
@dataclass
class IsaacVelocityRoughG1Args(IsaacLabArgs):
env_name: str = "Isaac-Velocity-Rough-G1-v0"
num_steps: int = 8
num_updates: int = 4
buffer_size: int = 1024 * 5 # To reduce memory usage
total_timesteps: int = 50000
@dataclass
class IsaacReposeCubeAllegroDirectArgs(IsaacLabArgs):
env_name: str = "Isaac-Repose-Cube-Allegro-Direct-v0"
total_timesteps: int = 100000
v_min: float = -500.0
v_max: float = 500.0
@dataclass
class IsaacReposeCubeShadowDirectArgs(IsaacLabArgs):
env_name: str = "Isaac-Repose-Cube-Shadow-Direct-v0"
total_timesteps: int = 100000
v_min: float = -500.0
v_max: float = 500.0

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from dataclasses import dataclass, replace
import functools
import os
import random
import sys
import copy
import time
import numpy as np
import tqdm
from omegaconf import DictConfig, OmegaConf
import wandb
try:
# Required for avoiding IsaacGym import error
import isaacgym
except ImportError:
pass
import hydra
import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim
from torchinfo import summary
from tensordict import TensorDict
from torch.amp import GradScaler
from reppo.torchrl.envs import make_envs
from reppo.network_utils.torch_models import Actor, Critic
from reppo.torchrl.reppo import (
EmpiricalNormalization,
hl_gauss,
)
try:
import jax.numpy as jnp
except ImportError:
pass
torch.set_float32_matmul_precision("medium")
os.environ["TORCHDYNAMO_INLINE_INBUILT_NN_MODULES"] = "1"
os.environ["OMP_NUM_THREADS"] = "1"
if sys.platform != "darwin":
os.environ["MUJOCO_GL"] = "egl"
else:
os.environ["MUJOCO_GL"] = "glfw"
os.environ["XLA_PYTHON_CLIENT_PREALLOCATE"] = "false"
os.environ["JAX_DEFAULT_MATMUL_PRECISION"] = "highest"
@dataclass(slots=True)
class TrainState:
device: torch.device
obs: torch.Tensor
critic_obs: torch.Tensor
actor: Actor
old_actor: Actor
critic: Critic
normalizer: EmpiricalNormalization
critic_normalizer: EmpiricalNormalization
actor_optimizer: optim.Optimizer
critic_optimizer: optim.Optimizer
scaler: GradScaler
def compile(self):
self.actor.compile()
self.old_actor.compile()
self.critic.compile()
self.normalizer.compile()
self.critic_normalizer.compile()
def get_autocast_context(cfg: DictConfig):
amp_enabled = (
cfg.platform.amp_enabled and cfg.platform.cuda and torch.cuda.is_available()
)
amp_device = (
"cuda"
if cfg.platform.cuda and torch.cuda.is_available()
else "mps"
if cfg.platform.cuda and torch.backends.mps.is_available()
else "cpu"
)
amp_dtype = torch.bfloat16 if cfg.platform.amp_dtype == "bf16" else torch.float32
return functools.partial(
torch.amp.autocast,
device_type=amp_device,
dtype=amp_dtype,
enabled=amp_enabled,
)
def make_collect_fn(cfg: DictConfig, env):
autocast = get_autocast_context(cfg)
asymmetric_obs = env.asymmetric_obs
def collect_fn(
train_state: TrainState,
) -> tuple[TrainState, TensorDict, list[dict]]:
transitions = []
info_list = []
obs = train_state.obs
critic_obs = train_state.critic_obs
for _ in range(cfg.hyperparameters.num_steps):
with autocast():
norm_obs = train_state.normalizer(obs)
norm_critic_obs = train_state.critic_normalizer(critic_obs)
with torch.inference_mode():
pi, _, _, _ = train_state.actor(norm_obs)
actions = pi.sample()
next_obs, rewards, dones, truncations, infos = env.step(actions)
if asymmetric_obs:
next_critic_obs = infos["observations"]["critic"]
else:
next_critic_obs = next_obs
with (
torch.inference_mode(),
autocast(),
):
if (
cfg.env.get("has_final_obs", False)
and cfg.env.get("partial_reset", False)
and "final_observation" in infos
):
_next_obs = infos["final_observation"]
_next_critic_obs = _next_obs
else:
_next_obs = next_obs
_next_critic_obs = next_critic_obs
norm_next_obs = train_state.normalizer(_next_obs)
next_pi, _, temperature, _ = train_state.actor(norm_next_obs)
next_actions = next_pi.sample()
next_log_probs = next_pi.log_prob(
next_actions.clip(-1 + 1e-6, 1 - 1e-6)
).sum(-1)
norm_next_critic_obs = train_state.critic_normalizer(_next_critic_obs)
next_value, _, _, next_embedding = train_state.critic(
norm_next_critic_obs, next_actions
)
rewards = (
rewards - cfg.hyperparameters.gamma * next_log_probs * temperature
)
transitions.append(
TensorDict(
{
"observations": norm_obs,
"critic_observations": norm_critic_obs,
"actions": actions,
"log_probs": pi.log_prob(actions.clip(-0.999, 0.999)).sum(-1),
"rewards": rewards.unsqueeze(-1),
"next_embeddings": next_embedding,
"next_values": next_value.unsqueeze(-1),
"dones": dones.unsqueeze(-1).float(),
"truncations": truncations.unsqueeze(-1).float(),
},
batch_size=(env.num_envs,),
)
)
info_list.append(infos)
obs = next_obs
critic_obs = next_critic_obs
train_state = replace(train_state, obs=obs, critic_obs=critic_obs)
return (
train_state,
torch.stack(transitions, dim=0),
info_list,
)
return collect_fn
def make_postprocess_fn(cfg: DictConfig, env):
@torch.compiler.disable()
def compute_gve(rewards, dones, truncated, next_values, device: torch.device):
gves = []
last_gve = 0
truncated[-1] = 1.0
for t in reversed(range(cfg.hyperparameters.num_steps)):
lambda_sum = (
cfg.hyperparameters.lmbda * last_gve
+ (1.0 - cfg.hyperparameters.lmbda) * next_values[t]
)
delta = cfg.hyperparameters.gamma * torch.where(
truncated[t].bool(), next_values[t], (1.0 - dones[t]) * lambda_sum
)
last_gve = rewards[t] + delta
gves.insert(0, last_gve)
return gves
def postprocess(train_state: TrainState, transition: TensorDict):
gve = compute_gve(
rewards=transition["rewards"],
dones=transition["dones"],
truncated=transition["truncations"],
next_values=transition["next_values"],
device=train_state.device,
)
# Flatten all time and environment dimensions into a single batch dimension
data = TensorDict(
{
"observations": transition["observations"],
"critic_observations": transition["critic_observations"],
"actions": transition["actions"],
"rewards": transition["rewards"],
"next_embeddings": transition["next_embeddings"],
"next_values": transition["next_values"],
"dones": transition["dones"],
"truncations": transition["truncations"],
"gve": torch.stack(gve),
},
batch_size=(
cfg.hyperparameters.num_steps,
cfg.hyperparameters.num_envs,
),
device=train_state.device,
)
return data.float().flatten(0, 1).detach()
return postprocess
def make_critic_update_fn(cfg: DictConfig, train_state: TrainState):
autocast = get_autocast_context(cfg)
def update(data: TensorDict):
qnet = train_state.critic
q_optimizer = train_state.critic_optimizer
with autocast():
critic_observations = data["critic_observations"]
actions = data["actions"]
targets = data["gve"]
target_embeddings = data["next_embeddings"]
truncations = data["truncations"].squeeze(-1)
if cfg.env.get("partial_reset", False):
truncation_mask = torch.ones_like(
truncations, dtype=torch.bool, device=train_state.device
)
else:
truncation_mask = 1.0 - truncations
qf_target_dist = hl_gauss(
targets,
cfg.hyperparameters.vmin,
cfg.hyperparameters.vmax,
cfg.hyperparameters.num_bins,
)
_, qf1, embedding, _ = qnet(critic_observations, actions)
qf_loss = -(
truncation_mask
* torch.sum(qf_target_dist * F.log_softmax(qf1, dim=-1), dim=-1)
).mean()
embedding_loss = (
truncation_mask
* F.mse_loss(
embedding,
target_embeddings,
reduction="none",
).mean(dim=-1)
).mean()
qf_loss = qf_loss + cfg.hyperparameters.aux_loss_mult * embedding_loss
q_optimizer.zero_grad(set_to_none=True)
train_state.scaler.scale(qf_loss).backward()
train_state.scaler.unscale_(q_optimizer)
critic_grad_norm = torch.nn.utils.clip_grad_norm_(
qnet.parameters(), max_norm=cfg.hyperparameters.max_grad_norm
)
train_state.scaler.step(q_optimizer)
train_state.scaler.update()
logs_dict = {
"critic_grad_norm": critic_grad_norm.detach(),
"qf_loss": qf_loss.detach(),
"qf_max": targets.max().detach(),
"qf_min": targets.min().detach(),
"qf_mean": targets.mean().detach(),
"embedding_loss": embedding_loss.detach(),
}
return logs_dict
return update
def make_actor_update_fn(cfg: DictConfig, train_state: TrainState):
autocast = get_autocast_context(cfg)
def update(data: TensorDict):
actor = train_state.actor
old_actor = train_state.old_actor
qnet = train_state.critic
actor_optimizer = train_state.actor_optimizer
scaler = train_state.scaler
critic_obs = data["critic_observations"]
with autocast():
pi, _, temperature, beta = actor(data["observations"])
actions = pi.rsample()
log_probs = pi.log_prob(actions.clip(-1 + 1e-6, 1 - 1e-6)).sum(-1)
entropy = -log_probs
qf, _, _, _ = qnet(critic_obs, actions)
actor_loss = -qf + temperature.detach() * log_probs
# compute KL
old_pi, _, _, _ = old_actor(data["observations"])
old_pi_actions = old_pi.sample((16,)).clip(-1 + 1e-6, 1 - 1e-6)
old_log_probs = old_pi.log_prob(old_pi_actions).sum(-1).mean(0)
new_pi_log_probs = pi.log_prob(old_pi_actions).sum(-1).mean(0)
kl = old_log_probs - new_pi_log_probs
if cfg.hyperparameters.actor_kl_clip_mode == "clipped":
actor_loss = torch.where(
kl < cfg.hyperparameters.kl_bound,
actor_loss,
kl * beta.detach(),
).mean()
elif cfg.hyperparameters.actor_kl_clip_mode == "full":
actor_loss = actor_loss + kl * beta.detach()
elif cfg.hyperparameters.actor_kl_clip_mode == "value":
actor_loss = actor_loss
else:
raise ValueError(
f"Unknown actor kl clip mode: {cfg.hyperparameters.actor_kl_clip_mode}"
)
# temperature updates
target_entropy = (
actions.shape[-1] * cfg.hyperparameters.ent_target_mult
) # -0.5 * np.prod(envs.action_space.shape)
entropy_loss = (target_entropy + entropy).detach().mean() * temperature
lagrangian_loss = (
-beta * (kl - cfg.hyperparameters.kl_bound).mean().detach()
)
actor_loss = (actor_loss + entropy_loss + lagrangian_loss).mean()
actor_optimizer.zero_grad(set_to_none=True)
scaler.scale(actor_loss).backward()
scaler.unscale_(actor_optimizer)
actor_grad_norm = torch.nn.utils.clip_grad_norm_(
actor.parameters(), max_norm=cfg.hyperparameters.max_grad_norm
)
scaler.step(actor_optimizer)
scaler.update()
logs_dict = {
"actor_grad_norm": actor_grad_norm.detach(),
"actor_loss": actor_loss.detach(),
"kl": kl.detach(),
"entropy": entropy.detach(),
"temperature": temperature.detach(),
"lagrangian": beta.detach(),
"entropy_loss": entropy_loss.detach(),
"lagrangian_loss": lagrangian_loss.detach(),
}
return logs_dict
return update
def make_evaluate_fn(cfg: DictConfig, eval_envs):
autocast = get_autocast_context(cfg)
@torch.inference_mode()
def evaluate(
train_state: TrainState, stochastic_eval: bool = False
) -> tuple[int | float | bool, int | float | bool]:
train_state.normalizer.eval()
num_eval_envs = eval_envs.num_envs
episode_returns = torch.zeros(num_eval_envs, device=train_state.device)
episode_lengths = torch.zeros(num_eval_envs, device=train_state.device)
done_masks = torch.zeros(
num_eval_envs, dtype=torch.bool, device=train_state.device
)
if cfg.env.type == "isaaclab" or cfg.env.asymmetric_observation:
obs, _ = eval_envs.reset(random_start_init=False)
else:
obs = eval_envs.reset()
# Run for a fixed number of steps
for i in range(eval_envs.max_episode_steps):
with autocast():
obs = train_state.normalizer(obs)
action_dist, det_actions, _, _ = train_state.actor(obs)
if stochastic_eval:
actions = action_dist.sample()
else:
actions = det_actions
next_obs, rewards, dones, _, infos = eval_envs.step(actions)
episode_returns = torch.where(
~done_masks, episode_returns + rewards, episode_returns
)
episode_lengths = torch.where(
~done_masks, episode_lengths + 1, episode_lengths
)
done_masks = torch.logical_or(done_masks, dones)
if done_masks.all():
break
obs = next_obs
train_state.normalizer.train()
if cfg.env.type == "maniskill":
# combine log_infos
info = {
"info_return": infos["log_info"]["return"].mean(),
"episode_len": infos["log_info"]["episode_len"].float().mean(),
"success": infos["log_info"]["success"].float().mean(),
"return": episode_returns.mean().item(),
}
else:
info = {}
return episode_returns.mean().item(), episode_lengths.mean().item(), info
return evaluate
def configure_platform(cfg: DictConfig) -> DictConfig:
cfg.platform.amp_enabled = (
cfg.platform.amp_enabled and cfg.platform.cuda and torch.cuda.is_available()
)
cfg.platform.amp_device = (
"cuda"
if cfg.platform.cuda and torch.cuda.is_available()
else "mps"
if cfg.platform.cuda and torch.backends.mps.is_available()
else "cpu"
)
return cfg
@hydra.main(
version_base=None,
config_path="../../config",
config_name="sac",
)
def main(cfg):
cfg.hyperparameters = OmegaConf.merge(cfg.hyperparameters, cfg.experiment_overrides)
cfg = configure_platform(cfg)
run_name = f"{cfg.env.name}_torch_{cfg.seed}"
scaler = GradScaler(
enabled=cfg.platform.amp_enabled and cfg.platform.amp_dtype == torch.float16
)
num_batches = cfg.hyperparameters.num_mini_batches
batch_size = (
cfg.hyperparameters.num_envs * cfg.hyperparameters.num_steps // num_batches
)
wandb.init(
project=cfg.wandb.project,
name=run_name,
config=OmegaConf.to_container(cfg),
save_code=True,
)
random.seed(cfg.seed)
np.random.seed(cfg.seed)
torch.manual_seed(cfg.seed)
torch.backends.cudnn.deterministic = cfg.platform.torch_deterministic
if not cfg.platform.cuda:
device = torch.device("cpu")
else:
if torch.cuda.is_available():
device = torch.device(f"cuda:{cfg.platform.device_rank}")
elif torch.backends.mps.is_available():
device = torch.device(f"mps:{cfg.platform.device_rank}")
else:
raise ValueError("No GPU available")
print(f"Using device: {device}")
envs, eval_envs = make_envs(cfg=cfg, device=device, seed=cfg.seed)
n_act = envs.num_actions
n_obs = envs.num_obs if type(envs.num_obs) == int else envs.num_obs[0]
if envs.asymmetric_obs:
n_critic_obs = (
envs.num_privileged_obs
if type(envs.num_privileged_obs) == int
else envs.num_privileged_obs[0]
)
else:
n_critic_obs = n_obs
if cfg.hyperparameters.normalize_env:
obs_normalizer = EmpiricalNormalization(shape=n_obs, device=device)
critic_obs_normalizer = EmpiricalNormalization(
shape=n_critic_obs, device=device
)
else:
obs_normalizer = nn.Identity()
critic_obs_normalizer = nn.Identity()
actor = Actor(
n_obs=n_obs,
n_act=n_act,
ent_start=cfg.hyperparameters.ent_start,
kl_start=cfg.hyperparameters.kl_start,
hidden_dim=cfg.hyperparameters.actor_hidden_dim,
use_norm=cfg.hyperparameters.use_actor_norm,
layers=cfg.hyperparameters.num_actor_layers,
min_std=cfg.hyperparameters.actor_min_std,
device=device,
)
old_actor = copy.deepcopy(actor)
qnet = Critic(
n_obs=n_critic_obs,
n_act=n_act,
num_atoms=cfg.hyperparameters.num_bins,
vmin=cfg.hyperparameters.vmin,
vmax=cfg.hyperparameters.vmax,
hidden_dim=cfg.hyperparameters.critic_hidden_dim,
use_norm=cfg.hyperparameters.use_critic_norm,
use_encoder_norm=False,
encoder_layers=cfg.hyperparameters.num_critic_encoder_layers,
head_layers=cfg.hyperparameters.num_critic_head_layers,
pred_layers=cfg.hyperparameters.num_critic_pred_layers,
device=device,
)
q_optimizer = optim.AdamW(
list(qnet.parameters()),
lr=torch.tensor(cfg.hyperparameters.lr, device=device),
)
actor_optimizer = optim.AdamW(
list(actor.parameters()),
lr=torch.tensor(cfg.hyperparameters.lr, device=device),
)
if envs.asymmetric_obs:
obs, critic_obs = envs.reset_with_critic_obs()
critic_obs = torch.as_tensor(critic_obs, device=device, dtype=torch.float)
else:
obs = envs.reset()
critic_obs = obs
train_state = TrainState(
obs=obs,
critic_obs=critic_obs,
actor=actor,
old_actor=old_actor,
critic=qnet,
normalizer=obs_normalizer,
critic_normalizer=critic_obs_normalizer,
actor_optimizer=actor_optimizer,
critic_optimizer=q_optimizer,
device=device,
scaler=scaler,
)
print(
summary(
train_state.critic,
input_data=(critic_obs[:1], torch.zeros((1, n_act), device=device)),
depth=10,
)
)
print(summary(train_state.actor, input_data=(obs[:1],), depth=10))
# create functions
collect_fn = make_collect_fn(cfg, envs)
postprocess_fn = make_postprocess_fn(cfg, envs)
update_critic = make_critic_update_fn(cfg, train_state)
update_actor = make_actor_update_fn(cfg, train_state)
evaluate = make_evaluate_fn(cfg, eval_envs)
if cfg.platform.compile:
mode = "max-autotune-no-cudagraphs"
update_critic = torch.compile(update_critic, mode=mode)
update_actor = torch.compile(update_actor, mode=mode)
postprocess_fn = torch.compile(postprocess_fn, mode=mode)
train_state.compile()
# TODO: Support checkpoint loading
# if cfg.checkpoint_path:
# # Load checkpoint if specified
# torch_checkpoint = torch.load(
# f"{cfg.checkpoint_path}", map_location=device, weights_only=False
# )
# actor.load_state_dict(torch_checkpoint["actor_state_dict"])
# obs_normalizer.load_state_dict(torch_checkpoint["obs_normalizer_state"])
# critic_obs_normalizer.load_state_dict(
# torch_checkpoint["critic_obs_normalizer_state"]
# )
# qnet.load_state_dict(torch_checkpoint["qnet_state_dict"])
# qnet_target.load_state_dict(torch_checkpoint["qnet_target_state_dict"])
# global_step = torch_checkpoint["global_step"]
# else:
global_step = 0
total_env_steps = (
cfg.hyperparameters.total_time_steps
// (cfg.hyperparameters.num_envs * cfg.hyperparameters.num_steps)
+ 1
)
pbar = tqdm.tqdm(total=cfg.hyperparameters.total_time_steps, initial=global_step)
start_time = None
desc = ""
eval_interval = total_env_steps // cfg.hyperparameters.num_eval
stochastic_eval = cfg.env.get("stochastic_eval", False)
while global_step < total_env_steps:
if start_time is None and global_step >= cfg.measure_burnin:
start_time = time.time()
measure_burnin = global_step
train_state, transition, infos = collect_fn(train_state)
data = postprocess_fn(train_state, transition)
for _ in range(cfg.hyperparameters.num_epochs):
indices = torch.randperm(
cfg.hyperparameters.num_envs * cfg.hyperparameters.num_steps,
device=device,
)
data = data[indices].contiguous()
for j in range(num_batches):
mini_batch = data[j * batch_size : (j + 1) * batch_size]
critic_logs_dict = update_critic(mini_batch)
actor_logs_dict = update_actor(mini_batch)
logs_dict = {
**critic_logs_dict,
**actor_logs_dict,
}
for param, target_param in zip(actor.parameters(), old_actor.parameters()):
target_param.data.copy_(param.data)
if start_time is not None:
# @TODO: shouldn't that be env_steps per second?
speed = (
cfg.hyperparameters.num_envs
* cfg.hyperparameters.num_steps
* (global_step - measure_burnin)
/ (time.time() - start_time)
)
pbar.set_description(f"{speed: 4.4f} sps, " + desc)
with torch.inference_mode():
logs = {
"critic/qf_loss": logs_dict["qf_loss"].mean(),
"critic/qf_max": logs_dict["qf_max"].mean(),
"critic/qf_min": logs_dict["qf_min"].mean(),
"critic/qf_mean": logs_dict["qf_mean"].mean(),
"critic/embedding_loss": logs_dict["embedding_loss"].mean(),
"critic/critic_grad_norm": logs_dict["critic_grad_norm"].mean(),
"actor/actor_loss": logs_dict["actor_loss"].mean(),
"actor/actor_grad_norm": logs_dict["actor_grad_norm"].mean(),
"actor/kl": logs_dict["kl"].mean(),
"actor/entropy": logs_dict["entropy"].mean(),
"actor/temperature": logs_dict["temperature"].mean(),
"actor/lagrangian": logs_dict["lagrangian"].mean(),
"actor/entropy_loss": logs_dict["entropy_loss"].mean(),
"actor/lagrangian_loss": logs_dict["lagrangian_loss"].mean(),
"train/rewards_batch": data["rewards"].mean(),
}
if cfg.env.type == "maniskill":
logs.update(
{
"train/return": torch.stack(
[info["log_info"]["return"] for info in infos]
).mean(),
"train/episode_len": torch.stack(
[info["log_info"]["episode_len"] for info in infos]
)
.float()
.mean(),
"train/success": torch.stack(
[info["log_info"]["success"] for info in infos]
)
.float()
.mean(),
}
)
if eval_interval > 0 and global_step % eval_interval == 0:
print(f"Evaluating at global step {global_step}")
if stochastic_eval:
eval_avg_return, eval_avg_length, stoch_eval_info = evaluate(
train_state, stochastic_eval=stochastic_eval
)
eval_avg_return, eval_avg_length, eval_info = evaluate(
train_state
)
eval_info = {
**eval_info,
**{f"stoch/{k}": v for k, v in stoch_eval_info.items()},
}
else:
eval_avg_return, eval_avg_length, eval_info = evaluate(
train_state
)
if cfg.env.type in [
"humanoid_bench",
"isaaclab",
"mtbench",
]:
# NOTE: Hacky way of evaluating performance, but just works
obs, _ = envs.reset()
logs["eval/avg_return"] = eval_avg_return
logs["eval/avg_length"] = eval_avg_length
for key, value in eval_info.items():
if isinstance(value, torch.Tensor):
logs[f"eval/{key}"] = value.mean().item()
elif isinstance(value, np.ndarray):
logs[f"eval/{key}"] = value.mean()
else:
logs[f"eval/{key}"] = value
print(
f"Eval return: {eval_avg_return:.2f}, length: {eval_avg_length:.2f}, env steps: {global_step * cfg.hyperparameters.num_envs * cfg.hyperparameters.num_steps} success rate: {eval_info.get('success', 0.0):.2f}"
)
wandb.log(
{
"speed": speed,
"frame": global_step
* cfg.hyperparameters.num_envs
* cfg.hyperparameters.num_steps,
**logs,
},
step=global_step
* cfg.hyperparameters.num_envs
* cfg.hyperparameters.num_steps,
)
global_step += 1
pbar.update(n=cfg.hyperparameters.num_envs * cfg.hyperparameters.num_steps)
if __name__ == "__main__":
main()

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reppo/torchrl/reppo_util.py Normal file
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@ -0,0 +1,777 @@
import os
import torch
import torch.nn as nn
from tensordict import TensorDict
class SimpleReplayBuffer(nn.Module):
def __init__(
self,
n_env: int,
buffer_size: int,
n_obs: int,
n_act: int,
n_critic_obs: int,
asymmetric_obs: bool = False,
playground_mode: bool = False,
n_steps: int = 1,
gamma: float = 0.99,
device=None,
):
"""
A simple replay buffer that stores transitions in a circular buffer.
Supports n-step returns and asymmetric observations.
When playground_mode=True, critic_observations are treated as a concatenation of
regular observations and privileged observations, and only the privileged part is stored
to save memory.
TODO (Younggyo): Refactor to split this into SimpleReplayBuffer and NStepReplayBuffer
"""
super().__init__()
self.n_env = n_env
self.buffer_size = buffer_size
self.n_obs = n_obs
self.n_act = n_act
self.n_critic_obs = n_critic_obs
self.asymmetric_obs = asymmetric_obs
self.playground_mode = playground_mode and asymmetric_obs
self.gamma = gamma
self.n_steps = n_steps
self.device = device
self.observations = torch.zeros(
(n_env, buffer_size, n_obs), device=device, dtype=torch.float
)
self.actions = torch.zeros(
(n_env, buffer_size, n_act), device=device, dtype=torch.float
)
self.rewards = torch.zeros(
(n_env, buffer_size), device=device, dtype=torch.float
)
self.dones = torch.zeros((n_env, buffer_size), device=device, dtype=torch.long)
self.truncations = torch.zeros(
(n_env, buffer_size), device=device, dtype=torch.long
)
self.next_observations = torch.zeros(
(n_env, buffer_size, n_obs), device=device, dtype=torch.float
)
if asymmetric_obs:
if self.playground_mode:
# Only store the privileged part of observations (n_critic_obs - n_obs)
self.privileged_obs_size = n_critic_obs - n_obs
self.privileged_observations = torch.zeros(
(n_env, buffer_size, self.privileged_obs_size),
device=device,
dtype=torch.float,
)
self.next_privileged_observations = torch.zeros(
(n_env, buffer_size, self.privileged_obs_size),
device=device,
dtype=torch.float,
)
else:
# Store full critic observations
self.critic_observations = torch.zeros(
(n_env, buffer_size, n_critic_obs), device=device, dtype=torch.float
)
self.next_critic_observations = torch.zeros(
(n_env, buffer_size, n_critic_obs), device=device, dtype=torch.float
)
self.ptr = 0
def extend(
self,
tensor_dict: TensorDict,
):
observations = tensor_dict["observations"]
actions = tensor_dict["actions"]
rewards = tensor_dict["next"]["rewards"]
dones = tensor_dict["next"]["dones"]
truncations = tensor_dict["next"]["truncations"]
next_observations = tensor_dict["next"]["observations"]
ptr = self.ptr % self.buffer_size
self.observations[:, ptr] = observations
self.actions[:, ptr] = actions
self.rewards[:, ptr] = rewards
self.dones[:, ptr] = dones
self.truncations[:, ptr] = truncations
self.next_observations[:, ptr] = next_observations
if self.asymmetric_obs:
critic_observations = tensor_dict["critic_observations"]
next_critic_observations = tensor_dict["next"]["critic_observations"]
if self.playground_mode:
# Extract and store only the privileged part
privileged_observations = critic_observations[:, self.n_obs :]
next_privileged_observations = next_critic_observations[:, self.n_obs :]
self.privileged_observations[:, ptr] = privileged_observations
self.next_privileged_observations[:, ptr] = next_privileged_observations
else:
# Store full critic observations
self.critic_observations[:, ptr] = critic_observations
self.next_critic_observations[:, ptr] = next_critic_observations
self.ptr += 1
def sample(self, batch_size: int):
# we will sample n_env * batch_size transitions
if self.n_steps == 1:
indices = torch.randint(
0,
min(self.buffer_size, self.ptr),
(self.n_env, batch_size),
device=self.device,
)
obs_indices = indices.unsqueeze(-1).expand(-1, -1, self.n_obs)
act_indices = indices.unsqueeze(-1).expand(-1, -1, self.n_act)
observations = torch.gather(self.observations, 1, obs_indices).reshape(
self.n_env * batch_size, self.n_obs
)
next_observations = torch.gather(
self.next_observations, 1, obs_indices
).reshape(self.n_env * batch_size, self.n_obs)
actions = torch.gather(self.actions, 1, act_indices).reshape(
self.n_env * batch_size, self.n_act
)
rewards = torch.gather(self.rewards, 1, indices).reshape(
self.n_env * batch_size
)
dones = torch.gather(self.dones, 1, indices).reshape(
self.n_env * batch_size
)
truncations = torch.gather(self.truncations, 1, indices).reshape(
self.n_env * batch_size
)
effective_n_steps = torch.ones_like(dones)
if self.asymmetric_obs:
if self.playground_mode:
# Gather privileged observations
priv_obs_indices = indices.unsqueeze(-1).expand(
-1, -1, self.privileged_obs_size
)
privileged_observations = torch.gather(
self.privileged_observations, 1, priv_obs_indices
).reshape(self.n_env * batch_size, self.privileged_obs_size)
next_privileged_observations = torch.gather(
self.next_privileged_observations, 1, priv_obs_indices
).reshape(self.n_env * batch_size, self.privileged_obs_size)
# Concatenate with regular observations to form full critic observations
critic_observations = torch.cat(
[observations, privileged_observations], dim=1
)
next_critic_observations = torch.cat(
[next_observations, next_privileged_observations], dim=1
)
else:
# Gather full critic observations
critic_obs_indices = indices.unsqueeze(-1).expand(
-1, -1, self.n_critic_obs
)
critic_observations = torch.gather(
self.critic_observations, 1, critic_obs_indices
).reshape(self.n_env * batch_size, self.n_critic_obs)
next_critic_observations = torch.gather(
self.next_critic_observations, 1, critic_obs_indices
).reshape(self.n_env * batch_size, self.n_critic_obs)
else:
# Sample base indices
if self.ptr >= self.buffer_size:
# When the buffer is full, there is no protection against sampling across different episodes
# We avoid this by temporarily setting self.pos - 1 to truncated = True if not done
# https://github.com/DLR-RM/stable-baselines3/blob/b91050ca94f8bce7a0285c91f85da518d5a26223/stable_baselines3/common/buffers.py#L857-L860
# TODO (Younggyo): Change the reference when this SB3 branch is merged
current_pos = self.ptr % self.buffer_size
curr_truncations = self.truncations[:, current_pos - 1].clone()
self.truncations[:, current_pos - 1] = torch.logical_not(
self.dones[:, current_pos - 1]
)
indices = torch.randint(
0,
self.buffer_size,
(self.n_env, batch_size),
device=self.device,
)
else:
# Buffer not full - ensure n-step sequence doesn't exceed valid data
max_start_idx = max(1, self.ptr - self.n_steps + 1)
indices = torch.randint(
0,
max_start_idx,
(self.n_env, batch_size),
device=self.device,
)
obs_indices = indices.unsqueeze(-1).expand(-1, -1, self.n_obs)
act_indices = indices.unsqueeze(-1).expand(-1, -1, self.n_act)
# Get base transitions
observations = torch.gather(self.observations, 1, obs_indices).reshape(
self.n_env * batch_size, self.n_obs
)
actions = torch.gather(self.actions, 1, act_indices).reshape(
self.n_env * batch_size, self.n_act
)
if self.asymmetric_obs:
if self.playground_mode:
# Gather privileged observations
priv_obs_indices = indices.unsqueeze(-1).expand(
-1, -1, self.privileged_obs_size
)
privileged_observations = torch.gather(
self.privileged_observations, 1, priv_obs_indices
).reshape(self.n_env * batch_size, self.privileged_obs_size)
# Concatenate with regular observations to form full critic observations
critic_observations = torch.cat(
[observations, privileged_observations], dim=1
)
else:
# Gather full critic observations
critic_obs_indices = indices.unsqueeze(-1).expand(
-1, -1, self.n_critic_obs
)
critic_observations = torch.gather(
self.critic_observations, 1, critic_obs_indices
).reshape(self.n_env * batch_size, self.n_critic_obs)
# Create sequential indices for each sample
# This creates a [n_env, batch_size, n_step] tensor of indices
seq_offsets = torch.arange(self.n_steps, device=self.device).view(1, 1, -1)
all_indices = (
indices.unsqueeze(-1) + seq_offsets
) % self.buffer_size # [n_env, batch_size, n_step]
# Gather all rewards and terminal flags
# Using advanced indexing - result shapes: [n_env, batch_size, n_step]
all_rewards = torch.gather(
self.rewards.unsqueeze(-1).expand(-1, -1, self.n_steps), 1, all_indices
)
all_dones = torch.gather(
self.dones.unsqueeze(-1).expand(-1, -1, self.n_steps), 1, all_indices
)
all_truncations = torch.gather(
self.truncations.unsqueeze(-1).expand(-1, -1, self.n_steps),
1,
all_indices,
)
# Create masks for rewards *after* first done
# This creates a cumulative product that zeroes out rewards after the first done
all_dones_shifted = torch.cat(
[torch.zeros_like(all_dones[:, :, :1]), all_dones[:, :, :-1]], dim=2
) # First reward should not be masked
done_masks = torch.cumprod(
1.0 - all_dones_shifted, dim=2
) # [n_env, batch_size, n_step]
effective_n_steps = done_masks.sum(2)
# Create discount factors
discounts = torch.pow(
self.gamma, torch.arange(self.n_steps, device=self.device)
) # [n_steps]
# Apply masks and discounts to rewards
masked_rewards = all_rewards * done_masks # [n_env, batch_size, n_step]
discounted_rewards = masked_rewards * discounts.view(
1, 1, -1
) # [n_env, batch_size, n_step]
# Sum rewards along the n_step dimension
n_step_rewards = discounted_rewards.sum(dim=2) # [n_env, batch_size]
# Find index of first done or truncation or last step for each sequence
first_done = torch.argmax(
(all_dones > 0).float(), dim=2
) # [n_env, batch_size]
first_trunc = torch.argmax(
(all_truncations > 0).float(), dim=2
) # [n_env, batch_size]
# Handle case where there are no dones or truncations
no_dones = all_dones.sum(dim=2) == 0
no_truncs = all_truncations.sum(dim=2) == 0
# When no dones or truncs, use the last index
first_done = torch.where(no_dones, self.n_steps - 1, first_done)
first_trunc = torch.where(no_truncs, self.n_steps - 1, first_trunc)
# Take the minimum (first) of done or truncation
final_indices = torch.minimum(
first_done, first_trunc
) # [n_env, batch_size]
# Create indices to gather the final next observations
final_next_obs_indices = torch.gather(
all_indices, 2, final_indices.unsqueeze(-1)
).squeeze(-1) # [n_env, batch_size]
# Gather final values
final_next_observations = self.next_observations.gather(
1, final_next_obs_indices.unsqueeze(-1).expand(-1, -1, self.n_obs)
)
final_dones = self.dones.gather(1, final_next_obs_indices)
final_truncations = self.truncations.gather(1, final_next_obs_indices)
if self.asymmetric_obs:
if self.playground_mode:
# Gather final privileged observations
final_next_privileged_observations = (
self.next_privileged_observations.gather(
1,
final_next_obs_indices.unsqueeze(-1).expand(
-1, -1, self.privileged_obs_size
),
)
)
# Reshape for output
next_privileged_observations = (
final_next_privileged_observations.reshape(
self.n_env * batch_size, self.privileged_obs_size
)
)
# Concatenate with next observations to form full next critic observations
next_observations_reshaped = final_next_observations.reshape(
self.n_env * batch_size, self.n_obs
)
next_critic_observations = torch.cat(
[next_observations_reshaped, next_privileged_observations],
dim=1,
)
else:
# Gather final next critic observations directly
final_next_critic_observations = (
self.next_critic_observations.gather(
1,
final_next_obs_indices.unsqueeze(-1).expand(
-1, -1, self.n_critic_obs
),
)
)
next_critic_observations = final_next_critic_observations.reshape(
self.n_env * batch_size, self.n_critic_obs
)
# Reshape everything to batch dimension
rewards = n_step_rewards.reshape(self.n_env * batch_size)
dones = final_dones.reshape(self.n_env * batch_size)
truncations = final_truncations.reshape(self.n_env * batch_size)
effective_n_steps = effective_n_steps.reshape(self.n_env * batch_size)
next_observations = final_next_observations.reshape(
self.n_env * batch_size, self.n_obs
)
out = TensorDict(
{
"observations": observations,
"actions": actions,
"next": {
"rewards": rewards,
"dones": dones,
"truncations": truncations,
"observations": next_observations,
"effective_n_steps": effective_n_steps,
},
},
batch_size=self.n_env * batch_size,
)
if self.asymmetric_obs:
out["critic_observations"] = critic_observations
out["next"]["critic_observations"] = next_critic_observations
if self.n_steps > 1 and self.ptr >= self.buffer_size:
# Roll back the truncation flags introduced for safe sampling
self.truncations[:, current_pos - 1] = curr_truncations
return out
class EmpiricalNormalization(nn.Module):
"""Normalize mean and variance of values based on empirical values."""
def __init__(self, shape, device, eps=1e-2, until=None):
"""Initialize EmpiricalNormalization module.
Args:
shape (int or tuple of int): Shape of input values except batch axis.
eps (float): Small value for stability.
until (int or None): If this arg is specified, the link learns input values until the sum of batch sizes
exceeds it.
"""
super().__init__()
self.eps = eps
self.until = until
self.device = device
self.register_buffer("_mean", torch.zeros(shape).unsqueeze(0).to(device))
self.register_buffer("_var", torch.ones(shape).unsqueeze(0).to(device))
self.register_buffer("_std", torch.ones(shape).unsqueeze(0).to(device))
self.register_buffer("count", torch.tensor(0, dtype=torch.long).to(device))
@property
def mean(self):
return self._mean.squeeze(0).clone()
@property
def std(self):
return self._std.squeeze(0).clone()
def forward(self, x: torch.Tensor, center: bool = True) -> torch.Tensor:
if x.shape[-1:] != self._mean.shape[-1:]:
raise ValueError(
f"Expected input of shape (*,{self._mean.shape[-1:]}), got {x.shape}"
)
if self.training:
self.update(x)
if center:
return (x - self._mean) / (self._std + self.eps)
else:
return x / (self._std + self.eps)
@torch.jit.unused
def update(self, x):
x = x.flatten(end_dim=-2)
if self.until is not None and self.count >= self.until:
return
batch_size = x.shape[0]
batch_mean = torch.mean(x, dim=0, keepdim=True)
# Update count
new_count = self.count + batch_size
# Update mean
delta = batch_mean - self._mean
self._mean += (batch_size / new_count) * delta
# Update variance using Chan's parallel algorithm
# https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Parallel_algorithm
if self.count > 0: # Ensure we're not dividing by zero
batch_var = torch.mean((x - batch_mean) ** 2, dim=0, keepdim=True)
delta2 = batch_mean - self._mean
m_a = self._var * self.count
m_b = batch_var * batch_size
M2 = m_a + m_b + (delta2**2) * (self.count * batch_size / new_count)
self._var = M2 / new_count
else:
# For first batch, just use batch variance
self._var = torch.mean((x - self._mean) ** 2, dim=0, keepdim=True)
self._std = torch.sqrt(self._var)
self.count = new_count
@torch.jit.unused
def inverse(self, y):
return y * (self._std + self.eps) + self._mean
class RewardNormalizer(nn.Module):
def __init__(
self,
gamma: float,
device: torch.device,
g_max: float = 10.0,
epsilon: float = 1e-8,
):
super().__init__()
self.register_buffer(
"G", torch.zeros(1, device=device)
) # running estimate of the discounted return
self.register_buffer("G_r_max", torch.zeros(1, device=device)) # running-max
self.G_rms = EmpiricalNormalization(shape=1, device=device)
self.gamma = gamma
self.g_max = g_max
self.epsilon = epsilon
def _scale_reward(self, rewards: torch.Tensor) -> torch.Tensor:
var_denominator = self.G_rms.std[0] + self.epsilon
min_required_denominator = self.G_r_max / self.g_max
denominator = torch.maximum(var_denominator, min_required_denominator)
return rewards / denominator
def update_stats(
self,
rewards: torch.Tensor,
dones: torch.Tensor,
):
self.G = self.gamma * (1 - dones) * self.G + rewards
self.G_rms.update(self.G.view(-1, 1))
self.G_r_max = max(self.G_r_max, max(abs(self.G)))
def forward(self, rewards: torch.Tensor) -> torch.Tensor:
return self._scale_reward(rewards)
class PerTaskEmpiricalNormalization(nn.Module):
"""Normalize mean and variance of values based on empirical values for each task."""
def __init__(
self,
num_tasks: int,
shape: tuple,
device: torch.device,
eps: float = 1e-2,
until: int = None,
):
"""
Initialize PerTaskEmpiricalNormalization module.
Args:
num_tasks (int): The total number of tasks.
shape (int or tuple of int): Shape of input values except batch axis.
eps (float): Small value for stability.
until (int or None): If specified, learns until the sum of batch sizes
for a specific task exceeds this value.
"""
super().__init__()
if not isinstance(shape, tuple):
shape = (shape,)
self.num_tasks = num_tasks
self.shape = shape
self.eps = eps
self.until = until
self.device = device
# Buffers now have a leading dimension for tasks
self.register_buffer("_mean", torch.zeros(num_tasks, *shape).to(device))
self.register_buffer("_var", torch.ones(num_tasks, *shape).to(device))
self.register_buffer("_std", torch.ones(num_tasks, *shape).to(device))
self.register_buffer(
"count", torch.zeros(num_tasks, dtype=torch.long).to(device)
)
def forward(
self, x: torch.Tensor, task_ids: torch.Tensor, center: bool = True
) -> torch.Tensor:
"""
Normalize the input tensor `x` using statistics for the given `task_ids`.
Args:
x (torch.Tensor): Input tensor of shape [num_envs, *shape].
task_ids (torch.Tensor): Tensor of task indices, shape [num_envs].
center (bool): If True, center the data by subtracting the mean.
"""
if x.shape[1:] != self.shape:
raise ValueError(f"Expected input shape (*, {self.shape}), got {x.shape}")
if x.shape[0] != task_ids.shape[0]:
raise ValueError("Batch size of x and task_ids must match.")
# Gather the stats for the tasks in the current batch
# Reshape task_ids for broadcasting: [num_envs] -> [num_envs, 1, ...]
view_shape = (task_ids.shape[0],) + (1,) * len(self.shape)
task_ids_expanded = task_ids.view(view_shape).expand_as(x)
mean = self._mean.gather(0, task_ids_expanded)
std = self._std.gather(0, task_ids_expanded)
if self.training:
self.update(x, task_ids)
if center:
return (x - mean) / (std + self.eps)
else:
return x / (std + self.eps)
@torch.jit.unused
def update(self, x: torch.Tensor, task_ids: torch.Tensor):
"""Update running statistics for the tasks present in the batch."""
unique_tasks = torch.unique(task_ids)
for task_id in unique_tasks:
if self.until is not None and self.count[task_id] >= self.until:
continue
# Create a mask to select data for the current task
mask = task_ids == task_id
x_task = x[mask]
batch_size = x_task.shape[0]
if batch_size == 0:
continue
# Update count for this task
old_count = self.count[task_id].clone()
new_count = old_count + batch_size
# Update mean
task_mean = self._mean[task_id]
batch_mean = torch.mean(x_task, dim=0)
delta = batch_mean - task_mean
self._mean[task_id] = task_mean + (batch_size / new_count) * delta
# Update variance using Chan's parallel algorithm
if old_count > 0:
batch_var = torch.var(x_task, dim=0, unbiased=False)
m_a = self._var[task_id] * old_count
m_b = batch_var * batch_size
M2 = m_a + m_b + (delta**2) * (old_count * batch_size / new_count)
self._var[task_id] = M2 / new_count
else:
# For the first batch of this task
self._var[task_id] = torch.var(x_task, dim=0, unbiased=False)
self._std[task_id] = torch.sqrt(self._var[task_id])
self.count[task_id] = new_count
class PerTaskRewardNormalizer(nn.Module):
def __init__(
self,
num_tasks: int,
gamma: float,
device: torch.device,
g_max: float = 10.0,
epsilon: float = 1e-8,
):
"""
Per-task reward normalizer, motivation comes from BRC (https://arxiv.org/abs/2505.23150v1)
"""
super().__init__()
self.num_tasks = num_tasks
self.gamma = gamma
self.g_max = g_max
self.epsilon = epsilon
self.device = device
# Per-task running estimate of the discounted return
self.register_buffer("G", torch.zeros(num_tasks, device=device))
# Per-task running-max of the discounted return
self.register_buffer("G_r_max", torch.zeros(num_tasks, device=device))
# Use the new per-task normalizer for the statistics of G
self.G_rms = PerTaskEmpiricalNormalization(
num_tasks=num_tasks, shape=(1,), device=device
)
def _scale_reward(
self, rewards: torch.Tensor, task_ids: torch.Tensor
) -> torch.Tensor:
"""
Scales rewards using per-task statistics.
Args:
rewards (torch.Tensor): Reward tensor, shape [num_envs].
task_ids (torch.Tensor): Task indices, shape [num_envs].
"""
# Gather stats for the tasks in the batch
std_for_batch = self.G_rms._std.gather(0, task_ids.unsqueeze(-1)).squeeze(-1)
g_r_max_for_batch = self.G_r_max.gather(0, task_ids)
var_denominator = std_for_batch + self.epsilon
min_required_denominator = g_r_max_for_batch / self.g_max
denominator = torch.maximum(var_denominator, min_required_denominator)
# Add a small epsilon to the final denominator to prevent division by zero
# in case g_r_max is also zero.
return rewards / (denominator + self.epsilon)
def update_stats(
self, rewards: torch.Tensor, dones: torch.Tensor, task_ids: torch.Tensor
):
"""
Updates the running discounted return and its statistics for each task.
Args:
rewards (torch.Tensor): Reward tensor, shape [num_envs].
dones (torch.Tensor): Done tensor, shape [num_envs].
task_ids (torch.Tensor): Task indices, shape [num_envs].
"""
if not (rewards.shape == dones.shape == task_ids.shape):
raise ValueError("rewards, dones, and task_ids must have the same shape.")
# === Update G (running discounted return) ===
# Gather the previous G values for the tasks in the batch
prev_G = self.G.gather(0, task_ids)
# Update G for each environment based on its own reward and done signal
new_G = self.gamma * (1 - dones.float()) * prev_G + rewards
# Scatter the updated G values back to the main buffer
self.G.scatter_(0, task_ids, new_G)
# === Update G_rms (statistics of G) ===
# The update function handles the per-task logic internally
self.G_rms.update(new_G.unsqueeze(-1), task_ids)
# === Update G_r_max (running max of |G|) ===
prev_G_r_max = self.G_r_max.gather(0, task_ids)
# Update the max for each environment
updated_G_r_max = torch.maximum(prev_G_r_max, torch.abs(new_G))
# Scatter the new maxes back to the main buffer
self.G_r_max.scatter_(0, task_ids, updated_G_r_max)
def forward(self, rewards: torch.Tensor, task_ids: torch.Tensor) -> torch.Tensor:
"""
Normalizes rewards. During training, it also updates the running statistics.
Args:
rewards (torch.Tensor): Reward tensor, shape [num_envs].
task_ids (torch.Tensor): Task indices, shape [num_envs].
"""
return self._scale_reward(rewards, task_ids)
def cpu_state(sd):
# detach & move to host without locking the compute stream
return {k: v.detach().to("cpu", non_blocking=True) for k, v in sd.items()}
def save_params(
global_step,
actor,
qnet,
qnet_target,
obs_normalizer,
critic_obs_normalizer,
args,
save_path,
):
"""Save model parameters and training configuration to disk."""
os.makedirs(os.path.dirname(save_path), exist_ok=True)
save_dict = {
"actor_state_dict": cpu_state(actor.state_dict()),
"qnet_state_dict": cpu_state(qnet.state_dict()),
"qnet_target_state_dict": cpu_state(qnet_target.state_dict()),
"obs_normalizer_state": (
cpu_state(obs_normalizer.state_dict())
if hasattr(obs_normalizer, "state_dict")
else None
),
"critic_obs_normalizer_state": (
cpu_state(critic_obs_normalizer.state_dict())
if hasattr(critic_obs_normalizer, "state_dict")
else None
),
"args": vars(args), # Save all arguments
"global_step": global_step,
}
torch.save(save_dict, save_path, _use_new_zipfile_serialization=True)
print(f"Saved parameters and configuration to {save_path}")
def hl_gauss(inp, vmin, vmax, num_atoms):
x = torch.clip(inp, vmin, max=vmax)
bin_width = (vmax - vmin) / (num_atoms - 1)
sigma_to_final_sigma_ratio = 0.75
support = torch.linspace(
vmin - bin_width / 2,
vmax + bin_width / 2,
num_atoms + 1,
device=inp.device,
)
sigma = bin_width * sigma_to_final_sigma_ratio
cdf_evals = torch.erf(
(support.unsqueeze(0) - x).squeeze()
/ (torch.sqrt(torch.tensor(2.0)) * sigma + 1e-6)
)
z = cdf_evals[..., -1] - cdf_evals[..., 0]
target_probs = cdf_evals[..., 1:] - cdf_evals[..., :-1]
target_probs = (target_probs / (z.unsqueeze(-1) + 1e-6)).reshape(
*inp.shape[:-1], num_atoms
)
return target_probs

View File

@ -0,0 +1,21 @@
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1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20
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1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20
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31578947.368421055,0.5164987664473684,0.3476690995065788,1.0118600945723684,13.908832750822377,0.4312872635690789,0.8241930509868421,0.8999794407894738,1.2379086143092106,1.0876529091282892,0.5647486636513158,2.105622944078946,0.6060855263157895,0.40881990131578944,1.953690378289474,0.6823280736019737,25.559685958059212,0.4373329564144738,0.5644145764802633,0.6739501953125001,0.8933298211348681,0.08574475740131585,0.44882684004934226,2.2047954358552637,0.5725932874177632
34210526.315789476,0.5630894711143094,0.2600290398848684,1.0167541503906252,16.49586085269325,0.4207217567845395,0.7727452328330591,0.9708814119037829,1.3840299907483553,0.896049097964638,0.6018098530016448,1.7122144197162839,0.5768898411800987,0.4026971114309211,1.8417840254934206,0.7199819464432566,26.103899504009043,0.5059396844161185,0.6886387875205593,0.7080977590460527,0.7641890676398028,0.1082281815378289,0.5099503366570723,2.496940211245888,0.5686276084498355
36842105.2631579,0.6720773797286184,0.3225386770148027,1.2828369140625002,12.712983783922697,0.4250199167351974,0.7478958932976975,0.9975907175164475,1.4516665810032894,0.8807822779605263,0.6336862664473684,2.3220953690378288,0.6012862356085528,0.39142488178453944,1.8977693256578956,0.7333438270970394,23.689783999794408,0.4865626284950657,0.9328099300986845,0.6889809056332237,0.9455245168585529,0.12684390419407904,0.4512039987664473,2.2551655016447367,0.5685746042351973
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50000000.0,0.4599609375,0.6884765625,7.0078125,23.0458984375,0.4267578125,0.76171875,0.8837890625,3.8232421875,0.9306640625,0.767578125,26.6025390625,0.9033203125,0.4033203125,2.2431640625,0.845703125,45.2783203125,1.70703125,5.8916015625,0.6376953125,0.880859375,0.2353515625,0.431640625,2.845703125,0.7529296875
1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20 trial_21 trial_22 trial_23
2 0.0 0.4677734375 0.23828125 0.314453125 0.548828125 0.3359375 0.783203125 0.60546875 0.408203125 0.939453125 0.1728515625 1.0234375 0.2978515625 0.3779296875 0.3232421875 0.3056640625 0.1416015625 0.25 0.6064453125 0.578125 0.2294921875 0.0869140625 0.255859375 0.4873046875 0.419921875
3 2631578.947368421 0.47522775750411184 0.24128482216282895 0.3237368935032895 0.5765429045024671 0.3386134097450658 0.7858517295435855 0.610547517475329 0.4032335783305921 0.9323537726151315 0.1807154605263158 1.0213623046875 0.2971689324629934 0.3782846551192434 0.3709443744860198 0.31467477898848684 0.15934994346217107 0.25442344263980265 0.6057899876644737 0.5763501619037829 0.2389124820106908 0.08705058850740131 0.2628495065789474 0.518732974403783 0.42560135690789475
4 5263157.894736842 0.7239990234375 0.3556422183388158 0.6561504163240132 1.6154014185855263 0.43136757298519735 0.8792403371710527 0.7970484683388158 0.24428518194901316 0.6889327199835527 0.4528455232319079 0.949109529194079 0.28201133326480265 0.39837967722039475 1.9478181537828947 0.627820466694079 0.7923680355674342 0.4122989052220395 0.5696828741776315 0.5241506476151316 0.5731779399671053 0.09092310855263158 0.5571385433799343 1.5620149311266447 0.615892912212171
5 7894736.842105264 0.5552175421463816 0.5139352898848684 0.8040996350740132 2.707399067125822 0.4177470960115131 0.897844816509046 0.9603383917557565 0.48065185546875 0.7569066097861843 0.4377023797286184 0.9480028654399671 0.4363419382195724 0.529706453022204 0.6677792197779608 0.6335127981085527 1.0373519094366777 0.4820187217310855 0.3935482627467107 0.6843245656866777 0.6967564633018093 0.07813784950657895 1.3374955026726971 0.7738085295024673 0.5054385536595395
6 10526315.789473685 0.6130949321546052 0.41277754934210525 0.6388967413651315 0.7638389185855263 0.3223941200657895 0.855115388569079 0.9168122944078947 0.5195633737664473 0.8672453227796053 0.49309339021381576 0.960205078125 0.5501901726973685 0.5303569592927632 1.663098787006579 0.7229196648848685 0.7749280427631579 0.4860968338815789 0.9209691097861842 0.687975431743421 0.7988345497532895 0.09818950452302631 0.4064748663651316 1.2171823601973684 0.609754060444079
7 13157894.736842105 0.5152780633223685 0.4240369294819079 0.6664589329769737 1.134177760074013 0.35869397615131576 0.8262039987664473 0.9690134148848685 0.55340576171875 0.8097598427220395 0.4206061112253289 0.9967137386924342 0.6259139211554277 0.47010080437911184 1.312556216591283 0.7749280427631579 0.8951432077508223 0.4720266241776316 0.8452373303865132 0.737871671977796 0.8056849429481908 0.08759669253700658 0.4248898154810855 0.9582888954564145 0.5981252569901315
8 15789473.684210528 0.49380653782894735 0.38178132709703955 0.7684968647203947 2.090666118421052 0.42508095189144735 0.8543155067845395 1.0089271946957237 0.534754702919408 0.8336502878289473 0.5039126747532895 0.9122282329358549 0.6273353978207237 0.31382028680098695 1.5233090049342106 0.7577129163240132 1.263851768092106 0.4648276881167762 0.6634200246710527 0.7173301295230262 0.7930876079358552 0.09032239412006579 0.4714644582648026 1.348619962993421 0.8901527806332236
9 18421052.63157895 0.4867312782689145 0.45927991365131576 0.7473546078330593 1.5748001901726971 0.39897236071134873 0.846234773334704 0.987749601665296 0.6122452585320723 0.8326913934004935 0.5028638337787829 0.378649259868421 0.5401852256373355 0.4641691509046053 1.6434165553042763 0.8027970163445723 2.168865003083881 0.34897974917763164 0.7622407612047699 0.6462787828947368 0.7712338096217105 0.08281667608963816 0.4293469880756579 1.3432633249383223 0.645525480571546
10 21052631.57894737 0.4948601973684211 0.4323473478618421 0.8724943462171053 1.1141293174342106 0.4361379523026316 0.8806923314144737 0.9792865953947368 0.6245502672697368 0.8836477179276316 0.501233552631579 0.5627826891447371 0.5207776521381579 0.5234760485197368 1.6124588815789473 0.7833701685855263 1.710809004934211 0.4428967927631579 1.060778166118421 0.7079178659539473 0.8216359991776316 0.08334189967105263 0.42953330592105265 1.373560855263158 0.6098375822368421
11 23684210.52631579 0.5287925318667763 0.40749158357319076 0.971117521587171 1.9908029656661186 0.4106862921463816 0.9523106625205592 0.9765046772203947 0.5373470908717105 0.9531844289679277 0.568036531147204 1.2821815892269737 0.5697166041324013 0.536572908100329 1.8591902883429277 0.7674030504728618 3.4662186472039473 0.4816653603001645 0.8218046489514803 0.6790787546258223 0.8194917377672697 0.08887361225328948 0.47222900390625 1.5904958624588816 0.6262287340666118
12 26315789.47368421 0.5157502826891447 0.41016588712993424 0.9317659076891447 4.164682488692434 0.41548879523026316 0.9117624383223685 0.9239823190789473 0.746264005962171 0.8560341282894737 0.5797376130756579 1.2406937448601973 0.6211869089226973 0.4827013517680921 1.7503469366776316 0.7565050627055921 9.043595163445723 0.4403943513569079 0.9655183490953947 0.7088655170641447 0.803052400287829 0.09070466694078948 0.4915353875411184 2.077427914268092 0.6154110557154605
13 28947368.42105263 0.5105879934210527 0.3934791966488487 0.9548371967516447 8.639731959292762 0.39632696854440785 0.8801928068462171 0.8585478130139803 1.0641286749588816 0.930394222861842 0.6612998560855263 1.5844967490748352 0.5991564298930921 0.4045956260279605 1.955535888671875 0.6564716539884868 22.66107980828536 0.3779232627467105 0.8646963019120066 0.6451303582442434 0.8990992495888157 0.08098240902549343 0.45110441509046056 1.9963186163651316 0.5763228567023027
14 31578947.368421055 0.5164987664473684 0.3476690995065788 1.0118600945723684 13.908832750822377 0.4312872635690789 0.8241930509868421 0.8999794407894738 1.2379086143092106 1.0876529091282892 0.5647486636513158 2.105622944078946 0.6060855263157895 0.40881990131578944 1.953690378289474 0.6823280736019737 25.559685958059212 0.4373329564144738 0.5644145764802633 0.6739501953125001 0.8933298211348681 0.08574475740131585 0.44882684004934226 2.2047954358552637 0.5725932874177632
15 34210526.315789476 0.5630894711143094 0.2600290398848684 1.0167541503906252 16.49586085269325 0.4207217567845395 0.7727452328330591 0.9708814119037829 1.3840299907483553 0.896049097964638 0.6018098530016448 1.7122144197162839 0.5768898411800987 0.4026971114309211 1.8417840254934206 0.7199819464432566 26.103899504009043 0.5059396844161185 0.6886387875205593 0.7080977590460527 0.7641890676398028 0.1082281815378289 0.5099503366570723 2.496940211245888 0.5686276084498355
16 36842105.2631579 0.6720773797286184 0.3225386770148027 1.2828369140625002 12.712983783922697 0.4250199167351974 0.7478958932976975 0.9975907175164475 1.4516665810032894 0.8807822779605263 0.6336862664473684 2.3220953690378288 0.6012862356085528 0.39142488178453944 1.8977693256578956 0.7333438270970394 23.689783999794408 0.4865626284950657 0.9328099300986845 0.6889809056332237 0.9455245168585529 0.12684390419407904 0.4512039987664473 2.2551655016447367 0.5685746042351973
17 39473684.21052632 0.6212816740337171 0.3954756887335526 1.5771227384868423 13.892448023745889 0.4088295384457236 0.8461464329769737 1.004625822368421 1.4943430047286186 0.922254060444079 0.5547501413445723 2.579575388055099 0.7662016216077303 0.37623034025493424 2.360335500616776 0.7340666118421053 25.917310212787832 0.4614177503083883 1.1736658999794407 0.6215290270353617 1.054962158203125 0.17379278885690785 0.4379449141652961 2.445249858655428 0.5527938039679275
18 42105263.15789474 0.6224814967105263 0.4769222861842106 1.8918328536184212 11.578150699013154 0.4010331003289474 0.8413856907894737 0.9921361019736843 1.2933028371710522 0.9226716694078947 0.5861687911184211 4.3059210526315805 0.7286698190789472 0.3924496299342105 2.6044150904605265 0.8162520559210527 23.7096525493421 0.5126953125 1.3959960937500004 0.6367958470394738 0.8885433799342104 0.1440686677631579 0.4612458881578947 2.6436574835526314 0.5451274671052632
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1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20 trial_21 trial_22 trial_23
2 0.0 0.4677734375 0.23828125 0.314453125 0.548828125 0.3359375 0.783203125 0.60546875 0.408203125 0.939453125 0.1728515625 1.0234375 0.2978515625 0.3779296875 0.3232421875 0.3056640625 0.1416015625 0.25 0.6064453125 0.578125 0.2294921875 0.0869140625 0.255859375 0.4873046875 0.419921875
3 2631578.947368421 0.47522775750411184 0.24128482216282895 0.3237368935032895 0.5765429045024671 0.3386134097450658 0.7858517295435855 0.610547517475329 0.4032335783305921 0.9323537726151315 0.1807154605263158 1.0213623046875 0.2971689324629934 0.3782846551192434 0.3709443744860198 0.31467477898848684 0.15934994346217107 0.25442344263980265 0.6057899876644737 0.5763501619037829 0.2389124820106908 0.08705058850740131 0.2628495065789474 0.518732974403783 0.42560135690789475
4 5263157.894736842 0.7239990234375 0.3556422183388158 0.6561504163240132 1.6154014185855263 0.43136757298519735 0.8792403371710527 0.7970484683388158 0.24428518194901316 0.6889327199835527 0.4528455232319079 0.949109529194079 0.28201133326480265 0.39837967722039475 1.9478181537828947 0.627820466694079 0.7923680355674342 0.4122989052220395 0.5696828741776315 0.5241506476151316 0.5731779399671053 0.09092310855263158 0.5571385433799343 1.5620149311266447 0.615892912212171
5 7894736.842105264 0.5552175421463816 0.5139352898848684 0.8040996350740132 2.707399067125822 0.4177470960115131 0.897844816509046 0.9603383917557565 0.48065185546875 0.7569066097861843 0.4377023797286184 0.9480028654399671 0.4363419382195724 0.529706453022204 0.6677792197779608 0.6335127981085527 1.0373519094366777 0.4820187217310855 0.3935482627467107 0.6843245656866777 0.6967564633018093 0.07813784950657895 1.3374955026726971 0.7738085295024673 0.5054385536595395
6 10526315.789473685 0.6130949321546052 0.41277754934210525 0.6388967413651315 0.7638389185855263 0.3223941200657895 0.855115388569079 0.9168122944078947 0.5195633737664473 0.8672453227796053 0.49309339021381576 0.960205078125 0.5501901726973685 0.5303569592927632 1.663098787006579 0.7229196648848685 0.7749280427631579 0.4860968338815789 0.9209691097861842 0.687975431743421 0.7988345497532895 0.09818950452302631 0.4064748663651316 1.2171823601973684 0.609754060444079
7 13157894.736842105 0.5152780633223685 0.4240369294819079 0.6664589329769737 1.134177760074013 0.35869397615131576 0.8262039987664473 0.9690134148848685 0.55340576171875 0.8097598427220395 0.4206061112253289 0.9967137386924342 0.6259139211554277 0.47010080437911184 1.312556216591283 0.7749280427631579 0.8951432077508223 0.4720266241776316 0.8452373303865132 0.737871671977796 0.8056849429481908 0.08759669253700658 0.4248898154810855 0.9582888954564145 0.5981252569901315
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11 23684210.52631579 0.5287925318667763 0.40749158357319076 0.971117521587171 1.9908029656661186 0.4106862921463816 0.9523106625205592 0.9765046772203947 0.5373470908717105 0.9531844289679277 0.568036531147204 1.2821815892269737 0.5697166041324013 0.536572908100329 1.8591902883429277 0.7674030504728618 3.4662186472039473 0.4816653603001645 0.8218046489514803 0.6790787546258223 0.8194917377672697 0.08887361225328948 0.47222900390625 1.5904958624588816 0.6262287340666118
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157894736.84210527,20.93860469564507,62.022362362975244,85.7289114500347,69.55898959088526,26.26827265615277,73.04686395481356,0.8089229023687726,8.604140950041796,64.26762188570652,30.216566548122927,50.80094005658687,75.29341152962556,22.38469854286173,0.3882291561348613,59.69005033382089,0.40628179618856586,52.88322378723907,16.521912056983677,1.1338901942456525,30.577961406549264,29.94445240200391,31.17389853046872,1.1057848758644673,19.46067774394873,104.03078655390858,41.552028037834674,31.17389853046872,37.56119133428855,16.692208673154877,11.793678569001175,46.478927374546544,18.78170444034143,31.220727645789495,14.545244100681634,32.50277000120803,27.967346059318402,38.47296557069816,37.630641369278095,6.612353773988846,87.07085215550052
168421052.63157895,21.833397904921767,44.453782226900636,99.24632165966932,89.49713815282257,34.06695036742826,87.55973976536801,0.1390235034382571,10.39505617770462,69.08605289195053,36.850569030254505,48.081508393432955,48.87818507144324,40.697050818445945,0.34828177581533504,22.084190558858836,1.0502881079169195,53.87098237352028,16.334211861988184,1.9927300957761647,29.734603966372163,83.20763551495415,26.171153525566456,0.5283944085033974,26.566136537166187,96.23106113761415,40.090914316784975,26.171153525566456,30.54276045273545,26.484150218171102,16.057352884984745,57.90814340015528,32.40687594849648,39.966278287512445,14.001846355744675,36.12048597679244,34.88797026657993,31.660333818345844,97.46280114340323,13.646429680060816,73.59145023419916
178947368.42105263,39.62290905453162,72.01485320537705,118.38136280672703,93.51537311902668,67.66455685729136,30.89697310270693,1.4005186630418098,17.01636497201682,93.24313926696777,72.31672083307834,69.29196774596323,108.4303757067863,42.841104417626546,0.5671681855854236,71.44353934734484,0.5683066534533724,73.4847314126604,28.15911824551316,1.0777454349803128,43.60697280535078,72.00125672612494,26.871987110359846,1.2908000629034073,30.494818246265528,114.58213631268023,42.717250821332854,26.871987110359846,98.78742092269941,33.78274945605165,34.93246751346747,55.59523259899953,45.13029844278775,56.46899472709508,26.481303296921332,60.838417283055534,15.159094945215447,63.26216114392903,76.43822607373266,13.146239798485077,115.92416219367877
189473684.21052632,82.69990513661561,83.0333305475124,157.83095485549885,95.52357798864307,83.45088402914539,138.61260967307473,1.0363624551619848,15.196170442322288,101.8697741289218,35.694249816218246,57.25018566268964,54.851957389852686,56.98084063543177,0.43187644937362035,94.84579836034379,0.8730964819149958,40.54276743754126,13.943557649438072,0.7616605732249431,70.40712352868923,89.06160556972853,42.06132338780115,3.9075127281970925,33.37288742910793,233.75306191272682,48.45792490359489,42.06132338780115,61.43184522908811,41.0789123440053,20.362468804018654,60.239098646634176,42.86614551174343,62.56966509515229,59.172065502388655,32.57754192722141,46.780091901234975,65.14912636986729,109.84514912211664,30.141611965739497,108.45218757248982
200000000.0,87.70932333092941,126.6426611950523,189.91159408970884,145.40460666857268,65.90140613756682,141.93519145564028,0.7105246594077662,37.30758431083277,116.48193359375,66.90076230701648,80.59385495436818,96.4539737701416,46.427630173532584,0.26785945892333984,99.67988074453254,1.172507737812243,84.90093833521793,17.944659383673418,7.393907848157381,40.68786365107486,117.31464355870297,46.02576140353554,4.258270364058645,66.42470209222091,114.95296382904053,86.08775515305369,46.02576140353554,94.29793714222156,55.6609713905736,56.793220269052604,66.8853511308369,26.22753499683581,89.84934094077663,56.36625440497147,31.966515290109736,56.7328139857242,46.12269250970138,128.4853956322921,39.81086439835398,144.08709255017732
1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20 trial_21 trial_22 trial_23 trial_24 trial_25 trial_26 trial_27 trial_28 trial_29 trial_30 trial_31 trial_32 trial_33 trial_34 trial_35 trial_36 trial_37 trial_38 trial_39
2 0.0 0.125 0.134765625 0.1162109375 0.1923828125 0.28125 0.1572265625 0.1875 0.150390625 0.1943359375 0.337890625 0.3193359375 0.15234375 0.1875 0.1669921875 0.1474609375 0.21484375 0.1650390625 0.15234375 0.2451171875 0.1640625 0.119140625 0.24609375 0.2158203125 0.1318359375 0.1865234375 0.2822265625 0.24609375 0.2578125 0.1806640625 0.2802734375 0.2412109375 0.1640625 0.140625 0.173828125 0.1552734375 0.1376953125 0.1240234375 0.1337890625 0.2451171875 0.3427734375
3 10526315.789473685 0.16475843920932254 0.16256330812406675 0.1471649312576759 0.21082231146476937 0.3008523502508359 0.1596630128136632 0.18949345934754264 0.16595068268498556 0.19173336557404155 0.3226628105396049 0.31468453235573385 0.15345122741530146 0.19923926060219552 0.16538634524781287 0.15958781519755103 0.23200964993717269 0.20352390268172588 0.15948697932869443 0.25286952940711027 0.17884732349427454 0.1445018578104035 0.24565075903387942 0.2509827204358215 0.13632122103197092 0.21598233674701894 0.2877639495765073 0.24565075903387942 0.2625746528857963 0.1901329944008275 0.27567740622649894 0.26773502159647006 0.17546951737760508 0.1581785170325282 0.17931013820574224 0.19231855704183395 0.1713626259251645 0.13160965779481504 0.13600401733060294 0.24650153426912683 0.3472587210319709
4 21052631.57894737 0.7925045615748355 0.5630920124846481 0.6950014542344535 0.49077717154970457 0.5689213084382033 0.2200191582338962 0.21778334937267357 0.4004401843633678 0.17800714698854908 0.08284716196667785 0.31826128655853697 0.16810957678797503 0.4033910693224117 0.14731019883935143 0.40518423064593795 0.49110941477429504 0.80587427239669 0.28817686149618305 0.3775167755803243 0.4189350571989022 0.6233305891464952 0.2653036989333557 0.7989477543289312 0.21880058964864038 0.706829921690711 0.5544212531515107 0.2653036989333557 0.3322725692284074 0.3443338177540956 0.1967822996863368 0.6891605292661038 0.38284326590329326 0.43524436739343025 0.28479427115738887 0.739708654768249 0.7331065286229522 0.32104946041371357 0.2075156055989358 0.2680915293601081 0.435496972208208
5 31578947.368421055 0.6475754629541964 0.14571632903038312 1.2066467475362765 0.37095567063941864 0.18533769538858272 0.42766055109758466 0.2752074270697513 0.20049200559917246 0.5050318577943418 0.22435883075576746 1.380596242783143 0.19614995285414602 0.4484024946048979 0.28610992167464927 0.7551901043286945 0.3142476993254348 0.6037904575590943 0.33533248478686045 0.32132358234014535 0.38949291461722674 1.3610656558641772 0.4393512588458708 0.5167427327163993 0.3133316383467487 0.8130619572140175 1.6885346362465303 0.4393512588458708 0.24269543328113502 0.3343070497803411 0.21428112970494834 0.5474694164836176 0.49210101679751744 0.3997589650246577 0.3478107425975006 0.20216860467377132 0.7321395345672015 0.783700459551613 0.5459609995918592 0.24637027592540117 0.6135906023992397
6 42105263.15789474 0.9944755681003559 0.49971903328089834 2.449571160398362 0.7257544393354505 0.5020932649311266 1.0112761500139318 0.6091996295960656 0.19593802581533504 0.9587020345672016 0.421342115322969 3.89199744565335 0.5073503721453807 0.45322961358152275 0.5812946330147106 1.2126524441790385 0.42372625884587084 0.9366905656217537 0.2864681465804082 0.3970842863384047 0.5450350267404995 3.9674184698807573 0.28084803023827043 0.5824551040776218 0.4568897363551766 1.309953145373231 1.2081189987732106 0.28084803023827043 0.2714977211569155 0.49561317211373035 0.3573603431934135 0.6778673504858467 0.3867399474590439 0.7534618853201827 0.1588590732902041 0.29717991160553914 0.9121374410275278 0.7950278622952195 0.9647056706394186 0.25135085721425404 1.0601271420634686
7 52631578.94736842 0.48655342197154033 0.7309763636285248 2.781361138721582 0.5829015293279843 0.7452132866983598 1.8104764140543845 0.15890281814617463 0.36336260555193367 0.8197659257376293 0.5689103900560711 5.588392791325366 0.7706739578881092 0.8531122815245736 0.4759909981175473 3.2873511327600875 0.3098878596297922 0.7088196508772155 0.4845670795176498 0.9125889226009971 0.7796082641939708 7.270052067130557 0.5578903266927873 0.6884916020232225 0.5075089858839716 1.491553116373078 2.6708549171933837 0.5578903266927873 0.6377059112295219 0.8262337502350107 0.27412831155877365 1.0517072466271735 0.5382079708279005 0.901442089239316 0.33363230803006244 0.6568204953729941 2.2373502208255336 1.5775630903376106 1.7442312768952006 0.4072204045641786 1.8016450755153666
8 63157894.73684211 1.0420178019769302 1.8103189970317652 5.545044193637671 1.7648259635777368 1.4199973922687221 1.5551879967348736 0.2229905537951357 0.36925956747208266 1.1995302342972276 1.5327045356137612 7.523034003302663 1.158937681414744 0.805724564021314 0.6856986439459212 4.756751147663824 0.2955948996081576 1.8540393797644628 0.20788887002791734 0.8148117171099976 1.0256419036527094 7.311451592273663 0.8515860539063849 0.798549905708292 0.7053573745769806 2.282229357479022 2.193101169660153 0.8515860539063849 1.109277989395438 0.8124757116851382 0.6429493764100647 1.667533314459212 0.5593464130179703 1.7188528964394019 0.3305101738081744 0.9957177856952533 3.8924312116036464 1.8392909940259934 3.733806340648198 0.3027439434442493 2.8920462706082417
9 73684210.5263158 1.3830839933781087 5.100327803487595 13.43898136001545 3.7048471086243184 1.6210746844389439 2.6957534541713897 0.44708755472030015 0.20198059874558377 2.7214035525546514 2.2359649969930455 11.240130662257652 1.3772276379064843 0.8208262477885323 0.824473415385323 3.905194047415355 0.20836535054891064 3.6135144458252975 0.5216871007987999 1.031909335022818 1.270225081087149 12.81709700344012 1.2153364192085592 0.9017106925351467 0.46933654140567505 7.1658145714334545 4.9027279565869275 1.2153364192085592 3.705652979272226 0.717919415714338 0.944001266500626 3.466930384120784 0.5417748131580301 1.5883855317768294 0.4837573730384216 1.7244084376707636 4.0685841858882315 1.1316749197624396 7.66055482246209 0.5972840634079195 3.450969931161305
10 84210526.31578948 4.014672276716154 12.016582013497395 23.181006053808325 3.612718534601692 3.1542508450241304 2.7617867593950183 0.46156744283322143 0.19719761560498184 3.8793698466715725 1.4529278403834294 14.404343877142487 2.9885022488327246 0.6980767289687391 0.755399603592722 8.341413820219175 0.31318774447876996 6.770764527888841 1.1650599640822479 0.7818840639743118 1.2950600494638378 16.08718688204018 2.8845401034791056 0.7440910656366322 0.7709036956533503 16.82825472084109 4.51887216330235 2.8845401034791056 5.652058567036551 1.4381194392069556 0.643355076332832 5.181146996833611 0.8622281399460051 2.1362054882947765 0.5899076382539278 2.9367576873863834 3.752791703242675 0.8795601377196589 9.607740534309535 1.2595998705919431 6.307293815295783
11 94736842.10526316 7.206987671574727 20.472733000969292 27.658756911259278 4.630834341709634 4.179353563409102 4.193443348533229 0.39152398466073246 0.34336410004676543 5.037000735380643 1.9169747439778082 18.562820011889176 8.97109312496027 0.593006905426279 0.3599191464875874 14.953387540463265 0.4500801239647694 13.060928857227442 1.1082677946856807 1.0216030215952865 2.47150509905617 17.433356670791753 4.715693341728063 0.7305781240278334 1.1777716184917248 27.34507172920037 5.5128052677143975 4.715693341728063 5.500632465711261 2.582225485191451 1.1256173786364103 9.04507803982975 1.893804344113844 3.3445423342844784 1.0345239982710652 3.8706329958590775 6.168476234182426 2.845837072652463 10.392869431556427 1.6238624673140676 10.91194662955329
12 105263157.89473684 8.615425152131396 16.700722343043278 44.27714042980585 9.23390510537948 7.044667981007753 6.372787887700047 0.6249945526968409 0.35853823400270246 8.856565808325263 8.447798821404369 21.272593569557422 17.973017911831757 1.7495619596867018 0.3543151475055726 13.826643724520782 0.5491730275246575 18.733312997791575 1.2025583536671138 0.8180130512100179 8.685578496832596 22.984352798673253 8.626647954502264 0.6113759672212469 1.0337551465655297 35.809171766455485 7.8992716612247875 8.626647954502264 10.082749300716326 3.2425235209372567 1.1161777200461096 16.167401453794866 3.1296436013937656 3.4180094277759667 2.1925999385168016 4.249838710161457 15.802954702826417 4.4951492795653625 21.30028856229914 1.143182014824611 13.192193160757133
13 115789473.68421052 9.898732985816173 33.9311675444204 40.799380836064145 17.085271122052728 10.80816331266366 13.7724383821778 0.42226769719427654 0.5424167522102841 12.583843027785875 12.710444487363018 27.33187628716973 19.28526973196014 4.420468710796324 0.28842294117090117 8.44861547306304 0.3847382458293208 15.227359153557355 0.8635894532348974 0.6124045168593979 14.121717038247063 34.8746522602282 9.723575922260654 0.6863716923298928 2.341130198534175 24.876571800570083 7.922004789526773 9.723575922260654 9.378431602858441 5.896153542473705 2.052391723252399 16.594550243705264 5.894031205005592 10.69688388581421 3.521378897563902 6.193912344956331 19.67007807153084 5.128197794145494 28.35557448897005 2.1761116704121846 36.51867231701879
14 126315789.47368422 19.2578698683974 31.084221160973183 50.78754471543756 32.0201824325604 19.85560531827553 10.872660935420399 0.364966754437814 1.7530347871648324 19.50133777523306 27.96229583867041 12.770933029724262 30.135337607682267 5.330696095390002 0.314728987844367 17.700676323634454 0.43210962142310344 31.615508378047394 3.5079920760812575 2.3745504257751664 22.52807503063594 34.323667933075704 7.553489547687222 1.135703617846207 3.462618587419928 31.315759949406782 16.31396907056139 7.553489547687222 14.806945304130926 9.015886724160321 2.898692165385323 21.914943642233226 11.082360972988315 13.824822888149777 4.217304145200101 8.77485626093899 23.833055480365285 5.954192534047811 33.394083134025095 1.8438913234383096 48.044342484830814
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147368421.0526316,1.5809387883321069,2.942739793138159,24.46977044208559,0.19035068839540747,0.301262514743118,92.9651444083766,0.1802890809288975,0.6619124637085974,0.19759649451089362,0.2397342692451792,1.025595979347123,0.5971677732599738,1.6888976691502282,0.459666968052407,0.5338327719564255,1.2614897466432355,1.1703646176409528,10.691914133087746,3.6039492007437826,0.37673535967797767,0.42433063475379024,3.383265249616883,1.7619237133670702,0.45273637639518605,0.7433922838966595,0.7100183006138678,9.00354647438282,0.4848791317926546,0.4673639598645663,9.506287693647137,15.884732909479968,0.23525210034484023,0.2523373315869276,25.088568727065336,0.1296907092065362,5.779394598878986,0.394397291780509,0.7482237723395424,0.502381052667084,0.6993510861806265
157894736.84210527,2.9801674866610295,7.916251938098689,30.649839908462486,0.5139713630781944,0.1331549747498741,105.55140764495343,0.5455583905249094,0.9567602427052001,0.2646005952787532,0.3000248330451776,1.2309275148978196,0.767323163737881,2.1125351358979034,0.23736857575392775,0.9186743052052001,0.5886688311674584,0.7597422956429686,20.325805722181165,7.5241419324584315,0.27535882881143414,0.37027918797120485,5.258753063275875,6.455622688885215,0.20460603772107894,0.730484500155885,0.27127240040956085,5.145708179209699,0.5080220468156557,0.35044543036463505,10.744365034341152,27.385786008966935,0.2085704327950517,0.21080486794257755,26.10407848041143,0.2019546408402293,4.837990808354849,0.8756125944142861,1.6123513462140628,0.5092587220041376,0.6135574087211628
168421052.63157895,2.2012294864390363,12.794544420744245,67.40622362469705,0.3322749256757486,0.39704738627510405,84.11273159544882,1.4717977423416946,0.6923321752997315,0.1968099747338123,0.44612193437824627,0.6601059086765276,1.862549927095958,5.20887955007791,0.29065605015635826,0.7924594192293541,1.0231935284474551,0.337568246096455,20.755509817699316,4.054029216396509,0.2967249481961998,0.4415703348175641,4.988143075536162,8.905153015643936,0.18628280512844098,0.23633146418098572,0.6656273923752383,5.213852266855848,0.7734655660275278,0.25874666758191217,22.028875715514637,21.01273990536,0.23670173285740567,0.24812891740878204,34.86719265670988,0.3735250964389284,4.803399252429233,3.130596847745521,0.9514161424293408,0.5211220527289647,0.3366142547691957
178947368.42105263,3.8616866114397137,9.760375588224203,79.11486676393123,0.12495895501979495,0.4003998500158252,127.34924911594129,1.1208985082990903,0.6215254553797502,0.1734148696519001,0.45145352857595006,0.5392217768196254,0.5643175553086717,10.181054773092931,0.6368100649762353,0.6783605638963693,0.48419990169704763,0.32069054865110613,22.161459478975335,2.53295685511877,0.4315944999208741,0.12075598814480842,10.938467210679836,5.85453545683969,0.3720761507832113,0.41795613825156097,0.44268630284021426,19.249580298764556,0.20200854589404138,0.20394397904668157,16.98866281218806,78.90181455849942,0.468042479327511,0.37248187448179293,61.57476029435685,0.24279693223102594,4.159137884335505,1.8680561678561471,5.944719874627705,1.4571920431882064,0.5195630699643798
189473684.21052632,1.3317146037093823,9.608790579925284,99.66854551954613,1.0431200804142409,0.4725663087374615,135.6688920916613,1.9935955301216102,0.44902561642126365,0.1685823033721163,0.5113464683046631,1.5655018180361084,0.7143379486168522,13.703403087203853,0.34229869789694156,0.42022511701504617,0.7113548289375622,0.18600527269358122,29.755003783841545,6.139354283129411,0.3477779874511043,0.23627998690195698,12.614510528268578,10.36519875354714,0.6902294845792396,0.6257143892409729,0.8616120874716634,24.394445683487234,0.557663703559178,0.21136645795235673,21.502688843787872,84.2396581021042,0.19899691108851553,1.6890823121216159,82.73021098319182,0.5526971315082752,19.676021480824478,0.30468205269684095,8.50576306710283,5.344249160005776,0.1122596402577747
200000000.0,2.8858423734966077,13.503776801259894,96.9629494516473,0.44552270989668996,0.20568897849635073,156.40123573102449,0.7199370233636153,0.3921194076538086,0.18664485529849403,0.21627355876721835,1.7926802886159796,1.2530435260973478,10.787358334189967,0.5791486940885845,0.720414211875514,0.5491467024150648,0.3646584560996608,36.99791065015291,15.644497871398926,0.6704824347245065,0.6044921875,20.147124089692767,9.650274226540013,1.3059104618273283,0.6453861939279657,0.33368873596191406,32.88845037159167,0.7028142025596217,0.1171731948852539,26.57983011948435,53.57619697169254,0.19112049905877365,2.0969105268779553,85.3630492561742,0.6357739599127519,20.90488092522872,0.4946517442402087,16.90790030830785,8.808686206215306,0.5628930643985146
1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20 trial_21 trial_22 trial_23 trial_24 trial_25 trial_26 trial_27 trial_28 trial_29 trial_30 trial_31 trial_32 trial_33 trial_34 trial_35 trial_36 trial_37 trial_38 trial_39
2 0.0 0.33203125 0.2978515625 0.3330078125 0.0908203125 0.1884765625 0.1005859375 0.1171875 0.2021484375 0.283203125 0.154296875 0.1748046875 0.408203125 0.162109375 0.2685546875 0.2568359375 0.3017578125 0.1552734375 0.2822265625 0.279296875 0.2353515625 0.0908203125 0.326171875 0.232421875 0.1708984375 0.13671875 0.171875 0.08984375 0.146484375 0.1689453125 0.0634765625 0.236328125 0.1982421875 0.1953125 0.28515625 0.2314453125 0.3134765625 0.130859375 0.25 0.0966796875 0.185546875
3 10526315.789473685 0.32483264680054047 0.3168448001724201 0.32691668671584195 0.10045536601312273 0.19545367021639923 0.12489506676586712 0.12820690028224957 0.21792999066804586 0.281708030489343 0.18779806681286926 0.18560259229918927 0.39945405341911844 0.16293998306147608 0.26700421911857797 0.2598261265213139 0.30951015440711027 0.1767584993568484 0.31290368690385056 0.282342437892079 0.23645903991530146 0.10106447859153854 0.31902864567130557 0.23917748723333893 0.1780970406994595 0.14679679447924332 0.17674790062732643 0.09615637126721835 0.15988485172514771 0.16811470443852392 0.06812796764426615 0.23455616113551767 0.1988513000784158 0.21425036380165502 0.2921887315871643 0.23814555086257386 0.3035092657622868 0.13534465853197092 0.25016612161229523 0.10354604747486908 0.18670972628606652
4 21052631.57894737 0.22102579978034106 0.6066760329988855 0.3322360125935309 0.333392705943776 0.3031066091437089 0.48544076935406205 0.3072042755803243 0.46806500294862363 0.2539564962202162 0.7089026760196422 0.3567067989021787 0.25811466417814555 0.20643820723007922 0.2354520549404324 0.3159936815087485 0.4239686083595508 0.5076002295327648 0.7554645696835505 0.37974335942572174 0.24624448866064857 0.2785722304579294 0.25025329167162613 0.3618620399623036 0.3030567063519169 0.33250500686941387 0.2565942748431684 0.2779200598803914 0.36332089749069424 0.17855063039510205 0.15757931632678596 0.25923377060824154 0.2092058704830603 0.5108020021644656 0.38647640048632 0.389700057433913 0.1424574653857963 0.21749178392404994 0.31395169308311066 0.2618510386289982 0.2770439898208238
5 31578947.368421055 0.3153028699499748 0.3760965352573553 1.2761542539517308 0.7925575314466311 0.2778383609000336 0.7975956422800513 0.2608122574655633 0.33870003560243217 0.2689887968787197 0.42046535840655297 0.3855589895697513 0.31859181264100644 0.4079101858376796 0.20421778132050322 0.31438099446389145 0.3142015504704948 0.3951584929574561 0.23804505842214146 0.798774468271356 0.36426877843376043 0.3155448760352306 0.5999050378138998 0.4598255817909981 0.37547922794838695 0.5081861078574057 0.26168901438197933 0.8005170161704276 0.34715722208208016 0.37248322441967574 0.29381577129839537 0.6774674175188482 0.28137306361317316 0.359399951395896 0.1980203485885155 0.6351812605712551 0.20792817409018735 0.36457776362876165 0.6969907924409057 0.6679103090492313 0.7610973215499411
6 42105263.15789474 0.19290715901805425 0.269974927822969 1.8890065222235597 0.27080006480547203 0.42508496736225326 4.282658658859803 0.2829440425967906 0.3337174412946623 0.4273409433972472 0.38146301649944275 0.7645147751573049 0.434962370389056 0.29090590754374246 0.285881581398919 0.10250010186615416 0.28706766693876057 0.7192589397905935 0.27025520768522227 1.004508517785746 1.2163723340655297 0.2802953218158923 0.3364590990906607 0.5748237652131395 0.5539734541874514 0.7181774678322748 0.36246671174701894 0.518980602148167 0.8323074087211629 0.3776070127196589 0.4887440647114677 0.9923393164975493 0.548584058344199 0.3177550466437089 0.357166913737881 0.37126705983338926 0.422119066655801 0.6651255219266685 0.22144759328741775 0.896673387437646 0.40042036061802067
7 52631578.94736842 0.25633175815571707 0.3007043352417669 1.982854586889209 0.28929869157785854 0.346788398446799 4.640484078108769 0.5248908864494176 0.7023599973345728 0.33446735688523904 0.42052860735526043 0.5691076210000838 0.3497898492786693 0.5105846278224956 0.4141455726940546 0.3324469093470692 0.2871746845192526 0.2989156384877551 0.25923480089351414 0.9541261942432857 0.7953873895872333 0.4166835219576088 0.16949016962024974 0.8531235908867579 0.6909701038265492 0.7876658373592302 0.36100270279226543 0.7829997361201659 0.20907461213933465 0.3531440777131395 0.3963968615122449 1.749352885745569 0.2847635052540956 0.3001372741530146 0.8835159233072127 0.6799165271325784 0.5923577781529308 0.19995296298632 0.2648429447924331 0.6243949847868605 0.38962451638937656
8 63157894.73684211 0.18771124018196253 0.41903319319199367 1.6856210661066537 0.2883788766623204 0.5540824847868605 3.662441026470999 0.3429422827638746 0.43071808643288245 0.2756008348966899 1.056775021751172 0.7039265355244896 0.27706140956720154 0.9086700608525582 0.5890073274311266 0.47117344758517177 0.6422448514901369 0.45912554521639926 0.8386874476298076 1.2766782332655464 0.26387560730825843 0.29502271086885656 0.3616634590804083 1.112771919229354 0.8366624879704948 0.5449803159507687 0.10584132757213308 0.5443253979458371 0.25610344165580107 0.39880904728686045 0.3900155677689742 0.7875540831082416 0.22952089283274804 0.2832721646802907 0.5668954135968748 0.6702776721309753 0.2891708437425607 0.2133459318377636 0.45507606442945475 0.5604566378606654 0.3856180936015542
9 73684210.5263158 0.16900547059288976 0.6859539486364643 1.96036018361015 0.3662618705770646 0.5802066596921462 9.480657101998373 0.38026601257746917 0.5093280813370383 0.2145521845513764 1.37036766041679 0.485417535100287 0.32364724811754736 1.0526359193542987 0.47608224176634045 0.32072097112597525 0.5349132136294716 0.4028851728360078 1.334013056556934 1.2206429669071102 0.3810699283251141 0.3481006146798174 0.6800440315394521 0.6058214800509718 0.8670070257213307 0.4502011270073973 0.26811172030969355 0.3245588445267188 0.3081678353518329 0.418731348666458 0.4965008236364643 1.3588814907126814 0.263484579704475 0.2214841736981083 0.8548473215499413 0.19819466493136328 0.23619517328996747 0.2982576296270058 0.3924844773522375 0.8822482101144555 0.23536319151479457
10 84210526.31578948 0.3034135813197932 0.3512483633786357 1.3963632768541159 0.4689537323082584 0.7979349786224789 14.164057702569089 0.47443263088236876 0.4813205792963341 0.4207836161690076 0.43259186889986573 0.6113011368093729 0.44130575755956764 1.048298674607211 0.29916787609829465 0.3151565720830267 0.3703154249534712 0.4851461606012488 1.6298015520513225 1.079589991688398 0.3172512107278501 0.3507147918447563 0.6799127256440983 0.27968618546166246 0.6210444865134284 0.3468765512397744 0.38244605658787434 0.37698835547280785 0.21172436320550556 0.49768317901526793 0.6269357528052504 2.1927492559121258 0.4238875962360414 0.31735445059567613 1.2255005559102323 0.13441458831533504 0.5421887553629784 0.27500985269731437 0.4239569793447563 1.3506467824497381 0.2608413062267356
11 94736842.10526316 0.42417369060569193 0.25796802288277326 3.7093396411377975 0.6298599216746491 0.7482683467072463 10.994220559286608 0.27164571239017055 0.5853092267572715 0.35743276960631815 0.4231947716583506 0.8141537082492479 0.3560446926761532 1.488667884361711 0.21109883739017055 0.30298219559265305 0.4064260572607828 0.8439807442746995 3.2509093588409 0.640345016014543 0.4061580694943584 0.19467568859829465 0.47928197760331004 0.9432084117899973 0.2692690767409729 0.2843844500935309 0.31267878091236234 0.6267083952631647 0.2914189684754263 0.32909265713678504 0.9214712893203355 2.3621894989647694 0.3826914969573721 0.40166969510656975 1.2336218984503495 0.1581569761450601 1.4035378057210401 0.23811682175401172 0.4523128657459883 1.1867794290473916 0.2166010177696841
12 105263157.89473684 0.3910283434754263 0.27153565150548875 5.3618300535672265 0.9706816316641598 0.8912686799701891 10.375362961576256 0.23942768804914732 0.30341387719658935 0.4643727881096076 0.6525064611038673 0.5487063875488958 0.24598231540162147 1.5324709250325972 0.3477711188826204 0.2980214380491473 0.4811711667977542 0.6395673778248626 4.643279950044161 0.3999377221612059 0.4754939832185444 0.17852158163392973 0.47963198400270246 1.3341740267428666 0.6560815457161773 0.30144298902178734 0.405022206398919 0.6214440998278166 0.26901647192619516 0.21565931853825365 1.5403868075553069 2.1788756616227847 0.4971144245602087 1.1098502256863663 1.134236222158839 0.2579574479290653 1.5722607694504334 0.17147337366669463 0.9840968282599197 1.0413588103825366 0.4419969363225794
13 115789473.68421052 0.3355929409037667 0.7794080374973961 11.520479833650455 0.9612577470055579 0.5783645307588448 21.252192354598527 0.2211666265683161 0.6031465292637366 0.41975501897922857 0.3417756299893283 0.4560752218780094 0.319640849105539 1.2349902467384233 0.6211043725053358 0.30107931681286926 0.8204862008134413 0.3221528166879247 5.6784187802977835 0.3564186439619831 0.2484433499069426 0.3598323674083086 0.5739709531831609 2.8284233283468225 0.5296857944816105 0.6097141355688881 0.5293105645853396 0.850388410679191 0.21781308499069427 0.21229142429425776 3.2014772726888467 5.442512189912662 0.3354763548790254 1.0993655804451814 1.8291128956379983 0.30783218161881465 1.433882615572858 0.36659892179959364 1.2793662581087148 1.1087925559596012 0.34890656722219376
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136842105.2631579,0.3119756534819457,0.13614315075227112,0.7586542985445898,0.7804659317735164,0.30378306803610855,0.4147002941353497,0.5311460494995114,0.6222439419859993,0.4090781885501092,0.22487255476848556,0.17107106047654091,0.4090115290929737,1.6516287927812496,0.2456370694485396,0.39678585232129715,0.23052000272967463,0.11553585232129715,0.691115714836649,0.2565563444945952,0.5896184292526451,0.38927929421210894,0.3687431198077851,4.022914598523085,0.32317552804286453,0.6394300328727576,0.7446390611643282,0.24048315455048314,0.603918162739507,0.17213170218005405,0.721224451989679,0.6768115167802724,0.40813099446389145,0.3729046269466998,1.3564408479304852,0.42936759642286676,0.3605286500460556,0.2506029546425943,0.43681296615389253,0.478324575767623,0.1874059851479991
147368421.0526316,0.29885820404644486,0.4263531428625051,2.003540044346016,0.4488618274804953,0.5765424395532162,0.4208707624525245,0.26172316701788634,0.34955122992602716,0.4289214908251141,0.18844648345355514,0.10687564416605341,0.37881360886169596,0.8840979050401165,0.5205984406193871,0.39605163933497717,0.6280042695867062,0.3760555616045925,0.4822133346938028,0.2651714103043574,0.2632435563528635,0.31279838646547936,0.2988441710326809,5.082009164910568,0.1723538607441486,0.6521215676600913,0.4365182385220087,0.3794388388002351,0.1592651166413958,1.0618438509362564,0.49622290022155213,0.9170270745443837,0.8664174647872803,0.20655680627373774,1.7252670879839536,0.4688795412016047,0.3593124379081408,0.5739576545778737,0.5410180289989694,0.40144339162557063,0.1866253036541292
157894736.84210527,0.6699639740412918,0.5021547967377131,1.0038571635111537,0.48041818412717374,0.21481497333980965,0.5784565801435562,0.258181323635281,0.3168653107746156,0.9343601739307523,0.6354896540126646,0.2379387752501259,0.2194401009261112,1.1198062130618958,0.5236312966597707,0.3077552668605814,0.488167387626838,0.5433242512541796,0.33163063017615313,1.585562045554376,0.30679445451646636,0.49251635649197667,0.5521847812092537,4.242530862380262,0.3227749557706459,0.71459423604104,0.22030250517615313,0.5270491174713727,0.09725290652457365,0.597749802544506,0.19523043381540384,0.7216772597252166,1.0209668732746155,0.663090793049567,3.5608185348088073,0.33175538715563313,0.24212390762286826,1.2001974443979875,0.3304684419711209,0.4459493114017054,0.2718743960943249
168421052.63157895,0.31982603627889084,1.0665047769731433,0.6447691349441654,0.6184696609623875,0.7359142778983079,0.41471089286487184,0.6811505262211092,0.6376751928778568,0.266899510433799,0.3568164688068082,0.18756800939501816,0.07738632244416545,1.4490854786373573,0.17220650881611388,0.45589884496461663,0.32995368767313016,0.4728346637081241,0.8372730455900497,0.5452033383694375,1.0780082132017186,0.1881938310871492,1.229814270526749,9.025932121805209,0.14106112239763666,0.42089873337679606,0.3812979489482342,0.30436786852384856,0.26385853099030476,0.49507754000930576,0.2610676097077346,0.5956097970048476,2.245478326263851,0.4926123368112663,7.2247872814907605,0.28564880032948836,0.30168980310498184,1.03001327725989,0.5584915879690748,0.6912022218149456,0.503107805331328
178947368.42105263,0.16908783265428196,1.0148261643512757,0.8389694208583673,0.865221763251561,0.19346593027299774,0.35314680136471904,0.21247661146760966,0.6793354330300624,0.536813416309304,0.1998189572152008,0.1476814026977877,0.5351662332001157,1.7974592087341479,0.1697014098022123,0.5027796356961998,0.40778817628559316,0.13721672385683337,0.7889585732753257,0.5600078561629616,0.4549047200633547,1.3676692983780545,0.6321721829866106,11.988294265937277,0.424139905174023,0.995881574636021,0.3862350812579126,0.26050496563686887,0.5617740292958606,0.5940299602096432,0.5821317899920604,0.4861889915783319,1.1209380369107145,1.0099591733346027,6.493331047966869,1.109713520039482,0.6578719596123102,1.4754903006091344,0.7525574771321052,0.6301217277294381,0.41901741926029445
189473684.21052632,0.5497069424869612,1.1784656873370143,0.9500587019563713,0.5782917846933296,0.7417523603360078,0.3938052317442326,0.3029391375935309,0.34313644662788373,0.44362463911484484,0.10192933439217783,0.18164371585581773,0.4847572886712665,2.629460189481191,0.3306831402131395,0.27274474674975124,0.5544075160145429,0.3823742694801901,1.4530799527577747,0.4352265566670003,0.7203882539701594,1.04530342926279,0.6526284468801398,19.052833002359918,0.47603741907346936,0.9852716282133911,0.6048613783395191,0.12569495647567797,0.27798909956068213,0.32314444248696117,0.43579123753259713,1.1412307496216159,0.90483520698019,0.38890225207046125,4.863410484757781,0.22094895634954992,0.4729533103034107,0.12646513434328213,0.3890868474902209,1.088537596599547,0.26863609060356164
200000000.0,0.6222849394145765,2.4296290247063888,1.6548071409526623,0.42989118475663035,0.7013195941322728,0.35227414181357936,0.4102591464394017,0.36949202888890315,0.5796488711708471,0.5352263199655634,0.289144566184596,1.376618134348016,1.9230283436022306,0.34192501871209396,0.9165915439003393,0.32346986469469574,0.2478114178306178,1.9161021082024825,0.20343368931820519,0.36306220606753703,1.6887894680625515,0.4443906482897307,46.86712370420757,0.13684900183426707,1.2336734470568205,0.8227253964072779,0.4287427099127519,0.30051085823460627,0.42170855873509455,0.23243934229800575,1.4553125281082957,0.7481388292814556,0.37096560628790604,7.274050461618524,0.6028052380210475,0.6749271593595806,0.8799737127203691,0.44110303176076787,0.5555447528236791,0.6040071688200298
1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20 trial_21 trial_22 trial_23 trial_24 trial_25 trial_26 trial_27 trial_28 trial_29 trial_30 trial_31 trial_32 trial_33 trial_34 trial_35 trial_36 trial_37 trial_38 trial_39
2 0.0 0.248046875 0.2529296875 0.31640625 0.154296875 0.2734375 0.2958984375 0.1181640625 0.236328125 0.173828125 0.1982421875 0.2265625 0.15625 0.49609375 0.150390625 0.23046875 0.33984375 0.3173828125 0.0830078125 0.15234375 0.1865234375 0.3037109375 0.2880859375 0.271484375 0.3203125 0.12890625 0.1845703125 0.3896484375 0.1875 0.1103515625 0.2978515625 0.3642578125 0.279296875 0.23046875 0.3330078125 0.203125 0.2392578125 0.677734375 0.2509765625 0.337890625 0.2216796875
3 10526315.789473685 0.25303052336885656 0.2818348480393682 0.3151880248431684 0.1530232759724033 0.27127791904016213 0.29373885654016213 0.20886646281318988 0.26102487136122265 0.17427111596612058 0.24669432441943903 0.2251227793601081 0.15901869353825365 0.5368489188830938 0.1704359662169565 0.2254851016311434 0.3528566096297922 0.3232524428010978 0.08483515023524742 0.16336315028224957 0.18967974813360916 0.2997240188049147 0.28160719462048645 0.27569278917814555 0.33570643607269035 0.14363569962350947 0.19442686149618302 0.3857168926756798 0.2030046838142205 0.15304481685987142 0.29547048605710186 0.36292883960163824 0.30105880621067377 0.2335696867628441 0.3363856186166695 0.19908270743414966 0.25321202793279846 0.6628941776349604 0.2595041385978213 0.3368385214554636 0.24250026290766752
4 21052631.57894737 0.3247519781054552 0.7037775140059621 0.2755410202322244 0.15343174709837853 0.25894083144592117 0.2796298050814388 1.5344859252676077 0.6107422466753593 0.1783181927540956 0.9530614076228683 0.19264429890217874 0.22412673654318516 1.153600248933829 0.47345062107920977 0.13438279212676918 0.5467433982278501 0.44637041805193367 0.13694093233990867 0.3770245686792601 0.26190059799236604 0.24535919358525582 0.18512439463607494 0.3808101590650564 0.5481622648371224 0.48889858108478246 0.37235265293279846 0.3824419829984121 0.48751695796723515 0.798936812170985 0.2401331957027192 0.31014318809614944 0.6102592647901202 0.28714970934754264 0.3766304502196589 0.14612239615738887 0.4649739780584531 0.3896576625158252 0.38885269270709344 0.32919248649618305 0.5444573431464114
5 31578947.368421055 0.2180345804737545 0.2539619672991893 0.17020524571807108 0.5804186105067715 0.4357177808344199 0.4126518281212803 0.2439287217370033 0.1284933380803243 0.17643138378280687 0.16602040922212466 0.18611258615086954 0.3673987401819625 0.64457055406227 0.2227263199655633 0.11632818660577586 0.3601498907622868 0.6028145581401285 0.32325278622952197 0.5918313948401454 0.40721117954835334 0.3053106218163656 0.25549636587211627 0.6572668968475426 0.21616793867623707 1.1649802543449927 0.4694845564147442 0.7458985558507183 0.6225512338146938 0.29157927558032426 0.1670239836885659 0.17164668350008405 0.20955862430984626 0.28296590313686887 0.2850113258467487 0.2701054993098463 0.30184326541720996 0.20336222186313113 0.3003184352885323 0.41007079708279004 0.21720021847542637
6 42105263.15789474 0.13598419358525582 0.3002172559912515 0.36671339970216194 1.5596519639287298 0.3951150677540956 0.22173984559288976 0.7765633643829261 0.11783216270383376 0.3005901769918088 0.17488672990878204 0.41149307420049014 0.31990915652457363 0.4778002054737545 0.1575888847710353 0.39087829167162613 0.28472248404970457 0.4007331235256882 0.37771741703276485 0.4939396401191352 0.3401148048464281 0.18324271331533504 0.1648678132371559 0.773753010335061 0.2722599526191352 0.6262277936010809 0.3841103635666443 0.25329544405527726 0.2946005739333557 0.24392835453276487 0.33839171348846514 0.5588118111988183 0.25602002553332215 0.3825469400083591 0.4070843619983282 0.34956972750930576 0.3018087455770646 0.2827495353043575 0.29542365034531354 0.38108940864203705 0.29717647732129715
7 52631578.94736842 0.17786528991530146 0.26807614640846145 0.2984565777131395 0.48377714923214055 0.414798430128441 0.23352047082790048 0.19221566060243223 0.16633317212979218 0.3055225488551766 0.3150263440245737 0.21540364664347217 0.2422626976161122 0.41017128952322246 0.19617490425004191 0.7063261095506663 0.21717013942898145 0.350719576066881 0.29652293303006244 0.5154834863551766 0.24064660006282731 0.3836147461571522 0.3076824970192526 1.2968951909495852 0.37243469534158047 0.5339568183032429 0.2966989665150312 0.49501291734690156 0.3737058903702078 0.1516590963770478 0.19563792220773457 0.22353813456696486 0.2891455726940546 0.8566958329684187 0.2955870483060293 0.401618418601081 0.34142361057101855 0.2852437634877551 0.1619545389740751 0.23120912092214146 0.25987705959837853
8 63157894.73684211 0.17999957605081912 0.27707303858199617 0.4620678920164665 0.19764880130165505 0.41907382341633204 0.2666196691032261 0.16284599198528943 0.23775896405249097 0.39197826121322354 0.2673063832967235 0.27476544261308916 0.24036597677214988 0.3899902491688398 0.3345182899623036 0.7855397221784508 0.31222928858199617 0.16956946460163824 0.6608618052052004 0.37667829244090567 0.18065346377047803 0.5571649715180543 0.5401549141162648 1.7198178299246072 0.5094227830458876 0.38991914891800383 0.344143775031177 0.2856922255328489 0.3368333938049147 0.17669834126395867 0.42355535301145086 0.3971519523049988 0.4327764643196253 0.3738525316655801 0.2834526389589599 0.37055026659344703 0.21014994993764596 0.4328284276819625 0.2617994186950853 0.4068888719722507 0.3450195016623204
9 73684210.5263158 0.21902311541697328 0.4048072122801044 0.5649795083127853 0.21383129394615785 0.44245359309822585 0.13812804816502283 0.36271556262494464 0.2710249707969602 0.42825595031484653 0.26083242463933465 0.3028328306457013 0.46015784879140265 0.37508101212350947 0.37426065936313113 0.3477154015834313 0.5182621155419179 0.182884488409576 0.9708832082986167 0.17069129468331373 0.31162429714467077 0.47253112581628165 0.29546229132654933 1.4554862051459228 0.477337734190711 0.3807958063986824 0.5142539993877887 0.4302764454046445 0.32755109411857797 0.3380550532459884 0.33365110149013694 0.5805108606650228 0.28719379763193736 0.4491401418754599 0.21764971080579262 0.3998526126724201 0.17420892107849978 0.40753316747184604 0.3288366655893934 0.8167627815394521 0.38297793475544684
10 84210526.31578948 0.27672950977103533 0.49609375 0.4557121889743118 0.26988640782575535 0.5044739741697866 0.23841559919954342 0.39831306267313016 0.24123213495904391 0.12370213643335572 0.25069490892404994 0.3359644881906271 0.5955277545960656 0.39878991039836176 0.3431641216753592 0.5136110300502619 0.534042590873063 0.32353787408971396 0.37822979110760035 0.13255067016939706 0.583048833704391 0.2897276733060293 0.4774314056142876 1.5770261558469314 0.39611930530157113 0.3430311461895126 0.5164658395867598 0.30432105658787434 0.3429149511448234 0.4549861707185444 0.34398346792627904 0.821226547959769 0.28823873673119377 0.5228529953890559 0.3338640588142205 0.4216230820420706 0.4141558279951524 0.4650375704355848 0.36534340559940914 0.8170744666102189 0.3284363891939707
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1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20
2 0.0 0.2802734375 0.17578125 0.2060546875 0.3681640625 0.1787109375 0.234375 0.2314453125 0.4072265625 0.1015625 0.1044921875 0.1455078125 0.1748046875 0.2431640625 0.158203125 0.3388671875 0.265625 0.1357421875 0.263671875 0.125 0.3681640625 0.1669921875
3 10526315.789473685 0.27517904138961324 0.21664716662462402 0.20527945330928898 0.35913812156529307 0.19925464355384215 0.23110794162486067 0.24473504148361758 0.40484548605710186 0.10831811223333893 0.13793800544210422 0.14761201958907277 0.1737525839554636 0.25252224665929734 0.1676720569008275 0.3313917149467151 0.26280093259098125 0.1611034203104035 0.27098122594098967 0.14105842252187123 0.3725939721612059 0.19274103740575904
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5 31578947.368421055 0.5593659171107074 1.0562601723499243 0.1592104534032933 0.35176998624511047 1.1225984129549063 0.9223344279788541 0.5239751688991556 0.31717466317385534 0.5847179011294715 0.19785628754676554 0.44676556679680757 0.10377779825902714 0.4440891471926195 0.38466581941641603 0.5153802702631648 0.4778849953099303 0.42733103152457363 0.6790356728508864 0.6700322793131059 0.6997957229614257 0.48823134720820804
6 42105263.15789474 0.9246354988077011 0.5353551743103195 0.3642817573864375 0.4714667301759165 0.942520205003733 1.6597057036085472 0.3733688629234927 0.677971573087317 0.36227426502513094 0.3999759959382033 0.8719267382846314 0.22967540920606283 0.39769165799888545 0.5895641569945951 0.873139516138304 1.0678873352727072 0.293752865778112 1.0677451347710354 0.6325612688989191 0.4016891754234927 0.4499201365124815
7 52631578.94736842 0.9867714356187308 0.49509397702203894 0.6614212870928059 0.3461020276817258 0.6589964895697512 0.8486628915464449 0.3478473230081912 0.22737362774455316 0.4114069582022458 0.3873740352091697 0.6964534907459883 0.4021058412800205 0.3044407096926195 0.8141957359630976 1.3091242782296897 2.0485787299201097 0.1649382266311434 0.9983521062581493 1.0205287140822477 0.3650928613551766 0.11630733257515609
8 63157894.73684211 1.6591425866631608 1.7824413320694616 0.44587821115086956 0.40847383641800383 1.6665435009055534 1.1877225733199614 0.28022147413766274 0.3380635914049651 0.5179783776196085 1.0235838216427624 0.7296962156850542 0.23140291758191212 0.4407968177689742 1.0733628946658322 1.792181199937646 4.195472807104898 0.14171196681310594 0.9286025937574394 2.554397059939906 0.2698115298622532 0.17777470934754264
9 73684210.5263158 6.238765642583537 3.59658643083229 0.6551404857899674 0.3245403944950685 3.8729239302658973 1.9344165067593477 0.26265259792930207 0.46801065936313113 0.4373612337825702 1.8031213765659495 0.3401677984940379 0.2482830903536727 0.8480729396323419 1.7971204403694978 1.7015861606333724 3.5507319389617997 0.12613277223962166 1.9583733445059237 3.313483999046262 0.23699467201972607 0.26459068340607966
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11 94736842.10526316 15.202643405037243 15.685721064538507 0.7532116607285603 0.5572941455154208 9.217766674601801 8.15010813134529 0.6283958889440816 0.4634296913886665 0.5443773613081745 4.50728197177031 0.42302452890496506 0.3292772525565446 1.4781875029165 1.9640556081840537 10.410305865913877 9.901060608945727 0.21344095319922282 10.328643532010657 6.292152698020196 0.1799496732590271 0.8677750716909477
12 105263157.89473684 25.396041542539304 21.818484546735345 0.4865458427703942 0.39040384794536387 12.66807343755072 8.59216557975621 0.3923658545327649 0.9828761991041188 0.44712239421305566 3.5509889607944647 0.6431069360875687 0.21256520279226543 3.083921020381008 2.7742421739319356 14.99383551262092 22.727189605586084 0.17520459669118443 19.471750449605928 12.117786713914528 0.334693660366238 0.6805385948878576
13 115789473.68421052 42.63585940754645 27.735247804847777 0.2831894354146604 0.4100106389899003 15.06661862613752 9.918502606843646 0.6394707344245381 2.134073925810837 0.772664373931462 4.038864748629837 1.9573007779108187 0.14512053883306866 6.462227501697487 4.790906855934544 9.35677797840573 18.159722560660665 0.1370267286855428 62.73333005825897 17.51345433686909 0.39889415677564627 0.31168131683011474
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15 136842105.2631579 16.033454924078857 28.467217551043838 0.25496142062454 0.6837882572924332 20.969380410424243 10.766100595532368 0.4718130064142709 2.0120291564603265 1.349581451627357 13.320209347310168 7.357996776823855 0.29395625465794617 17.497463712401675 6.682625110129571 13.461418257525757 23.01459267000742 0.17884972749324396 108.81330713076608 16.185095536081416 0.3766680609156221 0.4783474665929737
16 147368421.0526316 37.59070293394815 45.247559222488206 0.5489187531193871 0.2677650293154725 23.18473077282681 13.554130813091417 0.3090910607757989 1.9922845581561903 1.973272254922714 20.619481776229566 9.112065228068598 0.4696110543121593 27.280923315032375 6.106955874329458 18.48774893594251 33.81049475313225 0.07217057986272657 110.47327014151702 14.82299238823127 0.37575438016009133 0.4326448625474755
17 157894736.84210527 36.77550039793315 41.5172875739861 0.6474715362295219 0.09058684457372096 34.07405397304208 16.38433054609642 0.17504360272943803 3.4255914212594085 3.3810120210092824 28.359679169271796 8.069284127359573 0.5641930123115181 38.486584512810964 9.454989784642272 34.8980696326808 30.82037958213827 0.2703642858362596 93.73673477595531 29.67569741647991 0.7430602071027679 0.48935592471727707
18 168421052.63157895 39.882253588731935 87.91054042488587 0.4652204011615953 0.25461656565151064 29.904271683204204 35.48649123765096 0.2992554133618638 6.534593027384329 3.874464758875628 46.74972572220991 18.78880846863639 0.35086072250746614 41.29111356021955 18.411489893524937 76.87768503965765 41.29712421279866 0.24596077451415335 80.2293726110062 43.59896161615684 0.5038159653090373 0.38863801824088895
19 178947368.42105263 52.231146648650025 119.5222034692104 0.42840330224288137 0.25080975403085637 46.23489197865749 43.12637632111103 0.40478807539160566 9.235101374892977 10.007000925798497 29.432354541366443 18.630783300320527 0.8863489911827026 64.01402699848292 27.234131459053867 60.27029654854222 48.25192117823128 0.2684398423931936 134.70386039385176 65.43712950677423 0.5545542048615432 0.4268449825593309
20 189473684.21052632 72.26899539598799 96.20847314744776 0.6031557067279341 0.528297054470411 49.87977726373646 53.568232951071785 0.5338306638342522 11.775390931443825 6.6547322894067324 49.90554913655543 22.6669396429511 0.6017369352219178 55.97077158349373 31.042400545030425 76.6398057382853 55.76528996179639 0.2646484375 167.1103262597504 86.8981981568059 0.613903341531093 0.28348001812963936
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@ -0,0 +1,21 @@
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1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14
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3 10526315.789473685 0.19034423458279004 0.2400682533877048 0.34593077841888176 0.16407309872952194 0.4529544375940043 0.35159770669699375 0.25659940249371727 0.13492696239017055 0.15411571386448233 0.21215572515683162 0.22998576811476099 0.19686775260354672 0.16352961532296897 0.20850652076530984 0.30794908729616627
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1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20 trial_21 trial_22 trial_23 trial_24 trial_25 trial_26 trial_27 trial_28 trial_29 trial_30 trial_31 trial_32 trial_33 trial_34 trial_35 trial_36 trial_37 trial_38 trial_39
2 0.0 0.2275390625 0.2060546875 0.1025390625 0.220703125 0.318359375 0.3076171875 0.27734375 0.1376953125 0.1279296875 0.26171875 0.1572265625 0.220703125 0.1416015625 0.064453125 0.09375 0.3427734375 0.12109375 0.1435546875 0.419921875 0.146484375 0.3701171875 0.123046875 0.1904296875 0.126953125 0.1943359375 0.1904296875 0.0732421875 0.1455078125 0.1318359375 0.2138671875 0.2568359375 0.107421875 0.20703125 0.1513671875 0.15234375 0.3974609375 0.1669921875 0.265625 0.1806640625 0.4072265625
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5 31578947.368421055 0.3498253994040872 0.3549433731966731 0.37774921322133076 1.0402010629712046 0.22255644441641603 0.369544998760699 0.6786579438523901 0.21265067948528943 0.4280936301910317 0.5398124393663908 0.4577552076852222 0.2614384701377468 0.49887166855407883 0.19764298679425774 0.488345505458166 0.3782475780582164 0.2481736925500252 0.39283345346635723 0.2801226988393514 0.28250308842540117 0.2599375611196925 0.20115649204835334 0.27822904507539276 0.5606429266467319 0.4127451561164328 0.8448745775090691 0.1666052572614929 0.4018905037327817 0.46988311566804586 0.40820621585581784 0.20021650995904394 0.8358212811794967 0.31394040749674035 0.7036589149623036 0.4319632997803411 0.33588553663766274 0.37348849225242375 0.4581941012860665 0.6310042991532513 0.10114686442874486
6 42105263.15789474 0.31806849640822477 0.07151055798306029 0.4362800577010474 0.4209691943224117 0.3561332364491809 0.5947860337360413 0.2849552651191352 0.441506055583584 0.6402804409037666 0.48122244330324293 0.28668552092237815 0.505597545169397 0.5332985135656976 0.32151536598099906 0.2854676391939707 0.4303499258786357 0.38408062794862363 0.18500339159344703 0.2786310148371223 0.2349892402289647 0.34156409393056936 0.15931060241530146 0.17507642920327648 0.6638020438830938 0.5966882256589767 1.277095953183161 0.25712750294862363 0.3859339473650396 0.5371291987453471 0.7148686776200819 0.41922902664649525 0.689923791013596 0.4045176836262119 0.7694109338142205 0.46480204193876057 0.08634015661857795 0.17908385850055727 0.4975345009251645 0.5306378203415805 0.38499565864203705
7 52631578.94736842 0.4482678257527444 0.14452852634842045 0.24210170365436587 0.41767068318713074 0.5677116689919764 0.48819545365436584 0.3175738855081912 0.3406036012390644 0.35040818687291025 0.30685117832511416 0.15739199725544684 0.449594738080561 0.9795656679739912 0.6436442140066723 0.24983012445085268 0.2195354894918088 0.3465036540150312 0.21170794996858633 0.17861181877326437 0.22713571902457366 0.3089492512541795 0.17886749066804586 0.15466398149316002 0.708045055991725 0.3843110050190849 2.244460304027779 0.2854454352254683 0.4088365021174634 0.5351924869822663 0.17836946925958438 0.5028103778236791 0.5827360945725375 0.2932695404644488 1.2547355556752213 0.2702699037800205 0.155255674325198 0.22418655120765074 0.8493048543745131 0.841276649623036 0.21518077744671513
8 63157894.73684211 0.4295347007688062 0.30621711435080234 0.20832945699506847 0.30310592228686045 0.8611192412653784 0.38166194080976223 0.3134064925344367 0.3136676355081912 0.3328803318689406 0.28246959887052847 0.11680535398361758 0.5158625890673696 0.8010625601475259 0.3455479693214652 0.3236742363081744 0.3207179040459716 0.28131800939501805 0.3144657843000672 0.3050802447459044 0.17443210992786692 0.4905242233065026 0.24101029604755944 0.15488172303936823 0.3737284377671343 0.26674273271639926 2.792095971569789 0.4950980506115013 0.281389109645854 0.6222316498901705 0.3351752685377804 0.2236328125 0.8736371703425271 0.33585138400175585 2.463276892157473 0.15405486891474418 0.32283884402457363 0.30632104107547675 1.520006724011535 1.2819705709526086 0.23117460108199614
9 73684210.5263158 0.2705112230084279 0.35051314388285726 0.21319381946341817 0.21449543696691453 0.5097287249366994 0.302012477885323 0.2882756367944944 0.3608618997801044 0.43091733039581204 0.4181666678008611 0.22203962954788004 1.0264171140676062 1.1404507312087806 0.5620474168138159 0.3052070622959296 0.48204929742786695 0.2954103517400262 0.39570673681031954 0.3029958614021787 0.1881398784817091 0.4770393477252317 0.22991329415022826 0.28148381135470324 0.20030640366995434 0.3236865521798174 1.4399255557073454 0.5312441854926027 0.18736464429099806 0.6931245571358383 0.4508628660291846 0.24378890145848664 0.728100332857169 0.4541268335485061 3.702669172736087 0.15411640072133076 0.3717811510503458 0.3663739682564774 1.5483211982283234 1.6849394795637052 0.29650242242786695
10 84210526.31578948 0.19070142920327648 0.492338925517497 0.23267241924423257 0.14271826493112663 0.8555350898045253 0.3414714527922654 0.2616196312732644 0.38304184678518866 0.2617286618726736 0.4175031878611387 0.2767677835480328 1.3311480154951525 1.4286616740134284 0.45591729499626693 0.3480284841437089 0.35757909124908016 0.4469302909195918 0.30640990450111455 0.2568147400409561 0.2401848156366322 0.8117299172356519 0.24270399521592587 0.48214296885144353 0.31292591464816705 0.3422484041250974 2.5021138706365784 0.4130732781999329 0.39150656491435476 0.639573559536498 0.6972865265822479 0.24118974004095609 0.6500822791102189 0.256051821721888 6.55459848335245 0.19078209789836176 0.5345632072300792 0.3229434576060964 1.170348085524963 2.3973301176879547 0.34834262076507316
11 94736842.10526316 0.17653597358851553 0.34783738735970365 0.25224709444759297 0.12027852489017053 2.3185349118346323 0.30297365743367627 0.2515381525097791 0.318742551301655 0.2329345925032597 0.28731958489668996 0.32036173971075765 1.3045172572466144 0.7365030806480681 0.5753911697303159 0.28257212810569193 0.49299183050351136 0.27475962810569193 0.29303778968029076 0.22925599592214146 0.37817478444107355 1.6268421289333017 0.3673891717377132 0.8493909941485714 0.3928286692442326 0.4869940089386916 2.9320835684144924 0.31343622815245736 0.41808357133099244 1.134464586210383 0.8802078437276823 0.23555904874511044 0.4649360477098798 0.3257196590180542 7.203382246382018 0.392227112091149 0.47462645131795356 0.39892423582209113 1.0136547986820463 2.2716120801804136 0.2869592994203858
12 105263157.89473684 0.3387821017870282 0.1782775149781288 0.20618216813105958 0.17444373894266144 5.464725092837685 0.2481230791255708 0.1905305233688566 0.3568486559754263 0.4291105508143882 0.29361444298910633 0.31665404681683906 1.170143027054636 0.3531618408879415 0.7902175237597521 0.35131470318316094 0.5860526647594166 0.19953013919397075 0.25166121612295217 0.3724470112132233 0.4541812009098127 2.2518734865901875 0.41294614099729754 0.6939506530761719 0.22826984120207813 0.5904046531529308 4.055337160908284 0.23344627972124687 0.2560008886448234 1.0088251806031965 0.4132188654342187 0.24862009402457366 0.5294684676912683 0.28801346353546736 10.039715241197072 0.4992623527294381 0.2189058425353835 0.43283117510935604 0.8640386734642811 3.2897665758212185 0.38168181210673746
13 115789473.68421052 0.35314439736574976 0.1806343268819793 0.15484651634237442 0.3762486714075146 8.285631570789622 0.15975906446039512 0.22905535446970085 0.5511494105542465 0.4683985961110969 0.4266754504386077 0.19865919678495203 1.6609725767225438 0.4454222412320715 0.7236351689473415 0.7038178959051327 0.42741648444178365 0.30322147802632926 0.2803397535287112 0.28444046326951644 0.3528234397275296 1.9664447604784345 0.46053040258772154 0.3381155309914882 0.17458969338118532 0.40575298510099717 8.439830299229502 0.2024564161855428 0.22262958146198306 1.191928998255003 0.1278763504239661 0.2206070733532681 0.6033867706552436 0.6720951930968053 12.632351354879026 0.26584612827882215 0.23871879366296145 0.5428696312732644 0.4622343095055578 14.473562156064355 0.27923291541863027
14 126315789.47368422 0.4955267126870621 0.5303346734297909 0.17218707605081912 0.6911916230854238 8.054654530871275 0.27792109016566413 0.2247495149311266 0.5840927187425606 0.2945865409195917 0.6587421913886667 0.16299467007539276 1.9765327643819792 0.8072135481477779 0.5083539228360077 0.5573457416735192 0.30477464628351675 0.38727283213607494 0.3374086734000336 0.31044059182798456 1.3167003621024786 3.5454615225752333 0.5424273271639923 0.3866910749525246 0.4254158844247753 0.418333819698429 16.77756688337248 0.18916018583767957 0.2667649604607158 0.7247206669434931 0.14106013966399228 0.36904494055750653 0.8748363061624884 0.9645125370606822 15.219834303921944 0.1547596897114677 0.3760083586885659 0.43936833516382423 0.3190939314147442 19.21645830740889 0.226827764114845
15 136842105.2631579 1.0477754059260578 0.2945065115297265 0.14739974912183765 0.4752536467237812 16.179841926553586 0.5601767252026506 0.36046199058892014 0.6316120617937845 0.3598819267716766 0.663672478905675 0.22098718257491948 2.795400878399034 0.9910766120762706 0.6800262683646503 0.4020815767409729 0.463385603104272 0.31555307076578315 0.9395321716562209 0.3716574005803243 5.374017139551056 3.463400132768371 0.4060281373127013 0.49077513475497353 0.4028581608695665 0.39656298312454 24.874373198215988 0.13089320798329693 0.42243764407086587 0.22859423312454002 0.13495566772291862 0.19331114179870068 2.966870321131151 0.6447571387251324 15.260037863353611 0.3267564033867582 0.4562830277757302 0.49860951907086587 0.25948703850405364 26.696052022918117 0.5007571513632991
16 147368421.0526316 1.0926992463933463 0.5765981806282195 0.1859611606333725 0.3561028139743118 41.093773791664546 0.24100681421168912 0.351067202243118 1.1386770739779912 0.5901216734149122 0.8747156465482846 0.307135922756882 2.0717298502406907 0.7917234891009131 0.659126350423966 0.30908423975894317 0.8706614053150297 0.3741369326689238 0.5032413250191383 0.6344720465324594 7.085498334298174 3.316975738863536 0.5100527734307373 0.3526244916413958 0.4341700598803915 0.5145421543279844 23.39264359830819 0.1958587308339466 0.2851907460643312 0.26207287754048275 0.22575036574598836 0.17116232790114813 4.22579486878625 0.5021335992786693 18.357474704858674 0.4059283555049315 0.28120348394082173 0.9598434162932423 0.40768496019358136 57.03829002908725 0.37231536188944536
17 157894736.84210527 1.639772602725888 0.4988060156064019 0.20239522780738048 0.23239280246301364 72.52874119724265 0.15250030316804586 0.258544995844199 1.3656907121230362 0.5142266202171092 1.0361964048771317 0.4328824516148449 4.004721464542802 0.7054496722868605 0.9512272964223933 0.3218489591434722 0.6488756591923677 0.2818604625162985 0.6897765341888177 0.5278666990285433 10.423493290211688 4.304360183652419 0.5510731588770478 0.39443828920908586 0.1891375908891248 1.2933448569596315 35.360429372813904 0.2608191022582332 0.5173655586559689 0.7763932405086109 0.3218701566025161 0.1403012949343863 6.449813818997625 1.0750275688488402 17.91763835336363 0.4890640158402293 0.28611949011889853 0.4271299515404525 0.35066829956139217 64.87515323776287 0.46869943412717374
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19 178947368.42105263 6.0064985798336465 0.45278046467958066 0.25760879146755566 0.24032907670884915 97.45902445838063 0.33503549581089187 0.20646041119858166 7.178135068793048 0.6067646243235413 3.0048406553400526 0.6228297965348262 3.9085424032237723 0.8300118565229169 2.9102855772192786 0.6108745828559855 0.045538838880544205 0.392437298212025 1.1848476441613198 0.18454433081883143 19.95002200795013 7.838737102096431 0.5937725949485547 0.6001214769738534 0.3368494873892238 0.42213236526108844 51.87713701771237 0.2597563999841748 0.32713506756727045 0.0903643188053881 0.3074076406843444 0.4260595168433362 12.892902213120397 1.13466584319223 15.739320340249018 0.9442135607436754 0.21316305356012488 0.46911637208468354 0.332357335288769 64.48933502313504 0.3148328670174131
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1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9
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16 147368421.0526316 28.052590959290065 1.8088652433781087 4.110566865704398 22.06466674804688 26.32343972224607 0.601789099357795 0.9641266608832618 19.081813643183413 38.351053776833496 4.105917922677756
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1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11
2 0.0 0.201171875 0.1474609375 0.2626953125 0.2509765625 0.3779296875 0.3515625 0.5283203125 0.1025390625 0.2001953125 0.1552734375 0.201171875 0.40625
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7 52631578.94736842 0.26562227634842045 0.28747375784158047 0.7030830198377783 0.38061430183474043 0.7938516410764235 0.3176791621707483 0.7576070981012487 0.15861090926912683 1.325336115512161 0.18147347310243223 0.4715337330614761 3.8417730727684463
8 63157894.73684211 0.4130244056934134 0.419478197177031 2.552789867749836 0.5317743465180543 0.7291756944312946 0.2742431566655801 1.2819059482902042 0.15480002405901033 0.9884446479607158 0.16506129024431657 0.8301297924855415 6.062050874873872
9 73684210.5263158 0.4416308363388781 0.9029495233974303 4.578024922315434 0.5052830651196085 1.9550710794337909 0.3313127633937508 1.843442779498748 0.18985237111015008 1.7661487547644623 0.35013475180332687 2.1102747428450233 9.047234659379871
10 84210526.31578948 0.703158856759111 2.1783637260796294 8.389273244588331 0.6207991412471867 5.681757200457714 0.36671339970216194 4.353583232847939 1.3504192954615548 2.7489937018819792 0.43980553539836176 3.964401245117188 12.114645263164658
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12 105263157.89473684 0.7522874287951355 3.85286762311518 16.892098931394457 5.454146150076488 12.15275656681642 3.5993557768845488 5.601042216504379 4.577857131112646 4.791842325902712 0.8901967289044916 10.639487623177736 16.14216986785635
13 115789473.68421052 1.770855924759545 4.962410142216986 30.214912644383645 11.192647178417426 19.69669155797139 7.527202888869182 20.23894223876276 5.842226638688275 9.328721656693645 1.4675567975665063 16.8366599439584 20.60467112427603
14 126315789.47368422 6.458008087242747 6.281620659656474 41.81310676933987 13.325664308923104 26.887397945752767 12.208369627553676 35.33012637405185 10.183598441760633 12.488072213043468 2.5151763134055534 25.50017838200705 54.93078991580874
15 136842105.2631579 10.757425239541858 21.18903042801201 65.53680683305062 16.855921145621434 53.91626050003351 14.447411331113356 48.61652792193554 10.42493467780031 26.932806942271412 2.0457209114222636 36.71975068966769 44.305423652036005
16 147368421.0526316 17.106903144857565 19.493297022135295 74.71719628754084 22.694302107158464 60.21679335617953 32.81872818542651 73.32166379574595 18.40202304597047 74.92617977491051 3.3872946107816846 48.90670771612025 83.19890364649558
17 157894736.84210527 24.359525931508923 36.21356267744156 74.32568160979041 16.51164893628487 84.45178987180759 33.07684492074221 88.7824796349058 23.264234556055467 91.39014486328718 3.3141351631143414 42.45797127435742 115.99503649502913
18 168421052.63157895 48.62123260075367 46.22311392913565 64.09681967949273 33.462527626439154 128.38521421649122 45.96464652698126 102.65875184965266 42.08960518876602 111.09692758998713 3.5145066279783803 74.90180981918718 120.84549241845298
19 178947368.42105263 44.80953861933996 46.58364661314481 70.36745623802544 79.8354273661352 106.02552816808388 70.05180360735949 127.37867529438475 53.92728262660907 138.49816179407603 6.6758360691017735 74.96363218999636 130.2065561484762
20 189473684.21052632 80.78561290413388 50.879144642161535 65.52772759202445 113.54444279234825 128.26982405707446 69.0160346150068 117.7153404320376 49.49558243262801 153.671208717156 7.646348741906503 118.21148424861833 163.8649747431113
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1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9
2 0.0 0.1015625 0.3388671875 0.4326171875 0.2109375 0.955078125 0.4345703125 0.3984375 0.388671875 0.525390625 0.2646484375
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8 15789473.684210528 0.4758098369820297 0.3824696580458876 0.46029318072459047 0.8411207595360245 0.36577344138866674 0.5807384903080903 0.3193041413114341 0.6842254099753423 0.4427745269606318 0.8528741007036126
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View File

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115789473.68421052,46.656092494478514,49.3003974172217,40.88618461180922,0.25334020730861334,41.910199469146306,34.03389628243909,49.00269958253052,53.758933121477796,2.3499170736592903,0.3511508019677159,40.18175835094293,50.15375549971562,5.919387569057644,51.30893965507148,1.5903333402406472,51.3686523807346,35.98736973152266,14.98820638656616,19.71185778911094,43.69592754068137,51.63654300975007,8.098332146198135,0.22332978975079398,0.42853712441188146,43.709000233467926,40.5388273638041,36.95644398079024,41.39879911428013,32.6011972374533,0.41385128359385137,0.23226139618088992,39.2308258759348,42.3913648927641,49.19575073580332,0.2872866104844534,0.4159165062732644,50.36735196126795,44.85200709319181,0.3679334899395127,55.25720063735243
126315789.47368422,50.7570367110403,52.976161645059776,47.366475002257125,0.31013072428610855,44.14990248640488,34.19732289301061,49.38634661095955,58.1743103460592,0.4272218054351382,0.37309574750651936,45.080737893270985,55.0537393258219,5.963009271595287,54.12758286705968,3.548206762593871,56.25744196714788,40.83990379185558,21.697760658581178,22.474877867342038,45.57133719531453,55.972243332796815,8.525807214245573,0.2298403288188734,0.677621614239553,47.102193710876634,46.08562893748614,41.119568093001355,43.526330535761865,37.3657715181895,0.4213284257376292,0.3566150401107494,42.9950479945978,46.90616961133117,54.337957281815385,0.24798961227290178,1.2862201014384023,56.409569034946266,46.74809531425835,0.20578515430566663,63.949041636036384
136842105.2631579,53.9350477414118,60.46156376946997,50.39507691285617,0.23333228129759376,47.89338325067241,36.87274535805235,52.60365415610105,68.70991566967106,0.4601527092529467,0.18887406769221488,49.668169630531466,57.84740869622482,5.950966425549621,60.1147542858388,5.4075075358234965,59.828689462920636,43.388983726501465,27.622071433925896,26.959531791982894,50.158386805050924,60.51397173820771,8.5146870190417,0.16035500259610744,1.9383167652542255,48.087698569258166,51.13319751364373,43.27336407896554,47.40165236650082,40.66711062803824,0.22400793012159334,0.185431479086836,47.22096720692854,51.11769243884945,62.04953011251223,0.25980716134702736,3.4394111752179874,61.05483244396643,55.152264300475835,0.2738663219018658,70.90816192283525
147368421.0526316,55.426549438624505,67.26765538582842,54.96629402445954,0.20269226433497717,47.025430993690385,48.85590636499042,52.11518048051322,73.96457697744185,0.30798375507470954,0.19287811025688198,53.99958121017076,62.600232671172336,6.394833828934012,58.921657126365936,5.569509199781761,60.1442669686188,46.26557719476335,32.55457249110425,31.540916662136937,54.30574820246393,63.68158021329843,8.601941087569557,0.2437566139030986,4.160913982549864,49.16665086191447,55.80555607011114,42.6528623348458,52.275333370198176,50.99232035660678,0.2255374084219048,0.1864807229293021,50.14173426060135,54.075917346986046,71.33212466517314,0.2398154768587149,4.5656570688179,64.05983274729299,60.19737185005336,0.17605878243485962,59.13145895876051
157894736.84210527,64.25255515502761,74.46061060105005,63.49411354038524,0.09404599435441703,51.2797619484138,53.28576902273289,55.91283242920429,74.41781764413511,0.3046184603197093,0.18032839687907462,56.76242933907337,68.94851316837723,6.424376209026558,66.99848009542745,5.472073794071694,68.08767717498822,52.67536304796172,36.49175333910702,35.18614392795722,56.681206433726814,63.8464490911637,8.304588321833728,0.2629819220122868,7.969707409760961,56.353007364140986,59.631344845420436,43.98708957582299,50.09347830981098,55.1231301854522,0.1679714736515795,0.2552794947848756,51.8840199850933,57.710881399646034,76.3658868493796,0.2791322988156137,4.517977678874853,67.03021792889962,57.27909845790704,0.19710634818037465,78.43667520776681
168421052.63157895,66.25667553000834,77.70913510309362,76.04937911099675,0.07780796801284409,51.94030814553892,61.43769618744996,58.442686783640006,81.16076535465315,0.2247877887081241,0.21604813763309386,51.86910890278063,66.78434825273762,5.698441016707063,61.01313853594074,5.6116096306375525,75.84686744246126,53.525400684811075,37.03903276438198,34.26640053535102,57.08660542073342,68.74459581031694,8.277319657175164,0.24926971266474418,18.56597621421075,61.868744424835796,62.780055756714205,49.807558033274816,50.50667508619314,55.40086335158414,0.22349404628257014,0.12058579294305091,50.24718676115337,60.91642773910903,82.71585998112475,0.24551351446854439,5.083082246648308,69.59498067839985,62.904787628934656,0.1977284397114677,79.53383008793121
178947368.42105263,65.73572593382521,83.04939186143743,82.21289736015976,0.14307855040743084,58.02044856977595,71.76870822642319,58.05174952266619,81.45012706006332,0.2177030241060125,0.19056213595530333,54.24838673441034,70.10384824335411,5.556786910979041,67.51318451572324,5.438664361050255,74.89859534894991,55.49365537648716,43.63048864269521,37.042173616773866,61.76772238871398,76.03766362092502,8.568345916568408,0.24663484129549063,21.676341284014843,60.74922025897166,66.91877703785566,52.28359889059516,55.67508761704464,63.00039149387391,0.12880232327532568,0.2288039635423148,51.25826370418898,61.06184660364716,83.92521700766608,0.22897331206091884,6.270845864948473,70.55238805781441,68.32308550092323,0.22078191672665923,85.00873951238279
189473684.21052632,70.03839490156095,84.11796303270927,78.2207005387198,0.25439144039418227,59.15385215632473,67.67184759441174,63.57085884971302,68.03014485789798,0.17987481907133912,0.18274555047793403,53.248326032115486,71.29009116323371,5.828619095757397,68.09218141444832,5.7173553741539616,73.84181186961335,55.026133030075115,46.10458964191976,37.11788458309015,65.59806084831006,79.93420678294596,8.045755721855691,0.1616916788581996,23.026484946464898,67.00361081173546,69.48359441625114,52.17803209310093,56.08022738956018,67.23691428863441,0.1402910634091026,0.15547510923771315,56.131559609706386,65.1895280399481,92.5978728714412,0.21482203739831982,7.0279121795189345,74.47953558100228,71.90119198616853,0.2425749453811434,96.88982743239468
200000000.0,74.1640023181313,88.20140344218204,80.21218297356053,0.16139447061639084,61.21819438432392,72.84553038446526,64.21980923100521,80.9699421179922,0.2037934002123381,0.2522574976870888,56.771503498679714,73.2979884398611,5.8505777308815405,60.75899395189787,5.52407149264687,77.37758588790894,60.568656620226406,45.00232500779001,38.86378034792448,64.92305840943989,80.85791045741031,8.019417311015882,0.16745637592516446,24.14631193562558,66.12484121322632,74.87561394038953,53.085997129741465,56.55158790789152,68.79039694133557,0.23664617538452148,0.16919381994950144,60.330911761836,67.12918286574514,90.9565927354913,0.16649843517102694,8.009520580894069,80.6888095203199,77.13992292002628,0.2391904780739232,98.43607809669093
1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20 trial_21 trial_22 trial_23 trial_24 trial_25 trial_26 trial_27 trial_28 trial_29 trial_30 trial_31 trial_32 trial_33 trial_34 trial_35 trial_36 trial_37 trial_38 trial_39
2 0.0 0.494140625 0.9501953125 0.72802734375 0.23046875 0.484375 0.24462890625 0.5361328125 0.7392578125 0.220703125 0.208984375 0.43701171875 0.54833984375 0.31982421875 1.18408203125 0.13232421875 0.70751953125 0.2265625 0.0966796875 0.25537109375 0.5419921875 0.55859375 0.251953125 0.142578125 0.20703125 1.1865234375 0.564453125 0.24951171875 0.6279296875 0.27783203125 0.1484375 0.18310546875 0.22607421875 0.501953125 0.8427734375 0.33984375 0.28662109375 0.583984375 0.75830078125 0.23876953125 1.1474609375
3 10526315.789473685 0.49652170144289814 0.9977614674871979 0.8302475091823251 0.2288075338770478 0.5258777161384224 0.26179480618717266 0.5844465147425264 0.8223186186476098 0.21613478066188146 0.20795995839084613 0.44014034244822664 0.5774664997724285 0.3131793542581912 1.2775808120368262 0.14068567323552605 0.7143582042894865 0.22722698644918088 0.10673004504386079 0.2541805555285509 0.5312496565715759 0.5797465686322579 0.24948898775095424 0.15077345787323082 0.20888627467062995 1.2291059441183412 0.5879870200751561 0.25258496857746154 0.6318335453889377 0.28727327621544496 0.15109544579672352 0.18903047292186284 0.23094711937732643 0.5055524265997298 0.8665842019289814 0.33557996195108936 0.28424001730710186 0.6033929167031582 0.8217869240821564 0.23627770706557172 1.248075260680138
4 21052631.57894737 0.6849224032457516 2.0354762249045755 2.899330202562327 0.2083704781994595 1.5123926807308463 0.5181258774860413 1.8486727030323484 2.3948645472856773 0.15702574933334731 0.19307754970983784 0.48653936518196256 1.4385540399524976 0.2176984115980999 2.9038863670792936 0.2726973007920706 1.1934817993079527 0.28839460304239123 0.26190965129397914 0.23969089159344703 0.38155497078089834 1.128383987828305 0.23446643913881932 0.2949170907778753 0.2448958637311518 2.122116485130754 1.428297410050918 0.289313731101081 0.7537016828964952 0.43387027592540117 0.19929941869508527 0.27259133727266516 0.3060867145781372 0.5700257187735011 1.4916662681135775 0.2568407217221247 0.24473965399153014 1.2262851630551665 2.124011169179985 0.19919875454044078 3.114077705425569
5 31578947.368421055 2.24118826594049 4.627148058936207 6.956321308157122 0.2571729649467151 4.4241064512828725 0.30242520620287955 6.9978975642090715 4.626302251525204 0.2688787241061308 0.2056417755803243 0.4190427259725216 6.324368927287266 0.3265617124922057 4.997290672027506 0.2129659943303243 4.843616811852708 0.9436446583502185 0.18441478961722674 0.3087431268348589 0.8372309584366652 3.5895586449683883 0.45294930994345545 0.35903028107746154 0.27153427779179196 4.1995158816308535 5.935984034287304 0.26729409120089476 1.6712633949237525 0.3758061718082164 0.2163484129549063 0.1468012352729438 0.2813614345983786 0.7173415722939448 4.086182188789602 0.2085921453967319 0.22982391558195414 4.048961675068019 5.133871602879999 0.23165416057090019 4.987565718199078
6 42105263.15789474 5.191192600535555 10.389190272281045 15.12841030237087 0.22302882757213308 10.069237051247892 0.4511746224273936 16.082432427234597 10.240132302788817 0.17627978655109774 0.20904556337816235 0.33917533789975496 16.848162975998136 0.2657049818382369 14.023747753238414 0.17384264938058613 10.538108941920907 2.820839836987102 0.2887914451535719 0.423933229948345 4.502140309341728 10.21979456132799 0.49398851262565463 0.3515416459693803 0.1941140985885155 9.77537937639823 12.380305530622065 1.0742304265664226 5.395573312225765 0.5510600082101584 0.17625535029783806 0.14290148663718946 0.5723319648045253 2.1806129286493956 9.85613180461683 0.234670834528112 0.14906660803797503 7.448105281079576 12.058902481586319 0.20896882033414127 7.8542944361298375
7 52631578.94736842 10.83784787608646 20.385555940982048 23.572254878332078 0.22182034257376293 19.97872336617467 1.615725350842251 23.36556761416702 18.36757633758714 0.19532001976161123 0.2862509082889293 1.101568066182229 22.791972205249227 0.22986545192898145 20.553699007324894 0.1492667462356863 18.53281970697757 5.4521982636808355 0.32914804289545707 0.4060274861195741 15.137717310411448 19.36185924630416 0.699090618175813 0.2563520970437005 0.20477511413870095 19.20060614667771 18.830435314336974 5.432178082558586 11.44808975018953 1.4109826840852435 0.2726144117001351 0.2742455487766424 2.2851454742727517 6.6287669871322334 17.796421831664617 0.15306242020836827 0.13872229293442828 12.601487184825697 18.7865858936574 0.19123859484770292 13.378934909101998
8 63157894.73684211 17.681571799302038 24.965509924531975 25.528548031962814 0.18676971266474418 23.436591069123754 5.921458986657481 30.736879105713232 22.626395431581958 0.2350659832729858 0.22715007169094764 7.6920882301647655 30.14843616855442 0.40067605628861636 26.028098610959887 0.20446781042209947 25.811571707685903 8.995880586618865 0.34856634853289087 0.6106412628681047 21.48754160820282 25.737043610570176 2.587658182075481 0.21728037202787534 0.2831463774155381 22.96093462312651 23.087736861527464 14.609693767621579 16.40369266023927 5.065548767343456 0.24314816440571704 0.2669131234081828 7.416600829676582 14.068949282004239 23.940860328251638 0.28999975843772996 0.14751135543442828 17.590556440591154 24.487356196480118 0.2859974567909981 18.806900661077528
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10 84210526.31578948 27.914187317739895 38.72586870061394 34.37427745829659 0.25018611707185445 34.87612768157367 16.360396504071943 35.12214121726081 31.569806550678454 0.7241392479048543 0.16149017883469854 23.976321466081362 37.202182146320716 3.1595932809930103 36.29751395650848 0.28417679213420843 40.665853104102645 20.017524243722 3.322405807199241 5.020510792402021 33.043249019295224 33.58857228287039 6.7285567413076475 0.4223994944564523 0.4629706068382369 36.326130462815556 32.31678976973008 24.615091128362515 26.16703098962842 16.228713851886443 0.2158493612611723 0.2527393013486572 20.926730813742346 27.030312429834932 34.8623172833979 0.23361429018987512 0.22156211874161405 26.893434751727245 34.799212468958295 0.21807697539184234 30.454888457406593
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115789473.68421052,8.622501515945899,0.17303033152445532,30.4624208954893,34.4494729240185,32.32523063939694,29.10033617653675,32.68394685518048,35.03421277022428,29.25066611509244,36.44389487765832,31.956153038796295,27.203258828773393,32.48497857677639,31.02924344414159,32.335136919470706,0.2611046814852474,34.55427443617929,29.749940528763958,26.3664939489391,28.684378358465814,32.14956315138333,33.532602390754256,31.03434411178335,35.64516809706543,27.293726334611463,41.36981221909668,25.84496872973244,43.52629251163091,28.518349736020834,27.90022700381081,24.67630119270895,29.86176488274022
126315789.47368422,12.953163553803256,0.1676715417581912,33.4014120762368,36.214981232323474,36.62185140593891,33.39649893636519,37.98510644970839,37.83161627222626,32.14927361612505,37.06019579076371,37.07880169136703,28.69297118992687,36.598861699619455,35.13885881101656,37.91701086472277,0.24924954549097286,39.300789333776756,31.456702678817795,32.177538573246586,31.831940267885162,38.08447337480794,36.686553305205884,35.872348959756366,38.176747055265054,31.759865414733046,44.80667683292294,30.703182098938164,46.604350858778176,33.42258303845689,33.616753813302424,27.639321192479862,34.44234290611711
136842105.2631579,17.76422202752238,0.2581326228429737,35.67636442316536,38.85061561499937,39.09070651617077,36.82817951662059,43.90963821199793,40.68667470451207,40.04966179221621,41.721462842830334,39.7955187258628,32.505569522730866,40.11072799571664,39.583316231038104,40.304967028282356,0.1549811733066209,45.480007874338256,35.54768012567241,35.17292557660893,31.51637954526991,43.55536895841773,41.5929385367523,39.77065433095367,39.490757211753866,37.01248428762125,49.20768334000395,33.773233650133555,49.02499226784112,37.10005671297745,37.34949378491769,29.527241902338172,39.6905295723363
147368421.0526316,20.60570672476391,0.260494538621559,38.31259859301707,42.231486737893235,41.38264921563484,40.73568734832088,50.646387562527224,44.740820213698285,44.63164416706793,48.643137432531645,41.64506741573936,40.34868815466969,43.2403947190895,41.13025597654221,41.12120321913109,0.25687543705229626,50.849281604270196,37.71554495951476,41.43600509833762,33.58173339188595,45.139807246728616,43.83206370398609,42.460580910341896,44.589737517021376,36.15181583182633,47.555083031799654,38.0724171059944,51.82304479805056,41.23192626551578,42.69152521888966,32.82670638964117,40.99125826457861
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168421052.63157895,26.715029264751234,0.1977865372338123,40.6483221925857,46.188406376297124,47.896664352628335,44.920449106316816,57.66966511734305,47.51291468401035,55.239545975365466,58.429957276235996,46.36995255319696,49.251544962959606,42.72431286418207,49.434618350211274,46.68246104908782,0.1842773733376796,58.893274301967466,42.532215805265054,52.034736886909464,45.06114534922254,46.15300290009982,50.499782615091,56.667042190678565,49.380164931025206,37.5579634056197,45.91710508563181,44.579420158407366,58.330935301212726,47.099042094645405,48.48191630609148,39.709610872981955,50.18605172535059
178947368.42105263,28.837614544210673,0.21486973168116857,40.59004576516614,43.8768165065311,48.7303252946637,47.438980399736735,57.06440764450961,51.27431836220696,59.70055551740271,63.84417723156409,49.136360402252535,50.296337965122554,48.62306642400261,53.7552396306701,48.46115139382698,0.19997945981012488,63.31777568405025,47.1586730949106,61.79786850805098,51.845167277592374,48.759547636449504,49.15821553465402,61.260983023286855,50.79944745193228,39.82006362666714,57.308786665633775,45.93147571199158,59.319026052786704,50.68093549247594,46.91568566029092,43.8149001208699,49.19773148829917
189473684.21052632,31.99867078670174,0.1767333762467403,40.67618104295387,47.60233529320714,55.792366305216525,49.51787988234755,61.44642992627257,59.45849196204188,65.56626956284542,65.54279105484981,48.73579462743532,58.54962596734805,43.62327897977961,56.37715196477409,47.4302944886057,0.09778306755002517,64.34230051806759,52.26438877391023,64.09345422359054,53.15896337250263,51.936688737525834,53.397176240619864,69.45459241417967,52.13961957894534,46.31354668794246,62.875351150280224,49.85243285593894,63.38545828578875,56.71937128051166,50.516936875446355,46.2262927369728,53.113862914722056
200000000.0,35.77912157460263,0.19589767957988538,44.0443098419591,54.61983675705759,57.44728095907914,52.52605199813843,63.98921911340011,61.216058580498945,67.1724002486781,69.0598918262281,53.56565031252409,61.13422780287893,51.03659190629658,63.258964111930446,50.16908838874415,0.13556480407714844,69.07298070506046,51.32774358046682,73.0192215317174,52.29111724150808,54.54280444195396,53.68163495314749,70.86406047720658,53.29583193126478,50.12250875171862,64.98147881658454,49.4239363921316,66.28706073760986,57.06801630321302,55.12897709796303,48.3109793412058,56.84779302697433
1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20 trial_21 trial_22 trial_23 trial_24 trial_25 trial_26 trial_27 trial_28 trial_29 trial_30 trial_31
2 0.0 0.21337890625 0.21826171875 0.6845703125 0.41455078125 0.439453125 0.23779296875 0.291015625 0.294921875 0.22900390625 0.55078125 0.380859375 0.1962890625 0.44189453125 0.36474609375 0.29833984375 0.119140625 0.32421875 0.54736328125 0.26513671875 0.298828125 0.2861328125 0.3330078125 0.29638671875 0.826171875 0.396484375 0.54052734375 0.3359375 0.578125 0.65966796875 0.2255859375 0.3486328125 0.234375
3 10526315.789473685 0.21357271479767775 0.2228854369588836 0.7019023340494679 0.43993970099578605 0.4457103723964533 0.2440779030818358 0.28445382131433883 0.3020097304579294 0.23659012654481504 0.5688885057401789 0.4093215445732476 0.20769607987760508 0.46548380019592117 0.37152939291872145 0.3158102999763806 0.12055265870450936 0.324938610319946 0.5766560588847237 0.26416767601161123 0.31300383591585873 0.2913102694165343 0.34159076246858633 0.29804793487295217 0.8444452523524741 0.3994468770859314 0.5618462839945532 0.33319649339712887 0.5817519885351123 0.674480479179657 0.22874224813360916 0.34287392994043236 0.24068762126721835
4 21052631.57894737 0.21463729404016216 0.2847429946519001 1.2539801214540436 0.9711697174241338 0.5922764463768111 0.3674045546893598 0.19389858932706458 0.44744268877024135 0.3761380716043826 0.9280382563202665 0.9076199941027527 0.3867184065715758 1.0954640618321638 0.5039219763800709 0.6472004813830938 0.16120886868717269 0.38553232103173424 1.1500712127896888 0.25701744206394184 0.5633914530112143 0.4337566328180794 0.5333808756270898 0.36920745617134754 1.2941815278536726 0.46334917063197933 1.0828470140282798 0.30708925875930576 0.7122485380093477 1.0490335744503794 0.2927677651191352 0.2670602798461914 0.3565010297991893
5 31578947.368421055 0.20323591945574226 0.16300526880491473 4.20973530370443 1.9141308765992564 1.1303072054960723 0.47055323302250485 0.38454054729429976 0.6999750190164244 0.6068042361505146 1.9838808276316475 1.047240732779463 0.32258590766927875 3.300744557314633 0.820451130166939 1.2534598841891729 0.2838647041954822 0.8028362411541292 2.05955018098995 0.3327965723180375 0.7174475239254432 1.0429691172042386 1.0538034188119991 0.7856394154873583 2.6947369245280854 0.8043927195329749 2.747439355401122 0.49086964097379654 1.582021385678955 2.4064476219240656 0.3838922904799189 0.3872914538819373 0.4644241768897736
6 42105263.15789474 0.2500258099669565 0.16924816353499395 10.562775117868863 3.0364261901940006 2.5617434588825936 0.3306845139268363 0.6573641504937592 1.4167928193744863 1.5554985035819693 6.665296026214008 1.5902420847039478 0.5595294867856351 6.122559275323335 2.002881549401957 3.353673818699211 0.22144793671584195 1.312077567187703 3.7189625135088895 0.419380108735568 1.469084890265214 2.406639748993343 2.07946530603636 1.6489465348938497 5.053634876029314 2.681116569075228 5.717011200754267 0.684133651183913 4.126098395054361 4.518586874668618 0.42747887481943064 0.24465010370904391 0.5900655889114845
7 52631578.94736842 0.32888041044536387 0.2715100132527444 17.733460875429277 7.464843899259277 6.074702384399245 0.6656232355704268 1.4731523178290793 4.60719631253187 3.4147048775839344 14.414384933059566 6.434121141143122 1.7846566303284874 11.545327676630416 4.058305542224662 7.028147891617878 0.22477122753280682 3.516465171222211 6.5624148852277 0.9232236724811247 4.439537885776847 5.61043294843214 3.9165439922723744 5.178697201683911 10.395311174630457 6.622331314139749 11.543822865737113 1.2768046070003773 9.706652687527136 6.612446320023893 1.2700750121119277 0.41397620039963656 0.7761202492542214
8 63157894.73684211 0.5350462128911325 0.29962318293605816 19.781360399029595 15.19260876198555 12.498151311583799 0.9643479608762959 4.202989639007486 10.342126384005986 6.6210016662724485 19.07600781395825 12.518384072258863 5.658649148703285 16.467369206394185 7.578091576489058 12.856702910235718 0.22467789953765438 8.977922814704709 12.485103358852571 2.445170590091611 9.169885431960683 10.9500342604196 6.319276756857242 11.627668977774414 16.484819478275377 10.808324359460553 17.468208276003683 3.136212800678455 17.003232776293135 9.315752800812023 3.66637701208902 1.0774520467192852 1.8907644002391373
9 73684210.5263158 0.7852336561250554 0.2384258307248271 22.641011190546518 21.417244698532404 17.225132876155783 2.4014786405906796 8.874928936733767 17.268501571010688 12.455725827045391 20.028633709429375 15.736250269776237 11.799598576289467 20.206166419296057 13.716660425603557 19.380570267706368 0.13551659465166344 16.52533781627539 19.908879957701032 4.471161410418905 15.018252133662683 15.222444074636021 10.52112705753781 17.137029601596403 22.15234950638874 14.156446965447424 22.020987118380223 7.051836641211262 22.444470619560942 12.252371070787849 6.747187160058697 3.2735256950610907 5.643231167357387
10 84210526.31578948 1.0865307858115751 0.1625721897114677 24.922460529612703 26.028391206693783 21.931540470704476 7.427022326355827 15.49045526816244 23.244672812253157 18.479983554322303 23.264797252961475 20.318913594507446 17.263236872707378 24.036384677622788 19.661253857810742 22.65865376649471 0.19408470639891903 21.799998254326905 23.554826160547147 7.174491523045253 19.62782619402349 18.426508631402438 16.64619142527065 20.932012954246964 26.657700557127555 17.2458696021928 26.194125621933026 12.5986764754615 28.700997275989142 17.94214692472421 13.128704757901772 7.179397445636444 12.70919324288408
11 94736842.10526316 2.6582788205873276 0.23384656800457648 27.00726091696615 30.072886935891866 24.903228779578804 16.55449330971842 22.605368816291197 28.305850891525395 21.575907559275958 27.155014569079118 24.751330803636037 21.787139946734147 27.175793199988284 23.45812468383451 25.65341528763071 0.2079372273918004 26.26315112391337 26.554582058227624 15.029219785885799 22.826661364853877 22.64420315829671 22.053757330717474 22.635709687283164 30.819130501258407 19.947592706231198 30.637604253774207 17.19585534542221 33.978571811211076 23.49253982850389 19.76031255589958 13.753053688936948 20.234403689482207
12 105263157.89473684 5.158810243051798 0.2324192992868186 28.257206893033267 33.07061711044523 28.04394555025814 24.2341824185485 27.88982900159841 31.484295480469257 26.272313741435635 32.21083139646747 27.41051373521377 25.068851772107575 30.700618521988886 27.733159168275108 28.51371868165246 0.23559921137844095 29.91249806464874 28.84397799156379 21.897442701450675 25.46100950109001 26.490569035432344 29.707195385010948 25.814450047352967 34.304045774930074 23.846011732423733 35.449990415176856 21.909407502066067 39.53630973625712 26.544865684826288 23.703709055512235 20.16929844673981 25.416740750341866
13 115789473.68421052 8.622501515945899 0.17303033152445532 30.4624208954893 34.4494729240185 32.32523063939694 29.10033617653675 32.68394685518048 35.03421277022428 29.25066611509244 36.44389487765832 31.956153038796295 27.203258828773393 32.48497857677639 31.02924344414159 32.335136919470706 0.2611046814852474 34.55427443617929 29.749940528763958 26.3664939489391 28.684378358465814 32.14956315138333 33.532602390754256 31.03434411178335 35.64516809706543 27.293726334611463 41.36981221909668 25.84496872973244 43.52629251163091 28.518349736020834 27.90022700381081 24.67630119270895 29.86176488274022
14 126315789.47368422 12.953163553803256 0.1676715417581912 33.4014120762368 36.214981232323474 36.62185140593891 33.39649893636519 37.98510644970839 37.83161627222626 32.14927361612505 37.06019579076371 37.07880169136703 28.69297118992687 36.598861699619455 35.13885881101656 37.91701086472277 0.24924954549097286 39.300789333776756 31.456702678817795 32.177538573246586 31.831940267885162 38.08447337480794 36.686553305205884 35.872348959756366 38.176747055265054 31.759865414733046 44.80667683292294 30.703182098938164 46.604350858778176 33.42258303845689 33.616753813302424 27.639321192479862 34.44234290611711
15 136842105.2631579 17.76422202752238 0.2581326228429737 35.67636442316536 38.85061561499937 39.09070651617077 36.82817951662059 43.90963821199793 40.68667470451207 40.04966179221621 41.721462842830334 39.7955187258628 32.505569522730866 40.11072799571664 39.583316231038104 40.304967028282356 0.1549811733066209 45.480007874338256 35.54768012567241 35.17292557660893 31.51637954526991 43.55536895841773 41.5929385367523 39.77065433095367 39.490757211753866 37.01248428762125 49.20768334000395 33.773233650133555 49.02499226784112 37.10005671297745 37.34949378491769 29.527241902338172 39.6905295723363
16 147368421.0526316 20.60570672476391 0.260494538621559 38.31259859301707 42.231486737893235 41.38264921563484 40.73568734832088 50.646387562527224 44.740820213698285 44.63164416706793 48.643137432531645 41.64506741573936 40.34868815466969 43.2403947190895 41.13025597654221 41.12120321913109 0.25687543705229626 50.849281604270196 37.71554495951476 41.43600509833762 33.58173339188595 45.139807246728616 43.83206370398609 42.460580910341896 44.589737517021376 36.15181583182633 47.555083031799654 38.0724171059944 51.82304479805056 41.23192626551578 42.69152521888966 32.82670638964117 40.99125826457861
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7 52631578.94736842 32.37576011805653 0.1493764636919439 6.265924547517729 19.996075070135483 24.29708250473741 26.6585715655805 6.10779984704015 0.2001621544856444 11.340636197880034 3.9239011035401403 6.068390164679108 29.12424737396663 28.99433048544168 12.393097345188384 6.198827989213685 6.135541967407818 0.2632083734316839 18.486392133453876 18.32487551591403 22.473236131536 5.31832713499624 18.098600483997377 17.17883172920206 6.341349301906174 0.16022922721926194 20.96771786946009 0.2881647173387522 6.350126699727658 7.671597331514649 23.07540059684056 16.858973849182973 0.2855512151427546
8 63157894.73684211 35.80207819687693 0.15696968860573385 9.528466628859249 25.93645130168038 29.322925760475226 35.98826725925435 7.909809506170638 0.18297011304099808 19.6207221868626 11.841488027176371 7.1471137498554445 39.51367347590482 35.41464697555162 19.702830066311066 8.714586651556381 12.551106637864896 0.21265340313686887 27.894111997863266 22.868072269365733 32.63707952948489 8.056146447348135 22.01666963793895 28.06944986063358 11.067505207748626 0.17562572711722674 30.657168763496216 0.16387672635656977 10.259124906439531 9.602591168517222 27.649575761810897 27.45019500605618 0.26402906962048645
9 73684210.5263158 42.097688450377404 0.17120624447133076 15.057362825916748 30.882598448988475 35.760426465824374 42.40087026374162 9.17602476056593 0.19896648861364644 27.669871694823712 19.465457654725814 9.453078845861548 49.16960808312794 39.52166929139325 26.007552211634675 11.258532858291161 19.211206028005755 0.20455053968772996 32.89088746385231 29.191360765546975 41.76788461769717 14.800956604553395 29.16591713633234 38.925531135041304 15.4980167378349 0.1867820166484801 40.24636071408555 0.18143638943701237 15.044918992842996 13.2366541283943 33.978920569380236 34.34210071008952 0.23402207445900194
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11 94736842.10526316 50.64325562210294 0.2145757622335756 32.08468913899895 48.85426952171854 50.23131015492278 56.09562193587877 14.05611093816995 0.2411446214712888 42.76877510250441 35.598343096281354 20.581640330708257 62.13237791114236 51.9025301352102 42.574058651593916 16.533297886148382 33.64211386656827 0.3660697672836008 43.986269673482205 51.553368676732454 51.51794774380417 32.328315868272014 43.17469909250571 50.10774188688917 23.728150213194027 0.22334465755980432 49.67813453515811 0.24267287399630136 30.732595606193648 29.080394035561262 48.49142870546378 45.09694130995267 0.22637654275445065
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13 115789473.68421052 57.84781972060904 0.20530491984782126 45.051278077334246 71.35784784116242 62.39978758978381 65.62058491587969 19.464806851257578 0.2115729258001016 49.98107045641236 47.75888700168218 38.56563757397131 75.38356621179554 71.22856314492688 55.8925410954906 20.78477737315804 44.015384160250505 0.35737809448030855 52.25931945996271 59.534807744118645 61.15149383465669 37.80827363376142 53.19825499738022 62.83921505671789 34.050563824143765 0.19229207210593605 55.12566884534841 0.24111181877326435 43.069155896469496 44.387714350322604 52.746815015734725 54.64979370545152 0.22365110270534524
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15 136842105.2631579 64.805707676589 0.178621890472243 49.96782849700167 80.56781150495577 78.12921948181956 85.5370428304593 27.81163813598929 0.1914368441890812 59.664371242153344 57.8341243260455 54.869540851202046 92.0400896930959 74.93563837357836 64.55782760477463 27.63025651017715 58.11468744674218 0.2078662869672695 56.362652410100374 65.16038157074736 66.9500071784466 52.422797210989245 56.566700552308994 72.18032006741892 41.70922832673937 0.18247515871254028 71.61550764099715 0.30871339121683816 48.557396640407745 48.194826695397296 61.731607083138336 64.70955352175599 0.19316112565862176
16 147368421.0526316 67.4204287145937 0.13463367979942592 57.43094876994718 83.65467017641359 86.24994984095778 93.20914219885321 34.10741448864713 0.25084240879048275 63.46955779648884 58.9085684615159 60.04024309861033 99.38487338491424 76.63446779594527 69.46521978827396 30.494680172188463 60.46085262826936 0.24427377220005878 64.16851718141763 68.4582290966425 66.04493196915391 55.48238676340626 62.94392488801909 72.47080420919403 49.12282633583302 0.21459850512052842 77.12562282593957 0.291945866930848 56.65066451445181 56.30040905548265 62.69338523251859 70.59848607345963 0.19311754062895628
17 157894736.84210527 75.11101093714917 0.1446652438832122 57.72943945934898 92.0367622269818 93.08306409513521 98.0535777744494 38.80749326135313 0.3016834734549483 69.24901885140966 64.78287652192684 61.80310367283068 100.59991703403293 83.68771514601985 72.4255261711797 32.22426858833292 64.52351888725302 0.29508902689756783 64.9916165304316 70.51700372246825 66.72272138252153 58.48017675394497 65.68075569184533 78.80507130768162 51.575137197806235 0.16543983026224485 86.74412872916774 0.2097672887786273 66.2101844327932 61.90613622876746 68.62450473526509 72.37640202144506 0.10793013982165217
18 168421052.63157895 68.86239824796978 0.18781840570085268 65.21267645246765 102.54309010175457 96.48281004422259 103.50117281335213 44.30333961212074 0.24209981479803278 69.11582266260713 69.78110601367052 63.69698371781537 99.09766764125665 93.42920648886557 75.96690554632045 35.926341154568746 67.52480664874048 0.2804036655584531 70.10055818848333 74.4431859489293 72.2640332885066 64.72849307496132 62.235762725576464 81.15476841807696 53.232106258994655 0.1822505961494763 90.6124653274663 0.20475118114017055 65.16558201755512 71.49719470755876 75.32608146350469 74.67137184037396 0.3231740301665838
19 178947368.42105263 70.68408412880514 0.18012758371242196 65.07637613962231 105.87991427846893 95.10705247017816 102.94097472161798 46.1325226701858 0.18922512815269404 76.6458372713126 72.20303079097886 65.94735959362126 97.87624455554993 100.94739993061056 78.89789389375174 38.8776149247822 67.36650774287385 0.23784201297073151 71.51746272380332 73.53825630969948 73.58519468413165 61.01770497557199 73.00694562589693 86.19878709481364 62.40378995351184 0.18552927165150312 96.37348061453272 0.21309725267404994 64.1080729083011 68.78358301891845 80.49347682804942 79.12744323830856 0.14146412244463885
20 189473684.21052632 74.7780111793666 0.29193595505817443 69.56358931797693 111.95183009255956 101.04187843608064 109.19837586040973 47.49925733339093 0.3356706904572463 70.09297890280092 71.74511948318693 69.71643940563678 103.18923526457472 92.56247736806685 81.79213520958814 38.75901080894999 67.30001951782988 0.35302543111785295 71.10964035657635 75.65704755175477 79.51700720166235 67.64783785547907 75.54478327521326 87.4395329060647 62.86759142466199 0.26673964186058147 102.41595607186949 0.16846711483688565 68.2066048624773 77.31482650830804 87.25618293741073 80.94310684151266 0.18061518999348058
21 200000000.0 74.8451529553062 0.25142054808767217 70.38147190997475 114.76372851823506 107.85900936628643 107.15486784985191 50.362035149022155 0.18676373833104185 76.77851872695119 69.44340331930863 65.98918714021382 102.84718960209896 100.46886825561523 79.57574284704108 42.47697817651849 70.82723800759567 0.15393611004478053 67.85379028320312 77.56115122845299 77.00273456071552 68.15039315976594 76.66461758864553 88.43965093713058 64.11918256157323 0.18549868935032895 104.17709260237844 0.16769888526514956 69.53055404361926 78.6344186130323 86.94301341709338 81.56379895461232 0.22411835821051346

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13 289473684.2105263 16.5390625 0.5625 42.0390625 0.546875 0.578125
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View File

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1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19
2 0.0 0.2802734375 0.091796875 0.05859375 0.2421875 0.1259765625 0.2880859375 0.263671875 0.2119140625 0.22265625 0.421875 0.2109375 0.2177734375 0.341796875 0.0908203125 0.123046875 0.4404296875 0.1298828125 0.1025390625 0.1328125 0.1591796875
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1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11
2 0.0 0.248046875 0.0625 0.125 0.2177734375 0.1640625 0.263671875 0.142578125 0.1875 0.478515625 0.2314453125 0.40234375 0.2861328125
3 10526315.789473685 0.25125855950437426 0.07003084642404996 0.14266426477405836 0.21860404556147608 0.17630012543908116 0.264447109190711 0.15265616947924332 0.1891612161229522 0.47076328309288973 0.23604134377350108 0.4022883761292349 0.2895106186166695
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147368421.0526316,0.7728475480858971,0.5616922827638747,0.48851265735573385,1.4488068683655968,0.8492135393982778,0.4528009515059621,0.2296100996868101,0.4609651750474755,0.8119353191344031,0.3581742421411744,0.7743791754556163,0.48035765883004566,2.212994504173046,2.012104578625792,5.265597715932577,1.467720100423966,0.3576416533409393,1.092768629502061,1.7314870205612394,0.3049582114180039,0.8650442847254531,0.6616164812420874,0.41461795584977174,0.5268163601777562,1.5701039596938027,1.5939124152270714,0.4863445620127334,0.6644559316027527,0.25882836656227004,0.404190200847932,0.9695368632055056,0.2234106301600913,0.46242540628956286,1.4524841150088323,9.68162809778779,0.275538616233255,0.49670254292580573,0.9451460587350947,0.423587492628441,1.3606475449665099
157894736.84210527,0.7192808241064859,0.6800190801435562,0.5728573178320381,1.2741515220367345,0.8556359018975678,0.4740467547049483,0.36303961111898253,0.2809529396965892,1.1061982263158234,0.48192557073365955,0.39411760367184767,0.4335168352417668,2.4064089809428295,2.379179093315991,4.795482363397064,1.7448701013158234,0.5381122863854069,1.12182079854104,1.77721899302052,0.25270681830324293,1.0745448828403972,0.6176944029958624,0.5059574872172771,0.3636821657006428,1.6147141496230362,2.2455226628734137,0.43924357818434434,0.4325139238563599,0.5666076258609172,0.48670482371322343,1.0987070036066537,0.45532734308216394,0.5657506689140341,1.7637060989633493,8.537530539768884,0.21775224004095609,0.5235277371393346,0.7250793303809335,0.3510716430368185,1.8314840839840372
168421052.63157895,0.5446248146965893,0.6323370259884652,0.34956148522712505,1.4158399587192694,1.0243488005323753,0.44768741850707666,0.4242923134251645,0.3743092122170404,0.9926150842386599,0.36292471846054786,0.9373380708562373,0.4372990151191352,2.4998103007055055,2.07439745958492,4.894567854186505,1.4142213858395731,0.3392523768205721,0.988488025612448,2.074691180707345,0.35675091096238754,0.978722400612448,0.5606459937267356,0.46017046053984156,0.5432374483990868,1.3767637215823016,2.1346582639910836,0.3882076865748355,0.3480978672524238,0.5813151436169062,0.5434329384251645,0.8143628403090373,0.29506643194901305,0.5372990742944944,2.3193722458097086,8.333616261997381,0.34481135233617566,0.7004527253127165,0.6991791025093057,0.29527291168466496,1.8121038209698537
178947368.42105263,0.6591687691178679,0.4084881653085639,0.4136827579825869,1.317806986230232,0.7200132961748709,0.3972681473496878,0.4004350567128189,0.4140180682871811,1.0433635553164495,0.26677006433545053,1.1722329052531488,0.3622267424564942,2.2064730229470206,2.3212932074169044,4.882091609394782,1.0492908921598396,0.3220191781210437,0.8889107902294381,1.5547403985443538,0.18930645992881368,1.2453325725988669,0.7985338596756109,0.23758972780856394,0.4891798674564942,1.7873750300948972,1.7150877453283588,0.5259689954509366,0.2044293411550759,0.33710270773340784,0.5139275468947815,0.7210736420015879,0.36572557539160566,0.3731374317919448,1.6895521486234795,8.086900692567271,0.09764288006727045,0.4156334314319895,0.45265394300635164,0.3729135798615432,1.0947643977453172
189473684.21052632,0.6422042212657981,0.5305526870769807,0.5760128940571708,1.1364200676577243,0.9701035570900196,0.38320730531644953,0.30219295216399217,0.4370074496705116,1.0593717316181046,0.3910546923608331,0.9566542554099804,0.45032176284578695,2.449823030804663,2.4222031220835003,4.834490910791624,1.6343475616539613,0.2616466194638915,1.306795780678535,1.667646075219659,0.1756230034656472,1.191112280552407,0.6465099894769304,0.29377072405617,0.5455416100837518,1.876787227937059,2.7795739213515516,0.4502092979621359,0.36123891814593795,0.3971498917344535,0.4487176615115348,0.8336244567279341,0.2872303780426279,0.4650105346933296,1.638438407073721,6.3392494761712666,0.23643205172467432,0.5543819015376125,0.8812192932720659,0.2366795051130892,1.4850172587048645
200000000.0,0.8797569776836195,0.45245607275711863,0.34197531248393814,1.5450302425183748,0.8130079570569491,0.44204782184801605,0.36642114739668996,0.4647955643503289,1.1184805317928916,0.5815714785927221,1.2139172804983038,0.3197245848806281,2.1900277890657125,2.3103103637695312,4.651352882385254,1.4646324860422235,0.2180328871074476,1.1175750933195416,1.630814552307129,0.2488067024632504,1.108574766861765,0.5167208721763209,0.7578312221326327,0.6886364786248458,1.155426627711246,1.8101054241782741,0.2778626492148952,0.38942076030530426,0.42765336287649053,0.514480942174008,0.9143920195730109,0.3007494775872481,0.34607094212582235,1.5790150792975175,7.278399015727796,0.3382902145385742,0.45935219212582235,0.7952393983539782,0.21919335817035876,1.434862588581286
1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20 trial_21 trial_22 trial_23 trial_24 trial_25 trial_26 trial_27 trial_28 trial_29 trial_30 trial_31 trial_32 trial_33 trial_34 trial_35 trial_36 trial_37 trial_38 trial_39
2 0.0 0.2060546875 0.310546875 0.162109375 0.7412109375 0.216796875 0.2841796875 0.09375 0.2978515625 0.2666015625 0.1640625 0.3251953125 0.2177734375 0.3271484375 0.220703125 0.3154296875 0.7177734375 0.17578125 0.3427734375 0.060546875 0.3466796875 0.078125 0.1884765625 0.1708984375 0.228515625 0.0732421875 0.361328125 0.44921875 0.23828125 0.255859375 0.2412109375 0.1298828125 0.2978515625 0.3076171875 0.83203125 0.423828125 0.1923828125 0.138671875 0.240234375 0.4736328125 0.4345703125
3 10526315.789473685 0.2118135700595676 0.309827014680054 0.1672591449811518 0.7317973794699375 0.22122678466120585 0.27808856171584195 0.10172383739017053 0.2989036660445364 0.2818293769603951 0.17425129222077346 0.3266350331398919 0.2282944729453639 0.33362718037951355 0.2271264940087485 0.3453315777131395 0.6961776279016214 0.19366701025711863 0.33806665848496875 0.0710679104453639 0.40028159440059086 0.08726168867623707 0.20962938113225796 0.19659191353499395 0.23444062917186284 0.0897436009879918 0.3609405079046445 0.4458963177540956 0.25589014090329326 0.2610091449811518 0.24641608135191687 0.13519870409344703 0.29463987799562574 0.3138744348964533 0.8152529671581829 0.4520134252194222 0.23042466171560527 0.15279221204509366 0.2468792394918088 0.4610629438363284 0.4318569928325114
4 21052631.57894737 0.2927769901349604 0.32288055208581307 0.26201100230547203 0.5259125675190849 0.3001270188519169 0.20776718012844098 0.23404275677540956 0.31363755646174635 0.5216450255333221 0.3244798929737545 0.364983143898919 0.36455860296444875 0.43343241260982945 0.35569093233990867 0.8980365605235431 0.32783274769452797 0.4986310361825198 0.28147218233990867 0.26337039767870285 1.1860065988556499 0.2600783879076675 0.5349439795327648 0.5920173401977877 0.3222652815715758 0.3668050105551934 0.3563748991060125 0.3617198394606318 0.5455056927540957 0.36019091196667785 0.30620685904970457 0.2128902815715758 0.2638034767721499 0.39736967007539276 0.5721258284972975 0.8771530795955922 0.8021484966753593 0.37728502479616627 0.3725943155896301 0.2530606024153015 0.37586547133004566
5 31578947.368421055 0.2332391606803747 0.48416751375488953 0.4107527270541628 0.16305141765985465 0.4571054411066538 0.4224530032466983 0.25619743273198775 0.2826893772114677 0.42216212465492314 0.19176925912788373 0.4893336969729606 0.23811071136981854 0.44335665134842056 0.5305403949811518 1.3076517073401452 0.26181958586885656 0.5064718980868437 0.6136388118247249 0.3721902852573553 0.333998727666374 0.39477701002210785 0.3102040330458876 0.3756856839082248 0.25921257314919766 0.43090709887052847 0.3905299786385407 0.15384944324017896 0.4942807649311266 0.44405838128932623 0.11810937548608334 0.19219858428447872 0.4058763921425943 0.2501162188205032 0.8388969231180207 0.6187154209844955 0.31458369648687723 0.31998607128280687 0.6352383753599555 0.25224981809917246 0.44733606216980176
6 42105263.15789474 0.43082265246277696 0.37244460721425404 0.724254904031093 0.38941055255583457 0.8952821958758493 0.31834023811150125 0.34572226188849875 0.23198879590655297 0.41272224151526793 0.2885996852885323 0.45229642873325504 1.306264660695253 0.8862685945885994 0.7317529715329327 1.2945927226312273 0.30961133370439103 0.2506439758469854 1.3530910840655297 0.32188553955416277 0.3413275827001007 0.30875646110386734 0.24614468307706458 0.47301651170049014 0.4842581180984624 0.6128170615748355 0.4231113317600578 0.2669949941027528 0.3591329939147442 0.3290308056775883 0.3311890366995434 0.5226831198399087 0.2995449182399422 0.3530435852727071 0.6904976968950182 1.4620488026795957 0.2972585197300792 0.4525616928480999 1.1407596450763395 0.1912144901349604 1.0498197032474084
7 52631578.94736842 0.19438721400548875 0.5479718786857796 0.5071986031994595 0.6670940298783152 0.46532229109153855 0.544412248352558 0.22292252062430343 0.365314724042475 0.32787992683474043 0.4293990254071941 0.5465711900071755 1.7668202867798528 1.3394154789044916 1.08229509284952 1.8495260064291492 0.4306251018661541 0.19212542346309758 1.1372663307718294 0.6112785656366322 0.6913488155586898 0.4276017429425776 0.3104009205614761 0.27554273737434537 0.8042010838305191 0.7090213226149287 0.24748425470494828 0.2884362873278166 0.3571210845355512 0.28083161700135123 0.6189416769138664 0.5435207715655298 0.4377946325286274 0.4328021025723698 0.4033698718633678 2.9511417959535553 0.3701968259098127 0.509997375784158 0.5432278561790234 0.1688656740901873 0.7397989394592116
8 63157894.73684211 0.40211646378535665 0.45695911946389145 0.48651816772291856 0.35069634181310594 0.7141461412001848 0.7260753969736705 0.22915140611643284 0.5460429944490128 0.4650857560852558 0.5572298900572544 1.2152039641488617 1.1181630322147273 1.709709362970495 0.47841581941641603 3.0052941023808115 0.5139128507999832 0.31972426522801817 1.491355932980694 0.8555853360247416 0.5113759080458876 0.297368580614761 0.32412851286066535 0.4390528723803915 0.5042066970360245 1.3392025215804084 0.28469137471798706 0.216618461291876 0.3985967768196253 0.34366285371648325 0.4300706763016551 0.417485768114761 0.2037980246081576 0.8567441374971604 0.31820760605407883 4.014480765176284 0.2865351256901537 0.4968177076852222 1.0241515933641772 0.25751102267870285 1.4193305493722004
9 73684210.5263158 0.6832269869352642 0.3502434389743118 0.42469941083744295 0.330853359190711 1.0170202651512588 0.5658347481175474 0.28252735296444875 0.2504259146481671 0.4948707406210437 0.2926019869352642 0.6511313631263798 1.0467488693068232 2.124570059313999 0.9452250578396872 4.0766381002198955 0.5680250949806784 0.6984042117470189 1.908098463866849 1.0677054635045269 0.48898128657459883 0.5072851101777562 0.3462920704046445 0.47044264510727973 0.35083579488738414 1.5618416714866405 0.21649608453555125 0.4809097041713895 0.2367341921270058 0.5707660896956426 0.6125409028536727 0.43746992095355514 0.11579324135819961 1.339187043525505 0.503868343427241 6.064206678121043 0.3072712784658839 0.4929593236822831 1.168906623967136 0.31078409686313113 1.7903679189919768
10 84210526.31578948 0.6135799798939036 0.5060559428629784 0.46436111154318516 0.5034687538886665 0.9443499705137639 0.47750245831349536 0.3175468973175641 0.33357965781087684 0.7759932837657982 0.25440733848846514 0.7407016067293541 0.7270963674106754 2.426959093257661 1.6659178799869612 4.122235771031261 0.8202656880640258 0.4769264918615282 0.9828566236839399 0.913581235256882 0.4038808722245065 0.8500438278071438 0.41037980605360547 0.2831323681775883 0.29202329683171746 1.3165678832669665 0.6550338829653417 0.6089617446519001 0.18336302950111455 0.495234756258386 0.6062870184140191 0.6077090234307372 0.27082469654875785 0.49931500294862363 0.7141546318075332 6.310332934942272 0.29747658092889756 0.5628722341437089 0.6313560464705787 0.33018852931310594 1.6888859925838056
11 94736842.10526316 0.4518804497335756 0.6751762347868605 0.39460882783926754 0.6890296143508023 0.9811195468638412 0.30161391863202125 0.37235537658437795 0.2548223109786861 0.9490426927392173 0.21032976113528096 0.46526998430077715 0.24377452501629857 2.310550333060056 2.155622828369986 5.291314521324602 1.2526422669682806 0.24994258933450378 0.9459554931133408 1.1397841604132402 0.2403639162016047 0.8175007246868101 0.5286488017877383 0.26299200559917246 0.41787100498696117 1.189747461651831 1.154665698635281 0.5933121366844283 0.26866715238365113 0.4059389542344535 0.3046211839712888 0.5315634022128879 0.30814116681381604 0.4888602835319709 0.48115134305240703 7.620361396810685 0.2364952768975678 0.5756591574967402 0.754822310978686 0.45194131845912777 1.2548599216746492
12 105263157.89473684 0.41989179595355514 0.6957671199809151 0.4225029298143043 1.0848030819456993 0.8830141717377131 0.35927416413114344 0.3296959789836176 0.348857398838878 0.8554704671421209 0.22495084324041562 0.5843521921258223 0.17642694298910633 2.2409388048166714 2.4818770178797505 6.150779935461663 1.410464204909729 0.9096408801726026 0.8624748589259436 1.279065124215842 0.2494780574809151 0.79857861104104 0.5009341675819122 0.27660953701367996 0.45934532355733854 1.4530860393661542 1.0253147167512255 0.43124272882773274 0.448226141467319 0.4496822515683161 0.4034652604290653 0.5288118800958437 0.1902792922677756 0.3730027629397913 0.8583520165440779 8.402377559207483 0.27477672819945953 0.4730650407785854 0.7624741604453639 0.41050316554357474 1.331548268114761
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115789473.68421052,1.1999215577778062,0.35740205125465285,0.31415576881979307,0.1841297017570348,0.7656547356180207,0.4759899678322747,0.31301612801168766,1.1280127601940546,0.42551362943781373,1.0100018641294863,0.46344404405504047,0.6437597697461411,0.4433463960473227,0.9053329087360414,0.37020026019405455,0.5204719427219718,0.13159427484316838,0.5809357450279172,0.39714918110179115,0.6872217569324779,1.6812205486350442,0.40358793306218627,1.1986103480542465,0.30020494011960863,0.5049918430994093,0.4205149415457347,0.24509736375465288,0.6549487021491138,0.5059851622647525,0.9695901527299116,0.36040796665603764,0.45746737239763685,0.24247872202019943,0.24264108969564252,0.45196624607920977,0.2475635496863368,1.6110133015217873,1.1109668092384233,2.216639930851902,0.5585869052073302
126315789.47368422,1.4080035138328322,0.45896729868204655,0.3545007256589767,0.19093489712955558,0.8013565295951188,0.4192447292507519,0.2692191739491809,1.082088660665496,0.47498092228686045,0.9461704159047131,0.5686820497803411,0.6231275436950853,0.5511760553164496,0.8584579087360413,0.4771080439770982,0.43805849915396117,0.24780899005583468,0.6089015865590104,0.5185714679411577,0.5760785470048475,1.6961871963458708,0.3501337215180543,1.0807152322785012,0.47783818337395617,0.4474057649311266,0.6096805984623876,0.14864564932614466,0.6615976877820129,0.40255189932614466,0.8845044820262455,0.29682200635239014,0.3852708346295556,0.34347178070829204,0.27685119967051164,0.49738444912136437,0.20290213080324287,1.6539273882836847,1.0005626202950517,2.0815301615115347,0.46660374142126354
136842105.2631579,1.685544861981083,0.4700728149625403,0.3125950213614593,0.16522363414394553,0.8884927744350276,0.42189141323691925,0.4494963299864879,1.1374266616525412,0.4926113540776219,0.8855073696358383,0.6481579069945952,0.8028054990266501,0.6110823649778921,0.815212289382216,0.43217692018545883,0.4928058613700551,0.30057479404016213,0.4730144511299449,0.3645165276989709,0.8226372198384888,1.5476963592698367,0.41557435117600044,1.2330392298605968,0.36129083395664685,0.2951741126105394,0.6426731463614593,0.2899092016457854,0.6068756441660534,0.34729358430054047,0.7682989918294044,0.31180202399594636,0.5258473055514604,0.33267350870486434,0.1815466101479991,0.5071876610415134,0.2517237782148114,1.651451266703513,0.789756011434539,1.7992156945437272,0.43369424244043236
147368421.0526316,1.6932158007846314,0.47971436983990867,0.2692280555365818,0.5914688004681282,0.8043518224911675,0.39853696215515977,0.7656229869810831,1.3139441852094065,0.4294837676917416,0.750226599357795,0.766856227885323,0.863885234927867,0.46217074090423993,0.8744585771639922,0.4837734190711025,0.5152315683972473,0.19127190080045653,0.42965742095355514,0.32945569004048275,0.6457203788440311,1.5226831198399087,0.24773887253864302,1.0275053832669665,0.3256396771798174,0.37768223411158525,0.5706225154802739,0.2287329993419699,0.6734788054574561,0.4284518550967907,0.9492259619969082,0.3992752962825702,0.502061812170985,0.35453389556123943,0.17146311836559688,0.38371487139334626,0.30582608674701894,1.3928925574981603,1.1509581008446188,1.6121009551917416,0.3820256367944944
157894736.84210527,1.2549097531389988,0.5027943317909981,0.27886961041395025,0.664670238864719,0.6509453702171092,0.43518592644266146,0.8185955665778585,1.2093825670490634,0.42178476286066535,0.9018313997009786,0.7295506284507688,0.608284575126838,0.4582758002664244,0.9714858908402293,0.359380447303159,0.37672238072530045,0.24863856783203808,0.5427961507992732,0.4268108061476098,0.7069700853976517,1.7525844890985465,0.3420833365738888,1.0291030783402293,0.36598534465166344,0.19615127901621457,0.6143453259877552,0.1521208808032429,0.5312899671433043,0.3372326161392507,1.0011676355081913,0.23841145428263896,0.49033521086885656,0.26487675399991606,0.1753885052540956,0.4606640649304166,0.25533399819667313,1.3010068428483366,1.2435913270860497,1.7181952547828907,0.4073485958279005
168421052.63157895,1.0124180759419363,0.45978831452345914,0.2999462011448234,0.7901238523361757,0.8078746003127165,0.4522191943224117,1.013980220889781,1.2829143069787698,0.2519476301452128,0.9913637367311937,0.469789077040231,0.8026916842051162,0.26904174297470124,1.0704058279951525,0.36056383296723515,0.5218521921258225,0.30974293547654086,0.697169253700658,0.44317821386448236,0.6082032433507184,1.4083620108395731,0.2360621740283067,0.8826060202643481,0.2195908395867598,0.34425933077064585,0.6453775844415469,0.13832937647431182,0.6383943425651403,0.4458501926749698,0.7669867518205721,0.39574540156736937,0.5160184316027527,0.18859550497208272,0.4025020440859809,0.36608650017313016,0.2628368261448234,1.4146200164203169,0.8654640176619848,1.8252886404951525,0.43709803023827043
178947368.42105263,1.540162197440615,0.6781794503124798,0.3318811981961998,0.8592509298773684,0.6906166393671009,0.33169010141219457,0.8082542947785014,0.9945589604470206,0.49701326903874204,0.726901197037208,0.49893457407436215,0.81961759107595,0.4947173020846296,1.0621571580458875,0.5449629199802051,0.5494174138330686,0.18831144739716332,0.784363252634487,0.6636366329034611,0.3829567135205889,1.4962236584058428,0.18594337368275649,1.0215346449960303,0.4902737266138981,0.2427877072152008,0.8300839632832113,0.19700072808939337,0.5525600348813382,0.5907741874208741,1.186542645715941,0.4018600812579126,0.41406419336630695,0.29463852805774304,0.23845144520175748,0.4947542021479303,0.2025189545015879,1.438054082136075,0.9608209615268866,2.1982890707634164,0.3453175446993756
189473684.21052632,1.2474309651805424,0.22603579703460444,0.38242623284252725,0.7634182398999497,0.7871124658558177,0.610305046440822,1.0380975665147945,1.1121658737309421,0.4745372444638915,1.0006996693703607,0.4901133719573721,0.6686776919378138,0.2518988051903215,0.7926987729904725,0.47779505404739164,0.217048153652709,0.1977209318377635,0.5529709337820967,0.5048571980230696,0.7586704159047134,1.9725345125488958,0.2896589770541627,0.9778788135982946,0.5875942991050657,0.30496439312963936,0.6392621703425273,0.09999873301329049,0.8237719813212133,0.47105995241624826,0.9593535658395191,0.44698873187036064,0.5362910590343528,0.22654233282622868,0.2911622425195583,0.40635083586885656,0.3520519594736707,1.4246286302392173,0.6529200598803914,1.7648292076554655,0.37195549116900756
200000000.0,1.4503914180554842,0.42453429573460627,0.27918956154271174,0.6980528078581157,0.8648501446372584,0.4159773274471885,1.0562553405761719,0.8974411613062808,0.43092351210744756,0.8383592304430509,0.4834685074655633,0.7888030503925524,0.4189333162809673,1.1257642444811369,0.31813380592747736,0.5106129897268195,0.24825055975663035,0.6962507649471885,0.6283008675826224,0.5188404384412264,1.6482437033402293,0.3647110587672183,0.9155689038728413,0.7550875513177169,0.4355020523071289,0.5397270102249948,0.2954014226009971,0.7015758815564608,0.33128888983475535,1.1314397109182257,0.2894829197933799,0.4487545615748355,0.2337443703099301,0.16643162777549342,0.4068269729614258,0.25219174435264186,1.3003082275390625,0.7267135820890728,1.4779998879683645,0.5472253498278166
1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20 trial_21 trial_22 trial_23 trial_24 trial_25 trial_26 trial_27 trial_28 trial_29 trial_30 trial_31 trial_32 trial_33 trial_34 trial_35 trial_36 trial_37 trial_38 trial_39
2 0.0 0.4970703125 0.2109375 0.29296875 0.15234375 0.3076171875 0.3876953125 0.1015625 0.1220703125 0.669921875 0.2431640625 0.2548828125 0.126953125 0.2109375 0.25 0.3779296875 0.431640625 0.2421875 0.423828125 0.51171875 0.2763671875 0.7109375 0.2705078125 0.1689453125 0.31640625 0.2216796875 0.6982421875 0.30859375 1.2939453125 0.181640625 0.6875 0.16015625 0.2568359375 0.375 0.458984375 0.3271484375 0.3935546875 0.078125 0.2783203125 0.390625 0.5048828125
3 10526315.789473685 0.4929172721926195 0.2264421838142205 0.3127925957338962 0.15765964159344703 0.3105520026505489 0.3796107273682993 0.10372208095983786 0.1406205592062995 0.6496550382999832 0.2448252786229522 0.25322159637704783 0.12866971499371727 0.20711670291720996 0.2533778061166695 0.3785941739491809 0.4132564999059957 0.2630080754076675 0.4130855940715758 0.4925593907152847 0.27110666977731807 0.6936608523212971 0.27000944766311435 0.20754090042325601 0.3134160609786861 0.2247806242628441 0.6750405356494343 0.31280216417814555 1.236411860775089 0.18380020595983784 0.6765359735885155 0.15594783582185445 0.2676338422991893 0.3978694086259752 0.45289324921584195 0.32371525751256547 0.41077596130793775 0.11212455664975493 0.2816427447459044 0.39051425225846986 0.48810452965818285
4 21052631.57894737 0.43612112430984623 0.46610162264752586 0.6272949366688398 0.28729190984921443 0.3353427400879582 0.31898593110060763 0.16512041805193367 0.43448930037649053 0.3180373870765073 0.2894053419541124 0.261911196721888 0.16420367021639923 0.2680351489798845 0.3254072395388109 0.3856615188049147 0.12403403622952196 0.6241044496235094 0.23703294579672352 0.2352931215492312 0.2542508090962334 0.39196354134261113 0.28663699184428293 0.7726396946365482 0.2622321543601081 0.33761068856617094 0.29681484190711027 0.3706302484316839 0.2822870640213139 0.22980460697924332 0.46612144639287295 0.09712302189454478 0.43087495925353836 0.7051160553485732 0.3513410045169397 0.280223534708208 0.6536310148371224 0.6220282610103364 0.314986009677031 0.3989714149623036 0.20809839306775882
5 31578947.368421055 0.4798982546270058 0.30513493175982104 0.43554959865157944 0.5545548679425775 0.14364014041720996 0.7742188683507183 0.32588372005980426 0.4281455935533689 0.3309278699499748 0.40875139262867766 0.5120096285917752 0.3254000750935311 1.2878911105549566 0.4734725053951021 0.31030383862947153 0.30424109852545156 0.6860988965655297 0.27591975574017896 0.6359158169859993 0.7300585617319038 0.32844870506561374 0.45652707065571707 0.21276108379839537 0.23270318514752583 0.7795272520704613 0.33682279507539276 0.2675829092221247 0.3074914002352474 0.2908187374844115 0.30753857937546 0.1717789483532681 0.28977688924097283 0.1361349322459044 0.3437951185696673 0.40997577572133076 0.2909041904016214 0.2378550156992229 0.1789385909188818 0.477997092989343 0.27243804667464927
6 42105263.15789474 0.3247253333432523 0.22632118077159258 0.16629011413067007 0.252334584159534 0.23862718280993017 0.1927960678480999 0.15772048654318516 0.8096964194173627 0.18416765588142206 0.30685083489668996 0.4211021698082584 0.7878928039212636 1.2606836989976031 0.5113940146491137 0.10735180503443668 0.6468197090804082 0.5186784379700214 0.3704596860256882 0.37212467986130654 0.4138126426126158 0.6877355284968242 0.2984141827950517 0.3658267309130724 0.2968295617777226 0.5588542061169062 0.23787859338142206 0.2950548504858467 0.39437266003722304 0.2289090566027528 0.5544745426759164 0.16740681656179668 0.23453633739017055 0.37760465627231765 0.3331493261448234 0.550681444416416 0.2163347471453807 0.5305868872645159 0.37703448055193367 0.538037751850329 0.5237666523687726
7 52631578.94736842 0.5788017785450098 0.2895215607746156 0.42749202548632004 0.26031835719819213 0.5171669064466313 0.28096424905877365 0.3259285189768614 0.25731276144941756 0.22599987970494828 0.22978581351916877 0.605864218397484 0.4936391693072967 0.5059486056298761 0.46710625117505356 0.15675862013798342 0.922995799796403 0.6684014618892089 0.37360505450135123 0.7283874337362781 0.5947009242472556 1.0952697024781288 0.22920199576507314 0.31046007214490723 0.6634584912963191 0.6646743837816232 0.36803214107523996 0.42608032332232787 0.5906620421898332 0.7708647350195041 0.42080375956696486 0.3572051637390644 0.2810996047677756 0.891895484395965 0.49793443389216285 0.672349100297838 0.33734748502187123 0.6864332003606654 0.47328074553006244 1.0516460820248252 0.2050029273838878
8 63157894.73684211 0.7102440123412753 0.41137584887052847 0.3511793236983449 0.5651271798934302 0.27707303858199617 0.3617304381901537 0.5540219832655465 0.32454657620670424 0.3615509941967571 0.49057073936568096 0.48048037901479457 0.2420664969573721 0.5663385364817777 1.3289293305035117 0.28780771820829204 0.6771772020081072 0.3130253768033269 0.3962348610410401 1.0994761511889861 0.4257166273375955 1.249049786385407 0.4139934603197093 0.5435505071835504 0.3579079477410569 0.9808617906227002 0.5327553260359406 0.1721159757999832 0.4555727359000336 1.418757922101218 0.4455726126884819 0.34754584568689406 0.34735477267870285 0.20280129493438628 0.5550634643047467 0.5417843340506511 0.4094927938360917 0.8360923598017391 0.6312965752345375 2.3436475420922793 0.2630487531836344
9 73684210.5263158 1.1584573994052705 0.42419829857316366 0.2702647761294716 0.520240511590424 0.3005382136294716 0.6537985577147426 0.44178223808056094 0.8365821864796479 0.45694101286066535 0.7962525650404828 0.5197660678641617 0.40412120871926954 0.25367383613480765 1.4740025950931113 0.44445966419420735 0.6018889524930073 0.4067880123275799 0.6484816120602088 1.4740230581436784 0.36489327396382276 1.488372493648793 0.7808361053466799 0.4400178058655969 0.561081476819152 0.5061649734623875 0.3627213771323419 0.25026047989272027 0.4911541899155381 0.3797149737455838 0.3205080138018917 0.305370093052407 0.3742698843789563 0.4101658659958777 0.24073548726427926 0.2513423190552773 0.40597107007562944 1.1239899479451272 0.9245490156052185 2.559697674251989 0.297115632371559
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136842105.2631579,0.960159909361948,0.450690290604272,0.23012897512589126,0.3031537645081072,1.2008859338522602,0.31478742879513566,1.3341564299987634,0.32415108403340614,0.3303785958118387,1.8565622181773516,0.8373598008935143,0.5340105225835153,0.2586940411385407,2.385186588995343,0.4632587617784326,0.42975415945713547,0.3700331082964869,0.4503122181773516,0.3638722559751897,0.3153411437269722,0.5860544056773517,0.32595994796118904,0.5114446280735683,0.4670077955293525,0.8243640175816755,1.0210609594540592,0.8471702010347574,0.32536894198599936,1.3395810087631954,0.5504872567765928,0.2546490011452967,1.0243628097703255,0.2852512713614593,0.4995751394129197,2.809771297380865,0.37543580274502647,0.5132251300970273,0.2985157055207567,0.5266009988547032,0.3262549476940547
147368421.0526316,1.0055862595830267,0.6440014561787868,0.2858737300967907,0.3863602054416309,0.8479710734782128,0.4378958356017222,1.530421428733255,0.54462589253349,0.2567316673469014,1.553620309380613,1.45811728163109,0.37198208837958235,0.1532160423469014,2.7359078003098767,0.47535453014426615,0.3418036960168558,0.7782120163090676,1.4861997567385528,0.4293566304891064,0.44270003997718216,0.6637524845197261,0.36605131725195045,0.44276221108898883,0.329971450847932,0.7993510978043574,1.0415730938686887,0.6488028655752248,0.3565680326847489,1.4946403397747683,0.7484382935838358,0.5302830534958777,2.565739253881567,0.5837625836401438,0.4866890735573385,2.587823254910202,0.4213335771639922,0.45447173607316366,0.31662843233990867,0.4362479180840573,0.30952860443876057
157894736.84210527,0.9976090116844283,0.7096902260819962,0.49118156908621763,0.30583666170072676,2.533825134636624,0.43479590534833656,1.5473897780738048,0.47497304720891803,0.24082879148361758,1.6901296076682137,2.1395948520987984,0.4781837489796479,0.20542302752465758,2.631700877667794,0.3386815617949678,0.29715631014752586,0.5002949284054232,2.789382593783646,0.6829672414510206,0.5018177692909981,0.7628942605861337,0.3123116506433883,0.3546965828892927,0.3742781028853229,0.6146799256596868,1.1904109178157396,0.7768765182706459,0.6362036760493991,1.4573682774467152,0.5246160301145092,0.43812378489739995,3.921759954119654,0.4363299367170253,0.45301356540162147,2.1907006947948,1.1487924095005875,0.3566391091597707,0.3147901524467151,0.35226047600405364,0.43407128458208005
168421052.63157895,0.8819832418764066,0.6183622999534713,0.22751953463144897,0.3871347527754935,3.2939703352233383,0.2267976375167719,1.07802922045425,0.40803050202345914,0.42567634054168124,1.8516671135815228,1.5821111367349807,0.4174423429114006,0.3464219788104874,2.970000755753874,0.5660719937564925,0.4968351749832281,0.47434891888309383,4.935901631278676,0.5953465934605479,0.3941350709698537,0.5912875442293541,0.31495696091585873,0.4686734524460051,0.2391220895867598,0.6104732523994763,1.2840607450279173,0.6961646251731302,0.45934974057522493,1.0166076491083793,0.6046675579039344,0.39845732374534715,3.7994228373604138,0.38673857374534715,0.5138954310536055,2.1964220379858466,0.697549244043239,0.3853005702475762,0.2744933574813885,0.35074727489017055,0.6157125964389284
178947368.42105263,1.036737164632105,0.6620557182713559,0.30928696555774304,0.4473527950593309,2.256413634133801,0.32278280707277424,1.700483562543452,0.3760209942128189,0.4509254281210437,1.8510788312579125,1.4233721313053882,0.47974616602847453,0.3697299138330687,1.7596451186077082,0.290563018038002,0.3500167920648886,0.25259023227850147,4.41752291650323,0.5792071825909813,0.41858402051423726,0.5553212205458876,0.3079340477729438,0.39578193442643184,0.455206340039536,0.9051015489319356,1.1262431527769137,0.6798635334849688,0.8544854140347722,1.3124504881882602,0.3912973139754953,0.3701616192128189,4.179021024307716,0.26242457730618207,0.48850171519778773,1.7418606565269406,0.8900138744026671,0.3708213214398751,0.30816204462024976,0.40239571336233715,0.4134413912025514
189473684.21052632,1.237837572177031,0.5930154435852558,0.27973201466399217,0.4655953827326978,4.113130653994236,0.3874246010819961,1.522287971095035,0.5005732190245736,0.27539680671163547,1.5777712634395695,1.0808048776642438,0.5301438962983953,0.22412845368530612,0.3852786172459997,0.5128333918605815,0.2688028752968913,0.22640970076880626,2.662768128836254,0.4151313602098798,0.40941006457046125,0.5537225665147946,0.3220383387853564,0.4326978561950853,0.3504680253131898,0.9074135143671009,0.8324415095955382,0.9398728103849036,0.6542906932883645,1.1128848226446855,1.7575621089776796,0.4881168217540117,3.0816953241659997,0.5057438192605311,0.4500168987918759,2.6855392244714116,0.41633903418881746,0.3249307827936315,0.25339971420837576,0.2916004730393682,0.46179850676053114
200000000.0,1.1967784981978566,0.610686553151984,0.3437335867630808,0.37152069493343953,5.123102439077277,0.4199164039210269,1.4689820942125822,0.4834093796579461,0.44998404854222346,1.8275360308195416,1.4237405877364309,0.5493120896188837,0.29364314832185445,4.355327355234246,0.4096855364347759,0.4686908721923828,0.23630603991056742,1.0983883205213045,0.4730722527754934,0.36480743006656047,0.5995283628764906,0.43493602150364924,0.4425667210629112,0.44316557834022924,0.7875417910124126,1.3248418004889237,0.5543754477249948,0.4814408954821135,1.5615148042377673,0.5799588153236791,0.3838427192286441,3.5419572529039884,0.36495409513774674,0.5220931203741777,1.8803436379683645,0.7313085355256733,0.536768913269043,0.46199507462350947,0.32877856806704875,0.3125481856496711
1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20 trial_21 trial_22 trial_23 trial_24 trial_25 trial_26 trial_27 trial_28 trial_29 trial_30 trial_31 trial_32 trial_33 trial_34 trial_35 trial_36 trial_37 trial_38 trial_39
2 0.0 0.5126953125 0.341796875 0.1689453125 0.232421875 0.267578125 0.3916015625 0.1044921875 0.1884765625 0.3212890625 0.2333984375 0.4599609375 0.384765625 0.3291015625 0.5283203125 0.1376953125 0.455078125 0.25390625 0.1982421875 0.087890625 0.4580078125 0.140625 0.220703125 0.23046875 0.3603515625 0.333984375 0.2783203125 0.078125 0.1767578125 0.2294921875 0.2021484375 0.2421875 0.4267578125 0.796875 0.8671875 0.13671875 0.24609375 0.1328125 0.318359375 0.2880859375 0.1767578125
3 10526315.789473685 0.49093338128932623 0.3462821585319709 0.1852252305049315 0.2928347680046948 0.27106667885819963 0.38623029703578793 0.11983074970192527 0.1988314763330687 0.3117093828576423 0.23267857718005405 0.442573542079767 0.38980464723962166 0.3179714144762203 0.521509326395896 0.155857942110944 0.44749190470518496 0.27505906863225793 0.21468822711722674 0.09868852979918927 0.4620501050658503 0.1616670708907278 0.22291807983060294 0.25549773958581307 0.36278801281366324 0.32900072663114344 0.279040172819946 0.1068086650563079 0.19270548728034106 0.26188590189756783 0.21333395939454478 0.263395692503023 0.4162367770546361 0.7937186893663908 0.8380054701068065 0.1567087173461914 0.25711315028224957 0.15335620605384215 0.31996521725218713 0.2936233245765073 0.17786528991530146
4 21052631.57894737 0.14773336606012488 0.41170637495299783 0.43445887790162147 1.1673907229774876 0.3169193109316839 0.31370865671258225 0.387846738017497 0.40387508149292334 0.2171311787951356 0.2135045218005405 0.23726710057985093 0.4631117770546361 0.15972420119182557 0.426365754610944 0.4283274177699208 0.3453213224120418 0.6104517115120082 0.47045086361364646 0.27034647510982945 0.5193295782622869 0.510279029360108 0.24381795021965894 0.637100209159534 0.4475086613705284 0.2694615234628609 0.26598663541418693 0.5406820080617127 0.4469330383469854 0.7313424160605982 0.3769322709693803 0.5845370834223782 0.232129622694528 0.6846188415780952 0.38532039399292334 0.4707629396644656 0.4800773789677924 0.4946741965338794 0.34535071460163824 0.38374872815245736 0.19174840509726399
5 31578947.368421055 0.30206510432869443 0.5240726180353987 0.25200302779179196 0.16374085550493153 0.24011918646476937 0.4396643651819625 0.47582212907785854 0.5759325925663236 0.6530311272745316 0.17334035889263633 0.7837483017728598 0.3632504840967067 0.341378148572927 0.5027413381433882 0.21605753436313113 0.5028028699499748 0.4777906370295052 0.2948401760196421 0.2864172135033437 0.4068529546425943 0.47393907404342184 0.14073643459837856 0.35161240279179196 0.6927974177859825 0.40297644026061497 0.09805480925330169 0.21826223389263633 0.36566745409344703 0.20924176403690248 0.22758521135493992 0.3536923453418172 0.2098064449024994 0.25531110737132234 0.5960842407311098 0.4220240452943418 0.7280757011138831 0.489715842989343 0.3941002314770982 0.359857981885239 0.1763507150877216
6 42105263.15789474 0.3601710882213307 1.1924962601172955 0.18665435241530146 0.2274378832027192 0.36839684356943064 0.38353645768522227 0.45003534882352625 0.17367738633935143 0.34137508149292334 0.28982885260331004 0.27263287361969246 0.29196245188197933 0.21424010850055727 0.2311246982902041 0.33199160250930576 0.40100623894266146 0.4240786692442326 0.1392061333907278 0.5756957141316168 0.24957751963607494 0.32276808720216194 0.2485302003136632 0.5412050284176984 0.23178849788253658 0.15444761366064857 0.21346384402457366 0.329434836009863 0.38119127479616627 0.29703565053332215 0.3316378183972472 0.3469486817758829 0.4120478431934135 0.35543970123882773 0.3525383756431516 0.717103456196032 0.40850460232129715 0.6356967492777226 0.6420835140999664 0.3197789284661206 0.2659972341437089
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1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20
2 0.0 9.888734817504883 9.284497261047363 6.875021934509277 6.710487365722656 6.043292999267578 9.820124626159668 16.537796020507812 6.202973365783691 13.810953140258789 10.509878158569336 14.101040840148926 18.845413208007812 7.062399864196777 5.953526020050049 3.237598419189453 15.201939582824707 26.584564208984375 4.742987632751465 9.663023948669434 11.021127700805664 10.703713417053223
3 2631578.947368421 10.10537327277033 9.283902492962385 6.847756677552273 6.843581103964856 6.502802102189316 9.706934806547666 16.38613082546937 6.16217115521431 13.814598011343103 10.559696472004841 13.84272244807921 18.931698924616764 7.653529451081628 5.921330041006992 3.2969599005423094 15.300211296269769 26.58416327049858 4.995440086251811 9.93426430068518 10.886806641754351 11.527277304937966
4 5263157.894736842 17.75651438612687 9.914393174020868 5.956438364166963 11.625398419405284 22.537136435508728 5.852523133942955 11.18851415734542 4.71972844475194 13.519483784311696 12.223783179333335 4.817055474770696 21.689254810935573 28.765877899370697 4.9972495577837295 5.481313225470092 18.717195812024567 26.083637112065365 14.647366856273853 19.33682950546867 7.828131286721482 39.55978362183822
5 7894736.842105264 19.44448771131666 22.67342510348873 6.805056731167592 13.944712709439427 23.3878490266047 7.180790741976939 12.523353957816175 4.340164582980306 6.309299673689039 11.574244839580437 4.36824749174871 19.894484808570468 40.80036094941592 8.495043572626617 8.15164659525219 19.003879700836382 17.92720954041732 30.071821808815006 20.095726013183597 34.50449174956271 30.197650106329668
6 10526315.789473685 16.578101691446808 39.64854281827023 6.440792052369369 12.181270567994371 22.96099554864984 7.186699704120034 13.097670335518686 4.722508173239858 5.906746431400902 17.147330208828574 7.697360220708345 45.72458196941175 73.38811226894981 11.500692028748363 15.430165278284173 22.40508878858466 19.284776336268376 37.79571555790148 37.32427807858116 28.69454835590563 37.2967561295158
7 13157894.736842105 22.251839186015882 28.554213194470655 13.777229503581399 24.66804232095417 34.30007964686344 11.680851812425413 12.848895167049609 5.975417475951345 11.150909117962184 20.87581067336233 7.345379272573872 52.023328028227155 109.53894695482757 17.527399414464046 19.268240897279036 26.273384464414494 27.957743011022867 47.231798115529514 68.03209223872737 29.05422474208631 27.824859227004804
8 15789473.684210528 19.25550873656022 71.7214200873124 20.747600367194728 27.79745068989301 40.710212456552604 21.770903882227447 23.17712328308508 13.038783038917355 18.8152778430989 35.476379708239904 11.309572819032168 53.50583972428975 97.65787807263825 16.068686836644225 26.065466604734723 31.93282687036615 46.68305125989412 75.91218122683074 64.00905655559741 39.98445173313744 22.702275276184096
9 18421052.63157895 24.159047685171437 68.98515194340757 26.65492335118746 19.256001913233813 38.468064841471225 23.646104894186323 41.1612764408714 33.52059091392316 36.403322169655254 32.9737615146135 17.57789507508279 70.32805327365276 88.26997340352912 18.196330208527414 36.305894876781274 36.24021483095069 51.50751520458021 98.42132879558363 74.45273170973127 48.47059553861617 39.84074703643196
10 21052631.57894737 38.28674632624576 88.61726499858655 38.54707135652241 32.62826583259984 51.20372069509406 31.695851978502777 49.42035880841706 25.077611722444235 41.08017173566316 36.683732635096504 41.534054354617474 113.68805142452842 81.35287575972707 23.39544168271517 51.68273172880473 48.26376187173944 67.90966686449553 102.67105975903962 117.30013686732242 38.7832320614865 22.784806954233275
11 23684210.52631579 35.66065367272026 105.75405805989315 46.75854296433298 35.39752160875421 63.491124046476266 40.093452623015956 47.46454145406422 37.4789982093008 43.01326150015781 46.46034582665092 42.260203116818474 113.42279282369113 63.84576871520595 38.857609259454826 45.14887053088138 57.85811551621086 96.90247347480373 112.75141496407359 146.27356973447297 75.26643239824396 37.109446475380345
12 26315789.47368421 31.79018675653558 150.29831253854852 61.520441795650285 65.30472025118377 74.5737415614881 63.103047270523874 74.47154268465545 56.1377770022342 110.07281300896092 49.43393192793194 56.55144682683442 149.9051325446681 95.1966239778619 43.00841266230533 121.19370550858346 54.78556738401714 107.96995740187795 144.9742881875289 158.83448455208227 112.80655241012573 34.726112842559814
13 28947368.42105263 34.886604942773516 182.68540041070236 52.63218028294413 74.24405795649479 98.45311747099223 83.63654175557589 98.15259555766457 83.00712973193119 152.04949614876193 60.033586916170634 104.44645261764528 183.34212626908953 145.3882823994285 55.8120873350846 155.29590370780545 52.760886982867596 135.8035633689479 149.5857477941011 174.62654038479454 119.70657352397316 56.90697970515803
14 31578947.368421055 42.14771624615319 202.42679094013414 52.38267727902063 86.16361492558535 116.33401408948396 82.56993238549485 123.30445560656098 90.39040706032202 137.23200105365945 40.95219484128452 74.46030948036596 199.67874667519 197.26049192328207 95.94568357969584 134.3780511554919 49.24194752542601 126.69745851817879 172.39319590518346 173.57390514173008 134.63159445712444 63.719783306121826
15 34210526.315789476 43.65013820246645 217.50729831896336 62.131120148457974 115.80259094740214 128.52460966612168 95.68277384105482 124.53052769209206 97.55255219810887 81.50745273891249 47.45693647861479 80.01052587910702 156.18299102783214 207.39208640550308 110.61193823814396 156.5341895505002 80.74786253979332 121.23273363866309 162.08628305635955 190.38883532975854 143.8943206385562 77.16892081812811
16 36842105.2631579 41.94657889165378 245.93722017187818 55.185322447826984 135.67933988571173 147.6677642621492 95.9600271425749 107.22564328344245 93.87127048090883 117.41437731291124 48.61179826134132 79.67655578412509 242.42287349700928 182.9434824491802 137.05576708442285 161.4447242837203 81.30902413318032 131.1828931256344 160.34503550278512 207.20630570461876 137.0641293776663 112.80630558415466
17 39473684.21052632 58.79436187367691 212.42795580311824 56.41915478204427 164.73655364387912 139.29991523843063 94.7229819925208 131.44584129986015 105.2594486035799 168.36056754463598 73.8486905223445 83.05311863045942 250.90402429982237 201.20104995526768 139.37954770891292 153.56256239037768 83.17541534022281 118.41643432566998 162.2819593329179 186.46040652927596 159.94275539799742 120.8470532266717
18 42105263.15789474 64.42797510247482 147.64111830058846 60.26418444984837 158.13086258737667 136.83324552837172 105.07864440114875 175.86086995978107 145.38353729248047 174.84317819695724 85.31340006778115 98.05986544960426 264.37591231496714 194.34444628263773 150.8557458174856 168.78205148797284 93.2750462983784 154.0627132214998 184.64032062731292 187.95712240118732 183.14200230648646 126.56950057180306
19 44736842.10526316 63.05825469368383 119.0508030213808 67.56669671911943 184.729963001452 119.09256009051673 98.55030614451357 131.52183355783157 156.8359883208024 151.64848545977944 83.73348729233992 125.89496096811797 249.2035153539557 159.97292945259494 135.16470550235948 164.3975305557251 91.16130136188707 160.4443457001134 171.18832497847706 200.91943379452354 192.18329652987026 154.0876652817977
20 47368421.05263158 67.45054091905293 188.57196054960554 69.25454774655793 166.7225661026804 122.31587982177736 94.99036314612941 136.75466273960316 167.56895547164115 163.80847815463417 76.43427557694285 99.01034643775537 248.06674073871815 183.3102160002056 154.41465392865632 173.13884579507928 68.79246320222553 186.41125699093467 166.97562890303763 184.13067767494604 180.09653121546694 120.06530277352583
21 50000000.0 69.65415954589844 222.86355590820312 61.62987518310547 135.8297119140625 148.7770538330078 99.98258209228516 207.14266967773438 184.39578247070312 193.70370483398438 78.28141784667969 70.91169738769531 270.7571105957031 221.07476806640625 182.5941162109375 166.03514099121094 53.1497802734375 204.63912963867188 178.64535522460938 186.98333740234375 188.1245574951172 85.73209381103516

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1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20
2 0.0 9.888734817504883 9.284497261047363 6.875021934509277 6.710487365722656 6.043292999267578 9.820124626159668 16.537796020507812 6.202973365783691 13.810953140258789 10.509878158569336 14.101040840148926 18.845413208007812 7.062399864196777 5.953526020050049 3.237598419189453 15.201939582824707 26.584564208984375 4.742987632751465 9.663023948669434 11.021127700805664 10.703713417053223
3 2631578.947368421 10.10537327277033 9.283902492962385 6.847756677552273 6.843581103964856 6.502802102189316 9.706934806547666 16.38613082546937 6.16217115521431 13.814598011343103 10.559696472004841 13.84272244807921 18.931698924616764 7.653529451081628 5.921330041006992 3.2969599005423094 15.300211296269769 26.58416327049858 4.995440086251811 9.93426430068518 10.886806641754351 11.527277304937966
4 5263157.894736842 17.75651438612687 9.914393174020868 5.956438364166963 11.625398419405284 22.537136435508728 5.852523133942955 11.18851415734542 4.71972844475194 13.519483784311696 12.223783179333335 4.817055474770696 21.689254810935573 28.765877899370697 4.9972495577837295 5.481313225470092 18.717195812024567 26.083637112065365 14.647366856273853 19.33682950546867 7.828131286721482 39.55978362183822
5 7894736.842105264 19.44448771131666 22.67342510348873 6.805056731167592 13.944712709439427 23.3878490266047 7.180790741976939 12.523353957816175 4.340164582980306 6.309299673689039 11.574244839580437 4.36824749174871 19.894484808570468 40.80036094941592 8.495043572626617 8.15164659525219 19.003879700836382 17.92720954041732 30.071821808815006 20.095726013183597 34.50449174956271 30.197650106329668
6 10526315.789473685 16.578101691446808 39.64854281827023 6.440792052369369 12.181270567994371 22.96099554864984 7.186699704120034 13.097670335518686 4.722508173239858 5.906746431400902 17.147330208828574 7.697360220708345 45.72458196941175 73.38811226894981 11.500692028748363 15.430165278284173 22.40508878858466 19.284776336268376 37.79571555790148 37.32427807858116 28.69454835590563 37.2967561295158
7 13157894.736842105 22.251839186015882 28.554213194470655 13.777229503581399 24.66804232095417 34.30007964686344 11.680851812425413 12.848895167049609 5.975417475951345 11.150909117962184 20.87581067336233 7.345379272573872 52.023328028227155 109.53894695482757 17.527399414464046 19.268240897279036 26.273384464414494 27.957743011022867 47.231798115529514 68.03209223872737 29.05422474208631 27.824859227004804
8 15789473.684210528 19.25550873656022 71.7214200873124 20.747600367194728 27.79745068989301 40.710212456552604 21.770903882227447 23.17712328308508 13.038783038917355 18.8152778430989 35.476379708239904 11.309572819032168 53.50583972428975 97.65787807263825 16.068686836644225 26.065466604734723 31.93282687036615 46.68305125989412 75.91218122683074 64.00905655559741 39.98445173313744 22.702275276184096
9 18421052.63157895 24.159047685171437 68.98515194340757 26.65492335118746 19.256001913233813 38.468064841471225 23.646104894186323 41.1612764408714 33.52059091392316 36.403322169655254 32.9737615146135 17.57789507508279 70.32805327365276 88.26997340352912 18.196330208527414 36.305894876781274 36.24021483095069 51.50751520458021 98.42132879558363 74.45273170973127 48.47059553861617 39.84074703643196
10 21052631.57894737 38.28674632624576 88.61726499858655 38.54707135652241 32.62826583259984 51.20372069509406 31.695851978502777 49.42035880841706 25.077611722444235 41.08017173566316 36.683732635096504 41.534054354617474 113.68805142452842 81.35287575972707 23.39544168271517 51.68273172880473 48.26376187173944 67.90966686449553 102.67105975903962 117.30013686732242 38.7832320614865 22.784806954233275
11 23684210.52631579 35.66065367272026 105.75405805989315 46.75854296433298 35.39752160875421 63.491124046476266 40.093452623015956 47.46454145406422 37.4789982093008 43.01326150015781 46.46034582665092 42.260203116818474 113.42279282369113 63.84576871520595 38.857609259454826 45.14887053088138 57.85811551621086 96.90247347480373 112.75141496407359 146.27356973447297 75.26643239824396 37.109446475380345
12 26315789.47368421 31.79018675653558 150.29831253854852 61.520441795650285 65.30472025118377 74.5737415614881 63.103047270523874 74.47154268465545 56.1377770022342 110.07281300896092 49.43393192793194 56.55144682683442 149.9051325446681 95.1966239778619 43.00841266230533 121.19370550858346 54.78556738401714 107.96995740187795 144.9742881875289 158.83448455208227 112.80655241012573 34.726112842559814
13 28947368.42105263 34.886604942773516 182.68540041070236 52.63218028294413 74.24405795649479 98.45311747099223 83.63654175557589 98.15259555766457 83.00712973193119 152.04949614876193 60.033586916170634 104.44645261764528 183.34212626908953 145.3882823994285 55.8120873350846 155.29590370780545 52.760886982867596 135.8035633689479 149.5857477941011 174.62654038479454 119.70657352397316 56.90697970515803
14 31578947.368421055 42.14771624615319 202.42679094013414 52.38267727902063 86.16361492558535 116.33401408948396 82.56993238549485 123.30445560656098 90.39040706032202 137.23200105365945 40.95219484128452 74.46030948036596 199.67874667519 197.26049192328207 95.94568357969584 134.3780511554919 49.24194752542601 126.69745851817879 172.39319590518346 173.57390514173008 134.63159445712444 63.719783306121826
15 34210526.315789476 43.65013820246645 217.50729831896336 62.131120148457974 115.80259094740214 128.52460966612168 95.68277384105482 124.53052769209206 97.55255219810887 81.50745273891249 47.45693647861479 80.01052587910702 156.18299102783214 207.39208640550308 110.61193823814396 156.5341895505002 80.74786253979332 121.23273363866309 162.08628305635955 190.38883532975854 143.8943206385562 77.16892081812811
16 36842105.2631579 41.94657889165378 245.93722017187818 55.185322447826984 135.67933988571173 147.6677642621492 95.9600271425749 107.22564328344245 93.87127048090883 117.41437731291124 48.61179826134132 79.67655578412509 242.42287349700928 182.9434824491802 137.05576708442285 161.4447242837203 81.30902413318032 131.1828931256344 160.34503550278512 207.20630570461876 137.0641293776663 112.80630558415466
17 39473684.21052632 58.79436187367691 212.42795580311824 56.41915478204427 164.73655364387912 139.29991523843063 94.7229819925208 131.44584129986015 105.2594486035799 168.36056754463598 73.8486905223445 83.05311863045942 250.90402429982237 201.20104995526768 139.37954770891292 153.56256239037768 83.17541534022281 118.41643432566998 162.2819593329179 186.46040652927596 159.94275539799742 120.8470532266717
18 42105263.15789474 64.42797510247482 147.64111830058846 60.26418444984837 158.13086258737667 136.83324552837172 105.07864440114875 175.86086995978107 145.38353729248047 174.84317819695724 85.31340006778115 98.05986544960426 264.37591231496714 194.34444628263773 150.8557458174856 168.78205148797284 93.2750462983784 154.0627132214998 184.64032062731292 187.95712240118732 183.14200230648646 126.56950057180306
19 44736842.10526316 63.05825469368383 119.0508030213808 67.56669671911943 184.729963001452 119.09256009051673 98.55030614451357 131.52183355783157 156.8359883208024 151.64848545977944 83.73348729233992 125.89496096811797 249.2035153539557 159.97292945259494 135.16470550235948 164.3975305557251 91.16130136188707 160.4443457001134 171.18832497847706 200.91943379452354 192.18329652987026 154.0876652817977
20 47368421.05263158 67.45054091905293 188.57196054960554 69.25454774655793 166.7225661026804 122.31587982177736 94.99036314612941 136.75466273960316 167.56895547164115 163.80847815463417 76.43427557694285 99.01034643775537 248.06674073871815 183.3102160002056 154.41465392865632 173.13884579507928 68.79246320222553 186.41125699093467 166.97562890303763 184.13067767494604 180.09653121546694 120.06530277352583
21 50000000.0 69.65415954589844 222.86355590820312 61.62987518310547 135.8297119140625 148.7770538330078 99.98258209228516 207.14266967773438 184.39578247070312 193.70370483398438 78.28141784667969 70.91169738769531 270.7571105957031 221.07476806640625 182.5941162109375 166.03514099121094 53.1497802734375 204.63912963867188 178.64535522460938 186.98333740234375 188.1245574951172 85.73209381103516

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2 0.0 16.287094116210938 9.519023895263672 4.587231159210205 20.571439743041992 27.30125617980957 13.915904998779297 43.75962448120117 7.398332595825195 11.781911849975586 5.428969383239746 9.077356338500977 33.518253326416016 10.437522888183594 11.8486328125 6.978132247924805 33.936607360839844 18.351730346679688 5.592342376708984 7.198254585266113 17.855012893676758 18.936899185180664 4.449044227600098 14.971601486206055 5.235752582550049 6.302183151245117
3 2631578.947368421 16.421380137142382 10.056043079024867 4.662623287031525 21.04422082712776 27.586748220418627 14.44254457950592 43.875450799339696 7.770613846025969 11.924832394248561 5.583928081550097 9.636894740556416 33.95280931497875 10.44215615956407 12.334181158166183 7.188560103115282 34.73577610442513 18.441976864086953 5.693842956894323 7.268998602503224 17.906796514987946 19.13224710288801 4.521706488571669 15.107418784969731 5.526400786481406 6.619853305189233
4 5263157.894736842 21.361631732237967 28.318635200199328 7.797155866497442 37.381322434074 37.75667086400484 33.560849014081455 48.312501995187056 20.992702251986454 17.82285982056668 11.236212222199692 29.6345266229228 48.92006230354309 11.31641540715569 29.244621910546954 14.7860443717555 61.56724217063502 22.18982083546488 10.517626210262902 10.45357128193504 20.043819207894174 26.367242380192405 7.0919759022562125 20.14383306001362 15.893065179649152 18.051533636293914
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6 10526315.789473685 27.38552354511462 30.38068505337364 20.162110504351165 43.34544969859876 57.31569322786833 56.92737629539088 54.04297878867702 26.17458702388563 46.291572169253705 21.158217405018053 48.94438896681133 51.25651866511295 52.84580353686684 38.500591805106716 22.67075528596577 42.50031285536917 52.803925464027806 33.53385511197542 32.36817188011973 33.982845168364676 36.969710902163854 14.15533999392861 25.29677721073753 20.041901350021366 34.27549982070923
7 13157894.736842105 30.80395347821085 36.85353053870954 42.187363963378104 66.43124038294742 66.12823299357765 49.86494440781443 56.754242966049596 38.46823332811657 76.4212149067929 27.647250194298593 63.36426373531944 62.121768487127206 59.19179628397289 36.88565060339476 44.99805409029911 48.193437701777405 56.20987471781279 54.703254982044825 69.65226446954827 52.16454800806547 39.51263521846972 29.383961279141275 39.60771564433449 53.71195552223607 53.58391092325512
8 15789473.684210528 43.96609288767765 46.346220719186896 82.26313608571104 66.0013697272853 84.34098047959179 47.33048078888342 64.4124425210451 46.21369021817259 107.1608110227083 52.70972959618822 65.18659048331413 75.09479919232821 88.80393269187526 48.97378349304199 69.7719448491147 63.881811016484306 51.58831567513315 61.8734909735228 83.2185062107287 54.7519380418878 46.02017393865084 42.461149341181724 50.340063534284894 95.75055320639359 89.4950034994828
9 18421052.63157895 50.23525526649074 61.50189724721406 103.80597896324961 80.63195464485571 117.34456777572633 59.19724694051241 73.52777947877583 68.9801967269496 134.1733152991847 85.3421406871394 100.76200361000866 85.67804071777746 99.9848475456238 54.716643691062934 110.73270924467789 63.25767571047733 54.80461528426723 80.97548851213958 103.54271512282523 72.19664953256908 55.49492140192735 73.77047834898296 52.65499827108886 103.44908603868987 104.0086105246293
10 21052631.57894737 67.74022042123896 57.66859104758816 133.05308592946906 104.85747789081775 143.54523468017578 63.94674115431937 81.64914924220035 91.02104006315533 142.51776283665706 95.18521449440405 137.3905721965589 106.51264732762388 126.02176565872996 71.34742295114617 108.72206627695184 74.0683728268272 63.01840455908525 96.61264098318 132.38460601003547 71.63434545617356 65.51847979896947 82.19315830029939 68.17025305095471 125.74210197047182 140.32913770173727
11 23684210.52631579 89.8769181402106 84.87032641862568 152.11012310730783 149.80162592938072 159.56479511762922 89.89506904702438 89.92486411646793 117.66022782576712 128.3806041918303 137.5425827126754 152.77642390602514 128.68560053172865 137.7969227088125 83.73427398581254 126.21492806233859 82.64666007694446 65.93250309793572 120.96357506199887 139.9765312797145 116.575527078227 84.5733994308271 86.28288592790302 67.83383710760819 115.67570334986637 153.62613208670365
12 26315789.47368421 114.26601520337556 93.76450779563501 190.09130211880333 173.77456926044664 177.81273691277755 127.27064479024787 87.39835774271111 137.6591692472759 151.1868812159488 155.24181029671118 170.6516284942627 145.53067297684518 160.40461650647615 92.1872336738988 162.85533905029297 99.92150472339831 68.8617030946832 156.52020916185882 151.68310536836321 131.58652451163843 104.94969415664673 109.96378218500237 72.29348523993241 131.29652801312898 163.15333235891242
13 28947368.42105263 122.41626327916195 133.84884420194123 207.31056414152448 198.09824790452657 170.06713194596142 127.26082776722154 91.81295121343513 145.97237960915817 167.87781328904 145.58369874954224 188.92073912369577 133.8795719774146 169.23453162845811 96.16378713908948 173.42941249044318 100.4667820930481 90.6223213672638 174.71190690994263 161.78474742487856 135.2476440479881 96.78860313013979 130.6538378564935 82.91003312562641 111.33236460936696 175.15652127014963
14 31578947.368421055 145.70292944657174 154.49581999527786 196.8035216080515 206.22886898643094 152.96537298905224 146.67974883631658 101.19485046989043 156.73033664101052 177.02410768207747 169.2260831531726 198.04608967429715 127.78581794939554 184.50897548073218 109.48155041744835 167.64149655793844 103.55727562151453 91.79166778765226 178.19568603917173 160.45962825574372 133.88398933410645 125.93390976755246 136.4324505454616 79.36228762174906 120.42866807234914 168.53483611659
15 34210526.315789476 145.13476906324686 181.0156959985432 196.96632676375538 219.36357698942484 174.92123664052866 160.18036340412343 116.44782897045737 184.47489683251632 155.5202418628492 204.00147480713696 200.63506276983964 191.83462117847643 192.65076958505733 110.6756746392501 180.92265563262137 96.38060310012419 96.83216679723641 186.28922005703572 169.99148961117396 146.65858916232463 151.2074738050762 164.81994503422789 69.92559983855799 127.15519405666153 166.59142622194793
16 36842105.2631579 153.25818342911572 177.61119591562368 185.54612691778885 205.48416830364025 194.97514383416427 169.0116389927111 112.93625131406283 191.1707026331048 169.76137090984145 218.34308072140342 211.42340118006658 190.43515556736995 194.09800233339007 97.26928690860143 184.24711483403257 115.22883121590864 109.81641312649376 172.25729094053568 183.7776959067897 157.71640115035208 151.01735260612085 169.25614894063847 77.43704221123146 146.09945086428993 170.15413394727207
17 39473684.21052632 174.00993527864154 173.4664195462277 190.27979253467763 187.4821865182174 207.23032710426733 168.04096028679297 108.28894090652463 188.1237645149231 181.1585824615077 208.1002385992753 223.78642079704684 196.18918883173092 187.94592272607903 86.08651335615863 195.87506048302902 123.7816006384398 114.92910612256905 177.02735617286282 194.24528091832212 171.77286777998273 152.0886357959948 155.6707747108058 103.52223518020229 148.2211524812799 185.68032312393188
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19 44736842.10526316 112.16595446436028 195.17130994796753 217.09464494805587 203.96229997434114 218.59926120858444 184.17645692825317 116.61314033207141 189.38473520780866 215.5696160918788 190.83929910157858 195.87477217222514 182.3937087811922 205.65431386546084 160.96340656280518 201.25900002529747 155.24908404601248 129.4638685929148 197.94397042926988 198.7030984226026 191.8459028695759 185.69810520975216 166.76698185268202 95.27756620708264 140.59051365601388 195.0851933077762
20 47368421.05263158 146.875292627435 204.24813155124062 194.46876992677386 228.11076786643582 218.22915333195738 196.66796232524672 109.01915881508275 204.0876811178107 209.54677260549445 206.95813450060393 203.44305565482694 192.86889181639017 197.8119333166825 165.4711187262284 174.31547531328704 159.99122619628906 129.88634305251273 208.15185125250565 198.8398228695518 188.9094945004112 200.28832897387053 190.1343819467645 93.6343687960976 137.6984423085263 202.6962440390336
21 50000000.0 189.524169921875 208.85409545898438 187.1713104248047 241.01425170898438 217.15151977539062 205.97315979003906 101.03228759765625 212.29312133789062 203.9116668701172 204.74691772460938 216.1698455810547 173.5381317138672 196.7125701904297 169.46923828125 159.1580810546875 159.99122619628906 131.65098571777344 206.62130737304688 198.2906036376953 195.96603393554688 198.23983764648438 207.55056762695312 99.96365356445312 143.13748168945312 201.30123901367188

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28947368.42105263,122.41626327916195,133.84884420194123,207.31056414152448,198.09824790452657,170.06713194596142,127.26082776722154,91.81295121343513,145.97237960915817,167.87781328904,145.58369874954224,188.92073912369577,133.8795719774146,169.23453162845811,96.16378713908948,173.42941249044318,100.4667820930481,90.6223213672638,174.71190690994263,161.78474742487856,135.2476440479881,96.78860313013979,130.6538378564935,82.91003312562641,111.33236460936696,175.15652127014963
31578947.368421055,145.70292944657174,154.49581999527786,196.8035216080515,206.22886898643094,152.96537298905224,146.67974883631658,101.19485046989043,156.73033664101052,177.02410768207747,169.2260831531726,198.04608967429715,127.78581794939554,184.50897548073218,109.48155041744835,167.64149655793844,103.55727562151453,91.79166778765226,178.19568603917173,160.45962825574372,133.88398933410645,125.93390976755246,136.4324505454616,79.36228762174906,120.42866807234914,168.53483611659
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39473684.21052632,174.00993527864154,173.4664195462277,190.27979253467763,187.4821865182174,207.23032710426733,168.04096028679297,108.28894090652463,188.1237645149231,181.1585824615077,208.1002385992753,223.78642079704684,196.18918883173092,187.94592272607903,86.08651335615863,195.87506048302902,123.7816006384398,114.92910612256905,177.02735617286282,194.24528091832212,171.77286777998273,152.0886357959948,155.6707747108058,103.52223518020229,148.2211524812799,185.68032312393188
42105263.15789474,149.12492571379008,189.59115680895354,211.65512727436268,188.90756024812399,222.34170532226562,172.42721637926604,99.95464967426503,186.3722775107936,193.89571179841695,185.30610977975945,209.62792085346422,185.85879155209187,201.30312467876234,133.71206564652294,208.58982889275802,145.61541587428044,129.02138880679482,185.5816899349815,202.50917936626234,194.06424311587685,163.40277862548828,156.7138214111328,106.52769289518658,148.12367047761617,192.17261023270456
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47368421.05263158,146.875292627435,204.24813155124062,194.46876992677386,228.11076786643582,218.22915333195738,196.66796232524672,109.01915881508275,204.0876811178107,209.54677260549445,206.95813450060393,203.44305565482694,192.86889181639017,197.8119333166825,165.4711187262284,174.31547531328704,159.99122619628906,129.88634305251273,208.15185125250565,198.8398228695518,188.9094945004112,200.28832897387053,190.1343819467645,93.6343687960976,137.6984423085263,202.6962440390336
50000000.0,189.524169921875,208.85409545898438,187.1713104248047,241.01425170898438,217.15151977539062,205.97315979003906,101.03228759765625,212.29312133789062,203.9116668701172,204.74691772460938,216.1698455810547,173.5381317138672,196.7125701904297,169.46923828125,159.1580810546875,159.99122619628906,131.65098571777344,206.62130737304688,198.2906036376953,195.96603393554688,198.23983764648438,207.55056762695312,99.96365356445312,143.13748168945312,201.30123901367188
1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20 trial_21 trial_22 trial_23 trial_24
2 0.0 16.287094116210938 9.519023895263672 4.587231159210205 20.571439743041992 27.30125617980957 13.915904998779297 43.75962448120117 7.398332595825195 11.781911849975586 5.428969383239746 9.077356338500977 33.518253326416016 10.437522888183594 11.8486328125 6.978132247924805 33.936607360839844 18.351730346679688 5.592342376708984 7.198254585266113 17.855012893676758 18.936899185180664 4.449044227600098 14.971601486206055 5.235752582550049 6.302183151245117
3 2631578.947368421 16.421380137142382 10.056043079024867 4.662623287031525 21.04422082712776 27.586748220418627 14.44254457950592 43.875450799339696 7.770613846025969 11.924832394248561 5.583928081550097 9.636894740556416 33.95280931497875 10.44215615956407 12.334181158166183 7.188560103115282 34.73577610442513 18.441976864086953 5.693842956894323 7.268998602503224 17.906796514987946 19.13224710288801 4.521706488571669 15.107418784969731 5.526400786481406 6.619853305189233
4 5263157.894736842 21.361631732237967 28.318635200199328 7.797155866497442 37.381322434074 37.75667086400484 33.560849014081455 48.312501995187056 20.992702251986454 17.82285982056668 11.236212222199692 29.6345266229228 48.92006230354309 11.31641540715569 29.244621910546954 14.7860443717555 61.56724217063502 22.18982083546488 10.517626210262902 10.45357128193504 20.043819207894174 26.367242380192405 7.0919759022562125 20.14383306001362 15.893065179649152 18.051533636293914
5 7894736.842105264 26.056687750314413 22.142802790591592 16.60792303085327 36.10195835013139 43.11333872142591 48.11219581804778 55.122068442796404 25.632349409555133 34.312123913513986 16.133165528899745 39.53154394501134 46.8566004288824 25.81226831360868 30.529674677472368 19.601410341890237 45.22117100891314 34.154705210735926 32.26232831729086 23.132305261335876 26.22709031481492 34.101866264092294 8.21936057115856 25.312087752317126 20.015055273708544 25.26831566660028
6 10526315.789473685 27.38552354511462 30.38068505337364 20.162110504351165 43.34544969859876 57.31569322786833 56.92737629539088 54.04297878867702 26.17458702388563 46.291572169253705 21.158217405018053 48.94438896681133 51.25651866511295 52.84580353686684 38.500591805106716 22.67075528596577 42.50031285536917 52.803925464027806 33.53385511197542 32.36817188011973 33.982845168364676 36.969710902163854 14.15533999392861 25.29677721073753 20.041901350021366 34.27549982070923
7 13157894.736842105 30.80395347821085 36.85353053870954 42.187363963378104 66.43124038294742 66.12823299357765 49.86494440781443 56.754242966049596 38.46823332811657 76.4212149067929 27.647250194298593 63.36426373531944 62.121768487127206 59.19179628397289 36.88565060339476 44.99805409029911 48.193437701777405 56.20987471781279 54.703254982044825 69.65226446954827 52.16454800806547 39.51263521846972 29.383961279141275 39.60771564433449 53.71195552223607 53.58391092325512
8 15789473.684210528 43.96609288767765 46.346220719186896 82.26313608571104 66.0013697272853 84.34098047959179 47.33048078888342 64.4124425210451 46.21369021817259 107.1608110227083 52.70972959618822 65.18659048331413 75.09479919232821 88.80393269187526 48.97378349304199 69.7719448491147 63.881811016484306 51.58831567513315 61.8734909735228 83.2185062107287 54.7519380418878 46.02017393865084 42.461149341181724 50.340063534284894 95.75055320639359 89.4950034994828
9 18421052.63157895 50.23525526649074 61.50189724721406 103.80597896324961 80.63195464485571 117.34456777572633 59.19724694051241 73.52777947877583 68.9801967269496 134.1733152991847 85.3421406871394 100.76200361000866 85.67804071777746 99.9848475456238 54.716643691062934 110.73270924467789 63.25767571047733 54.80461528426723 80.97548851213958 103.54271512282523 72.19664953256908 55.49492140192735 73.77047834898296 52.65499827108886 103.44908603868987 104.0086105246293
10 21052631.57894737 67.74022042123896 57.66859104758816 133.05308592946906 104.85747789081775 143.54523468017578 63.94674115431937 81.64914924220035 91.02104006315533 142.51776283665706 95.18521449440405 137.3905721965589 106.51264732762388 126.02176565872996 71.34742295114617 108.72206627695184 74.0683728268272 63.01840455908525 96.61264098318 132.38460601003547 71.63434545617356 65.51847979896947 82.19315830029939 68.17025305095471 125.74210197047182 140.32913770173727
11 23684210.52631579 89.8769181402106 84.87032641862568 152.11012310730783 149.80162592938072 159.56479511762922 89.89506904702438 89.92486411646793 117.66022782576712 128.3806041918303 137.5425827126754 152.77642390602514 128.68560053172865 137.7969227088125 83.73427398581254 126.21492806233859 82.64666007694446 65.93250309793572 120.96357506199887 139.9765312797145 116.575527078227 84.5733994308271 86.28288592790302 67.83383710760819 115.67570334986637 153.62613208670365
12 26315789.47368421 114.26601520337556 93.76450779563501 190.09130211880333 173.77456926044664 177.81273691277755 127.27064479024787 87.39835774271111 137.6591692472759 151.1868812159488 155.24181029671118 170.6516284942627 145.53067297684518 160.40461650647615 92.1872336738988 162.85533905029297 99.92150472339831 68.8617030946832 156.52020916185882 151.68310536836321 131.58652451163843 104.94969415664673 109.96378218500237 72.29348523993241 131.29652801312898 163.15333235891242
13 28947368.42105263 122.41626327916195 133.84884420194123 207.31056414152448 198.09824790452657 170.06713194596142 127.26082776722154 91.81295121343513 145.97237960915817 167.87781328904 145.58369874954224 188.92073912369577 133.8795719774146 169.23453162845811 96.16378713908948 173.42941249044318 100.4667820930481 90.6223213672638 174.71190690994263 161.78474742487856 135.2476440479881 96.78860313013979 130.6538378564935 82.91003312562641 111.33236460936696 175.15652127014963
14 31578947.368421055 145.70292944657174 154.49581999527786 196.8035216080515 206.22886898643094 152.96537298905224 146.67974883631658 101.19485046989043 156.73033664101052 177.02410768207747 169.2260831531726 198.04608967429715 127.78581794939554 184.50897548073218 109.48155041744835 167.64149655793844 103.55727562151453 91.79166778765226 178.19568603917173 160.45962825574372 133.88398933410645 125.93390976755246 136.4324505454616 79.36228762174906 120.42866807234914 168.53483611659
15 34210526.315789476 145.13476906324686 181.0156959985432 196.96632676375538 219.36357698942484 174.92123664052866 160.18036340412343 116.44782897045737 184.47489683251632 155.5202418628492 204.00147480713696 200.63506276983964 191.83462117847643 192.65076958505733 110.6756746392501 180.92265563262137 96.38060310012419 96.83216679723641 186.28922005703572 169.99148961117396 146.65858916232463 151.2074738050762 164.81994503422789 69.92559983855799 127.15519405666153 166.59142622194793
16 36842105.2631579 153.25818342911572 177.61119591562368 185.54612691778885 205.48416830364025 194.97514383416427 169.0116389927111 112.93625131406283 191.1707026331048 169.76137090984145 218.34308072140342 211.42340118006658 190.43515556736995 194.09800233339007 97.26928690860143 184.24711483403257 115.22883121590864 109.81641312649376 172.25729094053568 183.7776959067897 157.71640115035208 151.01735260612085 169.25614894063847 77.43704221123146 146.09945086428993 170.15413394727207
17 39473684.21052632 174.00993527864154 173.4664195462277 190.27979253467763 187.4821865182174 207.23032710426733 168.04096028679297 108.28894090652463 188.1237645149231 181.1585824615077 208.1002385992753 223.78642079704684 196.18918883173092 187.94592272607903 86.08651335615863 195.87506048302902 123.7816006384398 114.92910612256905 177.02735617286282 194.24528091832212 171.77286777998273 152.0886357959948 155.6707747108058 103.52223518020229 148.2211524812799 185.68032312393188
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157894736.84210527,319.4371367487385,438.8960359651296,335.93308903248027,335.33164424166455,377.79123810354696,421.27432754767904,388.8802927061296,407.54358048600835,360.80726494650435,305.40035057439366,341.5672449482775,414.31668923394835,412.78808228741724,379.2012600539628,375.4074236975978,410.36587960931405,436.19841861345105,450.76744908721827,350.559084634454,285.4714257022846,217.08753348808534,417.39305680106884,324.2628801504661,394.5788551277566,354.9956076909631,10.619728304296114,334.2232698433287,430.5284344669525,337.3103654057695,369.5456475475983,412.953185415334,380.24785154901053,434.92694193950325,326.12409786454856,406.38966707872885,414.9345823381086,382.84838017581905,291.42020477408187,345.0068082401627,402.705297378044,354.4140480656043,338.21994598948726,447.5115759876296,305.68947555384807,379.82456534704676,371.5780525730092,430.40356882160063,414.55645047949616,323.8916691483883,407.7883412755428
168421052.63157895,359.9550312826839,356.08956733502833,387.15063165495604,314.36751110467884,423.2236417561687,335.90961637391274,369.4368377418729,353.9260972662315,408.7101379312637,310.6273126892766,421.4139342572221,362.9750264173069,441.14840749492276,369.1346163564772,368.1828386565655,403.6807277143167,372.8448023716828,425.7752558399105,417.2959520625276,308.55465713432295,347.0596264775771,391.7235765760955,351.8399038711083,327.7099130543315,342.1851323714217,10.851874733730696,331.604548842623,437.52680651699075,347.54702171262284,428.9528711231792,476.58806410918936,354.2465774240256,431.91340778541036,406.8365396951375,314.2840775888712,432.46192768339967,399.6192189134719,323.48628729268125,400.52607633268406,345.84652253069044,402.5480046945926,338.3828897185603,414.76752688812087,427.88150703874,367.0536686667445,345.73365704702866,350.4733094746386,349.17639883997697,378.95735212046026,453.15244681022835
178947368.42105263,424.1862716408978,429.5524229884478,430.3123633185417,390.67559176031244,453.1678893142625,358.8468738827349,425.82012368156643,360.54822518175,424.43842392615005,312.8583559502855,455.43650840705783,416.2684081839888,344.4092289948232,400.416601183672,420.6666319183696,443.16356836643246,412.2710924451536,330.1673371512804,436.6210455428035,291.73771567432175,338.29016915582883,411.74352206401215,392.2218581018686,449.42959771187685,341.7862329938735,8.032284210549559,401.14537573182685,387.03339982676704,403.91989352779046,433.5477445312154,418.250723131971,369.31728773277223,398.2252201601409,424.3135207842757,438.15765449545063,429.67754491494964,393.81013845068264,375.688338032885,437.01060984900784,355.7741284737792,298.3854456870014,313.70276352655856,389.4333854320967,450.6199733239297,467.6602152320982,394.4946728019338,421.4124408141398,479.807273483425,379.86767738496167,443.0825177725002
189473684.21052632,359.3258810434645,432.6553371269617,435.3871922674602,398.98991420592625,460.6816918128415,470.9855809632761,404.2624583510151,325.3524176059007,261.3128609076101,431.16090246614,458.3621986724663,470.5636248974919,412.2272390866874,448.3094219941842,470.9078854649351,438.91100251542565,458.0437994643922,471.1209647756204,380.87846808469857,308.2953936943057,369.45044155596366,369.60889945961435,310.60073033726445,442.6246018825806,432.8135956378855,8.83426236120824,443.8104823538801,430.6483456809435,397.1606999028092,426.6657524432502,341.84687051614566,381.31631883112016,378.68289827243774,455.13216278906344,385.9636085672392,455.7124659457035,366.83695224299,394.1719890448195,456.90076180689886,459.6371409292036,411.5598555766975,393.2819310040355,364.16218982492455,444.16721364632866,470.61743459807207,390.71233736907345,450.98516168736353,468.0763415600124,413.6251806238682,415.5071907162336
200000000.0,332.2180620714238,394.53579566666957,449.4133102486008,427.2775546233905,326.10394409612604,485.5193360573367,422.4752121457928,449.85337178801234,395.59909669976486,410.41199009355745,400.621340826938,469.92181377975567,418.13865042673916,454.0215923990074,441.5672948391814,359.02545880016527,363.5961473756715,474.97294805081265,461.20647636997074,278.60043747644676,328.6688987989175,418.5614862598871,395.1100215221706,373.59512803899617,413.9753353187912,6.649205576481395,428.64490203637826,473.9824835893355,365.0857575959281,386.9181992615524,463.28309116551753,354.24556859072885,445.01417607539577,446.487778963227,391.882612062128,384.9880537296596,424.6376469511735,392.9517190189738,444.9073190124411,446.20645395391864,354.5054558641032,425.5205393637481,389.0466575355906,463.7441430750646,440.292606507477,422.71178463101387,390.3505477920959,443.23616884256666,398.3211184802808,395.9731214140591
1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20 trial_21 trial_22 trial_23 trial_24 trial_25 trial_26 trial_27 trial_28 trial_29 trial_30 trial_31 trial_32 trial_33 trial_34 trial_35 trial_36 trial_37 trial_38 trial_39 trial_40 trial_41 trial_42 trial_43 trial_44 trial_45 trial_46 trial_47 trial_48 trial_49
2 0.0 13.131850242614746 19.088336944580078 18.534748077392578 9.736234664916992 26.78424072265625 14.534576416015625 14.604934692382812 30.73688316345215 30.384143829345703 13.160032272338867 16.67830467224121 32.946624755859375 16.287212371826172 11.276420593261719 20.979473114013672 31.550506591796875 10.902191162109375 25.663440704345703 12.663228988647461 20.764907836914062 15.645150184631348 9.958779335021973 16.15315818786621 13.715818405151367 21.309791564941406 17.166309356689453 24.48415756225586 31.02811622619629 21.977977752685547 15.927885055541992 10.854205131530762 43.514427185058594 36.47843933105469 18.705127716064453 9.01789665222168 14.974609375 28.061336517333984 14.599555015563965 29.38121795654297 16.62999725341797 28.061494827270508 23.176982879638672 18.30661392211914 21.846527099609375 31.955196380615234 5.222922325134277 24.149133682250977 14.076574325561523 4.547811508178711 12.979728698730469
3 10526315.789473685 14.578516896496788 21.27217122720467 20.773169099861484 11.257422922499003 28.163551497802015 16.108522453425334 16.305835927426404 31.914930359112134 31.654923331921204 14.13211430079843 16.807565564310327 34.1331594031913 17.809194357606515 12.24502856024332 21.403429960971312 32.16119472987929 11.984503532494122 26.32972139672188 13.772950235387915 22.997165271697614 16.157506279041087 10.109449690636092 17.32452764079862 15.751903628300969 24.12469719399871 16.5026787961214 26.012534148588653 31.82195441520301 23.63026851614798 17.90123860484861 12.514019008542714 44.73422487329826 38.433206619008594 20.170953891459348 9.993477400836028 16.077604318723868 29.58831166886722 15.352139616774659 31.53048250469227 17.583394926577974 29.377068005971754 24.721233597329697 19.636690188116727 24.486644240379995 34.68676498308365 6.277898443292651 25.389025488300792 15.99386529158543 5.199360155281186 14.043891634059415
4 21052631.57894737 41.9699082075724 60.350450819982555 56.61529349665727 38.22343111665626 49.91949587340088 44.55280600962877 44.23908254229708 54.835552537375214 53.801255558563234 31.40268119545318 21.69965727408507 56.909939696068086 45.43346053659091 31.12955591002082 31.30991787213698 45.604040135306995 31.727594151453133 40.37715117086417 34.95416063912357 63.39542901804903 27.402238714036603 14.382858662409426 38.32895942775331 56.13486680842503 73.60611767398188 5.658291847615341 50.882046328522165 47.28833870546392 52.344143393256 51.342227033135636 41.6641316787234 64.9429931675298 75.4204476021251 46.08789759267565 31.102428219582983 38.78266359739769 56.30345803088511 30.133151580133266 69.80889788439234 34.4516262237674 53.719430947526675 54.61095216531833 41.507692631715884 68.94802934005651 80.59594458799778 25.674573244480545 50.033174255341706 52.402261338034165 19.086892241988735 33.04253505725527
5 31578947.368421055 71.82923842570294 89.20940393795598 51.86431584007771 53.814702484065315 49.7774284479629 66.03723991206148 55.40710610526918 83.80683302745182 67.82404819045247 46.04743041713153 51.355510519874244 88.07472382372355 65.4418163264578 58.76778662556634 62.40782748641566 75.9722700920214 49.72562147342598 74.92825485667902 62.36576134101631 92.06652362562119 53.2729889456998 39.39577382732793 55.57664816308551 106.88883059851598 101.97433286661753 6.791727328639467 50.71064958073344 79.33624879409074 65.38555961405638 68.41926057046473 61.29456652914513 71.38773377045702 112.8603146817752 62.09150616413917 75.47236712142785 71.8000953380132 71.04090361107255 49.3084470618444 93.13644092860233 47.45984061021059 81.9267141872661 89.51191180896974 45.86237815521927 82.18942804762533 87.71783483899367 43.57849113421304 90.9641745901174 88.39200949594586 50.5276216131292 47.68582182062837
6 42105263.15789474 102.5467359871085 139.96036380843114 84.70142667164762 71.85725436332814 100.21967437582664 97.97964815849083 132.59601531183952 107.53529505188115 108.07909900032583 83.49446996815317 94.61736524187627 128.3878988167916 82.7371334286608 93.14794400160993 103.8310020354646 112.06424977079324 89.71856673082488 127.82209061395758 85.05144835137594 109.76285609776293 81.2382294116258 98.9263033129667 79.95390604556103 113.77420615778405 150.723114723479 5.329706375494888 78.32454566603883 156.57926234759782 93.74829114284212 129.1020234189205 107.35965868838937 108.43264617236368 127.01024321547176 94.02454384517472 105.26959627008173 81.21135687943641 97.52814887682817 60.013150132635296 123.49805149196588 82.51805546417461 128.46684939948807 104.98790308494648 88.01630801771486 135.03749597122135 108.96623901217929 65.43625644868926 143.03488636132423 121.14057619584896 86.40538589784313 84.16920916459567
7 52631578.94736842 144.13979146908196 185.54390390105854 98.2669547105884 92.4629613315052 131.94131366485456 154.6929700062133 173.89696222490056 143.52236334624547 138.64938037747575 126.52989631653905 117.31610031694257 132.54583404933481 119.88830440726719 116.41639239524706 114.50272682162615 183.89190203549953 162.20418576380223 147.86475339579368 75.40463155439933 119.0273981627665 107.91543696585454 143.05149236911717 88.33033488051052 148.59873948945892 195.68585212896076 7.092535126448668 113.32339880446236 172.85401617308403 141.3737898319547 149.02812729375515 141.0219228257763 127.66075503962357 155.6178410835461 150.22101113361168 120.67198953189347 149.87697301156962 130.38291655509755 78.48837357414808 175.19228991828962 129.24023185977893 144.72595483101802 136.07077052173852 127.4604304423788 163.9138241316143 164.69921980249254 106.42125280686444 166.73256900518555 219.82055856060452 100.12516405369436 148.2886260774327
8 63157894.73684211 135.7850016231682 186.65099440816368 131.3567391421409 111.08136356372253 159.88894375151543 177.29128979340484 227.09807373521406 163.60770072591933 126.39248155982045 160.13549264472937 155.82748588275712 133.4752865526155 149.64404376309335 155.55924040632237 163.01035111993966 248.5377308453054 201.9842170992882 232.17162564586735 129.61881628772892 130.58126931102984 142.20630389410707 215.9150707041458 136.95182849404887 210.03073203084878 222.81034131599927 7.556761387714967 135.04575778172452 151.86440633835886 163.43747750494288 201.3468350323944 193.7429336574435 161.28514621883548 205.6992639995843 205.4439744288902 178.9154333227064 193.28771711237872 171.36529199461197 100.57917860686945 207.75617558292407 176.79813569676844 155.1181606532299 174.86386330363825 134.68320627820128 183.36056676828963 273.55055915104055 171.79813773744326 183.36939666698845 229.14018003514602 147.75354186814909 201.9667309184154
9 73684210.5263158 137.4941390458897 213.71141381697973 171.73881925444357 147.01024638058573 167.2011874746583 189.50615948368474 269.9545277954799 184.40571114317697 150.01981112195847 179.63344627045035 206.2057923066567 184.64895688075768 157.94594263039798 219.3244845986449 180.9082957308048 249.44355805461757 240.05342299472593 257.1974964406847 165.72504083127032 160.59547806747898 170.02064665615393 228.51437470634724 170.99889279183753 277.1303765950441 251.35156073489347 7.395047835505198 144.02190146446642 169.80719205852694 184.7310018231499 235.6958190701345 262.6069913634468 175.63935190488758 198.98004524987655 260.599305703039 208.86079193449416 199.70475362142204 187.74416078457875 132.40912145433995 227.03161739733412 209.68270899640225 163.7439955285134 188.33631447461173 159.8010989797 221.83098979125063 271.07631585034966 200.3558374828249 211.7923857372801 259.0435818443668 171.81979007032442 237.65909953683698
10 84210526.31578948 190.6054479266798 236.52964512793312 194.63286740264735 165.86403157341184 201.63207120578375 233.25441333296556 273.13909049839856 211.0717185121494 197.94882644807865 236.06067579274693 263.21099116333306 217.37264484051525 202.85230090875706 245.39041472967313 193.4165912770829 257.1536286276793 276.4397002848232 270.20338615221993 179.17934460223876 207.43956020532224 177.23825545654404 265.18099309169685 184.90645077089854 256.629547566258 274.482604477214 7.136222053195383 213.64018115574635 204.45596312188707 218.21476130142108 254.27167203221626 270.367992820502 184.1062668436452 237.02938870379802 281.225585975145 242.78301077470226 239.44694030780212 217.7870300767164 163.65623399821675 232.40816722153957 228.95322476793856 206.36649878566615 207.62960287012223 193.73775794466448 224.61237972628047 286.75268723429735 249.82306382266438 242.21513200730828 290.3233504810492 206.97715675599687 259.40182058831
11 94736842.10526316 218.6093478828999 260.4235771085417 239.87491197194748 202.4542374744227 207.7642742862662 268.02659345870205 290.23976702662054 251.39520895018802 230.5822905680149 259.58972346543277 264.7963478177208 245.4519365710152 245.5206414316252 271.71887550476185 230.6868558583002 269.9336736153945 327.2937162067752 286.6697595445568 199.68922275746462 259.1918790185633 191.22278106906077 291.9408217033686 204.12259862751512 279.28572648763657 299.20330514892976 8.207333623845688 274.6120527493161 220.67371542929283 192.45959641002221 284.0899253319175 305.4111643114909 184.23090640990029 282.07258640407196 307.097376135908 301.8436694941032 267.99307128654954 224.09875334625926 182.24871467553348 235.69674135880788 250.1833234303876 208.02950419956133 239.22385424152637 235.79763301340168 235.00211449462788 317.38724400313606 253.67784693527585 252.19745760214957 316.03926547915984 227.03805852526608 283.6554968045854
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147368421.0526316,370.3942853876099,341.2557415130065,384.47379720425675,395.7937452228446,253.81901774157117,398.5665183508165,380.54408885237257,432.25985739551425,402.16225101990716,289.558074584463,333.1293403476559,345.9917329052809,373.18766408300144,453.0235213899877,343.9136790307935,332.00041786059126,236.9182789447895,273.0091116958378,402.3976468655211,319.8198612436363,341.0698728407849,356.8327299688331,296.1200630909188,434.86471840863084,441.19100512774696,381.0524857095404,366.1001347113515,358.6435228746353,278.96238650914046,326.7365833193972,379.69252581460995,352.68463947072917,404.6530310683304,436.63432705105174,413.19101009375504,346.4137888773657,358.03829574122653,375.7055694201646,403.512131685035,432.76447856310665,420.7434611452584,280.8673328042361,355.20467194081004,406.01481324714973,446.8363766077483,380.79529509683067,318.95795463244343,396.39719896831684,246.33690655115905,401.98747768808266
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168421052.63157895,405.66319603801105,436.92694349104016,371.0781460376328,436.085471494046,313.6614704488718,431.83860445286757,388.7779165304929,391.15441200805833,439.57102705567166,409.0776826285259,358.70014174559117,369.72447547225744,310.683538335182,455.6376533204499,399.6960995454868,322.52053370171967,323.93608347795015,244.5564996912208,352.69593422828945,385.4130186228871,373.22122557605735,360.1646905579395,353.46507820198076,473.2671767060446,439.74098881063696,467.58912187798205,397.3972447268521,424.1238789716916,309.34182845984805,315.16203010511526,281.6992490377452,361.0641497865608,350.1424059458387,429.14449884620734,451.26876141424,379.01408825950944,316.16020478964515,432.196519804133,396.7129494107001,447.0729596119508,409.9787525509863,334.0932743093644,432.1989708210953,436.9457453545441,469.29303387591716,436.3535582444674,267.05532896749855,450.26014419407727,387.5445527554879,334.56755607081914
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200000000.0,445.8689920039553,477.52782797186,471.2671553147467,488.94760429545454,439.9456694549636,480.6451155574698,398.4015148564389,465.5332888772613,437.0121902619538,403.0043455064297,401.88093809861886,326.7413901420016,423.57061845534724,429.4419846864123,362.4472447006326,389.56077324246104,357.7941360301093,339.4551521100496,380.07093806172674,413.3284254325064,408.90006056898517,420.30478690486206,467.6191948526784,496.21221445108716,387.0091969229673,439.06786423921585,433.34362527571227,455.5856535262183,423.07452937019497,364.95605689600893,447.886041175378,406.9709141426965,455.93409534033975,464.5003368148678,374.2333729910223,484.88693250951013,441.21791495618066,412.7518442429994,439.16432979859803,399.8890632610572,450.18339968511935,397.31223195791245,450.47006618976593,453.3742038058607,457.3968785514957,441.6868673343408,350.8426554516742,392.3017089006148,438.31347545824553,407.5624998290288
1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20 trial_21 trial_22 trial_23 trial_24 trial_25 trial_26 trial_27 trial_28 trial_29 trial_30 trial_31 trial_32 trial_33 trial_34 trial_35 trial_36 trial_37 trial_38 trial_39 trial_40 trial_41 trial_42 trial_43 trial_44 trial_45 trial_46 trial_47 trial_48 trial_49
2 0.0 12.017431259155273 23.287109375 10.888079643249512 14.205253601074219 15.467559814453125 20.44513511657715 12.091629981994629 9.831884384155273 15.037577629089355 22.472427368164062 17.966447830200195 18.04360008239746 52.83140182495117 30.300392150878906 14.272525787353516 28.776683807373047 14.87478256225586 26.560134887695312 22.791263580322266 13.031448364257812 7.465834617614746 15.859904289245605 15.654475212097168 35.36785888671875 41.679527282714844 13.489083290100098 12.026243209838867 10.55536937713623 10.937093734741211 20.357519149780273 9.97134017944336 6.53872013092041 22.88406753540039 16.057342529296875 8.918428421020508 31.07950782775879 12.095285415649414 11.247681617736816 17.473600387573242 14.213282585144043 21.809486389160156 16.25005340576172 18.457508087158203 14.448582649230957 19.33466339111328 21.741180419921875 36.0016975402832 7.962129592895508 11.582380294799805 12.768638610839844
3 10526315.789473685 12.776854911937773 24.663676115284336 11.50460004508547 14.671225372474858 17.374185145685548 20.682800526965483 13.288055084003368 11.440362194656212 16.873823473567963 23.09021612365119 18.51907138163714 20.278866849122494 52.724657441233994 31.825402611520897 14.734285683709086 29.528678925609903 15.09234152549563 27.171897841261448 23.14398767460148 13.934958505942138 7.821502990352501 16.55533397105107 16.789932060112193 36.67604927920899 41.60809650355718 14.087474481321335 13.008655385302582 11.17730214223111 11.321997185972961 21.453200092023224 10.50211116821709 6.6034694361033495 24.67641698757904 16.979849585824727 10.544376255139461 33.28799029645559 13.000915446476057 11.913011274697812 18.361130300697734 16.198423144201183 23.528672465677904 18.851392397878904 18.425226634631443 15.230230421186464 19.828224328405888 21.80370530696622 37.00908387222242 8.38620989546541 12.546300841990725 13.912173933393408
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5 31578947.368421055 49.20190873289084 63.3407311417018 33.114977303696314 48.51630176246744 66.29822704721232 34.01225583028781 65.06097386341925 50.047275764748996 43.282776942099986 61.40209562979495 57.700768603533106 82.31168388243033 105.80648966121211 88.26221817525473 110.843572811221 71.62837815443649 49.18897271648545 46.72247282685996 86.72634276908688 33.328892795028494 23.67281438119277 31.959782852453294 39.07779858889798 96.04975107021198 83.06608436031686 66.41134040049405 52.577474701324086 58.82678742664467 47.34819447817772 84.11480306084798 27.042457599915217 10.702444755188463 96.48672616551953 42.9159596922325 43.724018014337965 88.44290469566211 39.80999278071805 62.12509418082866 81.39175821873786 63.63133665324909 84.58056680833369 90.41854720717487 31.23196938182963 47.711000206728066 64.42433359302643 33.52378338944797 72.37739086817756 25.263175579370973 44.26823562103998 34.745594789106356
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168421052.63157895,374.20749622831056,300.8698926645633,393.02563713660203,344.3874844910365,421.54784317227944,386.81971816409,422.2265746111355,366.76998138427734,362.695848941803,341.3760617829426,410.4994723961954,423.44265975846486,403.233764142541,274.3367646473597,432.61980298219294,285.7924808557674,336.5352416698952,382.75353345976646,359.34346648002264,331.80881489280847,422.6831429605669,285.9784820126034,425.2275680465382,365.71028386060556,381.67256126641564,363.7023679331729,296.40756576411275,348.2884794708104,262.71160837818053,352.1786316649735,418.6676336827371,348.0470139115141,296.0973640227912,377.61352123778283,400.28931817453656,334.1318756338632,400.72983025447814,348.9818155323039,326.57440268762224,408.8445852800089,387.8502867281272,410.54368397403624,361.45651005906086,389.7398920138457,433.7308813052825,410.21367164992233,387.79224080458243,412.08511918007173,354.6767572260299,294.55531499656615,423.0860895542557,425.9015865008917
178947368.42105263,398.01404096074714,343.0975108570174,352.34444543983466,341.7874634552365,344.21429625739677,282.29907252947044,438.95200730748786,415.22266582224177,384.4037126287859,316.2727703955695,444.0847602010269,437.8799759261826,456.83454141136355,312.02938371863723,405.02045424146337,416.5735928360115,400.2747476744025,379.6909807688477,365.98834967109633,402.3423815390245,401.33779452134365,424.40306465158505,359.80635938188703,393.3847072848488,426.8554985335824,391.3710435760153,373.8681989105785,343.2895198200218,295.2621848998473,288.74132352192316,461.13590629064475,368.64064342188044,426.87068316637647,418.08778811112006,430.0503562543531,258.3060365077366,427.9050599097215,390.7223211107492,377.3263620782922,409.5508105064693,433.06401254760925,387.0293493639894,390.24354464632984,344.2173246845314,403.5795052540269,392.1088207283178,415.9190718847794,417.3374117802715,420.3628288448022,241.277399306152,403.91413826881353,394.01589216485905
189473684.21052632,385.2378914937418,323.18988571256153,371.40428784943686,337.7934095258528,409.0873669016064,350.0865441392333,386.67445789958634,438.3240877908353,348.0832089961731,393.9125860939396,441.1994237678533,432.8470368479428,354.38452062448306,362.3283076091486,423.22816584463595,389.48347414299394,460.3501194213566,376.732465519139,371.7489857191524,347.0449151358776,438.2062873435813,311.6641447796716,437.89386574119084,280.44927952890583,417.02974923363684,404.2108649728701,354.4117709971201,362.40806556325873,341.3597019408878,415.0093542162401,422.3552487041811,434.64257056082386,406.5943000494113,354.17875053430197,432.9376538988626,324.46613526938694,447.33863975830025,413.11104356450056,381.02392887606845,348.64680599885634,445.56152537687996,426.4302560138901,325.9977320700141,394.3317614556019,458.34285525601985,444.51259330237014,449.12709821211666,411.45975269934473,453.96155503450007,275.59770568850297,439.5296161207796,435.0594251375449
200000000.0,378.5197869319665,301.70494612737707,399.60696692372625,422.10956559526295,445.1377922955312,357.91642107304773,432.5184326407157,368.815842484173,417.42577834505784,376.1266447588017,387.5552142591853,417.07823802295485,486.6005549744556,263.66496690950896,464.6004346781655,411.08793175534197,463.1029889740442,399.80591059515353,385.4797520292433,410.11976740862195,460.4791630302605,359.92517642598403,453.4604589970488,437.12201295871483,449.5832874790618,429.516524446638,416.6843957383382,453.37773589397733,293.39611906754345,441.9698517746047,384.04286868007557,369.98577942816837,236.3446388048561,420.255173156136,461.411853818517,378.4628292855464,473.1667629103911,403.2194635993556,362.9362511697568,385.4418494277879,425.4589729607105,410.18619725421854,390.9898659649648,405.15032039974864,474.73755304907496,440.46052292930455,462.5142033633433,326.40245916812046,401.2219400923503,360.6054227493311,468.72995001548213,437.466227181648
1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20 trial_21 trial_22 trial_23 trial_24 trial_25 trial_26 trial_27 trial_28 trial_29 trial_30 trial_31 trial_32 trial_33 trial_34 trial_35 trial_36 trial_37 trial_38 trial_39 trial_40 trial_41 trial_42 trial_43 trial_44 trial_45 trial_46 trial_47 trial_48 trial_49 trial_50 trial_51
2 0.0 5.659590244293213 26.06021499633789 24.206058502197266 3.551205635070801 24.381572723388672 25.24798583984375 22.904619216918945 23.205829620361328 20.361244201660156 5.436698913574219 23.75769805908203 23.605976104736328 14.900619506835938 4.284371376037598 39.48065185546875 11.61447811126709 11.175546646118164 13.062265396118164 20.859821319580078 12.516582489013672 30.621231079101562 16.870220184326172 12.008752822875977 16.727144241333008 30.366870880126953 27.533985137939453 4.029427528381348 23.41136932373047 19.937116622924805 4.43222713470459 17.344379425048828 30.81283950805664 29.214832305908203 8.560333251953125 19.13614845275879 17.62757110595703 9.370306015014648 9.371320724487305 15.618865966796875 7.7243499755859375 19.97760009765625 12.78360366821289 9.0764799118042 14.895511627197266 13.307378768920898 16.089614868164062 3.8655829429626465 12.270563125610352 10.179352760314941 12.686513900756836 15.486466407775879 13.59727954864502
3 10526315.789473685 6.832179842082077 26.655761841632984 24.647387386978167 3.7951000110837025 24.625391447013683 26.989194710416477 23.52083598175847 23.68593773531658 21.505964871134786 6.178805253491673 24.291254072359806 24.02885478349542 15.25842534343085 5.6363645011167005 39.64680201991608 13.029074858113031 11.729220786970368 13.583531654648834 21.267860990647133 13.081201621509283 31.193171783724484 17.06456462561651 12.291960430014209 17.29320882652935 30.71530728474507 27.631295198425033 4.4305144800286005 23.872031043750592 21.072399616453 4.8248382069536815 18.455150071531534 31.757999885331973 29.120529306170187 8.690298646745218 19.795293378300574 18.47134473781589 10.036576541094238 10.714540822297295 16.085801157027152 8.390602115810001 21.141984764073776 14.268853959212096 11.663462633089038 16.354732738069963 13.993466110848448 17.041158165565985 5.519646887000589 12.77408562757983 10.878759518975182 12.874184006110474 16.49670249324581 15.477476564457852
4 21052631.57894737 28.147902433747564 37.22287948023001 33.6056732494704 8.76476968623636 31.189594262524658 57.853027596863356 35.680787060564576 33.39733524088054 41.07930637002404 20.98607490638947 35.37923510168316 31.28637695119528 23.60581588421089 29.482394350914497 43.46011415307624 36.97067757039602 22.661797813967986 23.621173048500292 30.616702312742905 23.55001003704862 43.07789826620154 21.385546275958873 19.710106381563435 27.632518249339427 38.985538164127895 29.504928318726883 11.446981073855074 31.393746199514563 43.00993741780437 14.809376867389995 39.59122657057652 51.235432717319675 30.593241051479225 13.376692822486824 33.07524504178201 34.797295711109015 22.10745354431199 33.52466998808602 26.082018015147742 20.24374039771443 41.394080985182704 39.4924360788595 56.2871973983056 41.513682820336314 31.357747317660717 33.01974145325102 32.66231393183574 23.712765755271153 22.531451086712345 16.743698832963354 34.49079740631531 50.443144228484826
5 31578947.368421055 41.92667163968334 47.081286884803035 53.31386547188929 15.734067988522618 50.92809671742475 82.65884691344735 55.39503933964014 50.652260361739806 49.82079556129275 40.99985525575454 54.66093580208079 35.508166313924704 46.11705220614527 41.22772324692014 56.816872034387 43.2228327223056 40.19663441021233 38.10794743479661 52.762171613780005 33.09947887429364 67.04472125703444 34.54369067007527 44.49081858767615 39.34411290972146 58.049930083908535 34.19552375136816 17.889195941370552 36.579066074445564 65.77434147692122 39.26487075412579 61.8704024942339 82.76812107233626 57.317669620598124 34.596338665479195 54.706077099001234 53.91412353304078 33.3593971645279 37.66723245261573 44.58308358777346 28.64237396818924 47.31604417122467 44.35868179637144 66.696906809806 53.72041435680067 89.43141169008128 44.489799806616 34.633037358083854 46.95936085364248 24.94592719816105 24.373070298593465 49.16865390767228 80.42390218921976
6 42105263.15789474 45.03420286743265 73.27525277117944 98.7415206533885 19.6023741904801 54.754309569080455 129.565376188121 78.54606731264874 81.8389400313931 77.15637892253511 44.15434618599692 68.51232993272534 50.155750891549765 67.66363900520135 50.85221590237935 88.36148197944806 62.49077229123367 71.73133739701103 64.20776773993329 65.93678008329505 43.32574237387762 102.95464571394089 64.28326158097576 67.88477996462271 67.6132686489837 54.94492945396999 57.28846560926319 42.152913433115245 66.50812302835266 76.14029259265625 30.933653839118264 76.36194617513804 92.22426402089998 83.57488780495534 47.93303664771639 74.12341055158433 72.26059684528869 52.23324800008222 46.95458285799482 58.34815755808453 43.72658182639329 49.740356901676044 50.15222640356199 66.78518838796589 85.88943360650968 140.95735328176013 119.37172471354214 65.49967622670276 62.988179742381845 40.105039974494 36.616043191578584 83.02653971157577 90.17971566170867
7 52631578.94736842 68.19982863906925 98.62902046740055 149.89563639292757 37.31145393718395 90.8538058003684 128.68682862083503 97.18668391627783 150.89161663157788 104.50409683882364 47.27786670418823 98.00339147436156 70.17052016663172 91.46424767593763 75.87357258311681 127.03667593448115 99.75405900906823 118.32361865695823 99.97577654869602 88.9501178143675 72.77759236561707 142.65313143012762 108.78447872647948 122.99013573985928 99.45447295109568 69.59848316240839 111.86518009029679 67.02958871088819 91.4430535141265 124.42946462968875 57.23680565259587 103.33874670533757 102.40711969170214 132.04876374395516 81.83370796749962 96.88298358625818 122.74303608513605 77.01863054526645 80.91640323483053 98.80274882351262 64.57210949987916 117.0932100008234 80.69520676672623 102.77821842197153 117.83863189564683 141.4332256555103 207.55719856368867 88.07973560133634 95.4651102644915 69.42282263108031 55.72770765317485 138.5041259121449 102.79626683517259
8 63157894.73684211 107.91899601388675 143.40176084695432 202.07172927747476 53.905907596040976 171.61163277994234 153.5450500102915 158.0027304757335 219.43945966054198 143.7749312539015 80.56461809305193 138.67242715736836 107.37028623312466 149.7808669954126 106.92668054329226 189.67774393692244 167.86396317840286 166.89563976133303 129.80476129983768 127.62876651095553 122.30031400762108 164.95216065835095 154.1963369258553 213.7809501466989 137.0633972818419 133.79106724489264 158.77895214328143 90.50216631364296 178.06996485698258 116.29014581247876 98.66104619972761 115.10021218579067 151.11044837489024 167.1813571567846 119.88039637140291 158.57706770986076 143.5445758474996 137.01065986015297 121.12346531413601 135.48091573101001 103.78291744695478 235.38945437592153 154.3679414960321 112.85369830011001 148.27576443858425 195.8013524470072 226.92724116546958 107.9768022773504 185.39239127847299 115.60783792883572 78.35283062774225 216.65210434654082 125.26208101093277
9 73684210.5263158 159.27213348667047 164.69235548550404 237.1428833089542 87.11527654062184 220.34895413102703 183.06053682344444 187.50815415200765 244.20376514538174 169.89169147573514 134.44562729344887 161.52370494434876 155.60801137554517 206.13444026908385 118.16709765420397 229.82704253040689 185.92471832164932 220.7179796937595 163.12295127269965 140.9532556124341 159.75447376629654 180.6877703009137 157.72269000822985 224.0692377513961 166.8458060386521 143.45255696424732 167.9714248380585 120.2691682845024 227.39046660973756 149.21119205164533 133.88103827830003 160.8760729027381 165.72361888433096 186.84776258163174 148.98402629351023 225.57498357253064 165.6156990489719 164.65016914796797 157.21168921594807 143.17523509206202 175.8885006343229 256.5494777203184 169.17628211880984 139.77598481714068 143.35689478010516 235.67630765993675 249.74661437585084 160.81853491881054 234.92553995694152 160.46660868703827 100.40524795591585 232.56014445836854 186.19126910879342
10 84210526.31578948 181.49334535110032 202.86809865226377 244.54835048276632 136.9738449730041 242.64559251581863 192.88516068260427 196.84616251533382 269.4718436574011 181.06986464027554 144.14859775294886 210.91982869857569 172.87517659584898 213.34077877813428 133.1486908771985 212.35303221779185 194.55898791997387 227.30744709301524 227.87541759905724 167.39779695513508 178.91156548146066 207.38431391161234 181.85070799757568 253.32659885229498 188.17152256450495 169.64988594454744 211.84758900308213 149.92824863925205 235.58682354731573 176.24888158108718 169.49650049638882 217.37305591179063 174.74953899786414 202.85201661738665 193.5160693376018 277.8905470549565 187.2670950717873 183.05075054287582 203.59228640481047 165.07513461416778 236.19514031456447 270.7366297529015 168.42355418403395 167.69085103124792 154.60634244842214 273.64416068478636 258.0338005814856 180.11805761058577 278.42032172541207 233.7866994251505 129.33775326915065 265.3804964094611 212.68048018497774
11 94736842.10526316 217.02513688414712 217.40887945081388 251.11152075486996 215.00448604307843 256.1565973265019 224.0008576076447 212.8130595597369 283.8795618796282 211.2892646598849 138.55405252032662 230.05362433942236 187.6279875877574 249.96236565820564 146.20013928817912 206.56550075311907 208.8869472236019 257.2059580760897 261.8355242179867 206.87350549872892 197.80102841865653 277.776471017718 197.17316929286042 268.01165100222147 203.4566460744248 225.54916045309105 218.13186058967563 199.26705589056675 238.4805408087959 175.1814991003754 189.9897630881322 239.72997726945832 182.3316647547434 243.28823338684282 219.53104953471973 311.4989064796479 184.86817445872234 219.15327002871732 263.98296699282866 209.68148471394403 233.19880699488098 307.6828768263233 197.80799960726847 162.5171639018607 178.39798249997756 276.5798949677693 280.23315778638846 196.88992108264293 272.6524273077867 251.78043104638022 164.45755950780458 283.25361567133024 230.48192281505078
12 105263157.89473684 234.10990122084473 217.3358140208054 268.8515427618641 256.3500708089806 289.30000748000316 220.46724514229805 246.1834609686833 288.6386668810884 226.11516149858028 179.30007085625155 234.0672507999346 268.1379677846491 272.1014634734045 178.48134565848721 226.5820130066033 216.65648028626006 284.4021098225731 252.4125197247455 236.43471294674515 204.11757548017184 303.5332206807969 234.57752460612815 292.4457925383074 236.94915928487302 258.0473381690371 240.2055082372351 232.65203548732558 280.9704074772111 190.91949436093302 200.74843618711276 257.47322858221975 179.76330357426752 257.6140380349021 239.513289012407 299.66237203500276 204.41949953877693 237.0964844879021 278.9093321056577 248.92210537360316 244.09034333846574 320.38562923339595 262.20589205564886 193.83135211368676 194.8333185571878 279.9745952908022 302.37976678306046 240.22126082064702 310.4425104144868 272.914372193351 208.41189419694885 319.2198248177024 226.18180656895413
13 115789473.68421052 249.18590030519914 201.9511145972892 287.2572264526029 267.4537149961635 322.91802707950166 212.04232808382062 253.9414979251633 277.4374415159556 245.63929299952414 200.66878382836848 299.10941293596227 323.05420755093445 315.3025903497871 205.4430230187247 261.71017522486625 242.5056815896173 343.54271122549045 270.9586794495252 261.1006143945076 197.63392752256254 335.2822739715556 290.29829008163176 287.67242846099293 282.4304266203804 309.06754603148164 270.7695217532134 263.9483717367094 326.35631039152514 207.29549197410944 220.54112385452783 317.8353903697303 184.20524202014767 217.4636432468231 243.75496271492042 343.43285579504726 232.37027203174011 244.5884135654841 309.7953513684035 255.47565112826402 281.1268229476303 289.6322519325153 276.7330301683035 207.6586179891782 240.92947756542392 333.9844641084486 296.96585101789054 296.62612143456107 319.80459124774484 329.46133025745934 229.17594435972023 316.6618266349189 251.2355852050299
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1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19
2 0.0 24.3169002532959 30.271114349365234 14.60433292388916 13.657001495361328 15.904391288757324 25.168766021728516 16.74152183532715 18.805774688720703 19.843246459960938 17.792728424072266 28.703142166137695 14.102890014648438 19.939960479736328 28.929645538330078 21.75873565673828 16.539203643798828 22.264387130737305 9.800703048706055 26.894725799560547 32.5867805480957
3 10526315.789473685 25.762511829450894 32.70700162324095 15.36123117126287 14.20298699588822 16.977084233606146 27.206356181229086 17.98280382835902 20.616100748913194 21.258175612259606 18.936890379843042 30.64417727490232 14.807493751677697 21.088349884453326 29.458373642250525 22.333996846869464 17.71215568628379 23.927833025356616 10.598851963769325 28.481777491094416 34.02556069740133
4 21052631.57894737 52.802071999108364 75.04354749463107 30.267817541069437 25.288711316099295 38.012291869298245 64.85328723063017 42.042211070986994 52.47638418300495 46.05687695710695 40.28956040942273 65.02992827057261 27.856611354529363 42.9228491768695 41.54559324632226 35.195920338075084 36.787317652822864 52.719722148247705 26.782328497897062 57.22022142766916 60.33896303517419
5 31578947.368421055 84.52866227786545 93.41449945824546 53.97153302651529 45.28002020109889 70.69617120562499 99.69342987901865 72.42625242659508 68.00371379939803 64.11864963197603 62.46243620925994 89.8273081147316 41.82106544763634 70.481348370189 70.67493571762068 66.56983537647946 36.14575144182117 68.54771589807693 51.84800787573459 78.83731343615749 84.86028521503852
6 42105263.15789474 136.46442768068525 118.56856599243724 84.13958934849319 70.35050390516292 110.45823494136499 130.1910540372381 100.96277890145944 82.83822812697234 112.17398193189642 86.58933386214883 132.764583095289 62.33591435507064 114.69852565588053 96.91321978394015 109.08007701034362 60.729169925989545 108.36251401166507 72.40169971529137 109.2776334890038 120.25627023031177
7 52631578.94736842 191.51177546324163 137.22077021597164 106.23935222382195 87.97524075899427 124.61782275210457 150.22093490071575 156.29813172224485 111.41645518593346 140.3074722253302 115.78617410634197 142.5488815822347 89.10208167889029 173.57055290959713 139.70335072068463 164.9673718009299 105.62017759594065 137.53337764397386 112.23756559820552 160.7608490121084 142.42668136504383
8 63157894.73684211 245.1352228659342 161.29114831633188 151.03451491021386 114.68412031303485 142.5274221086436 173.06202095614907 201.11275127546608 132.21238535436237 151.62592553242092 167.03167329039272 160.90778474282692 131.00744026156343 212.27889946763537 170.4728685084968 184.39648098100255 146.1250135044147 166.03865516903988 167.42173638188612 178.72940225771262 151.3985947890625
9 73684210.5263158 249.27998496492978 197.6212415887956 193.27252344361963 154.02377205500974 154.01569777826194 187.11299054287477 219.33901325359406 147.0810632117485 176.47623613344666 205.58722066045468 190.6559267956712 166.33897041415906 236.29937467821088 194.84835322436535 206.21267260978428 203.2651285276106 177.8257181515654 236.9242750494599 203.80678897654417 168.88351923441954
10 84210526.31578948 250.05047207426827 210.2934632373979 213.88962149289836 180.53644787010396 177.26351460294381 207.80069080746406 276.4014260207517 200.0965092172253 188.13320777951185 211.06099299942028 201.7714645083261 223.98842413636785 238.30537913182434 223.48484866506837 237.02326212034993 222.3086790936145 193.48866763801786 264.0820230691387 226.79453508213288 172.07964834744251
11 94736842.10526316 294.5232759923816 223.19554733751224 235.73416188788548 213.279825863787 189.82826234396146 246.07355888324102 297.954089518234 214.21506824222627 198.96135158915268 208.75851002686406 206.32593528183378 230.2881534641552 240.64756978346534 241.2582411316128 241.21360000629505 238.9790445958313 211.31644999138868 300.5051646675925 252.83925076551384 176.75785493268697
12 105263157.89473684 312.4253567648727 238.1863949382239 251.5679695626045 241.14316543235012 223.94594137275647 303.7945728098917 332.209810426856 233.15935256581886 203.5995933150981 226.25263951648634 212.51013239400868 243.95576424611903 279.6204641749489 247.2354274813158 240.10190256480695 256.00152441380425 247.13229266560307 300.38466452016723 252.686404169679 187.82689217228307
13 115789473.68421052 324.32314211856624 237.47856798784554 258.63967081153163 257.984210342499 266.8685342215022 340.9500689688152 351.23310166845033 248.54146900318997 211.9989426432389 224.41028554192707 238.99214235393953 281.8342053910867 345.6648225276589 244.35925231700625 273.7139865590925 253.95985308863285 265.05688116474494 311.2039019866663 284.98313567029965 214.07060069382356
14 126315789.47368422 328.4579964219038 265.98104875734975 243.26051586998463 256.57419957199915 244.8864680743283 318.77284372810504 394.7993501223356 261.81227400956726 278.32483848772563 292.56170795465783 240.0545474553372 290.1369752414999 386.78039891369787 311.5420004150875 278.0904132616487 328.6489255517475 295.55978971009773 345.9444580137565 268.62290552349293 258.3312623302693
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17 157894736.84210527 404.4930629034287 292.4332255012771 288.68266117250823 308.6885727366582 286.4357508496069 383.74028185175064 380.6973844009588 318.5002830120996 278.03917474652593 317.5929606722002 344.69870302832356 295.88010700851925 375.0334378563466 351.6014518791454 381.85084546875424 315.02968522658637 272.46775056103917 428.92158800635974 405.14476261558303 302.25783008427834
18 168421052.63157895 374.8085286808806 355.71886519117703 309.6698876100894 287.3859699188507 307.9483720113696 392.82563340829023 439.3696628633959 381.80300312095073 307.7508173385155 337.42833154287365 338.2521870658008 313.3624106510194 453.6570545312771 347.35719539584215 357.43786984863704 359.55321236792696 367.05916958436416 369.01141390443837 379.42239585939865 301.02159678440677
19 178947368.42105263 460.9219853769049 332.91101660160473 328.08016123178925 334.6597258260376 306.66642621894295 396.5225643712067 412.2956154452136 395.0246918517632 371.71390475130477 396.97516485173617 359.83094309480896 393.2392986393702 432.46183522396467 373.2472983816654 418.69614904384207 391.24885557430935 359.5810155994014 374.80882815921734 417.0380227778757 348.08028226843174
20 189473684.21052632 445.403046762514 369.06941627366393 325.17104752027427 389.51752933570884 359.73629539428987 442.19938579870393 348.85825205658284 388.412877708756 385.20297224353226 301.5269393285226 433.8218935376389 395.19299865297336 401.06453073916344 426.29952765369677 405.1504339382589 426.04661484025524 398.5646058910441 441.7296423570271 345.92167439503686 388.9061690963536
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1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20
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1 steps trial_0 trial_1 trial_2
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3 10526315.789473685 16.102586151376737 40.78576780318017 20.700928504932207
4 21052631.57894737 20.984169122213473 37.24624818101154 28.7622204513142
5 31578947.368421055 25.82256714434175 38.424179403952365 42.341857699176856
6 42105263.15789474 39.48025258162015 40.716315923841705 40.002442529079325
7 52631578.94736842 43.98444773285673 52.99415687117674 45.703030203930886
8 63157894.73684211 39.27736930485164 55.82250727950453 49.03863238927153
9 73684210.5263158 31.23113632902833 46.201162365520595 48.75332018531797
10 84210526.31578948 31.826514436349974 51.90484813293262 47.91930922213684
11 94736842.10526316 32.53973341677493 55.130621864824164 50.7900108620318
12 105263157.89473684 41.36943751460049 53.401270436117855 48.44223592207455
13 115789473.68421052 44.714684227558884 60.012540589130566 60.92519295511772
14 126315789.47368422 42.98434026097657 59.22982636841215 61.84121357259492
15 136842105.2631579 62.99426908009892 56.587936767580764 66.59265598977744
16 147368421.0526316 77.92241949874939 61.252681688609385 90.14325877082977
17 157894736.84210527 70.37777244506037 77.21775193396864 78.70447894526319
18 168421052.63157895 74.66005499673352 77.70293356441064 72.44301822938417
19 178947368.42105263 71.79797424576206 105.96007828187416 88.03305291743573
20 189473684.21052632 67.53728627341276 144.68886711541305 78.867013961861
21 200000000.0 107.00897326241983 185.26694365394744 75.47260350067364

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1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13
2 0.0 34.07563018798828 27.39107894897461 32.80567169189453 11.473906517028809 32.6915283203125 41.52360534667969 10.221007347106934 26.018232345581055 31.15937042236328 48.56639099121094 38.697105407714844 37.666847229003906 35.27167510986328 15.40784740447998
3 10526315.789473685 34.693340425057094 28.466272316099122 33.767087112193785 12.005439707666243 33.91737214306632 42.32214588046569 10.915249518949508 27.72251344163105 32.51209914389162 49.26564487689007 39.760808047743055 38.449470154290964 36.636273307111786 16.540240736355763
4 21052631.57894737 46.605396069317976 47.38682833124066 53.10789091414527 21.82512508974594 57.11047710593883 57.38776610069328 25.719181836992917 56.66012974326961 56.70195945948775 60.52967690337976 59.367012935951145 52.29420167548257 62.194769111407766 39.843515834154516
5 31578947.368421055 61.968588091887106 58.24731394931303 85.26092298027552 31.33459617987977 81.91333190423961 77.7057583341143 51.54766722090563 66.77549569180799 72.17442518026876 60.328853091467536 75.74856087581934 64.19739945540385 88.35469828818479 75.29088707734674
6 42105263.15789474 74.66357869405165 75.67919393754732 113.25921304214364 45.147771838711904 102.20273710147497 108.11046912531444 59.752879019919526 96.7805045069585 87.43265620195965 78.97479865788753 88.9880455654744 96.83215563746371 118.5438042279756 75.7881770619395
7 52631578.94736842 84.38171850854835 95.46336910881907 122.19150933140368 68.83146035619637 125.15598079184498 121.37136074962544 85.46424122311566 110.78881949954086 106.9781938457134 102.29312318148622 118.2612948984403 127.04891613806879 165.90072834355513 80.1240680132505
8 63157894.73684211 123.67189274468252 128.1529060870079 156.09194638111586 97.64308609146822 147.72156348370453 170.9338825688468 99.98624851077878 120.44933217999183 117.98263260495133 128.94726856639016 172.74328770242906 162.9343608088606 180.4248389148481 132.76766757320337
9 73684210.5263158 189.44089225260672 174.60681953382294 166.6089508168585 123.16339941591107 204.33567395748526 203.2163374052071 117.81474217694057 131.1928168328639 123.96500625182719 172.14135926850452 237.1300986244903 192.18679065172694 182.64418950817262 191.21565810836586
10 84210526.31578948 253.90335122733237 209.84569630761555 182.1127264123214 155.9007204186553 223.43832868915516 232.48352513551052 151.67509922624626 159.19444194923148 148.44663414697567 188.46213115516463 244.5940771317548 207.41653629022952 174.54944984569443 230.48675230830662
11 94736842.10526316 282.23801198502656 240.32092558165337 215.28548624426375 222.94720855850593 223.134930211091 248.48728750918545 168.44175812073692 191.83701406423404 153.52879191658502 245.16496599331458 257.64387554974604 234.5667038270146 217.1242185006759 238.60946873036778
12 105263157.89473684 305.2189948101453 260.2947119100437 220.2285285872766 264.80692383688245 272.08870855237967 277.20314323959917 175.79611189601493 233.0521011908959 197.3219953489766 299.6245480924432 260.8581662620534 274.84370013006503 291.4581044337756 238.92622016250593
13 115789473.68421052 306.8129309732828 273.96435129427846 219.93118351400724 298.0797184146837 298.53007116690895 310.30800368003236 234.46898241010894 269.80816667025437 235.87325119922696 296.2212512142275 331.9783073717372 290.51499383807845 302.25550691275714 252.14250298376888
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15 136842105.2631579 339.4164805219114 311.8416078567835 343.17631575234054 338.82721692043 319.2855823922521 340.98611734473144 273.45342522248666 315.33359135369517 311.196819595683 383.29897767140267 295.34617374172825 338.84044231767473 246.53617612712094 270.37147120673245
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19 178947368.42105263 425.58226314385183 359.20615979121004 467.4081493313128 370.8203348896345 437.96621125812675 375.5092861071188 332.4503836569859 343.17310706548744 319.7443415611735 387.809891144242 424.17714543165926 367.9691014586228 372.8765975498592 311.2588231146666
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168421052.63157895,291.8934986716823,292.8032875404464,303.6196940453759,310.7215798026637,338.8408755542829,338.22096556507654,377.3762954516424,363.7390118305703,388.64554795664105,420.05065055963405,378.4726949213615,207.1002508576887,192.2559747293055,362.39914556487446,393.45044374862204,377.83641522214685,370.9075768396795,448.9780755109074,272.7927068779013,286.2883612904852,385.07544864776065,294.31664315221053,341.0183441467233,360.32159218167334,350.3668509203311,307.06587868185915,422.5287315997391,238.88580998819614,402.5153885759475,262.52917306905306,414.1949773812228,278.41245042716366,284.3255839545971,355.59817077974867,319.1476166202091,378.6395647796568,283.31147490710106,411.21407767478115,319.01904493223606,309.0330916705885,245.08074630066295,353.4125390845323,337.34525808535125,355.4833657946283,331.7615326197194,258.2921636117793,250.11618260003192,265.5470217007349,396.1393336377976,280.4855040473621,335.74812761238076,312.44806572076686,318.4781535721882,330.91542130097787,275.1197319413817,176.67198796021313,349.0430592275393,383.1076037177089,284.15803462844804,350.77298175595143
178947368.42105263,323.4867910341543,306.59477210053115,338.9742059683701,272.44762310014204,349.6202698180715,356.21242533438425,415.3843328445077,406.45503196706403,363.5525320651128,368.83238811341016,322.88656639103414,210.61926726819405,195.73444180021326,393.5083012118564,353.9615836264024,354.97095883817224,420.2413749036036,402.9848650800389,278.0039345709571,266.9015686836434,405.04649478519065,278.25217117133894,363.5661960510006,299.80019076601945,366.57334774542716,399.6004834398009,315.69167166857505,367.6714489875243,363.48987470785994,266.5817015587953,450.8775974322224,296.9991092657944,344.28410071522575,365.41132432461774,332.17150423071064,341.8766899444885,281.2321838731581,384.17475245880615,253.21313249643816,361.2629809699891,367.6414440762964,363.0169169056614,308.1073904992636,356.2537413179214,326.57385522655505,254.51422596563924,280.81164139855935,293.0028404293794,428.4441351449721,239.6546129898021,311.5046668029558,326.63328962271567,282.41087649659437,367.72824119555656,271.8521433210109,206.54136326640761,333.58757517542534,422.88554984826465,284.63246393500935,331.5176258027719
189473684.21052632,291.1987604441075,392.81539487475504,303.93205805663587,314.49674255233725,370.4853718543317,358.1279445888263,370.9162837828295,408.34209462199516,376.9015187413078,421.59953840039776,401.91046565655523,229.21167370074343,215.54053490074386,384.1058138057466,407.30039984912423,448.3455321224112,373.25967925357685,357.59249067256985,291.3433544710072,328.6641294546735,394.9899036950352,273.3378584819157,385.9936726593575,319.5205416507668,326.6827584921158,385.2930974958676,335.6819358636468,362.249475315337,435.5602965889875,245.25459116218494,410.8941179183712,348.55669626403716,384.0513943154726,385.2983011131141,297.47666549534017,423.8761345331358,244.62352379116325,447.90094579454933,306.7216131251274,286.28587409928235,377.71188819028663,425.4318806633064,357.0208544665096,424.4997699016349,343.72069834523586,275.1054221634389,223.85850632116404,360.19619662593277,452.4859390943995,300.5850230996959,331.72917448351586,325.9052586149311,306.93792577496527,352.26298673199153,313.6327243098922,180.516361028699,378.100378198802,377.6579695760048,298.44257219990203,367.06861152708365
200000000.0,323.80988609477095,410.82074248947595,338.916478557022,342.94881952122637,366.69170150788204,377.3954415462519,355.05356556490847,451.865214932906,408.574218640202,425.3116951286793,352.9965223356297,279.53458236863736,198.7256152974932,438.31003459817487,481.4843272660908,369.4874466045907,425.41700550756957,441.6266595438907,282.14364730841237,295.30975777381343,368.03513252578284,406.2630075451575,334.8723376722712,336.7419066240913,414.0972129012409,410.93163867843776,434.83542439341545,328.48616526628797,431.39962866118077,281.5225012929816,424.4315608786909,320.1624299036829,371.7119784135568,407.4015055690941,345.5004364236405,419.4131177130498,225.1177396366471,445.5111840022238,337.37999242544174,309.45874505293995,389.9827517616121,383.01435690804533,375.1896372296308,409.1512322927776,348.62199642626865,280.99005907146557,273.87161913043576,364.73685055971146,427.10471819576463,351.24566193160257,387.2563348522312,326.1249270596002,335.38179971983556,355.090489161642,341.9574250124003,187.0701408150949,331.78061578618855,444.7386715020004,318.50800225138664,380.48608528940304
1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20 trial_21 trial_22 trial_23 trial_24 trial_25 trial_26 trial_27 trial_28 trial_29 trial_30 trial_31 trial_32 trial_33 trial_34 trial_35 trial_36 trial_37 trial_38 trial_39 trial_40 trial_41 trial_42 trial_43 trial_44 trial_45 trial_46 trial_47 trial_48 trial_49 trial_50 trial_51 trial_52 trial_53 trial_54 trial_55 trial_56 trial_57 trial_58 trial_59
2 0.0 11.785539627075195 20.944839477539062 23.589067459106445 4.790501117706299 22.078189849853516 12.267173767089844 14.26957893371582 21.009227752685547 19.944807052612305 18.501026153564453 25.534420013427734 7.656429290771484 11.978395462036133 30.33766746520996 21.306434631347656 19.665122985839844 14.038528442382812 23.657506942749023 23.632793426513672 10.11609935760498 12.907320022583008 23.30079460144043 41.12226104736328 11.626574516296387 15.905196189880371 7.155399799346924 20.783321380615234 15.256168365478516 14.738500595092773 12.945549011230469 22.072715759277344 18.5211181640625 17.723697662353516 20.409257888793945 20.436363220214844 23.49307632446289 22.489397048950195 6.639081954956055 14.212964057922363 9.581293106079102 10.174055099487305 33.60285949707031 29.099143981933594 23.81216812133789 20.28188705444336 3.913780450820923 7.905327796936035 5.953383445739746 19.593669891357422 18.583890914916992 11.005389213562012 8.893831253051758 7.85148811340332 34.27123260498047 18.74211311340332 2.6329994201660156 16.824853897094727 12.390493392944336 14.423970222473145 11.830799102783203
3 10526315.789473685 12.521245742531447 22.256282868632567 24.55918144395993 5.219488091394047 22.75625219845169 13.046124171811334 15.63517742965711 21.76460932920638 20.91708797276784 19.44213320676062 26.659236155708328 8.161998571069535 11.932931026639906 30.80523804897685 22.326499849258617 20.497244311377944 14.615842791815957 23.89519117160125 24.992365579773516 10.1887474426267 13.24259702148757 24.313732488380122 41.98179503458029 12.7265004822004 16.209588141985485 7.572079551724816 21.81090338517837 16.833174458160542 15.520192655329684 14.400838793583029 23.092565321918176 19.737784632953748 19.30846388389323 21.658559575702718 20.937224207368583 25.03969297730403 22.628890859293353 7.072514006635819 15.42048837645676 10.056394211813766 10.732709103385167 34.123126862885385 29.98765126550751 25.267955187006425 21.884178240863488 4.624378612145674 9.476415969408183 6.272993208236807 20.70372067752018 18.8132984805233 11.570610807282423 10.485109203858844 8.054299781924511 35.11227128675357 20.14071335479968 3.0408982231341035 16.79412118251593 13.366995056616426 14.714745934430892 11.781103757573833
4 21052631.57894737 27.359905527455737 49.479318940552815 41.858806247835844 13.839042351031651 34.94364612770378 27.764799880612014 38.974657996663424 37.03851566007593 39.81399748218439 35.757845150239746 47.356898906942554 18.77251762203315 12.216029037987179 39.274909262553145 40.153752324674436 38.17362284631445 26.165192488838926 32.342252766326524 50.03848534758484 13.340847326829577 20.57834614280849 45.55574190827123 55.86350044758779 31.95929233429546 22.4659324892051 15.345003433045711 42.527423986375666 44.96653949669523 31.570928304458757 40.67427721549434 42.73474488706635 40.36491466885293 46.17703216735511 45.47381193942063 32.415705007075275 52.75080671444164 26.9227886835624 16.150873613128454 37.98825536172971 20.124975139940794 22.849271784621678 44.29268284994397 48.548042858674755 49.458809519697425 51.59208857794383 16.537196890448435 35.62109787171897 12.408426848748427 40.29429169090005 25.139777841495345 21.60870932931096 37.92850724483874 15.746648905370542 51.34906750471638 45.55639018467176 12.545405540114832 18.44907268771381 30.79988395992326 22.440436530600294 11.963267911586735
5 31578947.368421055 50.19984218562822 95.7627434473165 57.44908338787236 27.490606025702366 46.31622227355632 46.42271329362431 48.928204724776705 63.00824045449744 66.87143983536109 45.18657296955834 66.36613860713973 38.22286283433272 21.760822755684487 47.23665355575217 49.001069785753614 67.30844743241275 46.722584111394156 70.83334652181726 74.37853096312021 28.897429747997148 36.768034405469734 87.24772420106586 63.39912562013458 38.99176335574187 34.148407234183395 23.03103437141575 81.61494452539327 61.37473770072091 57.3178523594818 61.37094538101613 70.54656969803358 45.375053538561616 55.36329639108641 70.50818928267157 57.26184309821917 70.64682318784111 47.023234357040934 40.141925605751815 58.13240398075483 39.35413919562613 46.422374490710425 57.443876964883714 78.75672523852778 54.05312604729572 77.97363730860549 16.882866950478622 39.18201143632017 21.974023716095996 52.12763368309453 46.8986691621821 29.569498028224366 47.83528931583395 50.204762281514604 75.5490172869446 62.50741971310981 35.72511847835251 41.644241008009786 41.4900454131066 47.981161816680284 20.521151958208872
6 42105263.15789474 71.7205637589386 118.302632463936 101.3021050756823 41.85173461216804 75.62955314020041 77.47314474226036 80.08230674894233 94.32690992340487 97.53938523190834 74.81742938395352 92.46111631979574 49.13239003230825 31.620140676869084 63.71013470691658 68.76809601126615 70.0006458041493 78.44450518480629 93.16119912332775 108.79861944261681 30.88315011556789 60.91928814652885 125.7514024069765 114.6559663261403 45.80562259574677 53.19936465218127 30.523363000137984 144.6606092083157 74.9237344968352 77.54316764508589 87.09789742838973 107.27080620036891 56.77543164269581 87.56150563445118 82.08937283376247 68.4969939636144 87.654038446927 77.37261080023654 90.40144906768839 73.7096477901754 52.11238302661937 53.35492494999537 70.59013371743325 94.91051908378127 91.85290913015523 99.01999473720377 17.911084433816313 56.15153539684341 39.55601663288978 76.28479543113643 60.075686107547 45.84764881770532 70.11813512910932 59.67213562618002 117.8326490924299 74.94229583070715 47.04145131621335 79.2642127621372 57.320525521799475 67.37550589916944 27.81922529158995
7 52631578.94736842 109.78308910789829 129.26172621110635 143.15915463621266 70.35662907563211 109.9685235915917 102.62451407835506 114.99960360120868 126.93669588186899 128.24316364514365 112.73028668901597 135.06876942480287 54.42914115612774 43.77966931216687 107.9545935538089 121.60569097819916 105.77133458014835 102.41545599575188 136.87449794553652 146.31507720490737 36.22220644149465 101.05313528900827 142.94836430338282 120.70437212296635 83.93320925632837 92.38767512342854 42.51138626750032 185.94786720824044 103.72868996765722 130.7558528629449 105.18739593431478 124.67650402260949 74.32735683133315 119.36600999503172 117.20324663696114 117.50127174950867 114.04186146522657 114.02449641890638 127.76820277305026 121.96723127621033 61.59412244536045 61.62199675129763 102.32576925821417 150.62751116878107 154.5477755263324 140.28159557518205 36.001864991019225 62.11321556833353 49.448539615595855 120.0330300271057 81.38011535655428 68.79558897083444 113.73096821822453 88.71656178920388 151.19500614170224 114.94237780649411 61.21451652956058 108.6644107342757 97.49090110531226 106.07466130311552 47.94170696323433
8 63157894.73684211 130.09573982561065 134.49164372715595 143.8041810326464 112.35440654594484 133.75277536496563 114.61320994587983 165.90329273123493 155.9917827339384 195.1349673762381 135.91990100057834 171.5284713233442 73.74760650218029 61.678494699196165 193.3532841608465 194.2357592271471 135.63697518404172 117.92179158144215 205.42551425627727 165.26021125128395 49.21965828575091 120.97795466637021 164.03316881303311 157.47767474421835 122.64910768777382 133.74001378687797 67.7638516430008 213.72451048536317 138.0508896129366 173.3742485086013 123.12391150199971 149.00704184397438 121.37970130694544 146.97009355754403 169.96131970463037 154.77483620356324 135.1718171618652 137.94731099569236 204.70469173863327 143.14453568410676 99.241259826435 98.25607884590647 134.35030867146986 195.68202826702696 192.57857306974418 162.87413804369288 56.59804398355969 86.14122690751613 59.62274795285636 153.94289153195155 117.11878372749464 119.8802781827397 144.6688488854761 115.76022774203993 164.79035527934 117.54453968366097 88.95088400792879 144.44883853874052 116.27139919017985 160.63054338221406 70.4290694657125
9 73684210.5263158 142.05119361358996 141.2739432390129 153.58242456284754 129.3530168546534 155.0370520251362 156.3233502617008 198.3129222332358 206.60054306590987 227.26284406096818 150.54703921389216 189.54458045369205 79.4871461187332 83.15570831575387 215.0559924036017 245.31307558826794 151.79886007036532 129.05333838950318 229.52851920795737 161.55290783149218 61.09510687228881 175.4535785511838 169.4010533898491 175.45690722800688 161.86104411968236 153.39613515741277 95.343237056255 250.12611998233768 175.67181219148176 186.91283098837346 138.30727918957905 168.6634191151636 166.74818455842725 185.13076690169586 196.06328659296202 159.00106996958277 147.53227785943784 144.29380331149227 252.92380828755054 161.83021639927273 158.37642650789172 134.95020751960556 161.92485472865383 219.44614581024877 204.8939925621669 163.87479544961388 62.28339529161309 114.36035383346174 73.26770117102899 184.90799060567102 133.55651756993126 149.25193044167642 172.65737803536274 127.64791199507145 187.47890424728394 127.4667265804438 100.58226624824664 192.5378447574179 122.82138388193216 166.08783444630143 97.68133479833521
10 84210526.31578948 156.98382791852026 171.49205648370727 167.96290058541496 169.58965982195414 165.14236203686352 190.55570776706918 213.81650753067473 227.07257700461759 244.72462381154216 172.39616706166572 210.56055105525041 86.66916269460214 97.76003269343497 216.62488078542694 274.47087871863243 187.37852013342268 174.906962667806 234.72810939771648 175.35142183634053 71.09189684123544 200.36326198828849 177.65034631480802 192.88590952960408 191.87133305488862 181.823534754835 121.08353809372541 260.37844490344503 197.72782769427735 199.1000146198801 155.6172585609547 188.3333606706762 216.63439847656895 237.46044434173615 219.88954279231234 167.9451337943777 184.12010345003281 171.86817226713714 255.55514081099025 192.7677592491509 177.55450556681097 172.40522007433663 184.57939248732254 211.90057499223798 220.12632777188955 176.32980910298568 66.19763033723567 147.89932422294513 91.83561926452738 227.15824218866237 148.3560436947524 177.9017477345929 176.77912095940346 148.9836894897873 186.8724168013998 138.17522092803364 103.79728987573587 196.31196953286093 181.15175239960575 176.38314548654898 134.11560053574414
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1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9
2 0.0 17.307758331298828 37.547828674316406 27.00891876220703 17.306774139404297 21.148475646972656 27.11147689819336 12.319110870361328 12.338271141052246 9.167003631591797 23.911279678344727
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4 21052631.57894737 29.213341455008845 67.41065765318778 33.44884940292531 27.89234048440805 55.86079928016811 44.259765687308324 25.886394279134407 19.283138154461525 22.713503041167918 35.75108932222851
5 31578947.368421055 47.85005487071304 94.13677850582346 44.793857524475904 55.930509796144236 62.01391163921382 90.32462446694973 43.72811458105031 39.81319235120784 43.460683282237724 54.5183416753801
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7 52631578.94736842 93.09273944642405 139.96234875847261 92.08393842274958 120.52496370991015 166.27367624178157 129.4817153519417 129.5151534611746 61.83638626024375 78.03499792798982 84.329490289381
8 63157894.73684211 127.35687766453239 151.7497832778418 118.49689206381915 140.2242629423201 173.43377406783713 150.53439266207806 186.04898702190195 90.96116083699418 124.220185591491 134.87419924222536
9 73684210.5263158 178.63772263677168 159.28665598459193 144.99850499357547 161.67004588097745 207.0625903145346 162.01191289029458 229.92634071422086 144.09537592864598 156.24973023911923 174.31626097779525
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11 94736842.10526316 235.2771218713796 191.76186071802704 184.81355733195335 288.1168865873543 213.87271481888612 262.9539938649147 329.8786438130606 165.87362296371577 206.2428021466468 223.4308408890487
12 105263157.89473684 277.33492727986334 185.62132651802577 238.3797582576975 329.5792514057701 230.78671148031373 294.2913171176765 321.5439626822181 172.01154988855535 242.44967724543858 219.0033588662042
13 115789473.68421052 307.9460944888334 196.83660464645092 249.20223194220392 365.42608106177596 244.3459545349563 246.85476109393747 347.049113987638 246.1799794863961 298.40788930472905 257.67848279502584
14 126315789.47368422 347.809756225166 242.00587657482015 248.1962690478877 344.42295861640457 288.91935710695645 261.3101041660415 393.9906976361685 306.75502706498656 294.1474340985686 280.94859180655175
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17 157894736.84210527 391.15023676873574 299.9427468393649 362.61438464210306 430.82592337580604 334.20080076219966 325.78666906327095 397.1084731393738 343.20987882054413 347.52650701289696 355.7689700402381
18 168421052.63157895 431.4388437244701 289.24209603576446 372.89117574955947 464.0627012543401 341.34415942215855 334.354972790483 430.0620384599364 375.63122438922153 389.5687670456736 354.5264400128182
19 178947368.42105263 352.4585110446092 273.3356909482763 355.1215074213423 374.1417406955089 403.7611349403363 313.9370236661791 407.1033625446693 347.8211592581959 368.04207233007264 344.00061052608356
20 189473684.21052632 417.68170600502117 367.0253049960757 396.2376656786557 426.6167923804796 440.9451707977998 309.5667177953879 440.08899143990385 364.85273147322795 404.96625137890476 361.7230547717734
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1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20 trial_21 trial_22 trial_23
2 0.0 20.56792640686035 20.694686889648438 27.230201721191406 19.650291442871094 25.915163040161133 22.800601959228516 16.541336059570312 28.28856658935547 25.41530418395996 14.245672225952148 12.60469913482666 18.117097854614258 12.392337799072266 17.59383773803711 17.011587142944336 15.569441795349121 26.47991180419922 26.600513458251953 29.363418579101562 19.30875015258789 18.296459197998047 19.347705841064453 18.06810760498047 15.1729154586792
3 10526315.789473685 20.455478189998097 20.959935733867898 27.619092415574514 20.65590083594963 25.82039531088664 23.03290929870778 16.91543911850477 28.276127692874407 26.26887520562104 14.66263271412113 13.103804543157755 18.24747444365762 12.340303664887712 17.722366440447868 17.767642831450477 15.994366657600281 26.591578622201556 27.16763295894721 29.601874473125484 19.339223734755844 18.515797695748695 19.498976440785498 17.81188729734591 15.337385750767824
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8 63157894.73684211 37.1513207678856 60.42686261744382 51.55921792934476 56.98365892399712 45.19351288771202 48.27100860907431 38.555211217119435 46.135930781714485 51.40481214790793 43.884528475496246 26.49556779081307 42.29194941619345 33.098247912575665 38.8559821986921 41.27332652750273 35.249141859071244 47.23070071129918 50.616800725769636 47.431705986797155 32.39677495160592 51.14264327826345 54.8855280071043 31.801127468057782 33.5308085133288
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12 105263157.89473684 47.47443305546227 148.13899773293255 61.61426323503669 45.788186711370116 117.0812779000839 63.84442637530555 51.76095406758571 72.52540222982621 40.606140865513495 50.042788749689706 41.255762772361166 32.880488908026685 30.62345660875172 54.25343176747293 62.724123380190775 45.95945261963682 75.76374827482198 70.8202111878306 57.14868385408724 54.657851671000266 95.58515290366975 102.84635889158685 36.60072861950319 35.43645039277146
13 115789473.68421052 44.535915883531445 164.82720318684287 64.3932838883674 52.10600800475833 127.98372183740139 93.77632044348607 55.341098148097124 93.41681771597456 56.43406792224444 50.50122993452851 44.65405796299021 50.973083292864196 32.55388350563944 59.9133537098497 75.7428189076669 55.140545387966476 80.8822842591811 87.3021288963236 66.77246057960383 51.14197987084821 120.97803712745618 118.79421289995767 45.34466498959139 37.189526810860286
14 126315789.47368422 75.81319968418902 182.57978809507273 73.35451628280148 61.34368185389406 110.73743592669096 121.93784806512072 68.49931875436758 143.28141910580723 68.89877746904325 56.49389529678136 47.967624305110235 65.11861085866957 43.44680387049998 65.01857131244898 106.05033310975399 55.09855855411109 111.40372865005217 113.57915672412213 80.53304962141033 57.55933259431676 141.57789722241856 123.65863279531868 45.65078847651005 38.39826784338648
15 136842105.2631579 93.10308516182398 196.30341812183983 83.9718467786578 65.13426848569075 131.0771817835332 133.80897478363025 81.53090939130067 113.99729728310717 88.03930388345614 71.30945767449872 58.2717024388509 86.07419400992406 43.610368646454276 84.8982153143992 113.31184844765554 55.792270862133634 149.76182951371595 125.51064462691464 79.83867698730359 74.7188103430159 161.5680981325889 142.72949009884016 36.32292799885872 39.173593412496544
16 147368421.0526316 107.82091506250678 203.20631955559895 134.84592485811743 70.9217153331497 146.82890448023738 164.2989379612528 83.06711849260694 117.28062497632493 85.3776231844009 63.62366568352871 58.73154523524964 117.0072014481655 48.85834209449652 113.4731640345585 117.42279105239298 65.21350358325442 174.03436241899502 125.53260034231928 77.42364286699454 92.31308578074476 145.05393613292898 160.44351972817054 53.31616459334906 37.4685000033012
17 157894736.84210527 132.3860596024594 210.68172586331573 155.47957892212347 66.57274173833738 161.28191481167426 173.6719290096096 109.13726121921951 183.694379375809 103.82564183266788 73.55421182474025 66.26501727413769 131.9231748201593 52.591262064977364 167.26997951182884 143.63448359175405 55.71610990632067 212.47818753800237 128.376423681645 91.2211974010986 112.1541069736111 169.60154679516677 188.11068707960465 62.62832676220964 36.958442079207735
18 168421052.63157895 129.3990554248197 202.39567406487927 190.3892880555996 83.04692684448328 180.50324491780881 168.4348282497015 135.22031588270394 191.88012423607782 119.62647360183526 80.45935500295539 74.34429707949842 107.99215858266624 59.44362404339862 185.14248205882362 148.64435478855037 81.82859276090633 206.11789878385548 131.96695798321775 61.96289417964928 130.12336313559408 159.84511655189323 171.2107347187243 59.16434668470948 49.84168935152303
19 178947368.42105263 130.14830403929767 238.74713514947496 193.5877089175161 98.45961401438201 170.09788606904056 191.2685152322797 141.23556813127115 207.35462354486833 114.41394540696427 72.64258853296576 113.46922786556536 128.85966795290773 62.42799756514977 213.08014986884893 120.7555092415486 77.83668065770759 226.45436477000695 157.28596079853105 90.02678856231954 109.7011419024081 157.77175503283988 176.71767578606296 85.91141996712237 45.8612212943135
20 189473684.21052632 148.10580558005793 257.848876953125 209.7747942681458 112.5199505459734 186.80492281055186 203.39924788640147 180.05037021001291 193.46168203301048 91.2469565833292 94.94104739548922 138.1341755989516 141.10012071218517 51.52152940643296 195.55914593040117 166.75279750412852 93.69295750727613 241.95503717528817 138.8859730967194 128.40282541430886 150.54730322362644 163.56386923872532 208.545816238402 68.5810945502939 47.12030731725643
21 200000000.0 163.92602742424137 257.848876953125 222.84618224752577 120.7504091686324 202.18845235125013 218.98799946904182 192.41719100114545 223.38270798796103 119.5254408921066 90.19675819458146 169.40402983285878 141.0112056222401 67.9249422052189 226.41533396745982 183.46244250394795 102.75374621231305 221.57285341542018 151.18313093326594 110.10695993272881 203.97469048907882 162.42532920994256 197.72680628770277 74.30333949625492 64.3154486315815

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1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14
2 0.0 47.869720458984375 58.712181091308594 44.333343505859375 41.355712890625 37.90257263183594 34.95667266845703 45.589073181152344 24.459699630737305 35.678009033203125 16.657047271728516 27.218734741210938 32.52488708496094 36.20814895629883 26.279478073120117 39.244510650634766
3 10526315.789473685 49.29063777627625 58.76334741311225 45.03257943829134 42.02801873600962 38.448579330172734 36.199575969490155 46.56510167942483 24.837706763864883 35.28293939353769 18.001048768398423 28.850799982072246 33.40719292761753 37.014281983200945 26.961627381097866 39.94536994595772
4 21052631.57894737 73.45035568829059 60.87957780814402 58.132507757074784 53.558576345485 49.752640293864665 59.215450858723095 62.62452806441573 31.785702308139395 30.832541590045693 41.35304042323392 55.98932058159829 48.09765991704781 51.33298249183599 38.26314907021552 51.61325548838958
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6 42105263.15789474 77.20904692702017 95.6457178643866 114.61005032838547 80.43264315300041 69.67968304021868 91.29662574575879 87.2257849085364 58.16996546097904 67.96853664059223 55.81807043942058 64.16077246981314 56.73561223037025 62.73421761657723 53.19722038854192 79.3265990124515
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8 63157894.73684211 109.64508339506767 86.83300030652508 114.31641004290279 122.29602599053173 104.2039977047087 178.79898665007462 92.65466195526545 94.88769507986028 120.22093783347896 67.7084982640773 113.80443493893935 75.44789627033423 83.91133156905876 104.04209863689636 107.37283942037341
9 73684210.5263158 135.0752723853922 130.5833125542901 145.55241227348097 142.50321737555092 160.42165486539338 191.55847590018342 96.83154423621554 133.60035480794156 192.03457746194508 83.07782337032363 155.14148683301136 106.94744174913029 124.88237557628317 163.59441809046632 119.80007983174518
10 84210526.31578948 195.86231121627247 143.80465263739185 169.00912825024358 165.55034481653547 229.1272350817176 212.1457455382783 131.9723182404801 175.7012977322713 230.4742121554478 111.33295470707304 188.8701921595761 142.50506885758398 164.68399536510583 210.84611961848188 171.88463378778124
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12 105263157.89473684 279.72017166877055 178.68899161605952 221.06454092057788 182.79071971328304 273.07925085843107 232.15890297145063 220.90591024155432 258.0034095441866 267.8309465451914 147.9430823000019 190.49524683214293 221.20472686384852 217.81632852892795 272.7247296703819 179.29262215097194
13 115789473.68421052 321.0871794149486 228.37973195673518 206.03242298527272 190.8365536065478 305.66065317961977 241.17183250556195 242.6524470752296 281.70605709059083 284.8530318427449 175.53607803872086 208.67567991405477 209.90171087580705 244.65127274195902 246.61435033220005 200.41697646710514
14 126315789.47368422 367.754370141888 230.6884329021802 278.35264386992054 230.2395017351801 325.0279333152269 261.89122750290215 275.95443328331714 314.7859843256071 307.28986924572996 220.26971481414387 225.67105506859986 231.3499813609837 260.7052821270977 278.55216303393456 225.71498346262695
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1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20
2 0.0 32.4077033996582 36.155517578125 25.75421142578125 29.606937408447266 27.17302703857422 16.026126861572266 13.865445137023926 31.84101104736328 30.781850814819336 18.447200775146484 27.443321228027344 23.80484390258789 23.779891967773438 27.92617416381836 31.59305191040039 39.16869354248047 33.610191345214844 36.45005416870117 20.54007911682129 38.84449005126953 34.24555969238281
3 2631578.947368421 33.296037207277614 36.785427371096745 26.648522366880545 30.070928266142957 27.658375122354798 16.909636004397083 14.5849724026046 32.483172309241795 31.134407273356977 18.28971532364879 27.769625172369864 24.67473756232998 24.22445243704352 27.639669323871505 32.86372066523436 39.94947247461021 34.48854379632466 36.91144894359638 22.061570849171595 39.57076941414058 35.02109238286593
4 5263157.894736842 47.85268858083398 48.244665590267104 42.69550373105957 39.864313121606436 37.426982542794 33.6573874229911 27.179000907564674 43.72329865292829 38.284123305014624 15.910192525081357 36.48614875559497 40.41140686373879 32.42776290967111 24.889028077021532 53.30326504027084 53.15286421536408 50.76808675710845 44.85972475671207 46.95364156745147 51.82332628598009 48.673801405484326
5 7894736.842105264 46.289031177160645 55.042522301737456 54.09337787392067 56.42648777237724 53.144822111121094 50.22762564730694 33.501808243249016 49.271767463927205 49.36965923597443 19.09700184072422 59.83897444905089 50.45623192499673 38.46070101455762 41.67901350319427 49.6850867264819 54.63208278024007 63.855021779825314 46.707314440304636 44.729709547167836 54.444386954762436 54.15614254775759
6 10526315.789473685 52.056275916066525 54.81231460751259 74.05637095030656 63.5784007053296 66.31524625313249 60.829015134609314 41.481055804071666 58.02204051089584 54.31379683443714 27.48259941575187 52.55809385921817 51.009362222167596 39.46608662262683 51.2882578602458 57.61938410989135 53.74984419733864 66.73611811273976 45.4475195833438 51.68484967947006 61.35790378470335 53.40799793085068
7 13157894.736842105 65.33051521372349 64.54581476310449 101.39453396258922 82.1989485288756 69.99954431695951 92.37778505030761 53.489512749841836 65.90184293982477 58.01873857391756 37.75656481033547 64.60210800154387 51.54042098185156 51.49881111311409 69.99729087472045 61.28976902142786 59.26768115029729 81.32731635404178 50.51788533190033 61.01289577361124 66.07327938235656 56.682834893857176
8 15789473.684210528 62.288964994437485 74.67267434872753 117.30094707945051 85.57247418495427 70.64805491359445 99.1536963618363 76.71144264556695 70.18010282099578 77.18331596618546 46.548501034006684 66.02018492836042 62.126340740605414 68.03360012194292 73.19627934867654 79.54463746351219 77.18552978357451 99.40059083489666 64.95080359490625 85.92186557210552 73.2946830179305 74.03522284188597
9 18421052.63157895 74.93735160680689 107.81465900012412 139.2873089840207 96.71375098380769 86.87840321203927 113.47289029651239 93.44800781175867 97.10603002875715 96.94276465686075 51.13459859087733 84.31004567019167 85.57612551139911 87.22768531824332 79.04176998198281 80.70959805724033 93.1210169256394 116.47493457860234 79.01124874019474 122.10848017792293 73.69862018011696 113.93861476468165
10 21052631.57894737 97.10230527558156 93.96989148475457 96.52644659277475 116.53272218007461 113.20687297011347 174.57018046960278 153.29147939602757 141.83370591646417 106.18938247516876 56.92739289635767 88.59680833182506 98.30280876638487 116.02657619374611 102.99297806893028 95.20292315324589 94.353535294863 122.6360879416611 110.15239549921492 138.70916615166493 85.8180380409114 147.08891463263214
11 23684210.52631579 116.27735660887656 116.03497409178692 128.7576511145629 148.53811679045745 147.7007118017307 180.4411057644934 218.819252871658 178.99188914985868 144.46769188926493 102.97105440930812 107.9235355442911 124.23589051595356 148.52493570150597 141.86054870983654 114.07920847511193 115.40575793876708 159.42236704381384 135.99380406923075 180.29462874637417 116.24597945662829 188.09331493859807
12 26315789.47368421 131.7258633593113 170.21886141296898 192.91515870132275 187.39992579083034 202.23182970912833 207.65967708380268 238.20913633349198 208.33421997944734 208.33317792514686 153.72142048283297 151.02752303053467 181.4257410114987 205.62764731066048 184.45465234458612 191.9764393842121 164.1790215488616 241.4987096171465 155.8979871799741 238.7906318729604 140.21512545286123 200.8675222978037
13 28947368.42105263 158.33178354729574 202.37646896315744 227.33339871899574 216.93278682467184 211.331247086629 248.69978439911085 246.6390119787316 253.57222508443027 235.39637340138825 180.44286899309904 189.12914332953846 230.71455120359266 239.18017664613652 190.25308435701268 272.071464554755 170.13196379375592 248.429662619849 141.57710379225892 260.24952784708995 191.00687052491133 233.41085929751725
14 31578947.368421055 154.90293820891682 259.51886878713685 238.00155754465806 230.06350551450683 204.04818964120093 268.90613665128353 278.3264847906343 297.9188012779585 263.6566409047621 233.0199083050203 187.61077770929256 248.62723383299203 286.4701455133114 232.60310746163879 239.4052901964768 236.2464176310728 265.57598176194034 147.03692383069415 277.6510531974962 227.1836707213909 257.47360423760404
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17 39473684.21052632 223.78152848932882 311.36378852218144 290.2786089949661 268.27760689707674 288.8315125849934 331.56831176228144 316.60071037895466 327.69570335721045 335.2528018445355 312.5851707836598 276.15293550821553 300.10106629042417 325.54629257461704 258.3734440263619 323.2678803412703 266.3304482982429 308.70753486351293 217.55363201649232 287.675268513344 294.6170784805455 293.491367597329
18 42105263.15789474 234.71857714785102 314.98354696236817 283.7284783920753 305.4871167595037 327.815720531749 342.18832026294064 347.4369622518482 359.1234421835712 321.55971752705665 296.5348788998464 328.4429737894159 320.2516846670008 323.5348077546857 268.7956971871225 305.5235315637245 316.0435993308176 319.21332096855394 211.6789066732095 343.86831283833516 292.32147242421917 354.51419196696827
19 44736842.10526316 197.38530471809517 334.59399147756875 341.7113641431127 325.66671816942767 310.07803450322547 327.6141084031385 331.2294814979601 414.69330027823304 375.55925973110584 289.038970218636 351.0568013585836 363.8722931092961 352.0182927139413 286.6342829280943 351.55434802859776 334.9405559625817 316.564209680478 194.9518083879657 334.9490503408737 338.65567082843626 398.9040526068277
20 47368421.05263158 273.97604445753996 355.3467957329552 358.03872707494406 338.0551271167819 360.6422533754497 398.6396637395478 368.90517846666216 321.8780714666414 387.91837769185406 400.57232862760486 339.23682612345823 374.71732094908685 346.9451931840495 288.66709963832864 350.67221955265694 337.94357375557075 374.24965236342183 219.90429991178235 365.6490119190427 295.2192700559743 430.01798900672935
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1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20 trial_21 trial_22 trial_23 trial_24 trial_25 trial_26 trial_27 trial_28 trial_29 trial_30 trial_31 trial_32 trial_33 trial_34 trial_35 trial_36 trial_37 trial_38 trial_39 trial_40 trial_41 trial_42 trial_43 trial_44 trial_45 trial_46 trial_47
2 0.0 20.115737915039062 18.025856018066406 11.86644172668457 15.197259902954102 12.585914611816406 14.272492408752441 22.784841537475586 12.306120872497559 21.898910522460938 23.83329963684082 18.866573333740234 17.847206115722656 18.518878936767578 11.115408897399902 17.001426696777344 20.172229766845703 23.71015739440918 29.406579971313477 13.539291381835938 13.235689163208008 9.226959228515625 28.54927635192871 17.407058715820312 27.34342384338379 23.04488182067871 39.098270416259766 21.33762550354004 15.688055038452148 11.3455228805542 18.1380558013916 27.41034507751465 12.818075180053711 38.510257720947266 15.566980361938477 23.278188705444336 4.447911262512207 20.364103317260742 19.513654708862305 13.808625221252441 15.358587265014648 10.231523513793945 12.558725357055664 18.58182144165039 10.572517395019531 25.525001525878906 12.722334861755371 17.007261276245117 9.125801086425781
3 10526315.789473685 20.99003336489861 19.695332581450817 13.650125059936393 16.44222663773786 13.994926114285422 15.526145540980153 24.344568278676626 13.808757747776312 23.41892435648311 25.006169808192638 20.652298254020245 19.592732201477414 20.191323842450853 12.348489230661201 18.275268850275353 21.965644733428213 24.94986858646646 30.745484584374896 15.153443824417291 15.179515028537518 10.87049962257208 29.597357828340332 18.80037345636089 28.493466136512705 24.846022199297586 40.2290630431077 22.872938856859165 17.53301496731009 12.749183071619855 19.82421601453791 28.9575134141737 15.31352581225666 39.233430306842536 16.845108690968306 24.40671003022208 5.8899246726644305 21.59961258426536 21.441238509418852 14.984651757313914 16.51844825390778 11.679132875380136 14.182769498062886 20.10140677708668 12.74538051319461 27.32918151902484 14.16414267478196 18.750413315442916 10.568386891521412
4 21052631.57894737 36.50103998070691 48.59159159090711 45.24867933996827 38.93564758810971 38.96691085718098 38.30157363365232 50.733868247109605 40.54464261921076 50.08773664391272 45.59309800592486 51.92510816789235 50.117045375180545 49.58327570072584 34.28846075197997 41.19828154004264 53.50697724562438 47.01492937953518 55.01123516096468 42.70081296658087 49.515068548145884 40.79992686232702 48.41331993367451 42.85124744652381 50.58103277092578 56.10343209107167 60.647490753898 50.17434636988468 49.53187714591416 38.43725805453069 49.40967888911345 55.559622110958905 57.82486044066517 53.47086184738085 40.272871666626585 44.7027670638094 32.78702423170498 44.108258088209624 54.76228181128274 37.3025376836968 38.372731013579546 37.38045675720287 42.3322039080211 46.4966869555682 49.76637190268723 57.09628902780217 39.63602644892363 48.574570999849705 36.17749075414071
5 31578947.368421055 46.0092408909176 59.06723302288027 61.75543097333359 54.06830382067452 54.1453695506002 55.76161229071773 55.80993557464424 55.86212922269453 62.277380621550904 55.397391830093724 64.94820228066305 63.43323923434825 63.92296468014533 47.377278103031365 56.06188437200237 68.88896825408094 60.25719345096819 71.86782118096082 50.415891036638925 66.34984256197129 62.23151603073831 61.85701596101236 50.38871411986422 74.93790714135213 67.12088183792427 75.12919006255196 64.6519909787851 61.705406404691146 58.42517961904283 63.907506613932824 62.6379648724318 66.48832262732563 73.37214997660503 58.467918055250706 60.22513375056707 56.99836651269873 63.12220958281835 70.08047386622083 61.24544590806532 60.20770052682165 53.021089184172766 54.50503218504201 58.58654492207058 58.421589191992695 56.701568782174775 53.18032981471838 57.52358756825287 52.00068682149425
6 42105263.15789474 59.13485917382954 72.17071119858949 75.03923971897348 64.62930561403984 74.5333023693753 70.78636066297746 66.81600480140742 66.16120931291515 70.89693105402415 63.92526383223296 72.9717496605461 73.9231096617568 78.44358913802705 60.161263377877816 66.75150536487803 83.56791378223335 73.9409593853924 81.67364461765395 63.01517705379926 74.84088675888292 67.8074348117341 79.59179036116997 55.047547126080524 86.96195082783369 74.80049916746874 87.89306677791221 71.05857437849045 76.18306966039283 70.32247327470384 77.84671556049767 67.5417610318542 73.66021137587582 88.09372345983486 67.23367932042586 81.32396608797467 66.39543448665135 84.7797823220574 99.1923789553695 79.29654767036108 71.71791404791156 70.21733166974998 75.53018094545587 79.44781452912703 70.86087699469768 69.44502858252076 66.41357255039783 74.20543114019563 70.53072454757638
7 52631578.94736842 74.12287566691141 92.64629672880483 98.35459462101275 88.42794013766371 96.37462676194731 84.01929215036353 80.2651875079545 74.68868268136751 80.8093271000192 72.3610943320344 90.27917632181972 85.8752041417187 102.15085274796324 75.22330158195585 87.20856945148547 108.08583835836427 90.08596844217867 97.60818125385987 75.36059574764273 88.06487334977804 73.4886192490148 100.20308109401748 65.2900314744758 110.40513653584712 91.05952323318931 102.92840158103493 85.53425837933521 96.25011465700544 94.34933309777126 89.77800156518693 82.14671428522244 87.53234132480424 99.30892465901341 80.14131626309285 97.00569510594052 76.72960226142835 101.06439402280505 110.5411619077594 105.80331898488909 88.56557575759795 88.36190002539564 93.97652771625245 103.29841013285757 87.02789230644703 95.21211416321778 84.44847093526677 92.478146303022 86.37305143285656
8 63157894.73684211 92.73054026104408 115.21297844810996 116.61447448087368 119.51207331070611 117.07241269566347 103.58924159890564 89.34486535274091 85.97095979374532 95.73118289669466 84.2034599781862 104.42320336698661 97.53755253895993 132.9138573489031 96.8023282341102 119.82758588672017 132.77700927779284 101.01236790381476 114.8423849349207 107.29050684156843 108.45178906768149 95.26287550390428 112.98168701932372 88.4342502980929 127.90862654157789 106.39067165322416 115.4095493593457 101.79841552484895 111.7681924914967 138.4894709360484 111.48859915603727 100.6182267592802 104.87999526822007 117.74069062473868 94.47991004771968 112.1836414605049 89.69569966477701 121.403965453527 122.9033747895355 126.88489477856504 115.16950885906115 116.83623353447611 107.95046465057582 129.01982703078488 100.58142067397071 120.92605304412565 100.28352709824524 105.70647929257964 115.73200970867501
9 73684210.5263158 129.43767368155753 161.43375981588775 145.28661221261666 140.03078686258138 147.42051968758622 139.65465338953317 106.03460404712327 105.5526431297414 115.70200272967364 99.8605795783143 119.94506746751368 103.95190989659517 173.9106457938861 133.24997963442615 166.92250320034677 142.66956609945714 116.55016722408358 136.39818662987028 142.75602436503215 135.23853294625673 110.84562988213969 126.41170682597112 104.26585467921318 148.8353853734659 119.82041712371515 130.0881805175972 114.85789213424492 125.0251404775353 185.33347453643412 131.78167202125545 128.23394026671255 129.03586922488964 132.88233660198645 106.99317895036985 126.02903215345667 117.00723915088955 144.5281678812986 133.92475179007013 159.23491072770304 139.8584267906948 132.2037467723119 128.39707942643406 155.88648075893153 112.5340477782521 141.17353151734517 113.2994548214646 122.78248973258893 158.44374976556884
10 84210526.31578948 167.84364720791 197.72169350818254 173.0057276863801 151.83991206253665 176.96259821815173 166.11068757287023 129.32439358957586 123.10738529624041 134.20174325404076 117.60739936260636 135.4960705743602 120.89349277643616 220.5485154284665 162.94731330706472 192.5469118663809 147.56028175816311 133.76977655844675 152.95613575410977 168.39320200434022 163.15280230190615 130.81318299905746 143.23171177002862 117.75827022685239 160.66686938343946 137.35922040437399 149.51469685199189 137.7903189041608 135.27010727027778 212.40673679261988 147.95112377058436 145.02937692651457 145.20685848734055 150.42192583863425 122.89223735715544 136.64024815764122 161.56927404278204 163.52099033537993 148.13309601436362 195.5809310717596 169.01824574985665 153.59108119327936 141.8396488378583 188.92313787547505 124.75621543861823 163.1779825476068 131.64064526458856 142.79359726694483 194.8275684035716
11 94736842.10526316 210.42991110975558 198.45931177786514 187.79628941792365 171.31469841198248 194.83413372616027 180.90297067268568 144.23602922046118 142.41991722980035 144.13573494371946 137.22669442443802 153.5328669202955 148.71281150647974 238.0424058758486 182.07556616108337 211.91917187970267 150.74389963446396 149.74523880310005 162.77277383905863 192.87233389158658 182.4646193817299 147.23400476620304 147.70000912112872 142.7666377428496 169.2730219198231 147.91166343843344 157.28189860049048 165.90790930922836 150.55306552069834 213.78126109826928 160.69546859936372 161.18234937776325 163.71650310995835 161.46304166449073 139.97138275416603 144.067942897864 189.80113415812193 182.53297036939875 155.79055231826126 217.7112299536569 184.98418330749976 198.83440633312156 156.23077577608444 213.22766363496925 137.05515959631867 179.91230441778487 146.2535017409731 156.93443005884947 209.7809814709623
12 105263157.89473684 232.5801353111987 210.83904519561585 185.72850215682692 166.77719458904622 220.5477372796747 186.13173794531755 154.62417247726316 171.639151733833 156.0919977452121 152.20878486760435 166.50943799329266 164.6489291205961 230.354676880995 199.02276820026935 227.88404665041168 161.5140254497528 156.42884391166496 170.94303089933382 202.43936624355263 195.69182442396962 151.8656806564397 150.89317305026952 157.27811861170295 170.85700879161377 158.96333008690885 162.69854021972236 182.72345238635083 157.13774660477347 231.25600339724087 167.04195160210298 182.64008852591806 186.90907099141307 163.65269184962864 152.0107054392552 150.6032050322958 209.0794615457428 199.3099481070471 163.12400664203386 227.6026524288007 189.57571642402135 234.09679511701302 159.58689975259708 226.87821574942558 148.78214669962338 187.18196412986995 161.67987710476913 159.57432784424924 222.24016834684025
13 115789473.68421052 232.4767570370122 227.47387753493072 221.4324579790771 176.83288685890776 234.15810001680725 204.70220843469338 168.00981230790265 191.91092183504904 164.94040890029757 163.26578362290218 178.55722537492287 174.70932164920333 235.0951385550882 207.00482358327366 230.78202790302583 170.0275976103511 168.32032679033742 172.83196632646622 216.13220818018814 206.37882833042468 163.6619249382095 161.52165259297038 166.10232201532313 172.0077243709003 165.81229848416723 166.13864536637084 205.7490314993997 169.05401633283603 235.73331700430518 164.95262678264746 198.03975982770035 198.40192957020201 168.92522583303358 167.1581140057367 157.39720997433088 223.2544048594058 211.23558287665125 172.75166822569523 234.62923694787924 185.95312652260148 241.36291810828894 169.29496041798856 231.95262842586166 154.46332546350368 195.42994595432546 172.01909221923418 171.5661897031059 235.71806607517178
14 126315789.47368422 237.74994240986013 230.10673851649847 232.0332693685455 203.61070237843288 231.33603592922813 213.18060231572042 177.86646551240514 196.20678927759715 171.51279136133988 168.28731757600553 190.10289658899123 196.0843304899261 240.50558058178655 225.33390156582124 242.52187639326272 169.10735171620536 173.91888784256008 179.15063322878282 237.12494802904263 221.69332591021163 172.60797658422317 161.9300862458274 168.13524186396532 171.44152466015802 173.38684486121022 172.51443457966698 222.59329681482342 168.43196232365108 235.13038362773173 168.6263231489797 208.86748438148948 207.31945915367464 175.9803743030556 171.90525147161986 168.97818181290194 226.2786681936058 218.48649966980943 173.63634192662886 230.521205268243 198.45611639019526 238.67826682477775 178.15388675145496 235.43788943511956 164.73387055846135 202.34781084579114 176.35829869003507 176.69225537446727 229.37513830605636
15 136842105.2631579 233.96077022942973 233.57024914315204 236.953998254318 215.01258751741736 210.6179108208979 206.91990264829175 183.19354167671415 194.60672727813352 189.21258608877164 177.08455648349593 186.23701474376 204.11578502702085 227.1077566847329 230.73563459119308 244.78455359144058 176.12253371260834 178.5201465171295 191.41994825207792 242.48000501492513 216.2777831280743 183.38279897717558 151.465997012492 175.3276890827926 179.37439983662148 181.3717215355496 177.4659062167449 233.24426814777536 168.2825952687422 245.84654184589758 178.3651224168384 199.3093997997095 217.85347828442372 176.7597097006118 189.74696836820766 172.33770708236173 237.67759244511333 219.86177831619895 176.5656075977883 228.51614144630216 217.68078957493947 242.2092498444289 185.11801623233137 242.91128908828355 168.1520120859394 206.40260213563977 181.49276373124684 182.61431055447898 239.44464660305894
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1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20 trial_21 trial_22 trial_23 trial_24 trial_25 trial_26 trial_27 trial_28 trial_29 trial_30 trial_31 trial_32 trial_33 trial_34 trial_35 trial_36 trial_37 trial_38 trial_39
2 0.0 8.45626449584961 6.79600715637207 11.114153861999512 6.566476821899414 6.975578784942627 6.019253730773926 13.187922477722168 9.610929489135742 11.058207511901855 8.138980865478516 8.241827964782715 4.533395290374756 9.133914947509766 7.11447811126709 8.011873245239258 4.775976181030273 6.504958152770996 6.739677429199219 8.172922134399414 5.260425090789795 12.010283470153809 9.059353828430176 5.858153343200684 9.182978630065918 4.886148929595947 8.927388191223145 11.782123565673828 7.7661285400390625 4.323923587799072 6.703610420227051 5.1463422775268555 5.8211894035339355 6.207094192504883 9.287851333618164 4.452250957489014 7.079854965209961 11.736565589904785 13.737770080566406 8.21053695678711 4.320318222045898
3 10526315.789473685 10.009982198703819 7.293472492314071 11.877441951233656 7.262770368534443 8.175056939375771 6.525961906669812 15.0992217638099 11.253482130142007 12.444622852003661 10.052993200853509 9.659487795159531 4.875226873812882 10.655476437958985 7.828629460843626 8.98008916088976 5.087962464837053 7.872664695200601 7.204090728963677 10.022698724797188 5.604066545400418 13.609666500913903 9.635663715315019 6.117543101947951 10.573231855280946 5.345820382029758 9.715044028156662 13.370590102866583 9.290915342156165 4.673137092231476 7.865581077889868 6.138127724366608 6.715619771580091 6.9514799458993775 10.871857570412047 4.848607417775209 8.174443679482488 13.325478092246172 15.441990286988979 9.627932193072468 4.6575822993246145
4 21052631.57894737 38.18205327278525 19.23387150066051 27.439888810857596 21.833078328581976 30.819563517909383 17.949183065774452 48.52724730865282 40.91852479502352 38.39768967936409 44.74188149710111 36.17542252962031 11.96534862320798 38.02968546550029 23.339854307730693 28.29620426913873 12.897475992104974 33.08549053936041 16.578491293120912 42.640002246523004 12.87019920368212 42.09351143154246 22.3604550088067 12.348915678487673 36.006850027332185 15.366465796755211 25.753232260077286 42.08869685339961 36.92182561045208 13.977509982445358 30.24490268212689 25.195678819043156 24.949501106427814 22.797075661069552 38.86162909277176 13.576542959752341 29.2741754908125 41.7144245714816 45.663469470831004 35.18268819978858 12.325642516088372
5 31578947.368421055 58.013910893144455 50.67936909048099 52.318839514963436 48.60969466486962 54.174062730109846 44.707791336788866 63.013155839212466 61.40298973524381 63.01978642646213 69.40506853351056 60.11700600976965 25.726848224358548 56.3552013331111 54.772534936294996 55.98441710273563 36.384902458379976 54.828825582066486 32.82055692039327 58.67891034716096 29.794846534517465 58.0189348286704 49.43809348515073 31.231169633041052 56.670483489982644 36.94967785506533 51.05759884649243 62.64895246372948 56.07791274976904 44.89888386500592 56.481478592767864 47.505170420637754 53.405977329007065 52.64539229819278 54.378019095364955 34.875119445644266 52.9066852514743 58.851417333991826 62.362998697710665 53.04047671239049 31.59892114180649
6 42105263.15789474 67.16482135628729 66.14724005350115 65.99457742203636 65.88242422774888 68.29126735712683 64.48606450158144 74.34230360743742 73.98893932622556 74.48689122923193 82.14153906645207 66.12357135699067 40.220219802328096 69.01546774073981 71.62547107474296 69.84803427850771 53.96573019952325 69.30090123423248 52.09925923882429 69.07723416970047 56.2727919710475 65.64607713394219 64.51118986568623 52.50437225335358 70.869917626196 54.837937330192474 64.74198234696303 77.85259279897669 66.13422684326066 64.48479921327403 70.47406649861969 61.79015246921134 66.47448670236687 67.8938870813873 68.55993982167125 59.7832056796204 59.947047325547715 70.41620238756869 73.93636627548949 66.73692670167318 50.14127413821188
7 52631578.94736842 72.39728682882402 73.85714769179718 73.07820563909915 69.2525891040831 78.57301801383248 79.44638966436696 88.61256873840853 82.33217617165596 81.37845979053063 88.33625116806033 72.74142276889894 46.68622040593806 77.03961924779283 79.56834631786782 75.30002029632267 66.7609730666075 78.83269765351865 65.02206354806009 79.37277631721668 68.89787210047328 73.30938844172248 74.4511260131472 64.50051780402083 77.34975363889973 67.60310479676625 74.65888580021517 88.3820510723543 77.59928844297444 74.43479855170789 78.77381094419229 74.61289349243746 76.77708783921194 77.53904222583506 74.23028400833422 69.04162342464578 68.71021679328584 82.05520417446327 80.31058287550373 75.7045200116664 62.083673207465964
8 63157894.73684211 77.96186640771968 77.88192279314896 79.90939156508843 74.59772101593646 81.95450827012928 91.32023482420934 99.8219248004815 88.71310677616715 87.05812763003762 96.66909369991427 83.85186222373119 58.91816984942581 84.70048816729121 84.30572490179473 82.699403670521 79.1708958555952 85.94157966649433 73.81358258946285 86.92019426967134 78.1754470913364 82.84876727397423 82.02697752816526 77.95594730424254 84.60909789255781 76.16912031656653 85.08030606839301 98.90300199393586 84.50312371704717 84.08359830816202 82.87125030126928 82.58972449869 85.47248331339736 91.35298261479824 83.54609760419154 75.5701546082041 75.47427564335167 90.62633216851636 86.56694207903917 83.08580821203559 68.41902974780412
9 73684210.5263158 85.20590856124407 81.63994845240235 87.5536801860851 80.02211912042381 88.93895388714495 101.66903585119178 103.37438984995404 95.74795153291272 90.27874880733995 104.7106697629322 94.23625790080123 70.3899351770982 92.9502840445395 89.58890648277017 91.02809318582273 93.11215345229222 93.00044250232361 83.37840738091774 96.38188635392781 84.69166377052623 90.95690393782223 93.58000030876279 85.33535254897339 89.766755722071 85.47888010135566 94.94427861931665 109.41930468729245 94.07833133751419 94.37431791011977 91.07855648976697 89.65548677730098 92.03973163144245 100.83050526488687 91.16842168468435 86.46374962338533 81.56014853678747 96.1543835915233 97.22680180177217 89.64854993021059 76.84670810420015
10 84210526.31578948 94.58850524333045 90.83613501906065 95.3034353195135 87.10750257011266 99.6640167285861 110.56034452267961 110.83371086530077 105.54086266825404 95.57707602049835 116.70126111685735 103.4113903040701 84.48521418122374 100.21657412633341 99.15831680079907 96.7834836779539 106.77713621603816 101.31314210036454 99.64253775168655 108.07471593595278 90.08850997554299 99.46355560842974 101.27142288116868 91.54180394860185 94.90197676321147 95.64812839146796 103.65011057777748 115.76212588935017 100.13870888882397 108.95919690683608 100.59892966476504 97.21905508364998 103.31965357593552 107.68338891591392 96.90379751999953 93.71759573095723 92.03145708189116 106.78001212793045 110.79734578076493 98.82696552520974 87.42132459667582
11 94736842.10526316 101.88429206826433 99.8938707395191 99.14809043627037 100.76287327209421 108.37623480725982 121.46893862669984 116.83811802307655 114.04406868684985 104.81740577085527 127.59927797798387 108.38569930503326 100.743737881286 111.05183225240651 110.1534130271741 109.64443115089243 124.00553335309276 108.91868194906748 114.74200134024726 123.8274421608514 104.30303329357315 108.79121520411522 111.31312831736832 99.55750597928782 105.24583764570325 104.61805018256328 112.71411208948766 126.85815563199428 107.85342714006798 124.77597780818755 116.60481493026431 102.22960813126818 116.8053509888763 116.2450770734296 105.78968097283982 102.0391513479466 104.50903597449332 119.26716255988936 120.32318122658126 106.96064208208524 96.76329541963801
12 105263157.89473684 111.88603721228829 109.70143845173791 109.40784566178712 120.98175197472368 121.3114516633947 134.780379322262 131.72081355721667 128.20252870361725 118.03989737272428 143.36412465539334 113.22776764160709 109.64102217435341 121.19535848263062 116.03230664678888 131.2139862133938 145.4731281469073 118.53652354707513 131.00931832082878 132.2579038516306 121.75001301436873 120.51721003816729 122.21878272422958 110.75283410728308 113.11012512098719 116.92501035761966 114.78063356546154 134.47534718399564 117.2748983751291 146.00184947318317 129.52482397912115 109.84680408870909 128.9956928406148 125.41471709348158 114.95474209576598 111.84281066906254 115.01606822203732 127.06839895293818 128.95356210814452 115.09946180492062 109.78053243115669
13 115789473.68421052 122.60972126728115 122.95534448994329 122.96286662279981 137.06600378061594 131.99550881515415 142.2984627663594 149.21274357902047 139.15723138878386 134.29736175092964 156.59085089756675 120.22325258631868 115.90000440039958 130.83590036591417 123.52368846411851 150.31279879304842 166.98742200747915 125.53196502524399 143.90746519378183 144.42663199704273 132.56288756764496 133.69792656292958 131.17964799281137 121.72636962244468 121.33427487247704 130.81087104185713 117.4281842420471 138.12385699280907 128.90960083200164 162.3300031091285 139.35922574860732 122.14053971846678 148.77687064605738 132.8697192714733 122.45246475511888 119.64158058870284 123.56158002449452 136.25863906419178 137.66648146757788 126.75669043253168 125.90588279619524
14 126315789.47368422 126.85695797832389 134.28583930073682 134.9243479001225 151.37521788139424 140.21280420883213 144.62339296945245 163.84559288150388 144.1045494399903 150.9614755559166 167.67398843573733 130.45619186470054 124.95830020118619 135.2700953762617 136.77639995189256 167.81090206386642 174.77412622919374 129.76628504144517 157.2553264000079 162.37243566073872 147.02536539803583 145.03258706905837 142.08734372233423 135.1896556891563 140.27134785609235 133.7065102471209 128.25321889782217 149.95095576820614 141.6027406969229 172.91866216071756 148.55347630918192 137.87239560063858 159.6526409143226 140.00874730028275 132.2734392104552 131.14642235521137 132.78090331660084 142.92996688034395 143.44610237332262 135.26064672826732 140.25254454870304
15 136842105.2631579 128.25246481388973 147.71527992709028 145.00722832664064 167.41595134613755 143.0661991436313 149.30622178188156 167.95497013938063 157.74698866812972 168.7108649037304 168.8626981082055 144.16069731974866 144.00697861783146 141.85380575077357 147.8173775117731 186.94637737057877 178.88245540795398 134.71520058674497 160.6708919626359 157.9662813112924 167.13078010102885 152.3738460931669 148.7167743189761 150.05542535526766 161.2204795634565 139.43851340584808 138.57832816342238 162.37730958261153 144.69840190070488 185.15795489204558 157.26213668315697 140.91641295286428 165.11060669390778 148.6120298835462 141.3425099924826 146.77010574301195 139.72182381524604 152.89198275868088 146.2648896236086 139.31816132329507 156.75999156156573
16 147368421.0526316 134.77661006123736 163.22143277872632 154.96791705687292 174.7445341323056 142.4531365738681 164.0062487229416 179.1334203721909 168.04421263091123 177.22472287858952 169.5565973941309 156.76209875817446 166.15327856340897 151.50470790894408 151.55741512362647 217.21657504624278 191.6683819564756 140.26085027639556 172.76058940511 165.78387243604067 189.32316427052518 157.58407029996619 156.04412420238484 167.82283924796576 179.03455921239802 152.783394252577 145.01445177692787 168.14986296902072 155.1739957870869 191.07194103180868 167.6409816995387 143.29448019120832 183.1490840509823 157.3619156405536 149.21267782139316 160.39338348389003 139.87974457364334 161.35556538423674 155.4813307823402 145.56563454932453 165.64636754015476
17 157894736.84210527 136.23639003713706 163.8631174365817 158.57466104486312 186.48805579481197 157.06537044461083 165.02104080292986 174.38983147746143 176.514878952561 195.1106327815482 174.77758008406764 162.44861303546423 182.54323082369783 163.26382600988708 159.11155832379313 222.54600961968674 218.71034922205183 146.62281801747648 185.4798412069142 173.8299399800908 200.39737295604974 167.57263379971243 157.7886441031734 184.49155916145634 191.88277577264157 152.08469013423965 154.23577465372898 175.35115161922005 165.82630178419012 193.5049134458201 168.76205435952485 150.4369752606444 185.74660883517808 152.67771580134237 161.93311256384916 167.23404639410344 141.37671673277242 178.96127353303157 167.4840652854324 156.21128387885412 173.81255692685247
18 168421052.63157895 139.6767140788715 179.29714142912974 163.9306062951973 202.61394998175285 160.75181686250787 176.68706361672886 181.61770352366227 186.2762466203473 217.93236788223987 180.73991708081846 154.53878704530712 190.05474930060538 162.52324899345885 168.75508809816145 244.9614926282719 231.2320996479975 152.12870720747105 224.8866804504659 174.52597083411388 210.20824376169665 167.3110150438927 162.59094451272918 192.76136448310683 197.26422471881244 159.32390785679593 160.64695354313733 186.7008671133142 173.6902160287894 209.8485705872322 175.39101470210215 154.86256685415464 192.97556720480034 162.95017685256175 165.04581404326694 172.13883195821597 143.9112652087806 181.38266882011433 165.1702125488556 168.67916444464075 179.65576557307364
19 178947368.42105263 152.1773001259384 187.78848363975078 172.71605956950677 228.25923802313548 167.60074508706123 176.77090451740492 188.96848370110064 190.18331680783274 214.38406492241367 177.1231710149228 165.43429649301348 201.93324024909256 171.46795913209712 160.94297722192516 247.65322664264497 242.92557070959472 158.65025637928304 218.67045822657045 181.4624049275123 235.76302255780908 180.5963450416386 167.0881583495401 192.86693630282898 217.72460795464278 167.95777068602908 170.51874512293662 180.6173929217532 179.95675759958593 226.86208948687008 182.95824959977347 169.5371000146767 204.63095265465927 158.99093024312955 165.78888877627756 164.25471335954944 149.21484890316003 174.30290365846534 163.73526394705692 173.40510318636728 190.7973366211326
20 189473684.21052632 151.5611848667718 192.523295115566 172.48407511384204 240.28192562244607 168.5187837294099 177.28882083998494 192.08789655318552 194.6066968843052 216.42897035928644 187.1353163027367 171.6872317234565 204.17419042299989 174.06555168078876 180.1811453005779 237.52306122206915 247.26534311989337 175.63854791203363 232.8222674091767 185.56134612829402 243.0356346525644 177.98689555725562 165.72059787541545 207.72896230344628 219.45322499298322 173.64358805239695 169.4350698038812 188.87591009894567 180.77158077156113 242.5699783759269 186.196442212507 161.08386867313834 207.74302595465798 168.9096205596118 172.26485912439895 174.6773919341802 153.4163679908187 181.72981270718444 180.64700451295133 165.20710539751767 189.6273595542954
21 200000000.0 169.8640814752955 194.23091325242268 190.5104549174246 252.9276318848133 175.20456174408136 186.4562118947506 185.4500541239977 200.59314903381625 227.82707963883877 193.05572496433007 181.82379878273136 205.98679436351122 177.09725610206002 181.77721870337663 241.6123682872245 256.39578675125773 174.02710151907644 235.72361347392984 191.75352107615848 246.22038053681976 183.59360968439202 173.57362318980066 213.383493435226 221.69393600994036 183.60875355648366 177.18748693874008 184.21683073592814 184.46073462147461 232.9164292961359 198.74460786737893 168.4230472523915 217.64467298827674 168.59258995009097 170.57408494149385 186.11799173370787 159.83466629291834 190.49950953612202 193.4700266232616 168.05141248828485 201.34765830400744

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200000000.0,233.3627727023865,223.80396291692006,239.77410919650606,223.2427730474033,219.3700780766575,259.3557613209674,237.12765725113843,296.86745795607567,228.5117539614439,232.06042272323057,221.5428994470521,226.27285162084982,293.36829774160134,233.21333471097444,214.7782752443301,227.2409575769776,228.57191316234437,242.49128405279234,246.86727137393072,217.1853632675974,298.617594296995,249.63688149028704,223.22638544048132,233.73226100755366,217.80707008979823,229.38289530888983,298.8386672107797,234.02891624601264,230.70007269006027,302.4543564429409,220.78411024965737,292.27454152703285,233.72480676127108,225.3258987429895,292.12308772614125,214.41391163515416,291.9945796179144,223.05400930266632,211.99844315491225,225.65526270787967
1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20 trial_21 trial_22 trial_23 trial_24 trial_25 trial_26 trial_27 trial_28 trial_29 trial_30 trial_31 trial_32 trial_33 trial_34 trial_35 trial_36 trial_37 trial_38 trial_39
2 0.0 16.36858558654785 26.00448226928711 16.071184158325195 18.28192138671875 13.429677963256836 17.10512924194336 25.6998291015625 10.222268104553223 28.574752807617188 11.341191291809082 30.163766860961914 20.912904739379883 14.828292846679688 15.408313751220703 20.8553466796875 14.672196388244629 13.907516479492188 15.634739875793457 16.230104446411133 18.430156707763672 17.961626052856445 13.207015037536621 12.6388521194458 18.22677993774414 35.21895980834961 11.414321899414062 20.768640518188477 16.839088439941406 19.221025466918945 12.757458686828613 20.066017150878906 13.08200454711914 23.689924240112305 15.852598190307617 15.245919227600098 12.187602043151855 13.174694061279297 28.60873794555664 17.09139633178711 14.216440200805664
3 10526315.789473685 18.11368068621863 27.425026894472232 18.38610494032069 20.559494980381302 15.357595737471435 19.554993659495235 26.761648597376333 10.970705721973651 30.780688186410888 13.062509208275237 31.809527941909813 22.208616002811084 15.833878229993946 17.418129372144755 23.389531875251073 17.08550101876455 16.076059786835042 17.629000143648494 18.291182536348042 20.612136182021814 19.07975352904824 14.941778097541647 14.993891973799183 20.705034495576434 36.287913665020646 13.346746479426809 22.259029439503426 19.006784267496535 21.414071171314887 14.07391811784233 22.40518033229991 14.151989958437362 24.98784505076954 17.72551954455591 17.327674104739238 14.617211791113991 15.160476124466209 30.06212252066819 18.816248280065874 16.63664920676056
4 21052631.57894737 49.808253384466155 53.586484389952346 58.33789627190029 59.641477115844424 49.485490342111966 62.088607374362006 45.23082691309277 25.395185544209717 69.2804608328108 43.39822179718856 60.78165504336357 46.121952212335664 34.171111139316636 52.522181122545724 67.04657731302227 58.607984166705876 53.388078167085176 52.57056698946081 54.04979319342121 58.269837626047085 40.3598502209601 45.84551030737954 56.20714531717125 63.3390201349379 55.6848138251298 47.73393425372251 47.87616282530191 56.20832159549741 58.82206584021986 38.75625651626954 62.57557550233652 34.6567980071473 47.78055875756652 51.22342188313728 54.576655816276485 55.85619692370254 50.49176067109749 55.432243933534856 49.919930236347 58.87255255747948
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168421052.63157895,205.9888778148926,197.95220443185346,242.27585374037645,229.92877350817756,201.3382438044799,233.7308674368832,290.61178702594833,171.2707621143135,187.79079740727707,191.07411632709557,232.29201785283075,251.40304134856302,220.8044729853601,207.40489982749617,256.0445701128228,248.04761227610368,201.3066829274566,268.9784077610666,201.21632215273348,187.78481378234986,182.18753470294695,248.0711262919566,176.90307019853196,183.9438369790933,176.20218866105887,198.10063838694563,254.7428497556504,196.45825596397273,240.3647540234793,194.78226263272134,203.0281613170275,194.22603240832066,236.4290188430419,196.70714229873673,182.0284070950466,267.3135290301077,239.57377240086527,158.20646169971562,173.81722267199092,212.26023321997096,205.24530170862033,229.74410170828537,270.6985091935234,192.47675646077894,199.6954621984688,268.1604115414818,247.00093365012773,200.40598084837447,238.12187796517424,196.37514748847386,266.69776600483715,187.5134183681903,269.63889756361203,188.6837065989291,191.20129164021432,265.1613543522325,192.69453564756796,244.54224160041176,195.22499685356823,190.28928300796125,194.21637746848558,180.18536685196648,181.5141567984116,225.63029411360827,249.55610435193927,258.91630720052035,262.8972055007216,190.00298770395344,220.6122901646054,186.18810867190032,186.1181991683149,183.69386154396713,196.6215860751197,199.46599709096049,201.1814751354281,197.09940585436254,232.83689637180842,209.42987146420492,191.95207515548802,196.68333470226986
178947368.42105263,213.79684700022278,198.8288263168155,250.43149276962117,230.90171214174532,217.896638375756,236.65636270698624,294.4587490721257,176.63285667486386,187.57181728459958,193.29724587384518,230.94606646924302,260.3358776120474,221.34511089960623,209.74876189862385,261.72908029321405,254.87267819228595,206.71074021308377,273.1983583712553,205.13758764860745,190.70736642139565,185.36037222191774,253.51159158266483,186.40558371069608,189.19434938855323,180.76825314860307,201.1405939431732,263.24197848030775,199.56169173100812,254.0131243082109,198.4519492972054,208.13047395824066,199.29937021112343,239.33103756071003,200.32317230294245,183.09828728244452,278.97962613562714,240.32778331477434,176.6459230968414,182.17326696923936,214.69311995808437,214.47828633994524,242.21870483629345,277.5378851648472,200.5692740383447,206.89749124609037,274.1144909127267,252.68175143319237,205.5812989568178,245.2242848430025,203.29606658809527,274.86423633497344,193.90062481405374,273.906938021079,194.909983373972,196.14358561693425,269.31262475974506,198.0334801668007,251.87542331115526,201.6852127976633,199.2343775468499,201.08143495003645,195.38223021905713,182.93351674937435,229.17010997343095,255.44158414053703,272.101217124735,271.3804964206886,196.94813312227913,223.25253564822088,192.66623032442874,189.39168273144688,186.35477397200805,199.89816141636254,201.3846892843286,204.46537077530104,203.70303273698383,238.78326443728275,213.1463298384936,196.33729682505708,199.53309954816368
189473684.21052632,221.60481618555298,199.70544820177753,258.58713179886587,231.87465077531306,234.45503294703207,239.5818579770893,298.3057111183032,181.99495123541422,187.35283716192205,195.5203754205948,229.6001150856553,269.26871387553183,221.8857488138524,212.09262396975154,267.4135904736053,261.6977441084682,212.1147974987109,277.41830898144406,209.05885314448142,193.62991906044144,188.53320974088854,258.95205687337307,195.90809722286016,194.4448617980132,185.33431763614726,204.18054949940077,271.7411072049651,202.66512749804355,267.6614945929425,202.12163596168944,213.2327865994538,204.3727080139262,242.23305627837817,203.93920230714815,184.16816746984244,290.6457232411466,241.08179422868338,195.08538449396718,190.5293112664878,217.1260066961978,223.71127097127015,254.6933079643015,284.3772611361709,208.6617916159105,214.09952029371195,280.06857028397167,258.362569216257,210.7566170652611,252.32669172083078,210.2169856877167,283.03070666510973,200.2878312599172,278.17497847854594,201.13626014901496,201.0858795936542,273.46389516725765,203.37242468603347,259.2086050218988,208.1454287417584,208.1794720857386,207.9464924315873,210.57909358614782,184.35287670033708,232.70992583325366,261.3270639291348,285.28612704894965,279.86378734065556,203.89327854060483,225.89278113183636,199.14435197695718,192.66516629457885,189.01568640004896,203.17473675760536,203.30338147769675,207.749266415174,210.3066596196051,244.7296325027571,216.8627882127823,200.72251849462617,202.3828643940575
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1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20 trial_21 trial_22 trial_23 trial_24 trial_25 trial_26 trial_27 trial_28 trial_29 trial_30 trial_31 trial_32 trial_33 trial_34 trial_35 trial_36 trial_37 trial_38 trial_39 trial_40 trial_41 trial_42 trial_43 trial_44 trial_45 trial_46 trial_47 trial_48 trial_49 trial_50 trial_51 trial_52 trial_53 trial_54 trial_55 trial_56 trial_57 trial_58 trial_59 trial_60 trial_61 trial_62 trial_63 trial_64 trial_65 trial_66 trial_67 trial_68 trial_69 trial_70 trial_71 trial_72 trial_73 trial_74 trial_75 trial_76 trial_77 trial_78 trial_79
2 0.0 89.20394897460938 80.8363265991211 90.47622680664062 83.14705657958984 64.39078521728516 80.56387329101562 85.53324890136719 70.99172973632812 87.89069366455078 75.88204193115234 84.02256774902344 68.24169158935547 98.6713638305664 90.78836059570312 69.00027465820312 74.3541488647461 84.44625854492188 89.91865539550781 69.98278045654297 73.83918762207031 80.39730834960938 78.81390380859375 75.34542083740234 78.56448364257812 82.18145751953125 93.45423126220703 83.18026733398438 97.29779052734375 76.18155670166016 80.51220703125 96.50995635986328 86.4296875 81.37446594238281 83.57403564453125 75.21205139160156 76.11017608642578 93.61534118652344 84.02777862548828 79.27843475341797 97.04215240478516 78.34747314453125 69.44991302490234 77.99539947509766 80.59425354003906 82.23249053955078 77.73381042480469 75.1167221069336 78.68003845214844 81.82601165771484 87.6048812866211 74.93865203857422 81.61906433105469 74.98188781738281 79.41499328613281 86.32952880859375 81.18024444580078 83.0518569946289 71.0606689453125 86.39849090576172 73.83191680908203 80.37627410888672 74.10311126708984 79.9956283569336 74.34557342529297 74.59795379638672 76.42047119140625 80.4571762084961 87.75067138671875 71.04902648925781 73.02156066894531 79.36551666259766 79.2263412475586 94.48149871826172 84.76939392089844 92.80410766601562 90.59996795654297 77.6960678100586 80.04590606689453 72.02660369873047 78.71775817871094
3 10526315.789473685 89.20394897460938 80.8363265991211 90.47622680664062 83.14705657958984 64.39078521728516 80.56387329101562 85.53324890136719 70.99172973632812 87.89069366455078 75.88204193115234 84.02256774902344 68.24169158935547 98.6713638305664 90.78836059570312 69.00027465820312 74.3541488647461 84.44625854492188 89.91865539550781 69.98278045654297 73.83918762207031 80.39730834960938 78.81390380859375 75.34542083740234 78.56448364257812 82.18145751953125 93.45423126220703 83.18026733398438 97.29779052734375 76.18155670166016 80.51220703125 96.50995635986328 86.4296875 81.37446594238281 83.57403564453125 75.21205139160156 76.11017608642578 93.61534118652344 84.02777862548828 79.27843475341797 97.04215240478516 78.34747314453125 69.44991302490234 77.99539947509766 80.59425354003906 82.23249053955078 77.73381042480469 75.1167221069336 78.68003845214844 81.82601165771484 87.6048812866211 74.93865203857422 81.61906433105469 74.98188781738281 79.41499328613281 86.32952880859375 81.18024444580078 83.0518569946289 71.0606689453125 86.39849090576172 73.83191680908203 80.37627410888672 74.10311126708984 79.9956283569336 74.34557342529297 74.59795379638672 76.42047119140625 80.4571762084961 87.75067138671875 71.04902648925781 73.02156066894531 79.36551666259766 79.2263412475586 94.48149871826172 84.76939392089844 92.80410766601562 90.59996795654297 77.6960678100586 80.04590606689453 72.02660369873047 78.71775817871094
4 21052631.57894737 89.20394897460938 80.8363265991211 90.47622680664062 83.14705657958984 64.39078521728516 80.56387329101562 85.53324890136719 70.99172973632812 87.89069366455078 75.88204193115234 84.02256774902344 68.24169158935547 98.6713638305664 90.78836059570312 69.00027465820312 74.3541488647461 84.44625854492188 89.91865539550781 69.98278045654297 73.83918762207031 80.39730834960938 78.81390380859375 75.34542083740234 78.56448364257812 82.18145751953125 93.45423126220703 83.18026733398438 97.29779052734375 76.18155670166016 80.51220703125 96.50995635986328 86.4296875 81.37446594238281 83.57403564453125 75.21205139160156 76.11017608642578 93.61534118652344 84.02777862548828 79.27843475341797 97.04215240478516 78.34747314453125 69.44991302490234 77.99539947509766 80.59425354003906 82.23249053955078 77.73381042480469 75.1167221069336 78.68003845214844 81.82601165771484 87.6048812866211 74.93865203857422 81.61906433105469 74.98188781738281 79.41499328613281 86.32952880859375 81.18024444580078 83.0518569946289 71.0606689453125 86.39849090576172 73.83191680908203 80.37627410888672 74.10311126708984 79.9956283569336 74.34557342529297 74.59795379638672 76.42047119140625 80.4571762084961 87.75067138671875 71.04902648925781 73.02156066894531 79.36551666259766 79.2263412475586 94.48149871826172 84.76939392089844 92.80410766601562 90.59996795654297 77.6960678100586 80.04590606689453 72.02660369873047 78.71775817871094
5 31578947.368421055 89.20394897460938 80.8363265991211 90.47622680664062 83.14705657958984 64.39078521728516 80.56387329101562 85.53324890136719 70.99172973632812 87.89069366455078 75.88204193115234 84.02256774902344 68.24169158935547 98.6713638305664 90.78836059570312 69.00027465820312 74.3541488647461 84.44625854492188 89.91865539550781 69.98278045654297 73.83918762207031 80.39730834960938 78.81390380859375 75.34542083740234 78.56448364257812 82.18145751953125 93.45423126220703 83.18026733398438 97.29779052734375 76.18155670166016 80.51220703125 96.50995635986328 86.4296875 81.37446594238281 83.57403564453125 75.21205139160156 76.11017608642578 93.61534118652344 84.02777862548828 79.27843475341797 97.04215240478516 78.34747314453125 69.44991302490234 77.99539947509766 80.59425354003906 82.23249053955078 77.73381042480469 75.1167221069336 78.68003845214844 81.82601165771484 87.6048812866211 74.93865203857422 81.61906433105469 74.98188781738281 79.41499328613281 86.32952880859375 81.18024444580078 83.0518569946289 71.0606689453125 86.39849090576172 73.83191680908203 80.37627410888672 74.10311126708984 79.9956283569336 74.34557342529297 74.59795379638672 76.42047119140625 80.4571762084961 87.75067138671875 71.04902648925781 73.02156066894531 79.36551666259766 79.2263412475586 94.48149871826172 84.76939392089844 92.80410766601562 90.59996795654297 77.6960678100586 80.04590606689453 72.02660369873047 78.71775817871094
6 42105263.15789474 91.83890336714788 83.37862017327646 93.38319495671179 86.11032741058649 65.59998702883225 82.802158690762 90.36925149599601 72.92086281559308 89.91974067405238 78.65103180613627 85.27209212108828 70.35783520844504 100.39711517163674 93.48102061809595 72.1783904838595 75.62877706764395 87.38326875031655 92.81064837440394 72.77644977355351 75.63981741466598 82.29444355113107 80.66863387292689 76.674734631156 80.8799628138212 84.51592516975472 95.8623842300842 84.8222124846936 99.30070928940317 78.54292610308305 82.05789682066838 99.1743735451241 88.77804447440147 83.97995970524084 86.19764531529677 77.44173004791925 77.56665337874124 96.28442318778784 84.5284150889004 81.07855277031743 99.7750480334143 80.49402177736287 71.09090211112414 80.39085019615136 83.74238441467615 84.66842691447596 79.73682998461324 76.04671674904895 79.65702344751672 84.30187994780385 89.92895681869207 77.11726170997045 83.9215963991395 79.65131888701646 81.60676160617795 88.64996913257067 83.00430863354758 85.68049400720818 73.09730952945112 88.45758819014577 76.72754542868059 83.23132882250727 75.5819695531868 81.82479689078318 75.70032069745405 76.13718041682672 78.71135311621212 81.74163673432167 90.45945818375517 73.48493777289781 75.21757633792149 82.17086121417232 81.70204255081858 96.63803022173221 86.93000881472949 95.52408690668044 92.92724565573428 80.56230631514022 83.82137228212116 73.79306175654698 82.11033787105718
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9 73684210.5263158 128.6672653102334 118.9118757695424 134.01345234978274 127.5275189218955 82.50081920414297 114.08633767587452 157.9613337031981 99.88406623221955 118.27942609292174 117.35278756381464 102.73650667088886 99.93485686319192 124.5176825684307 131.1159254859648 116.59843822956663 93.44406409200973 128.4334194402512 133.23160004827332 111.82314638716589 100.8069496864809 108.81041743457214 106.59191752041993 95.2543539486392 113.24306755358162 117.14442902937057 129.52077671172938 107.77143334113372 127.29520411656299 111.5474317002928 103.661770943738 136.41453251866443 121.60067733276605 120.39655485038242 122.86744378541192 108.60561387231084 97.9236178238079 133.58978159425374 91.5257357744722 106.23853203006233 137.97231992883633 110.49600974429616 94.02676019776314 113.87170528100901 127.74333700180631 118.71514390514251 107.73273364677922 89.04511223625072 93.31219604719234 118.90671932149854 122.41221160312129 107.5673619994063 116.1037414218828 144.91525589773778 112.24077835219327 121.08241515924479 108.49897992804419 122.42055887906939 101.56312920095353 117.23728178942014 117.19931190680722 123.13599990838185 96.25174978814525 107.39081086441256 94.63541992415784 97.65071979743993 110.7306658354513 99.69434866006293 128.31976455960867 107.53130406643834 105.91095764226593 121.38074082841484 116.3045479746747 126.77954727279698 117.12859879980003 133.5408283867396 125.45525664924399 120.62329157517703 136.59049673907336 98.48258082175994 129.52791488274852
10 84210526.31578948 139.68291226813668 128.94681896578902 148.62833511490902 143.0844506842608 91.20545182362653 129.27292150440638 180.69630025108435 109.37763755300038 128.53894398070437 128.70190337919462 114.10592263854443 110.60160879080811 135.48891710194854 144.33773898021667 134.58994552765526 102.73288828555567 138.5170013085627 153.4985014977878 125.25831002640922 109.8377665566523 118.19698081217149 117.17608292516414 102.38698935314724 124.64108090230633 126.44978389494803 139.41901772017295 118.71161188825016 137.45320586558856 125.09871083229697 113.46550792241031 146.36297607735582 133.35785752027155 134.72326402832596 134.08462554505329 119.93194249152643 114.8597193193155 151.10453830647006 96.17101366756035 116.89370439476089 149.12408896603742 119.83257702872199 102.80520067886137 134.0615314108183 140.29797241900766 130.82674936463133 125.34865163539091 97.57429407148976 100.09496637844478 130.82673135061344 133.1458388654479 120.9796613688862 127.27521115706568 167.08111139314659 122.42681659989245 131.00404553689125 118.70512334973529 134.2743756131287 116.48327395022741 128.6186399674069 130.0710934009661 136.1661843050715 104.11886874790667 116.35198655654354 104.10131657552851 106.60930670888635 124.35127449431909 114.72998590565125 139.92858233527795 123.17997080013363 117.42721537989758 132.4576990519369 128.53139771607775 136.7404064673136 129.0214081451173 145.61363782182625 138.34311157976822 135.8183032487238 151.20700613101764 108.23916551404713 142.00782020864725
11 94736842.10526316 149.02279099586764 136.57610998092184 164.6677019707033 160.96956070021332 103.9929312065481 150.785844141798 203.70284194811933 119.54370630657368 139.87040346999166 137.98837939973848 132.85119192954411 122.3422370976059 150.3569031538767 158.45940123799767 156.8155975931239 116.47597904231947 143.81473689998947 182.7968600224136 139.25131884196622 119.72180427839449 128.31197073089263 130.34351241159823 110.7685720600714 136.85048847603213 133.66678206644787 147.56072560841233 134.02634576869062 148.71002330105762 142.03985503759142 126.72913121190592 153.0343399083144 146.2002915459378 151.9586572308413 143.96424327370738 132.50580701469818 145.29058568534077 175.3725456277378 103.89115136233352 130.5648075121602 158.17441682873547 128.28624613454613 113.09014164964434 166.25590649195573 150.04429299176937 143.95234511803494 153.97787399710236 111.68246255192255 109.84385671462977 143.25867842129557 143.7543301829795 138.7290616745795 139.03708485699673 189.7936600615526 132.57921824305527 139.743526753905 131.18190321852543 145.60587944343192 138.62451281436716 142.37726821925315 142.12018603159223 148.83558557806873 113.28514030526219 125.89702914948795 117.76063909119516 117.94420665790975 141.89051652400448 141.79923287737816 150.19292287315935 144.54521769946672 130.6520221409468 140.88501145479134 141.67914986894195 146.58651448092797 143.34265334660657 156.88950980114146 153.94998825917284 153.46134356570295 161.87072216839093 120.02551948577371 150.065953343859
12 105263157.89473684 158.36266972359857 144.20540099605464 180.7070688264976 178.85467071616583 116.78041058946968 172.29876677918963 226.70938364515428 129.70977506014697 151.2018629592789 147.27485542028234 151.5964612205438 134.0828654044037 165.22488920580483 172.58106349577864 179.0412496585925 130.21906979908326 149.11247249141624 212.0952185470394 153.24432765752323 129.60584200013665 138.42696064961376 143.5109418980323 119.15015476699557 149.05989604975792 140.88378023794772 155.70243349665174 149.34107964913105 159.9668407365267 158.98099924288587 139.99275450140155 159.7057037392729 159.04272557160408 169.19405043335667 153.8438610023615 145.07967153786993 175.72145205136604 199.64055294900555 111.61128905710669 144.2359106295595 167.2247446914335 136.73991524037027 123.37508262042729 198.45028157309315 159.79061356453107 157.07794087143859 182.6070963588138 125.79063103235535 119.59274705081476 155.69062549197773 154.36282150051105 156.47846198027278 150.7989585569278 212.5062087299586 142.73161988621808 148.48300797091875 143.65868308731558 156.93738327373512 160.76575167850692 156.13589647109944 154.16927866221837 161.50498685106595 122.45141186261772 135.44207174243235 131.41996160686182 129.27910660693314 159.42975855368985 168.86847984910506 160.45726341104077 165.91046459879985 143.876828901996 149.31232385764574 154.82690202180618 156.43262249454236 157.66389854809583 168.16538178045664 169.55686493857746 171.10438388268207 172.53443820576422 131.81187345750033 158.12408647907077
13 115789473.68421052 167.70254845132953 151.83469201118743 196.74643568229186 196.73978073211833 129.56788997239127 193.81168941658126 249.71592534218922 139.87584381372025 162.5333224485662 156.5613314408262 170.3417305115435 145.82349371120148 180.09287525773294 186.70272575355963 201.26690172406114 143.96216055584705 154.410208082843 241.39357707166522 167.23733647308026 139.48987972187885 148.54195056833493 156.6783713844664 127.53173747391973 161.2693036234837 148.10077840944757 163.84414138489112 164.6558135295715 171.22365817199577 175.9221434481803 153.25637779089718 166.37706757023147 171.88515959727033 186.42944363587202 163.72347873101563 157.6535360610417 206.1523184173913 223.90856027027328 119.33142675187986 157.9070137469588 176.27507255413153 145.1935843461944 133.66002359121026 230.64465665423063 169.53693413729275 170.2035366248422 211.23631872052528 139.89879951278814 129.34163738699976 168.12257256265988 164.97131281804263 174.22786228596607 162.56083225685887 235.21875739836463 152.88402152938093 157.2224891879325 156.13546295610573 168.2688871040383 182.90699054264667 169.8945247229457 166.2183712928445 174.17438812406317 131.61768341997322 144.98711433537676 145.07928412252846 140.61400655595654 176.96900058337525 195.93772682083198 170.7216039489222 187.27571149813295 157.10163566304522 157.73963626050016 167.97465417467038 166.27873050815677 171.98514374958512 179.44125375977183 185.16374161798205 188.74742419966122 183.19815424313754 143.5982274292269 166.18221961428253
14 126315789.47368422 175.8350267487467 161.8061472119717 208.03998840503252 207.5285752009487 143.1370844519452 206.5322182061682 262.9093908576754 147.4373956341245 170.21033228892534 164.85177601750044 186.61592005445027 165.94827330141354 191.33288729269253 194.05506209282004 216.3226515594612 164.73235903866075 163.1639558660109 254.12751875640282 176.57977594373298 150.19921869827937 156.79100413562685 175.32154168795353 137.01920083866887 167.96755922241059 154.34686713746214 171.63340669874506 183.2646974514231 178.38948431792682 189.8972654332745 163.70381406535734 173.8379736809767 178.73959604916976 199.60412640399056 171.7256522931138 165.35930926408466 223.84505093299947 233.63456976838884 125.53268858893591 163.4329808375842 184.71556278679344 156.55853860096755 151.22210737757408 245.9729120910498 175.13738877980498 178.04721135668808 228.51011787610867 161.45716021145978 143.55529653386233 182.66647041215464 172.4374555043484 194.01013558954415 169.34834222867053 247.16227268466824 161.06461024977824 164.863327717682 177.76237437347794 174.9926809654094 198.86354254623694 177.32570665150138 172.56719936479988 180.32495410467945 140.36866652049187 153.81399892229288 162.30112614426918 161.6359521892758 194.16625012634864 214.0882600325049 176.0203774171853 198.874505284668 165.01138273653396 164.57930624509783 174.14524410248134 173.87135472493324 180.6116648077387 185.9919314511595 190.8415762522049 200.59258663901994 190.2688025673258 154.66611321472726 173.33574270104108
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9 73684210.5263158 31.90788460505347 36.59270049295185 36.1496786073036 43.6141872660275 44.875909703290944 51.95149808441008 59.59644322438873 44.32102376363986 41.89194138402795 15.68377083752026
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1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19
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73684210.5263158,74.93735160680689,107.81465900012412,139.2873089840207,96.71375098380769,86.87840321203927,113.47289029651239,93.44800781175867,97.10603002875715,96.94276465686075,51.13459859087733,84.31004567019167,85.57612551139911,87.22768531824332,79.04176998198281,80.70959805724033,93.1210169256394,116.47493457860234,79.01124874019474,122.10848017792293,73.69862018011696,113.93861476468165
84210526.31578948,97.10230527558156,93.96989148475457,96.52644659277475,116.53272218007461,113.20687297011347,174.57018046960278,153.29147939602757,141.83370591646417,106.18938247516876,56.92739289635767,88.59680833182506,98.30280876638487,116.02657619374611,102.99297806893028,95.20292315324589,94.353535294863,122.6360879416611,110.15239549921492,138.70916615166493,85.8180380409114,147.08891463263214
94736842.10526316,116.27735660887656,116.03497409178692,128.7576511145629,148.53811679045745,147.7007118017307,180.4411057644934,218.819252871658,178.99188914985868,144.46769188926493,102.97105440930812,107.9235355442911,124.23589051595356,148.52493570150597,141.86054870983654,114.07920847511193,115.40575793876708,159.42236704381384,135.99380406923075,180.29462874637417,116.24597945662829,188.09331493859807
105263157.89473684,131.7258633593113,170.21886141296898,192.91515870132275,187.39992579083034,202.23182970912833,207.65967708380268,238.20913633349198,208.33421997944734,208.33317792514686,153.72142048283297,151.02752303053467,181.4257410114987,205.62764731066048,184.45465234458612,191.9764393842121,164.1790215488616,241.4987096171465,155.8979871799741,238.7906318729604,140.21512545286123,200.8675222978037
115789473.68421052,158.33178354729574,202.37646896315744,227.33339871899574,216.93278682467184,211.331247086629,248.69978439911085,246.6390119787316,253.57222508443027,235.39637340138825,180.44286899309904,189.12914332953846,230.71455120359266,239.18017664613652,190.25308435701268,272.071464554755,170.13196379375592,248.429662619849,141.57710379225892,260.24952784708995,191.00687052491133,233.41085929751725
126315789.47368422,154.90293820891682,259.51886878713685,238.00155754465806,230.06350551450683,204.04818964120093,268.90613665128353,278.3264847906343,297.9188012779585,263.6566409047621,233.0199083050203,187.61077770929256,248.62723383299203,286.4701455133114,232.60310746163879,239.4052901964768,236.2464176310728,265.57598176194034,147.03692383069415,277.6510531974962,227.1836707213909,257.47360423760404
136842105.2631579,185.3483334431771,288.244503821445,200.98698775078117,262.38887776108334,234.9703059204728,300.94985060984084,285.87677064917756,294.33157443199457,279.39890948160865,259.3397508126547,236.45249789400123,271.87452206742074,303.82141308936383,244.9907631181036,278.33346704069606,268.4523852427911,303.5926700412732,189.8020199536452,273.70698676413116,265.58575844009334,302.29368292558894
147368421.0526316,217.15594078315593,313.3082447720697,242.89344419353233,264.4147583865393,269.04264408052796,311.566828934935,285.8760857961845,345.1251253437798,287.88174234070607,267.13349160510745,288.908934617637,254.7768222093582,299.069269646568,258.82332522543845,286.61811474733406,278.37361948642047,313.9588218418845,245.4122034481358,295.88553080961645,285.4122809714888,306.8542738398356
157894736.84210527,223.78152848932882,311.36378852218144,290.2786089949661,268.27760689707674,288.8315125849934,331.56831176228144,316.60071037895466,327.69570335721045,335.2528018445355,312.5851707836598,276.15293550821553,300.10106629042417,325.54629257461704,258.3734440263619,323.2678803412703,266.3304482982429,308.70753486351293,217.55363201649232,287.675268513344,294.6170784805455,293.491367597329
168421052.63157895,234.71857714785102,314.98354696236817,283.7284783920753,305.4871167595037,327.815720531749,342.18832026294064,347.4369622518482,359.1234421835712,321.55971752705665,296.5348788998464,328.4429737894159,320.2516846670008,323.5348077546857,268.7956971871225,305.5235315637245,316.0435993308176,319.21332096855394,211.6789066732095,343.86831283833516,292.32147242421917,354.51419196696827
178947368.42105263,197.38530471809517,334.59399147756875,341.7113641431127,325.66671816942767,310.07803450322547,327.6141084031385,331.2294814979601,414.69330027823304,375.55925973110584,289.038970218636,351.0568013585836,363.8722931092961,352.0182927139413,286.6342829280943,351.55434802859776,334.9405559625817,316.564209680478,194.9518083879657,334.9490503408737,338.65567082843626,398.9040526068277
189473684.21052632,273.97604445753996,355.3467957329552,358.03872707494406,338.0551271167819,360.6422533754497,398.6396637395478,368.90517846666216,321.8780714666414,387.91837769185406,400.57232862760486,339.23682612345823,374.71732094908685,346.9451931840495,288.66709963832864,350.67221955265694,337.94357375557075,374.24965236342183,219.90429991178235,365.6490119190427,295.2192700559743,430.01798900672935
200000000.0,281.7031864978765,311.4724302511466,355.67379710391947,346.4399628294142,322.5400290457826,406.9658508630175,337.0044558989374,410.9943090128271,380.6061951141608,320.96123184342133,373.0588185175469,321.95514380461293,389.21944143113336,300.4861226395557,379.84359742465773,346.62374156713486,362.50578028277346,193.65573316655662,406.5343745429265,325.86513288240684,355.2923764508021
1 steps trial_0 trial_1 trial_2 trial_3 trial_4 trial_5 trial_6 trial_7 trial_8 trial_9 trial_10 trial_11 trial_12 trial_13 trial_14 trial_15 trial_16 trial_17 trial_18 trial_19 trial_20
2 0.0 32.4077033996582 36.155517578125 25.75421142578125 29.606937408447266 27.17302703857422 16.026126861572266 13.865445137023926 31.84101104736328 30.781850814819336 18.447200775146484 27.443321228027344 23.80484390258789 23.779891967773438 27.92617416381836 31.59305191040039 39.16869354248047 33.610191345214844 36.45005416870117 20.54007911682129 38.84449005126953 34.24555969238281
3 10526315.789473685 33.296037207277614 36.785427371096745 26.648522366880545 30.070928266142957 27.658375122354798 16.909636004397083 14.5849724026046 32.483172309241795 31.134407273356977 18.28971532364879 27.769625172369864 24.67473756232998 24.22445243704352 27.639669323871505 32.86372066523436 39.94947247461021 34.48854379632466 36.91144894359638 22.061570849171595 39.57076941414058 35.02109238286593
4 21052631.57894737 47.85268858083398 48.244665590267104 42.69550373105957 39.864313121606436 37.426982542794 33.6573874229911 27.179000907564674 43.72329865292829 38.284123305014624 15.910192525081357 36.48614875559497 40.41140686373879 32.42776290967111 24.889028077021532 53.30326504027084 53.15286421536408 50.76808675710845 44.85972475671207 46.95364156745147 51.82332628598009 48.673801405484326
5 31578947.368421055 46.289031177160645 55.042522301737456 54.09337787392067 56.42648777237724 53.144822111121094 50.22762564730694 33.501808243249016 49.271767463927205 49.36965923597443 19.09700184072422 59.83897444905089 50.45623192499673 38.46070101455762 41.67901350319427 49.6850867264819 54.63208278024007 63.855021779825314 46.707314440304636 44.729709547167836 54.444386954762436 54.15614254775759
6 42105263.15789474 52.056275916066525 54.81231460751259 74.05637095030656 63.5784007053296 66.31524625313249 60.829015134609314 41.481055804071666 58.02204051089584 54.31379683443714 27.48259941575187 52.55809385921817 51.009362222167596 39.46608662262683 51.2882578602458 57.61938410989135 53.74984419733864 66.73611811273976 45.4475195833438 51.68484967947006 61.35790378470335 53.40799793085068
7 52631578.94736842 65.33051521372349 64.54581476310449 101.39453396258922 82.1989485288756 69.99954431695951 92.37778505030761 53.489512749841836 65.90184293982477 58.01873857391756 37.75656481033547 64.60210800154387 51.54042098185156 51.49881111311409 69.99729087472045 61.28976902142786 59.26768115029729 81.32731635404178 50.51788533190033 61.01289577361124 66.07327938235656 56.682834893857176
8 63157894.73684211 62.288964994437485 74.67267434872753 117.30094707945051 85.57247418495427 70.64805491359445 99.1536963618363 76.71144264556695 70.18010282099578 77.18331596618546 46.548501034006684 66.02018492836042 62.126340740605414 68.03360012194292 73.19627934867654 79.54463746351219 77.18552978357451 99.40059083489666 64.95080359490625 85.92186557210552 73.2946830179305 74.03522284188597
9 73684210.5263158 74.93735160680689 107.81465900012412 139.2873089840207 96.71375098380769 86.87840321203927 113.47289029651239 93.44800781175867 97.10603002875715 96.94276465686075 51.13459859087733 84.31004567019167 85.57612551139911 87.22768531824332 79.04176998198281 80.70959805724033 93.1210169256394 116.47493457860234 79.01124874019474 122.10848017792293 73.69862018011696 113.93861476468165
10 84210526.31578948 97.10230527558156 93.96989148475457 96.52644659277475 116.53272218007461 113.20687297011347 174.57018046960278 153.29147939602757 141.83370591646417 106.18938247516876 56.92739289635767 88.59680833182506 98.30280876638487 116.02657619374611 102.99297806893028 95.20292315324589 94.353535294863 122.6360879416611 110.15239549921492 138.70916615166493 85.8180380409114 147.08891463263214
11 94736842.10526316 116.27735660887656 116.03497409178692 128.7576511145629 148.53811679045745 147.7007118017307 180.4411057644934 218.819252871658 178.99188914985868 144.46769188926493 102.97105440930812 107.9235355442911 124.23589051595356 148.52493570150597 141.86054870983654 114.07920847511193 115.40575793876708 159.42236704381384 135.99380406923075 180.29462874637417 116.24597945662829 188.09331493859807
12 105263157.89473684 131.7258633593113 170.21886141296898 192.91515870132275 187.39992579083034 202.23182970912833 207.65967708380268 238.20913633349198 208.33421997944734 208.33317792514686 153.72142048283297 151.02752303053467 181.4257410114987 205.62764731066048 184.45465234458612 191.9764393842121 164.1790215488616 241.4987096171465 155.8979871799741 238.7906318729604 140.21512545286123 200.8675222978037
13 115789473.68421052 158.33178354729574 202.37646896315744 227.33339871899574 216.93278682467184 211.331247086629 248.69978439911085 246.6390119787316 253.57222508443027 235.39637340138825 180.44286899309904 189.12914332953846 230.71455120359266 239.18017664613652 190.25308435701268 272.071464554755 170.13196379375592 248.429662619849 141.57710379225892 260.24952784708995 191.00687052491133 233.41085929751725
14 126315789.47368422 154.90293820891682 259.51886878713685 238.00155754465806 230.06350551450683 204.04818964120093 268.90613665128353 278.3264847906343 297.9188012779585 263.6566409047621 233.0199083050203 187.61077770929256 248.62723383299203 286.4701455133114 232.60310746163879 239.4052901964768 236.2464176310728 265.57598176194034 147.03692383069415 277.6510531974962 227.1836707213909 257.47360423760404
15 136842105.2631579 185.3483334431771 288.244503821445 200.98698775078117 262.38887776108334 234.9703059204728 300.94985060984084 285.87677064917756 294.33157443199457 279.39890948160865 259.3397508126547 236.45249789400123 271.87452206742074 303.82141308936383 244.9907631181036 278.33346704069606 268.4523852427911 303.5926700412732 189.8020199536452 273.70698676413116 265.58575844009334 302.29368292558894
16 147368421.0526316 217.15594078315593 313.3082447720697 242.89344419353233 264.4147583865393 269.04264408052796 311.566828934935 285.8760857961845 345.1251253437798 287.88174234070607 267.13349160510745 288.908934617637 254.7768222093582 299.069269646568 258.82332522543845 286.61811474733406 278.37361948642047 313.9588218418845 245.4122034481358 295.88553080961645 285.4122809714888 306.8542738398356
17 157894736.84210527 223.78152848932882 311.36378852218144 290.2786089949661 268.27760689707674 288.8315125849934 331.56831176228144 316.60071037895466 327.69570335721045 335.2528018445355 312.5851707836598 276.15293550821553 300.10106629042417 325.54629257461704 258.3734440263619 323.2678803412703 266.3304482982429 308.70753486351293 217.55363201649232 287.675268513344 294.6170784805455 293.491367597329
18 168421052.63157895 234.71857714785102 314.98354696236817 283.7284783920753 305.4871167595037 327.815720531749 342.18832026294064 347.4369622518482 359.1234421835712 321.55971752705665 296.5348788998464 328.4429737894159 320.2516846670008 323.5348077546857 268.7956971871225 305.5235315637245 316.0435993308176 319.21332096855394 211.6789066732095 343.86831283833516 292.32147242421917 354.51419196696827
19 178947368.42105263 197.38530471809517 334.59399147756875 341.7113641431127 325.66671816942767 310.07803450322547 327.6141084031385 331.2294814979601 414.69330027823304 375.55925973110584 289.038970218636 351.0568013585836 363.8722931092961 352.0182927139413 286.6342829280943 351.55434802859776 334.9405559625817 316.564209680478 194.9518083879657 334.9490503408737 338.65567082843626 398.9040526068277
20 189473684.21052632 273.97604445753996 355.3467957329552 358.03872707494406 338.0551271167819 360.6422533754497 398.6396637395478 368.90517846666216 321.8780714666414 387.91837769185406 400.57232862760486 339.23682612345823 374.71732094908685 346.9451931840495 288.66709963832864 350.67221955265694 337.94357375557075 374.24965236342183 219.90429991178235 365.6490119190427 295.2192700559743 430.01798900672935
21 200000000.0 281.7031864978765 311.4724302511466 355.67379710391947 346.4399628294142 322.5400290457826 406.9658508630175 337.0044558989374 410.9943090128271 380.6061951141608 320.96123184342133 373.0588185175469 321.95514380461293 389.21944143113336 300.4861226395557 379.84359742465773 346.62374156713486 362.50578028277346 193.65573316655662 406.5343745429265 325.86513288240684 355.2923764508021

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