
from math import factorial


class     lowercase :



		def __init__(			self    ,				A_    ,				A_	)  -> List[str]:
				"""simple docstring"""
				UpperCamelCase          =					real
				if isinstance(A_    ,				A_	):
						UpperCamelCase          =					[1] * rank
				else:
						UpperCamelCase          =					rank



		def __repr__(			self	)  -> str:
				"""simple docstring"""
				return (
				    F'''{self.real}+'''
				    F'''{'+'.join(str(A_	)+'E'+str(n+1	)for n,dual in enumerate(self.duals	)	)}'''
				)



		def __UpperCamelCase			(			self	)  -> Tuple:
				"""simple docstring"""
				UpperCamelCase          =					self.duals.copy()
				while cur[-1] == 0:
						cur.pop(-1	)
				return Dual(self.real    ,				A_	)



		def __add__(			self    ,				A_	)  -> Optional[Any]:
				"""simple docstring"""
				if not isinstance(A_    ,				A_	):
						return Dual(self.real + other    ,				self.duals	)
				UpperCamelCase          =					self.duals.copy()
				UpperCamelCase          =					other.duals.copy()
				if len(A_	) > len(A_	):
						o_dual.extend([1] * (len(A_	) - len(A_	))	)
				elif len(A_	) < len(A_	):
						s_dual.extend([1] * (len(A_	) - len(A_	))	)
				UpperCamelCase          =					[]
				for i in range(len(A_	)	):
						new_duals.append(s_dual[i] + o_dual[i]	)
				return Dual(self.real + other.real    ,				A_	)

		__lowercase	:	List[str]     					=    __add__



		def __sub__(			self    ,				A_	)  -> List[str]:
				"""simple docstring"""
				return self + other * -1



		def __mul__(			self    ,				A_	)  -> Any:
				"""simple docstring"""
				if not isinstance(A_    ,				A_	):
						UpperCamelCase          =					[]
						for i in self.duals:
								new_duals.append(i * other	)
						return Dual(self.real * other    ,				A_	)
				UpperCamelCase          =					[0] * (len(self.duals	) + len(other.duals	) + 1)
				for i, item in enumerate(self.duals	):
						for j, jtem in enumerate(other.duals	):
								new_duals[i + j + 1] += item * jtem
				for k in range(len(self.duals	)	):
						new_duals[k] += self.duals[k] * other.real
				for index in range(len(other.duals	)	):
						new_duals[index] += other.duals[index] * self.real
				return Dual(self.real * other.real    ,				A_	)

		__lowercase	:	Tuple     					=    __mul__



		def __truediv__(			self    ,				A_	)  -> Union[str, Any]:
				"""simple docstring"""
				if not isinstance(A_    ,				A_	):
						UpperCamelCase          =					[]
						for i in self.duals:
								new_duals.append(i / other	)
						return Dual(self.real / other    ,				A_	)
				raise ValueError



		def __floordiv__(			self    ,				A_	)  -> Optional[Any]:
				"""simple docstring"""
				if not isinstance(A_    ,				A_	):
						UpperCamelCase          =					[]
						for i in self.duals:
								new_duals.append(i // other	)
						return Dual(self.real // other    ,				A_	)
				raise ValueError



		def __pow__(			self    ,				A_	)  -> Dict:
				"""simple docstring"""
				if n < 0 or isinstance(A_    ,				A_	):
						raise ValueError('power must be a positive integer'	)
				if n == 0:
						return 1
				if n == 1:
						return self
				UpperCamelCase          =					self
				for _ in range(n - 1	):
						x *= self
				return x






def 				A	( lowercase   ,	lowercase   ,	lowercase			)       ->  Union[str, Any]:
		'''simple docstring'''

		if not callable(lowercase			):
				raise ValueError('differentiate() requires a function as input for func'			)
		if not isinstance(lowercase   ,	(float, int)			):
				raise ValueError('differentiate() requires a float as input for position'			)
		if not isinstance(lowercase   ,	lowercase			):
				raise ValueError('differentiate() requires an int as input for order'			)
		UpperCamelCase          =					Dual(lowercase   ,	1			)
		UpperCamelCase          =					func(lowercase			)
		if order == 0:
				return result.real
		return result.duals[order - 1] * factorial(lowercase			)


if __name__ == "__main__":
					import doctest

					doctest.testmod()


					def 				A	( lowercase			)       ->  Optional[Any]:
							'''simple docstring'''

							return y**2 * y**4


					print(differentiate(f, 9, 2))


import darl  # noqa
import gym
import tqdm
from diffusers.experimental import ValueGuidedRLPipeline


_UpperCAmelCase :			Optional[Any]              =	{
    "n_samples": 64,
    "horizon": 32,
    "num_inference_steps": 20,
    "n_guide_steps": 2,  # can set to 0 for faster sampling, does not use value network
    "scale_grad_by_std": True,
    "scale": 0.1,
    "eta": 0.0,
    "t_grad_cutoff": 2,
    "device": "cpu",
}


if __name__ == "__main__":
					_UpperCAmelCase :			int              =	"hopper-medium-v2"
					_UpperCAmelCase :			Tuple              =	gym.make(env_name)

					_UpperCAmelCase :			Any              =	ValueGuidedRLPipeline.from_pretrained(
					    "bglick13/hopper-medium-v2-value-function-hor32",
					    env=env,
					)

					env.seed(0)
					_UpperCAmelCase :			Optional[Any]              =	env.reset()
					_UpperCAmelCase :			Union[str, Any]              =	0
					_UpperCAmelCase :			Union[str, Any]              =	0
					_UpperCAmelCase :			Dict              =	1_000
					_UpperCAmelCase :			Tuple              =	[obs.copy()]
					try:
										for t in tqdm.tqdm(range(T)):
															# call the policy
															_UpperCAmelCase :			int              =	pipeline(obs, planning_horizon=32)

															# execute action in environment
															_UpperCAmelCase       ,_UpperCAmelCase       ,_UpperCAmelCase       ,_UpperCAmelCase :			List[Any]              =	env.step(denorm_actions)
															_UpperCAmelCase :			int              =	env.get_normalized_score(total_reward)

															# update return
															total_reward += reward
															total_score += score
															print(
															    F'''Step: {t}, Reward: {reward}, Total Reward: {total_reward}, Score: {score}, Total Score:'''
															    F''' {total_score}'''
															)

															# save observations for rendering
															rollout.append(next_observation.copy())

															_UpperCAmelCase :			Union[str, Any]              =	next_observation
					except KeyboardInterrupt:
										pass

					print(F'''Total reward: {total_reward}''')
