





"""simple docstring"""




from math import factorial


class 			__UpperCamelCase							:






							def __init__(  self ,   lowerCAmelCase__ ,   lowerCAmelCase__ )      ->					int:
								a :						int      =							real
								if isinstance(lowerCAmelCase__ ,   lowerCAmelCase__ ):
									a :						int      =							[1] * rank
								else:
									a :						str      =							rank






							def __repr__(  self )      ->					Dict:
								return (
								    f"""{self.real}+"""
								    f"""{'+'.join(str(lowerCAmelCase__ )+'E'+str(n+1 )for n,dual in enumerate(self.duals ) )}"""
								)






							def        __a  (  self )      ->					Optional[Any]:
								a :						Optional[int]      =							self.duals.copy()
								while cur[-1] == 0:
									cur.pop(-1 )
								return Dual(self.real ,   lowerCAmelCase__ )






							def __add__(  self ,   lowerCAmelCase__ )      ->					List[str]:
								if not isinstance(lowerCAmelCase__ ,   lowerCAmelCase__ ):
									return Dual(self.real + other ,   self.duals )
								a :						Tuple      =							self.duals.copy()
								a :						Optional[Any]      =							other.duals.copy()
								if len(lowerCAmelCase__ ) > len(lowerCAmelCase__ ):
									o_dual.extend([1] * (len(lowerCAmelCase__ ) - len(lowerCAmelCase__ )) )
								elif len(lowerCAmelCase__ ) < len(lowerCAmelCase__ ):
									s_dual.extend([1] * (len(lowerCAmelCase__ ) - len(lowerCAmelCase__ )) )
								a :						Optional[Any]      =							[]
								for i in range(len(lowerCAmelCase__ ) ):
									new_duals.append(s_dual[i] + o_dual[i] )
								return Dual(self.real + other.real ,   lowerCAmelCase__ )

							lowerCamelCase  :   int    =__add__






							def __sub__(  self ,   lowerCAmelCase__ )      ->					Optional[Any]:
								return self + other * -1






							def __mul__(  self ,   lowerCAmelCase__ )      ->					Any:
								if not isinstance(lowerCAmelCase__ ,   lowerCAmelCase__ ):
									a :						int      =							[]
									for i in self.duals:
										new_duals.append(i * other )
									return Dual(self.real * other ,   lowerCAmelCase__ )
								a :						Tuple      =							[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 ,   lowerCAmelCase__ )

							lowerCamelCase  :   List[str]    =__mul__






							def __truediv__(  self ,   lowerCAmelCase__ )      ->					Dict:
								if not isinstance(lowerCAmelCase__ ,   lowerCAmelCase__ ):
									a :						Dict      =							[]
									for i in self.duals:
										new_duals.append(i / other )
									return Dual(self.real / other ,   lowerCAmelCase__ )
								raise ValueError






							def __floordiv__(  self ,   lowerCAmelCase__ )      ->					List[Any]:
								if not isinstance(lowerCAmelCase__ ,   lowerCAmelCase__ ):
									a :						Dict      =							[]
									for i in self.duals:
										new_duals.append(i // other )
									return Dual(self.real // other ,   lowerCAmelCase__ )
								raise ValueError






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






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       str       ,			_lowercase		:       Optional[int]       ,			_lowercase		:       Optional[Any]   )					->List[str]:






	'''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"   )
	a :						Dict      =							Dual(_lowercase       ,			1   )
	a :						Any      =							func(_lowercase   )
	if order == 0:
		return result.real
	return result.duals[order - 1] * factorial(_lowercase   )


if __name__ == "__main__":
		import doctest

		doctest.testmod()






		def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       int   )					->List[Any]:






			'''simple docstring'''






			return y**2 * y**4







		print(differentiate(f, 9, 2))









"""simple docstring"""




import gc
import threading
import time

import psutil
import torch


class 			__UpperCamelCase							:






							def __init__(  self )      ->					Any:
								a :						str      =							psutil.Process()
								a :						str      =							False






							def        __a  (  self )      ->					str:
								a :						List[Any]      =							-1

								while True:
									a :						str      =							max(self.process.memory_info().rss ,   self.cpu_memory_peak )

									# can't sleep or will not catch the peak right (this comment is here on purpose)
									if not self.peak_monitoring:
										break






							def        __a  (  self )      ->					List[str]:
								a :						Dict      =							True
								a :						Optional[Any]      =							threading.Thread(target=self.peak_monitor )
								a :						List[Any]      =							True
								self.thread.start()






							def        __a  (  self )      ->					List[str]:
								a :						Optional[int]      =							False
								self.thread.join()
								return self.cpu_memory_peak
a		:					Tuple	      =     PeakCPUMemory()






def  _SCREAMING_SNAKE_CASE						(      )					->List[Any]:






	'''simple docstring'''






	a :						List[str]      =							{"time": time.time()}

	gc.collect()
	torch.cuda.empty_cache()

	# CPU mem
	a :						Tuple      =							psutil.Process().memory_info().rss
	cpu_peak_tracker.start()

	# GPU mem
	for i in range(torch.cuda.device_count()   ):
		a :						Any      =							torch.cuda.memory_allocated(_lowercase   )
	torch.cuda.reset_peak_memory_stats()

	return measures






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       List[str]   )					->Union[str, Any]:






	'''simple docstring'''






	a :						int      =							{"time": time.time() - start_measures["time"]}

	gc.collect()
	torch.cuda.empty_cache()

	# CPU mem
	a :						List[Any]      =							(psutil.Process().memory_info().rss - start_measures["cpu"]) / 2**20
	a :						Union[str, Any]      =							(cpu_peak_tracker.stop() - start_measures["cpu"]) / 2**20

	# GPU mem
	for i in range(torch.cuda.device_count()   ):
		a :						Optional[Any]      =							(torch.cuda.memory_allocated(_lowercase   ) - start_measures[str(_lowercase   )]) / 2**20
		a :						Optional[Any]      =							(torch.cuda.max_memory_allocated(_lowercase   ) - start_measures[str(_lowercase   )]) / 2**20

	return measures







def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       str       ,			_lowercase		:       Union[str, Any]   )					->Optional[int]:






	'''simple docstring'''






	print(F"""{description}:"""   )
	print(F"""- Time: {measures['time']:.2f}s"""   )
	for i in range(torch.cuda.device_count()   ):
		print(F"""- GPU {i} allocated: {measures[str(_lowercase   )]:.2f}MiB"""   )
		a :						str      =							measures[F"""{i}-peak"""]
		print(F"""- GPU {i} peak: {peak:.2f}MiB"""   )
	print(F"""- CPU RAM allocated: {measures['cpu']:.2f}MiB"""   )
	print(F"""- CPU RAM peak: {measures['cpu-peak']:.2f}MiB"""   )


