





from math import factorial



class   _SCREAMING_SNAKE_CASE		:







 '''simple docstring'''

 def __init__(self							:  Union[str, Any]			,					UpperCAmelCase_							:  Dict			,					UpperCAmelCase_							:  List[str])			->Optional[Any]:



   '''simple docstring'''



   lowerCamelCase__: Optional[Any]         =real
   if isinstance(UpperCAmelCase_			,					UpperCAmelCase_):
     lowerCamelCase__: Optional[int]         =[1] * rank
   else:
     lowerCamelCase__: str         =rank

 def __repr__(self							:  Optional[int])			->Optional[Any]:



   '''simple docstring'''



   return (
       F"""{self.real}+"""
       F"""{"+".join(str(UpperCAmelCase_)+"E"+str(n+1)for n,dual in enumerate(self.duals))}"""
   )

 def 				SCREAMING_SNAKE_CASE_   (self							:  Tuple)			->Any:



   '''simple docstring'''



   lowerCamelCase__: Any         =self.duals.copy()
   while cur[-1] == 0:
     cur.pop(-1)
   return Dual(self.real			,					UpperCAmelCase_)

 def __add__(self							:  Union[str, Any]			,					UpperCAmelCase_							:  List[str])			->List[Any]:



   '''simple docstring'''



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

 lowercase_						=     __add__

 def __sub__(self							:  Union[str, Any]			,					UpperCAmelCase_							:  List[Any])			->str:



   '''simple docstring'''



   return self + other * -1

 def __mul__(self							:  str			,					UpperCAmelCase_							:  Optional[int])			->Union[str, Any]:



   '''simple docstring'''



   if not isinstance(UpperCAmelCase_			,					UpperCAmelCase_):
     lowerCamelCase__: Dict         =[]
     for i in self.duals:
       new_duals.append(i * other)
     return Dual(self.real * other			,					UpperCAmelCase_)
   lowerCamelCase__: Any         =[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			,					UpperCAmelCase_)

 lowercase_						=     __mul__

 def __truediv__(self							:  Tuple			,					UpperCAmelCase_							:  str)			->List[str]:



   '''simple docstring'''



   if not isinstance(UpperCAmelCase_			,					UpperCAmelCase_):
     lowerCamelCase__: Tuple         =[]
     for i in self.duals:
       new_duals.append(i / other)
     return Dual(self.real / other			,					UpperCAmelCase_)
   raise ValueError

 def __floordiv__(self							:  Union[str, Any]			,					UpperCAmelCase_							:  Dict)			->int:



   '''simple docstring'''



   if not isinstance(UpperCAmelCase_			,					UpperCAmelCase_):
     lowerCamelCase__: Any         =[]
     for i in self.duals:
       new_duals.append(i // other)
     return Dual(self.real // other			,					UpperCAmelCase_)
   raise ValueError







 def __pow__(self							:  List[Any]			,					UpperCAmelCase_							:  Optional[Any])			->Tuple:



   '''simple docstring'''



   if n < 0 or isinstance(UpperCAmelCase_			,					UpperCAmelCase_):
     raise ValueError("power must be a positive integer")
   if n == 0:
     return 1
   if n == 1:
     return self
   lowerCamelCase__: Union[str, Any]         =self
   for _ in range(n - 1):
     x *= self
   return x





def 	lowerCAmelCase_					(			__a      ,       __a      ,       __a						)	->						Any:







  """simple docstring"""





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


if __name__ == "__main__":
     import doctest

     doctest.testmod()





     def 	lowerCAmelCase_					(			__a						)	->						str:







       """simple docstring"""





       return y**2 * y**4






     print(differentiate(f, 9, 2))







# Copyright 2021 The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

from argparse import ArgumentParser

from accelerate.commands.config import get_config_parser
from accelerate.commands.env import env_command_parser
from accelerate.commands.launch import launch_command_parser
from accelerate.commands.test import test_command_parser
from accelerate.commands.tpu import tpu_command_parser







def      lowerCamelCase_						(			)	->			Union[str, Any]:





				"""simple docstring"""


				__lowerCamelCase									=       ArgumentParser('Accelerate CLI tool'					,	usage='accelerate <command> [<args>]'					,	allow_abbrev=UpperCamelCase__ )
				__lowerCamelCase									=       parser.add_subparsers(help='accelerate command helpers' )

				# Register commands
				get_config_parser(subparsers=UpperCamelCase__ )
				env_command_parser(subparsers=UpperCamelCase__ )
				launch_command_parser(subparsers=UpperCamelCase__ )
				tpu_command_parser(subparsers=UpperCamelCase__ )
				test_command_parser(subparsers=UpperCamelCase__ )

				# Let's go
				__lowerCamelCase									=       parser.parse_args()

				if not hasattr(UpperCamelCase__					,	'func' ):
								parser.print_help()
								exit(1 )

				# Run
				args.func(UpperCamelCase__ )


if __name__ == "__main__":
					main()


