






import timeit

import numpy as np

import datasets
from datasets.arrow_writer import ArrowWriter
from datasets.features.features import _ArrayXD







def      snake_case		(							UpperCAmelCase	:       Tuple   ):
				def wrapper(*UpperCAmelCase	:       List[str],						**UpperCAmelCase	:       str   ):
								A	 =      timeit.default_timer()
								A	 =      func(*UpperCAmelCase,						**UpperCAmelCase   )
								A	 =      timeit.default_timer() - starttime
								return delta

				A	 =      func.__name__

				return wrapper







def      snake_case		(							UpperCAmelCase	:       dict,						UpperCAmelCase	:       int=1_00,						UpperCAmelCase	:       Optional[Any]=None   ):
				A	 =      []
				A	 =      seq_shapes or {}
				for i in range(UpperCAmelCase   ):
								A	 =      {}
								for col_id, (k, v) in enumerate(features.items()   ):
												if isinstance(UpperCAmelCase,						_ArrayXD   ):
																A	 =      np.random.rand(*v.shape   ).astype(v.dtype   )
												elif isinstance(UpperCAmelCase,						datasets.Value   ):
																if v.dtype == "string":
																				A	 =      'The small grey turtle was surprisingly fast when challenged.'
																else:
																				A	 =      np.random.randint(10,						size=1   ).astype(v.dtype   ).item()
												elif isinstance(UpperCAmelCase,						datasets.Sequence   ):
																while isinstance(UpperCAmelCase,						datasets.Sequence   ):
																				A	 =      v.feature
																A	 =      seq_shapes[k]
																A	 =      np.random.rand(*UpperCAmelCase   ).astype(v.dtype   )
												A	 =      data

								dummy_data.append((i, example)   )

				return dummy_data







def      snake_case		(							UpperCAmelCase	:       Union[str, Any],						UpperCAmelCase	:       Dict,						UpperCAmelCase	:       Dict=1_00,						UpperCAmelCase	:       str=None   ):
				A	 =      generate_examples(UpperCAmelCase,						num_examples=UpperCAmelCase,						seq_shapes=UpperCAmelCase   )

				with ArrowWriter(features=UpperCAmelCase,						path=UpperCAmelCase   ) as writer:
								for key, record in dummy_data:
												A	 =      features.encode_example(UpperCAmelCase   )
												writer.write(UpperCAmelCase   )

								A ,		A	 =      writer.finalize()

				if not num_final_examples == num_examples:
								raise ValueError(
								    f'Error writing the dataset, wrote {num_final_examples} examples but should have written {num_examples}.'   )

				A	 =      datasets.Dataset.from_file(filename=UpperCAmelCase,						info=datasets.DatasetInfo(features=UpperCAmelCase   )   )

				return dataset













from math import factorial
class      UpperCamelCase :







		"""simple docstring"""



		def __init__(  self		:       Any						,_SCREAMING_SNAKE_CASE		:       List[Any]						,_SCREAMING_SNAKE_CASE		:       List[str]		)    ->   List[str]:


						'''simple docstring'''
						A	 =      real
						if isinstance(_SCREAMING_SNAKE_CASE						,_SCREAMING_SNAKE_CASE		):
										A	 =      [1] * rank
						else:
										A	 =      rank
		def __repr__(  self		:       Any		)    ->   Optional[Any]:


						'''simple docstring'''
						return (
						    f'{self.real}+'
						    f'{"+".join(str(_SCREAMING_SNAKE_CASE		)+"E"+str(n+1		)for n,dual in enumerate(self.duals		)		)}'
						)
		def       A(  self		:       Optional[Any]		)    ->   Tuple:


						'''simple docstring'''
						A	 =      self.duals.copy()
						while cur[-1] == 0:
										cur.pop(-1		)
						return Dual(self.real						,_SCREAMING_SNAKE_CASE		)
		def __add__(  self		:       Optional[Any]						,_SCREAMING_SNAKE_CASE		:       int		)    ->   Any:


						'''simple docstring'''
						if not isinstance(_SCREAMING_SNAKE_CASE						,_SCREAMING_SNAKE_CASE		):
										return Dual(self.real + other						,self.duals		)
						A	 =      self.duals.copy()
						A	 =      other.duals.copy()
						if len(_SCREAMING_SNAKE_CASE		) > len(_SCREAMING_SNAKE_CASE		):
										o_dual.extend([1] * (len(_SCREAMING_SNAKE_CASE		) - len(_SCREAMING_SNAKE_CASE		))		)
						elif len(_SCREAMING_SNAKE_CASE		) < len(_SCREAMING_SNAKE_CASE		):
										s_dual.extend([1] * (len(_SCREAMING_SNAKE_CASE		) - len(_SCREAMING_SNAKE_CASE		))		)
						A	 =      []
						for i in range(len(_SCREAMING_SNAKE_CASE		)		):
										new_duals.append(s_dual[i] + o_dual[i]		)
						return Dual(self.real + other.real						,_SCREAMING_SNAKE_CASE		)

		snake_case    =   __add__
		def __sub__(  self		:       Tuple						,_SCREAMING_SNAKE_CASE		:       Dict		)    ->   Optional[Any]:


						'''simple docstring'''
						return self + other * -1
		def __mul__(  self		:       Any						,_SCREAMING_SNAKE_CASE		:       Union[str, Any]		)    ->   Union[str, Any]:


						'''simple docstring'''
						if not isinstance(_SCREAMING_SNAKE_CASE						,_SCREAMING_SNAKE_CASE		):
										A	 =      []
										for i in self.duals:
														new_duals.append(i * other		)
										return Dual(self.real * other						,_SCREAMING_SNAKE_CASE		)
						A	 =      [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						,_SCREAMING_SNAKE_CASE		)

		snake_case    =   __mul__
		def __truediv__(  self		:       Union[str, Any]						,_SCREAMING_SNAKE_CASE		:       int		)    ->   List[str]:


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


						'''simple docstring'''
						if not isinstance(_SCREAMING_SNAKE_CASE						,_SCREAMING_SNAKE_CASE		):
										A	 =      []
										for i in self.duals:
														new_duals.append(i // other		)
										return Dual(self.real // other						,_SCREAMING_SNAKE_CASE		)
						raise ValueError







		def __pow__(  self		:       int						,_SCREAMING_SNAKE_CASE		:       Union[str, Any]		)    ->   str:


						'''simple docstring'''
						if n < 0 or isinstance(_SCREAMING_SNAKE_CASE						,_SCREAMING_SNAKE_CASE		):
										raise ValueError('power must be a positive integer'		)
						if n == 0:
										return 1
						if n == 1:
										return self
						A	 =      self
						for _ in range(n - 1		):
										x *= self
						return x







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


if __name__ == "__main__":
					import doctest

					doctest.testmod()







					def      snake_case		(							UpperCAmelCase	:       int   ):
									return y**2 * y**4



					print(differentiate(f, 9, 2))





