



"""simple docstring"""






from math import factorial

class 	__SCREAMING_SNAKE_CASE     :


					'''simple docstring'''





					def __init__(	self							:  List[str],  lowerCamelCase							:  List[Any],  lowerCamelCase							:  Dict					)-> Any:
								lowerCamelCase__		:		Any		     =real
								if isinstance(lowerCamelCase,  lowerCamelCase					):
											lowerCamelCase__		:		int		     =[1] * rank
								else:
											lowerCamelCase__		:		int		     =rank



					def __repr__(	self							:  List[Any]					)-> List[Any]:
								return (
								    F'''{self.real}+'''
								    F'''{"+".join(str(lowerCamelCase					)+"E"+str(n+1					)for n,dual in enumerate(self.duals					)					)}'''
								)



					def 		snake_case	(	self							:  Optional[int]					)-> Optional[int]:
								lowerCamelCase__		:		Tuple		     =self.duals.copy()
								while cur[-1] == 0:
											cur.pop(-1					)
								return Dual(self.real,  lowerCamelCase					)



					def __add__(	self							:  int,  lowerCamelCase							:  Union[str, Any]					)-> List[Any]:
								if not isinstance(lowerCamelCase,  lowerCamelCase					):
											return Dual(self.real + other,  self.duals					)
								lowerCamelCase__		:		Any		     =self.duals.copy()
								lowerCamelCase__		:		List[str]		     =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					))					)
								lowerCamelCase__		:		Any		     =[]
								for i in range(len(lowerCamelCase					)					):
											new_duals.append(s_dual[i] + o_dual[i]					)
								return Dual(self.real + other.real,  lowerCamelCase					)

					_a             =							__add__



					def __sub__(	self							:  int,  lowerCamelCase							:  str					)-> Optional[int]:
								return self + other * -1



					def __mul__(	self							:  Dict,  lowerCamelCase							:  Optional[int]					)-> Union[str, Any]:
								if not isinstance(lowerCamelCase,  lowerCamelCase					):
											lowerCamelCase__		:		Optional[Any]		     =[]
											for i in self.duals:
														new_duals.append(i * other					)
											return Dual(self.real * other,  lowerCamelCase					)
								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,  lowerCamelCase					)

					_a             =							__mul__



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



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




					def __pow__(	self							:  Dict,  lowerCamelCase							:  Optional[Any]					)-> Dict:
								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
								lowerCamelCase__		:		Dict		     =self
								for _ in range(n - 1					):
											x *= self
								return x






def 					snake_case__       (		__lowerCamelCase    :   List[Any]							,		__lowerCamelCase    :   List[str]							,		__lowerCamelCase    :   Tuple     ):
			"""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'''     )
			lowerCamelCase__		:		Optional[Any]		     =Dual(lowercase__							,		1     )
			lowerCamelCase__		:		Dict		     =func(lowercase__     )
			if order == 0:
						return result.real
			return result.duals[order - 1] * factorial(lowercase__     )


if __name__ == "__main__":
		import doctest

		doctest.testmod()






		def 					snake_case__       (		__lowerCamelCase    :   Any     ):
					"""simple docstring"""
					return y**2 * y**4



		print(differentiate(f, 9, 2))









"""simple docstring"""






from typing import List

import jiwer
import jiwer.transforms as tr
from packaging import version

import datasets
from datasets.config import PY_VERSION


if PY_VERSION < version.parse("3.8"):
		import importlib_metadata
else:
		import importlib.metadata as importlib_metadata


_lowercase			:			List[str]										=						""


if version.parse(importlib_metadata.version("jiwer")) < version.parse("2.3.0"):

		class 	__SCREAMING_SNAKE_CASE     (				tr.AbstractTransform       ):


							'''simple docstring'''





							def __init__(	self							:  List[Any],  lowerCamelCase							:  str = " "					)-> List[str]:
										lowerCamelCase__		:		List[str]		     =sentence_delimiter



							def 		snake_case	(	self							:  Any,  lowerCamelCase							:  str					)-> Optional[Any]:
										return list(lowerCamelCase					)




							def 		snake_case	(	self							:  Optional[Any],  lowerCamelCase							:  List[str]					)-> Tuple:
										lowerCamelCase__		:		Optional[int]		     =[]
										for sent_idx, sentence in enumerate(lowerCamelCase					):
													chars.extend(self.process_string(lowerCamelCase					)					)
													if self.sentence_delimiter is not None and self.sentence_delimiter != "" and sent_idx < len(lowerCamelCase					) - 1:
																chars.append(self.sentence_delimiter					)
										return chars





		_lowercase			:			Optional[int]										=						tr.Compose(
		    [tr.RemoveMultipleSpaces(), tr.Strip(), SentencesToListOfCharacters(SENTENCE_DELIMITER)]
		)
else:
		_lowercase			:			List[str]										=						tr.Compose(
		    [
		        tr.RemoveMultipleSpaces(),
		        tr.Strip(),
		        tr.ReduceToSingleSentence(SENTENCE_DELIMITER),
		        tr.ReduceToListOfListOfChars(),
		    ]
		)


_lowercase			:			Dict										=						"\\n@inproceedings{inproceedings,\n    author = {Morris, Andrew and Maier, Viktoria and Green, Phil},\n    year = {2004},\n    month = {01},\n    pages = {},\n    title = {From WER and RIL to MER and WIL: improved evaluation measures for connected speech recognition.}\n}\n"

_lowercase			:			List[Any]										=						"\\nCharacter error rate (CER) is a common metric of the performance of an automatic speech recognition system.\n\nCER is similar to Word Error Rate (WER), but operates on character instead of word. Please refer to docs of WER for further information.\n\nCharacter error rate can be computed as:\n\nCER = (S + D + I) / N = (S + D + I) / (S + D + C)\n\nwhere\n\nS is the number of substitutions,\nD is the number of deletions,\nI is the number of insertions,\nC is the number of correct characters,\nN is the number of characters in the reference (N=S+D+C).\n\nCER's output is not always a number between 0 and 1, in particular when there is a high number of insertions. This value is often associated to the percentage of characters that were incorrectly predicted. The lower the value, the better the\nperformance of the ASR system with a CER of 0 being a perfect score.\n"

_lowercase			:			Dict										=						"\nComputes CER score of transcribed segments against references.\nArgs:\n    references: list of references for each speech input.\n    predictions: list of transcribtions to score.\n    concatenate_texts: Whether or not to concatenate sentences before evaluation, set to True for more accurate result.\nReturns:\n    (float): the character error rate\n\nExamples:\n\n    >>> predictions = [\"this is the prediction\", \"there is an other sample\"]\n    >>> references = [\"this is the reference\", \"there is another one\"]\n    >>> cer = datasets.load_metric(\"cer\")\n    >>> cer_score = cer.compute(predictions=predictions, references=references)\n    >>> print(cer_score)\n    0.34146341463414637\n"

@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION		,       _KWARGS_DESCRIPTION       )
class 	__SCREAMING_SNAKE_CASE     (				datasets.Metric       ):


					'''simple docstring'''





					def 		snake_case	(	self							:  Dict					)-> Optional[Any]:
								return datasets.MetricInfo(
								    description=_DESCRIPTION,  citation=_CITATION,  inputs_description=_KWARGS_DESCRIPTION,  features=datasets.Features(
								        {
								            '''predictions''': datasets.Value('''string''',  id='''sequence'''					),
								            '''references''': datasets.Value('''string''',  id='''sequence'''					),
								        }					),  codebase_urls=['''https://github.com/jitsi/jiwer/'''],  reference_urls=[
								        '''https://en.wikipedia.org/wiki/Word_error_rate''',
								        '''https://sites.google.com/site/textdigitisation/qualitymeasures/computingerrorrates''',
								    ],  )




					def 		snake_case	(	self							:  Optional[Any],  lowerCamelCase							:  Union[str, Any],  lowerCamelCase							:  List[str],  lowerCamelCase							:  Dict=False					)-> List[Any]:
								if concatenate_texts:
											return jiwer.compute_measures(
											    lowerCamelCase,  lowerCamelCase,  truth_transform=lowerCamelCase,  hypothesis_transform=lowerCamelCase,  )["wer"]

								lowerCamelCase__		:		Optional[Any]		     =0
								lowerCamelCase__		:		Union[str, Any]		     =0
								for prediction, reference in zip(lowerCamelCase,  lowerCamelCase					):
											lowerCamelCase__		:		int		     =jiwer.compute_measures(
											    lowerCamelCase,  lowerCamelCase,  truth_transform=lowerCamelCase,  hypothesis_transform=lowerCamelCase,  )
											incorrect += measures["substitutions"] + measures["deletions"] + measures["insertions"]
											total += measures["substitutions"] + measures["deletions"] + measures["hits"]

								return incorrect / total




