

from math import factorial





class        lowerCAmelCase__  :



       '''simple docstring'''







       def __init__(							self ,   lowercase__ ,   lowercase__     ):







             '''simple docstring'''



             __A    =real
             if isinstance(lowercase__ ,   lowercase__     ):
                   __A    =[1] * rank
             else:
                   __A    =rank

       def __repr__(							self     ):







             '''simple docstring'''



             return (
                 f'''{self.real}+'''
                 f'''{'+'.join(str(lowercase__     )+'E'+str(n+1     )for n,dual in enumerate(self.duals     )     )}'''
             )

       def     __UpperCamelCase     (							self     ):







             '''simple docstring'''



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

       def __add__(							self ,   lowercase__     ):







             '''simple docstring'''



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

       lowercase_						=    __add__

       def __sub__(							self ,   lowercase__     ):







             '''simple docstring'''



             return self + other * -1

       def __mul__(							self ,   lowercase__     ):







             '''simple docstring'''



             if not isinstance(lowercase__ ,   lowercase__     ):
                   __A    =[]
                   for i in self.duals:
                         new_duals.append(i * other     )
                   return Dual(self.real * other ,   lowercase__     )
             __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 ,   lowercase__     )

       lowercase_						=    __mul__

       def __truediv__(							self ,   lowercase__     ):







             '''simple docstring'''



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

       def __floordiv__(							self ,   lowercase__     ):







             '''simple docstring'''



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


       def __pow__(							self ,   lowercase__     ):







             '''simple docstring'''



             if n < 0 or isinstance(lowercase__ ,   lowercase__     ):
                   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      A__					(			__A  :						List[str]     ,				__A  :						Union[str, Any]     ,				__A  :						List[str]			)					->Optional[int]:
      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'''			)
      __A    =Dual(__A     ,				1			)
      __A    =func(__A			)
      if order == 0:
            return result.real
      return result.duals[order - 1] * factorial(__A			)


if __name__ == "__main__":
   import doctest

   doctest.testmod()





   def      A__					(			__A  :						List[str]			)					->Dict:
         return y**2 * y**4


   print(differentiate(f, 9, 2))





import numpy as np
from nltk.translate import meteor_score

import datasets
from datasets.config import importlib_metadata, version


_lowerCamelCase      :					List[str]					    =      version.parse(importlib_metadata.version('''nltk'''))
if NLTK_VERSION >= version.Version('''3.6.4'''):
   from nltk import word_tokenize


_lowerCamelCase      :					Dict					    =      '''\
@inproceedings{banarjee2005,
  title     = {{METEOR}: An Automatic Metric for {MT} Evaluation with Improved Correlation with Human Judgments},
  author    = {Banerjee, Satanjeev  and Lavie, Alon},
  booktitle = {Proceedings of the {ACL} Workshop on Intrinsic and Extrinsic Evaluation Measures for Machine Translation and/or Summarization},
  month     = jun,
  year      = {2005},
  address   = {Ann Arbor, Michigan},
  publisher = {Association for Computational Linguistics},
  url       = {https://www.aclweb.org/anthology/W05-0909},
  pages     = {65--72},
}
'''

_lowerCamelCase      :					str					    =      '''\
METEOR, an automatic metric for machine translation evaluation
that is based on a generalized concept of unigram matching between the
machine-produced translation and human-produced reference translations.
Unigrams can be matched based on their surface forms, stemmed forms,
and meanings; furthermore, METEOR can be easily extended to include more
advanced matching strategies. Once all generalized unigram matches
between the two strings have been found, METEOR computes a score for
this matching using a combination of unigram-precision, unigram-recall, and
a measure of fragmentation that is designed to directly capture how
well-ordered the matched words in the machine translation are in relation
to the reference.

METEOR gets an R correlation value of 0.347 with human evaluation on the Arabic
data and 0.331 on the Chinese data. This is shown to be an improvement on
using simply unigram-precision, unigram-recall and their harmonic F1
combination.
'''

_lowerCamelCase      :					Union[str, Any]					    =      '''
Computes METEOR score of translated segments against one or more references.
Args:
    predictions: list of predictions to score. Each prediction
        should be a string with tokens separated by spaces.
    references: list of reference for each prediction. Each
        reference should be a string with tokens separated by spaces.
    alpha: Parameter for controlling relative weights of precision and recall. default: 0.9
    beta: Parameter for controlling shape of penalty as a function of fragmentation. default: 3
    gamma: Relative weight assigned to fragmentation penalty. default: 0.5
Returns:
    \'meteor\': meteor score.
Examples:

    >>> meteor = datasets.load_metric(\'meteor\')
    >>> predictions = ["It is a guide to action which ensures that the military always obeys the commands of the party"]
    >>> references = ["It is a guide to action that ensures that the military will forever heed Party commands"]
    >>> results = meteor.compute(predictions=predictions, references=references)
    >>> print(round(results["meteor"], 4))
    0.6944
'''





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



       '''simple docstring'''







       def     __UpperCamelCase     (							self     ):







             '''simple docstring'''



             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/nltk/nltk/blob/develop/nltk/translate/meteor_score.py'''] ,   reference_urls=[
                     '''https://www.nltk.org/api/nltk.translate.html#module-nltk.translate.meteor_score''',
                     '''https://en.wikipedia.org/wiki/METEOR''',
                 ] ,   )

       def     __UpperCamelCase     (							self ,   lowercase__     ):







             '''simple docstring'''



             import nltk

             nltk.download('''wordnet'''     )
             if NLTK_VERSION >= version.Version('''3.6.5'''     ):
                   nltk.download('''punkt'''     )
             if NLTK_VERSION >= version.Version('''3.6.6'''     ):
                   nltk.download('''omw-1.4'''     )


       def     __UpperCamelCase     (							self ,   lowercase__ ,   lowercase__ ,   lowercase__=0.9 ,   lowercase__=3 ,   lowercase__=0.5     ):







             '''simple docstring'''



             if NLTK_VERSION >= version.Version('''3.6.5'''     ):
                   __A    =[
                       meteor_score.single_meteor_score(
                           word_tokenize(lowercase__     ) ,   word_tokenize(lowercase__     ) ,   alpha=lowercase__ ,   beta=lowercase__ ,   gamma=lowercase__     )
                       for ref, pred in zip(lowercase__ ,   lowercase__     )
                   ]
             else:
                   __A    =[
                       meteor_score.single_meteor_score(lowercase__ ,   lowercase__ ,   alpha=lowercase__ ,   beta=lowercase__ ,   gamma=lowercase__     )
                       for ref, pred in zip(lowercase__ ,   lowercase__     )
                   ]

             return {"meteor": np.mean(lowercase__     )}


