





import colorsys

from PIL import Image  # type: ignore




def     a__ (					lowercase__  ,    lowercase__  ,    lowercase__  ):






   '''simple docstring'''






   UpperCAmelCase_											=x
   UpperCAmelCase_											=y
   for step in range(lowercase__  ):  # noqa: B007
      UpperCAmelCase_											=a * a - b * b + x
      UpperCAmelCase_											=2 * a * b + y
      UpperCAmelCase_											=a_new

      # divergence happens for all complex number with an absolute value
      # greater than 4
      if a * a + b * b > 4:
         break
   return step / (max_step - 1)




def     a__ (					lowercase__  ):






   '''simple docstring'''






   if distance == 1:
      return (0, 0, 0)
   else:
      return (2_5_5, 2_5_5, 2_5_5)




def     a__ (					lowercase__  ):






   '''simple docstring'''






   if distance == 1:
      return (0, 0, 0)
   else:
      return tuple(round(i * 2_5_5  ) for i in colorsys.hsv_to_rgb(lowercase__  ,    1  ,    1  )  )




def     a__ (					lowercase__ = 8_0_0  ,    lowercase__ = 6_0_0  ,    lowercase__ = -0.6  ,    lowercase__ = 0  ,    lowercase__ = 3.2  ,    lowercase__ = 5_0  ,    lowercase__ = True  ,    ):






   '''simple docstring'''






   UpperCAmelCase_											=Image.new("RGB"  ,    (image_width, image_height)  )
   UpperCAmelCase_											=img.load()

   # loop through the image-coordinates
   for image_x in range(lowercase__  ):
      for image_y in range(lowercase__  ):
         # determine the figure-coordinates based on the image-coordinates
         UpperCAmelCase_											=figure_width / image_width * image_height
         UpperCAmelCase_											=figure_center_x + (image_x / image_width - 0.5) * figure_width
         UpperCAmelCase_											=figure_center_y + (image_y / image_height - 0.5) * figure_height

         UpperCAmelCase_											=get_distance(lowercase__  ,    lowercase__  ,    lowercase__  )

         # color the corresponding pixel based on the selected coloring-function
         if use_distance_color_coding:
            UpperCAmelCase_											=get_color_coded_rgb(lowercase__  )
         else:
            UpperCAmelCase_											=get_black_and_white_rgb(lowercase__  )

   return img


if __name__ == "__main__":
     import doctest

     doctest.testmod()

     # colored version, full figure
     __lowercase  :   Tuple						      =get_image()

     # uncomment for colored version, different section, zoomed in
     # img = get_image(figure_center_x = -0.6, figure_center_y = -0.4,
     # figure_width = 0.8)

     # uncomment for black and white version, full figure
     # img = get_image(use_distance_color_coding = False)

     # uncomment to save the image
     # img.save("mandelbrot.png")

     img.show()











import math_equivalence  # From: git+https://github.com/hendrycks/math.git

import datasets


__lowercase  :   int						      ="""\
@article{hendrycksmath2021,
  title={Measuring Mathematical Problem Solving With the MATH Dataset},
  author={Dan Hendrycks
    and Collin Burns
    and Saurav Kadavath
    and Akul Arora
    and Steven Basart
    and Eric Tang
    and Dawn Song
    and Jacob Steinhardt},
  journal={arXiv preprint arXiv:2103.03874},
  year={2021}
}
"""


__lowercase  :   List[Any]						      ="""\
This metric is used to assess performance on the Mathematics Aptitude Test of Heuristics (MATH) dataset.
It first canonicalizes the inputs (e.g., converting \"1/2\" to \"\\frac{1}{2}\") and then computes accuracy.
"""


__lowercase  :   str						      =R"""
Calculates accuracy after canonicalizing inputs.

Args:
    predictions: list of predictions to score. Each prediction
        is a string that contains natural language and LaTex.
    references: list of reference for each prediction. Each
        reference is a string that contains natural language
        and LaTex.
Returns:
    accuracy: accuracy after canonicalizing inputs
        (e.g., converting \"1/2\" to \"\\frac{1}{2}\")

Examples:
    >>> metric = datasets.load_metric(\"competition_math\")
    >>> results = metric.compute(references=[\"\\frac{1}{2}\"], predictions=[\"1/2\"])
    >>> print(results)
    {'accuracy': 1.0}
"""

@datasets.utils.file_utils.add_end_docstrings(_DESCRIPTION		,      _KWARGS_DESCRIPTION						)
class      A       (	datasets.Metric						):



      def 	lowerCAmelCase__    (	self:						Any       )						->    Optional[Any]:
         '''simple docstring'''

         return datasets.MetricInfo(
             description=_DESCRIPTION		,  citation=_CITATION		,  inputs_description=_KWARGS_DESCRIPTION		,  features=datasets.Features(
                 {
                     "predictions": datasets.Value("string"       ),
                     "references": datasets.Value("string"       ),
                 }       )		,  homepage="https://github.com/hendrycks/math"		,  codebase_urls=["https://github.com/hendrycks/math"]		,  )






      def 	lowerCAmelCase__    (	self:						Any		,  _lowerCAmelCase:						Tuple		,  _lowerCAmelCase:						Union[str, Any]       )						->    Dict:
         '''simple docstring'''

         UpperCAmelCase_											=0.0
         for i, j in zip(_lowerCAmelCase		,  _lowerCAmelCase       ):
            n_correct += 1.0 if math_equivalence.is_equiv(_lowerCAmelCase		,  _lowerCAmelCase       ) else 0.0
         UpperCAmelCase_											=n_correct / len(_lowerCAmelCase       )
         return {
             "accuracy": accuracy,
         }




