code: import numpy as np
  def 		snake_case__  (		lowercase       ,							lowercase				):
     lowerCAmelCase_:       str         =  np.array(lowercase				)
     lowerCAmelCase_:       int         =  np.array(lowercase				)
  
     lowerCAmelCase_:       List[str]         =  abs(predict - actual				)
     lowerCAmelCase_:       Tuple         =  difference.mean()
  
     return score
  def 		snake_case__  (		lowercase       ,							lowercase				):
     lowerCAmelCase_:       int         =  np.array(lowercase				)
     lowerCAmelCase_:       Dict         =  np.array(lowercase				)
  
     lowerCAmelCase_:       Tuple         =  predict - actual
     lowerCAmelCase_:       Optional[Any]         =  np.square(lowercase				)
  
     lowerCAmelCase_:       Dict         =  square_diff.mean()
     return score
  def 		snake_case__  (		lowercase       ,							lowercase				):
     lowerCAmelCase_:       Any         =  np.array(lowercase				)
     lowerCAmelCase_:       Tuple         =  np.array(lowercase				)
  
     lowerCAmelCase_:       Optional[Any]         =  predict - actual
     lowerCAmelCase_:       Dict         =  np.square(lowercase				)
     lowerCAmelCase_:       Tuple         =  square_diff.mean()
     lowerCAmelCase_:       Union[str, Any]         =  np.sqrt(lowercase				)
     return score
  def 		snake_case__  (		lowercase       ,							lowercase				):
     lowerCAmelCase_:       List[Any]         =  np.array(lowercase				)
     lowerCAmelCase_:       int         =  np.array(lowercase				)
  
     lowerCAmelCase_:       Tuple         =  np.log(predict + 1				)
     lowerCAmelCase_:       Dict         =  np.log(actual + 1				)
  
     lowerCAmelCase_:       Union[str, Any]         =  log_predict - log_actual
     lowerCAmelCase_:       Optional[Any]         =  np.square(lowercase				)
     lowerCAmelCase_:       str         =  square_diff.mean()
  
     lowerCAmelCase_:       List[str]         =  np.sqrt(lowercase				)
  
     return score
  def 		snake_case__  (		lowercase       ,							lowercase				):
     lowerCAmelCase_:       Union[str, Any]         =  np.array(lowercase				)
     lowerCAmelCase_:       Dict         =  np.array(lowercase				)
  
     lowerCAmelCase_:       Tuple         =  predict - actual
     lowerCAmelCase_:       List[str]         =  np.sum(lowercase				) / len(lowercase				)
     lowerCAmelCase_:       Optional[Any]         =  np.sum(lowercase				) / len(lowercase				)
     # print(numerator, denumerator)
     lowerCAmelCase_:       int         =  float(lowercase				) / denumerator * 100
  
     return score
  
  
  
  
  
  
  
  def 		snake_case__  (		lowercase       ,							lowercase				):
     return np.mean(np.array(lowercase				) == np.array(lowercase				)				)
style_context: import random
  
  class 				_lowercase						:
  
  
  
  
  
  
      '''simple docstring'''
  
  
  
  
      def __init__(						self					,	lowerCamelCase__					,	lowerCamelCase__   ):
         lowerCAmelCase_:       int         =  x
         lowerCAmelCase_:       List[str]         =  y
  
  
  
  
      def     _a						(						self   ):
         return (self.x**2 + self.y**2) <= 1
  
  
  
  
      @classmethod
      def     _a						(						cls   ):
         return cls(x=random.random()					,	y=random.random()   )
  
  
  
  
  
  def 		snake_case__  (		lowercase				):
     if number_of_simulations < 1:
        raise ValueError("At least one simulation is necessary to estimate PI."				)
  
     lowerCAmelCase_:       List[Any]         =  0
     for _ in range(lowercase				):
        lowerCAmelCase_:       Tuple         =  Point.random_unit_square()
  
        if random_point.is_in_unit_circle():
           number_in_unit_circle += 1
  
     return 4 * number_in_unit_circle / number_of_simulations
  
  
  if __name__ == "__main__":
   # import doctest
  
   # doctest.testmod()
   from math import pi
  
   a     :			Union[str, Any]					    =						"""Please enter the desired number of Monte Carlo simulations: """
   a     :			int					    =						estimate_pi(int(input(prompt).strip()))
   print(f'''An estimate of PI is {my_pi} with an error of {abs(my_pi - pi)}''')