
'''simple docstring'''





import math as m





def        snake_case							(		UpperCAmelCase      ,  UpperCAmelCase      ,  UpperCAmelCase=0.001	)->			Union[str, Any]:







      """simple docstring"""
      return (f(a + h	) - f(a - h	)) / (2 * h)





def        snake_case							(		UpperCAmelCase      ,  UpperCAmelCase=0      ,  UpperCAmelCase=1_0_0      ,  UpperCAmelCase=0.0001      ,  UpperCAmelCase=1e-6      ,  UpperCAmelCase=False	)->			Union[str, Any]:







      """simple docstring"""
      __A       	=			xa  # set the initial guess
      __A       	=			[a]
      __A       	=			abs(f(UpperCAmelCase	)	)
      __A       	=			lambda UpperCAmelCase	: calc_derivative(UpperCAmelCase      ,  UpperCAmelCase      ,  h=UpperCAmelCase	)  # noqa: E731  Derivative of f(x)
      for _ in range(UpperCAmelCase	):
            if fa(UpperCAmelCase	) == 0:
                  raise ValueError('No converging solution found'	)
            __A       	=			a - f(UpperCAmelCase	) / fa(UpperCAmelCase	)  # Calculate the next estimate
            if logsteps:
                  steps.append(UpperCAmelCase	)
            if error < maxerror:
                  break
      else:
            raise ValueError('Iteration limit reached, no converging solution found'	)
      if logsteps:
            # If logstep is true, then log intermediate steps
            return a, error, steps
      return a, error


if __name__ == "__main__":
 from matplotlib import pyplot as plt

 a__		:   int            =       lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
 a__       ,		a__       ,		a__		:   Optional[int]            =       newton_raphson(
     f, xa=1_0, maxiter=1_0_0_0, step=1E-6, logsteps=True
 )
 plt.plot([abs(f(x)) for x in steps])
 plt.xlabel("step")
 plt.ylabel("error")
 plt.show()
 print(f'''solution = {{{solution:f}}}, error = {{{error:f}}}''')








'''simple docstring'''





from .hash_table import HashTable
from .number_theory.prime_numbers import is_prime, next_prime


class  UpperCamelCase__  (    SCREAMING_SNAKE_CASE):






 def __init__(			self  :Union[str, Any]	,				*_A  :int	,				**_A  :Optional[Any]			)				->			Union[str, Any]:







       '''simple docstring'''



       super().__init__(*_A	,				**_A			)






 def 	lowercase_						(			self  :Dict	,				_A  :Union[str, Any]	,				_A  :Dict			)				->			Dict:







       '''simple docstring'''



       __A       	=			(
           next_prime(value % self.size_table			)
           if not is_prime(value % self.size_table			)
           else value % self.size_table
       )  # gt = bigger than
       return next_prime_gt - (data % next_prime_gt)






 def 	lowercase_						(			self  :List[Any]	,				_A  :int	,				_A  :Tuple	,				_A  :Union[str, Any]			)				->			List[Any]:







       '''simple docstring'''



       return (increment * self.__hash_function_a(_A	,				_A			)) % self.size_table






 def 	lowercase_						(			self  :List[Any]	,				_A  :List[str]	,				_A  :str=None			)				->			List[Any]:







       '''simple docstring'''



       __A       	=			1
       __A       	=			self.hash_function(_A			)

       while self.values[new_key] is not None and self.values[new_key] != key:
             __A       	=			(
                 self.__hash_double_function(_A	,				_A	,				_A			)
                 if self.balanced_factor() >= self.lim_charge
                 else None
             )
             if new_key is None:
                   break
             else:
                   i += 1

       return new_key






