


import math as m







def 						_lowercase       (     __lowerCamelCase			:					str		,__lowerCamelCase			:					List[str]		,__lowerCamelCase			:					Tuple=0.0_0_1			)  ->   Union[str, Any]:





     '''simple docstring'''





     return (f(a + h			) - f(a - h			)) / (2 * h)







def 						_lowercase       (     __lowerCamelCase			:					Optional[int]		,__lowerCamelCase			:					Union[str, Any]=0		,__lowerCamelCase			:					int=100		,__lowerCamelCase			:					Optional[Any]=0.0_0_0_1		,__lowerCamelCase			:					int=1e-6		,__lowerCamelCase			:					List[str]=False			)  ->   Any:





     '''simple docstring'''





     UpperCamelCase__							:  str								=     xa  # set the initial guess
     UpperCamelCase__							:  Any								=     [a]
     UpperCamelCase__							:  Optional[Any]								=     abs(f(UpperCamelCase__			)			)
     UpperCamelCase__							:  Tuple								=     lambda __lowerCamelCase			: 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'''			)
          UpperCamelCase__							:  List[Any]								=     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

   _SCREAMING_SNAKE_CASE :					List[str]			=	lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
   _SCREAMING_SNAKE_CASE,       _SCREAMING_SNAKE_CASE,       _SCREAMING_SNAKE_CASE :					Any			=	newton_raphson(
       f, xa=10, maxiter=1000, 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}}}')








import math







def 						_lowercase       (     __lowerCamelCase			:					int			)  ->   str:





     '''simple docstring'''





     if number == 0:
          UpperCamelCase__							:  List[str]								=     '''Zero'''
          return words
     else:
          UpperCamelCase__							:  str								=     math.logaa(__lowerCamelCase			)
          UpperCamelCase__							:  Tuple								=     digits + 1
          UpperCamelCase__							:  List[str]								=     {}
          UpperCamelCase__							:  Optional[int]								=     ''''''
          UpperCamelCase__							:  str								=     '''One'''
          UpperCamelCase__							:  int								=     '''Two'''
          UpperCamelCase__							:  str								=     '''Three'''
          UpperCamelCase__							:  Dict								=     '''Four'''
          UpperCamelCase__							:  List[str]								=     '''Five'''
          UpperCamelCase__							:  int								=     '''Six'''
          UpperCamelCase__							:  str								=     '''Seven'''
          UpperCamelCase__							:  List[str]								=     '''Eight'''
          UpperCamelCase__							:  Tuple								=     '''Nine'''

          UpperCamelCase__							:  int								=     {}
          UpperCamelCase__							:  Any								=     ''''''
          UpperCamelCase__							:  Union[str, Any]								=     '''Twenty'''
          UpperCamelCase__							:  Optional[int]								=     '''Thirty'''
          UpperCamelCase__							:  Optional[int]								=     '''Forty'''
          UpperCamelCase__							:  Any								=     '''Fifty'''
          UpperCamelCase__							:  Optional[Any]								=     '''Sixty'''
          UpperCamelCase__							:  Union[str, Any]								=     '''Seventy'''
          UpperCamelCase__							:  Tuple								=     '''Eighty'''
          UpperCamelCase__							:  Dict								=     '''Ninety'''

          UpperCamelCase__							:  Any								=     {}
          UpperCamelCase__							:  str								=     '''Ten'''
          UpperCamelCase__							:  List[Any]								=     '''Eleven'''
          UpperCamelCase__							:  List[str]								=     '''Twelve'''
          UpperCamelCase__							:  List[str]								=     '''Thirteen'''
          UpperCamelCase__							:  List[Any]								=     '''Fourteen'''
          UpperCamelCase__							:  Union[str, Any]								=     '''Fifteen'''
          UpperCamelCase__							:  str								=     '''Sixteen'''
          UpperCamelCase__							:  int								=     '''Seventeen'''
          UpperCamelCase__							:  Tuple								=     '''Eighteen'''
          UpperCamelCase__							:  int								=     '''Nineteen'''

          UpperCamelCase__							:  Union[str, Any]								=     {}
          UpperCamelCase__							:  Dict								=     '''Hundred,'''
          UpperCamelCase__							:  Union[str, Any]								=     '''Thousand,'''
          UpperCamelCase__							:  List[Any]								=     '''Lakh,'''
          UpperCamelCase__							:  str								=     '''Crore,'''

          UpperCamelCase__							:  int								=     number
          UpperCamelCase__							:  int								=     ''''''
          UpperCamelCase__							:  int								=     0
          UpperCamelCase__							:  int								=     int(__lowerCamelCase			)
          while counter < digits:
               UpperCamelCase__							:  str								=     temp_num % 10
               if counter % 2 == 0:
                    UpperCamelCase__							:  List[Any]								=     ''''''
                    if counter in placevalue and current != 0:
                         UpperCamelCase__							:  Optional[Any]								=     placevalue[counter]
                    if counter == 2:
                         UpperCamelCase__							:  Tuple								=     singles[current] + addition + words
                    elif counter == 0:
                         if ((temp_num % 100) // 10) == 1:
                              UpperCamelCase__							:  Optional[Any]								=     teens[current] + addition + words
                              UpperCamelCase__							:  int								=     temp_num // 10
                              counter += 1
                         else:
                              UpperCamelCase__							:  Optional[Any]								=     singles[current] + addition + words

                    else:
                         UpperCamelCase__							:  Tuple								=     doubles[current] + addition + words

               else:
                    if counter == 1:
                         if current == 1:
                              UpperCamelCase__							:  Optional[Any]								=     teens[number % 10] + words
                         else:
                              UpperCamelCase__							:  Union[str, Any]								=     ''''''
                              if counter in placevalue:
                                   UpperCamelCase__							:  Optional[int]								=     placevalue[counter]
                              UpperCamelCase__							:  Optional[Any]								=     doubles[current] + addition + words
                    else:
                         UpperCamelCase__							:  List[Any]								=     ''''''
                         if counter in placevalue:
                              if current == 0 and ((temp_num % 100) // 10) == 0:
                                   UpperCamelCase__							:  Dict								=     ''''''
                              else:
                                   UpperCamelCase__							:  List[Any]								=     placevalue[counter]
                         if ((temp_num % 100) // 10) == 1:
                              UpperCamelCase__							:  Optional[int]								=     teens[current] + addition + words
                              UpperCamelCase__							:  Dict								=     temp_num // 10
                              counter += 1
                         else:
                              UpperCamelCase__							:  Optional[int]								=     singles[current] + addition + words
               counter += 1
               UpperCamelCase__							:  List[str]								=     temp_num // 10
     return words


if __name__ == "__main__":
   import doctest

   doctest.testmod()




