code: 
  
  
  
  
  
  import math as m
  def   _A (	SCREAMING_SNAKE_CASE  :     Optional[Any] , SCREAMING_SNAKE_CASE  :     int , SCREAMING_SNAKE_CASE  :     Union[str, Any]=0.0_0_1		):
  
  
  
  
  
    """simple docstring"""
  
  
  
    return (f(a + h		) - f(a - h		)) / (2 * h)
  def   _A (	SCREAMING_SNAKE_CASE  :     int , SCREAMING_SNAKE_CASE  :     Dict=0 , SCREAMING_SNAKE_CASE  :     List[Any]=100 , SCREAMING_SNAKE_CASE  :     str=0.0_0_0_1 , SCREAMING_SNAKE_CASE  :     Optional[int]=1e-6 , SCREAMING_SNAKE_CASE  :     Any=False		):
  
  
  
  
  
    """simple docstring"""
  
  
  
    a__			:      int            =xa  # set the initial guess
    a__			:      List[str]            =[a]
    a__			:      Any            =abs(f(SCREAMING_SNAKE_CASE		)		)
    a__			:      List[str]            =lambda SCREAMING_SNAKE_CASE		: calc_derivative(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , h=SCREAMING_SNAKE_CASE		)  # noqa: E731  Derivative of f(x)
    for _ in range(SCREAMING_SNAKE_CASE		):
      if fa(SCREAMING_SNAKE_CASE		) == 0:
        raise ValueError("No converging solution found"		)
      a__			:      Any            =a - f(SCREAMING_SNAKE_CASE		) / fa(SCREAMING_SNAKE_CASE		)  # Calculate the next estimate
      if logsteps:
        steps.append(SCREAMING_SNAKE_CASE		)
      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
  
       UpperCAmelCase			:			Optional[int]	  = lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
       UpperCAmelCase  ,			UpperCAmelCase  ,			UpperCAmelCase			:			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}}}""")
  
  
  
  
  
  
  
style_context: 
  
  
  
  
  
  def   _A (	SCREAMING_SNAKE_CASE  :     int		):
  
  
  
  
  
    """simple docstring"""
  
  
  
    if not isinstance(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE		) or number < 0:
      raise ValueError("Input must be a non-negative integer"		)
  
    a__			:      List[str]            =number & ~(number - 1)
    a__			:      Optional[int]            =0
    while intermediate:
      intermediate >>= 1
      index += 1
    return index - 1
  
  
  if __name__ == "__main__":
       import doctest
  
       doctest.testmod(verbose=True)
  
  
  
  
  
  
  