

'''simple docstring'''






import math as m


def 					__lowerCamelCase			(      SCREAMING_SNAKE_CASE_     :	str  ,  SCREAMING_SNAKE_CASE_     :	List[str]  ,  SCREAMING_SNAKE_CASE_     :	Any=0.001    )							->   List[Any]:
      """simple docstring"""

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


def 					__lowerCamelCase			(      SCREAMING_SNAKE_CASE_     :	List[str]  ,  SCREAMING_SNAKE_CASE_     :	Dict=0  ,  SCREAMING_SNAKE_CASE_     :	str=1_0_0  ,  SCREAMING_SNAKE_CASE_     :	Optional[int]=0.0001  ,  SCREAMING_SNAKE_CASE_     :	List[Any]=1E-6  ,  SCREAMING_SNAKE_CASE_     :	Optional[int]=False    )							->   Union[str, Any]:
      """simple docstring"""

      SCREAMING_SNAKE_CASE_      :			Optional[Any]     =       xa  # set the initial guess
      SCREAMING_SNAKE_CASE_      :			Optional[int]     =       [a]
      SCREAMING_SNAKE_CASE_      :			Optional[Any]     =       abs(f(SCREAMING_SNAKE_CASE_    )    )
      SCREAMING_SNAKE_CASE_      :			int     =       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"    )
            SCREAMING_SNAKE_CASE_      :			Union[str, 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

      snake_case_       =       lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
      snake_case_  ,	snake_case_  ,	snake_case_       =       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'''






def 					_snake_case   (     A ,    A       )						->    float:
							return a + b


if __name__ == "__main__":
		__UpperCAmelCase    				=							5
		__UpperCAmelCase    				=							6
		print(f"""The sum of {a} + {b} is {add(a, b)}""")