





import math as m





def 							__lowerCAmelCase(					_SCREAMING_SNAKE_CASE       ,    _SCREAMING_SNAKE_CASE       ,    _SCREAMING_SNAKE_CASE=0.001							)       ->   Optional[int]:




    """simple docstring"""




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





def 							__lowerCAmelCase(					_SCREAMING_SNAKE_CASE       ,    _SCREAMING_SNAKE_CASE=0       ,    _SCREAMING_SNAKE_CASE=100       ,    _SCREAMING_SNAKE_CASE=0.0001       ,    _SCREAMING_SNAKE_CASE=1e-6       ,    _SCREAMING_SNAKE_CASE=False							)       ->   Optional[Any]:




    """simple docstring"""




    _A    =       xa  # set the initial guess
    _A    =       [a]
    _A    =       abs(f(_SCREAMING_SNAKE_CASE							)							)
    _A    =       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    =       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

       __A       : Tuple						    = lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
       __A       : int						    = newton_raphson(
           f, xa=10, maxiter=1_000, 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 numpy as np





def 							__lowerCAmelCase(					_SCREAMING_SNAKE_CASE       ,    _SCREAMING_SNAKE_CASE							)       ->   List[Any]:




    """simple docstring"""




    _A    =       np.array(_SCREAMING_SNAKE_CASE							)
    _A    =       np.array(_SCREAMING_SNAKE_CASE							)

    _A    =       abs(predict - actual							)
    _A    =       difference.mean()

    return score





def 							__lowerCAmelCase(					_SCREAMING_SNAKE_CASE       ,    _SCREAMING_SNAKE_CASE							)       ->   Optional[int]:




    """simple docstring"""




    _A    =       np.array(_SCREAMING_SNAKE_CASE							)
    _A    =       np.array(_SCREAMING_SNAKE_CASE							)

    _A    =       predict - actual
    _A    =       np.square(_SCREAMING_SNAKE_CASE							)

    _A    =       square_diff.mean()
    return score





def 							__lowerCAmelCase(					_SCREAMING_SNAKE_CASE       ,    _SCREAMING_SNAKE_CASE							)       ->   Tuple:




    """simple docstring"""




    _A    =       np.array(_SCREAMING_SNAKE_CASE							)
    _A    =       np.array(_SCREAMING_SNAKE_CASE							)

    _A    =       predict - actual
    _A    =       np.square(_SCREAMING_SNAKE_CASE							)
    _A    =       square_diff.mean()
    _A    =       np.sqrt(_SCREAMING_SNAKE_CASE							)
    return score





def 							__lowerCAmelCase(					_SCREAMING_SNAKE_CASE       ,    _SCREAMING_SNAKE_CASE							)       ->   List[Any]:




    """simple docstring"""




    _A    =       np.array(_SCREAMING_SNAKE_CASE							)
    _A    =       np.array(_SCREAMING_SNAKE_CASE							)

    _A    =       np.log(predict + 1							)
    _A    =       np.log(actual + 1							)

    _A    =       log_predict - log_actual
    _A    =       np.square(_SCREAMING_SNAKE_CASE							)
    _A    =       square_diff.mean()

    _A    =       np.sqrt(_SCREAMING_SNAKE_CASE							)

    return score





def 							__lowerCAmelCase(					_SCREAMING_SNAKE_CASE       ,    _SCREAMING_SNAKE_CASE							)       ->   Optional[int]:




    """simple docstring"""




    _A    =       np.array(_SCREAMING_SNAKE_CASE							)
    _A    =       np.array(_SCREAMING_SNAKE_CASE							)

    _A    =       predict - actual
    _A    =       np.sum(_SCREAMING_SNAKE_CASE							) / len(_SCREAMING_SNAKE_CASE							)
    _A    =       np.sum(_SCREAMING_SNAKE_CASE							) / len(_SCREAMING_SNAKE_CASE							)
    # print(numerator, denumerator)
    _A    =       float(_SCREAMING_SNAKE_CASE							) / denumerator * 100

    return score





def 							__lowerCAmelCase(					_SCREAMING_SNAKE_CASE       ,    _SCREAMING_SNAKE_CASE							)       ->   Dict:




    """simple docstring"""




    return np.mean(np.array(_SCREAMING_SNAKE_CASE							) == np.array(_SCREAMING_SNAKE_CASE							)							)





