# -*- coding: utf-8 -*-
import numpy as np

def function(point, a, b, c, d):
    x, y = point

    return a*x + b*y + np.exp(c*x**2+d*y**2)

def derivative(point, a, b, c, d):
    dx = a + np.exp(c*(point[0]**2)+d*(point[1]**2))*2*c*point[0]
    dy = b + np.exp(c*(point[0]**2)+d*(point[1]**2))*2*d*point[1]

    return [dx, dy]

def grad(point, alpha, a, b, c, d):
    new_point = [None, None]
    der = derivative(point, a, b, c, d)
    new_point[0] = point[0] - alpha*der[0]
    new_point[1] = point[1] - alpha*der[1]

    return new_point

def criterion(point, a, b, c ,d):
    der = derivative(point, a, b, c, d)
    if np.sqrt(der[0]**2 + der[1]**2) < 0.0001:
        return False
    elif (np.abs(der[0]) < 0.0001/2) and (np.abs(der[1]) < 0.0001/2):
        return False

    return True

point = [0, 0]
alpha = 1

a, b, c, d = map(float, input("Введите a, b, c, d через пробел: ").split(" "))

while criterion(point, a, b, c, d):
    new_point = grad(point, alpha, a, b, c, d)
    if function(new_point, a, b, c, d) > function(point, a, b, c, d):
        alpha/=2
    elif function(new_point, a, b, c, d) < function(point, a, b, c, d):
        point = new_point

    print(f'''
        x:{point[0]}, y:{point[1]}
        f(x):{function(point, a, b, c, d)}
        grad(x):{new_point[0]}, grad(y):{new_point[1]}
        alpha:{alpha}''')