#include<cmath>
#include<cstdio>
#include<iostream>

#define SIZE 1000

using namespace std;

double f(double x,double y){ 
  return x*x*x*x + y*y + 2*y + cos(0.2*x + 0.15*y);
}
double dx(double x,double y){
  return 4*x*x*x - sin(0.2*x + 0.15*y)*0.2; 
}
double dy(double x,double y){ 
  return 2*y + 2 - sin(0.2*x + 0.15*y)*0.15;
}
double antyGrad(double x, double y, double k){ 
  return f(x - k*dx(x,y), y - k*dy(x,y)); 
}
double norma(double x, double y){ 
  return sqrt(x*x + y*y);
}

double findFactor(double a, double b, double eps, double x, double y)
{  
  while ((b-a)>=eps) {
    if( antyGrad(x,y,(a+b-0.5*eps)/2) <= antyGrad(x,y,(a+b+0.5*eps)/2) )
      b=(a+b+0.5*eps)/2;
    else a=(a+b-0.5*eps)/2;
  } 

  return (a+b)/2;
}

double descent(double bx, double by,double eps){
  double x = bx, y = by, x1 = 0, y1 = 0, factor;
  int k = 0;
  do {
    k++;
    x = x1; y = y1;
    factor = findFactor(-10000, 10000, eps, x, y);
    x1 = x - factor * dx(x, y);
    y1 = y - factor * dy(x, y);

  } while (norma(x1 - x,y1 - y) > eps);

  std::cout << "steps = " << k << std::endl;
  std::cout <<"min: " <<"x = " << x1 << "; y = " << y1 <<std::endl;
  return f(x1,y1);
}

int main(){
    double x = 10, y = 10, eps = 0.001;
    std::cout << "f(x, y) = " << descent(x,y,eps) << std::endl;
    
    return 0;
}