#define _USE_MATH_DEFINES
#include <random>
#include <math.h>
#include <iostream>
int main()
{
    std::default_random_engine rnd(7);
    std::weibull_distribution<double> distribution(0.5, 1.0);
    double eta = 0;
    double k = 1;
    double s = 0;
    double s1 = 0;
    int N = 100000;
    for (int i = 0; i < N; i++)
    {
        double x = distribution(rnd);
        double y = distribution(rnd);
        eta = 4 * cos(2 * k * pow(x * y, 0.5)) * (exp(-(x+y)+pow(x,0.5)+pow(y,0.5)));
        s += eta;
        s1 += eta * eta;
    }
    std::cout << s << '\n';
    double d = s1 / N - pow(s / N, 2);
    std::cout <<"precise value"<<"\n"<<M_PI/sqrt(1+k*k) << "\n";
    std::cout <<"approximate value"<< "\n" << s / N << "\n";
    std::cout<<"miscalculation"<< "\n" << 3 * sqrt(d / N);
    return 0;
}