I don't understand why my code doesn't work and take longer to run

Question

there is my robbinsmonro.hpp:

#include <utility>

#ifndef ROBBINS_HPP
#define ROBBINS_HPP


template <class Func, class DetermSeq, class RandomV, class RNG> 
std::pair<double,double> robbins_monro( const Func & h, double x_init, 
    double alpha, const DetermSeq & epsilon,RandomV & U, RNG & G, 
    long unsigned N)
{
    for(unsigned i=0; i<N; i++) 
    {
        x_init = x_init - epsilon(i+1)*(h(x_init) - alpha + U(G));
    }
    return std::make_pair(x_init, h(x_init));
}

#endif

And there is my test1.cpp:

#include "robbinsmonro.hpp"
#include <ctime>
#include <random>
#include <cmath>
#include <iostream>


int main() {
    auto f = [](double x) {return 1./(1.+exp(-x));};
    std::mt19937 G(time(nullptr));
    double alpha = 2./3.;
    auto epsilon = [](long unsigned N) { return 1./(N+1.);};
    std::uniform_real_distribution<double> U(-0.1,0.1);
    long unsigned N = 1000000;
    double variance=0.;
    double esperance=0.;
    int K = 100;    
    std::pair<double,double> y = std::make_pair(0,0);   
    for(int i=0; i<K; i++) {
        y = robbins_monro(f,0.,alpha,epsilon,U,G,N);
        variance += std::get<0>(y)*std::get<0>(y);
        esperance += std::get<0>(y);
    }
    variance /= double(K);
    esperance /= double(K);
    std::cout << "La variance empirique pour N=1000000 est de " << variance - esperance*esperance << std::endl;
return 0;
}

And there is another code of the test1.cpp (not from me):

#include <random>
#include <iostream>
#include "robbinsmonro.hpp"

int main() {
    auto h=[](double x) { return 1./(1.+exp(-x)); };
    double alpha=2./3.;
    auto epsilon=[](long unsigned n) { return 1./(n+1.);};
    std::uniform_real_distribution<double> U(-0.1,0.1);
    std::mt19937 G(time(nullptr));
    std::pair<double,double> p;
    long unsigned N;
    double m;
    double v;
    int K=100;
    
    N=100000;
    m=0.;
    v=0.;
    for (int i = 0; i < K; i++)
    {
        p=robbins_monro(h,0.,alpha,epsilon,U,G,N);
        m += p.first;
        v += p.first*p.first;
    }
    return 0;
}

When I calculate the empirical variance, my code takes much longer to run to give a factor 2 error. Yet my code is exactly the same, isn't it?

Answer 1

As I said in my comment, the value of N is different in each program, which seems to have solved the issue.

If you are using c++14 or newer this can be easily avoided by writing long numbers using the digit separator - you can optionally place a single quote anywhere in the number to aid readability.

eg

int N=1'000'000

and

int N=100'000

are very clearly different.