#include <iostream>
#include <random>
#include <cmath>
#include <limits>
#include <ctime>

const std::string currentDateTime() {
    time_t now = time(0);
    struct tm tstruct;
    char buf[80];
    tstruct = *localtime(&now);
    strftime(buf, sizeof(buf), "%Y-%m-%d.%X", &tstruct);

    return buf;
}

int main()
{
    typedef std::numeric_limits< double > dbl;

    std::default_random_engine generator;
    std::normal_distribution<double> distribution(0.0, 1.0);

    std::cout.precision(dbl::digits10);

    const long long N=1390737600000;
    long long i, in;

    double x, y, xz1, yz1, diff;
    xz1 = 0.0;
    yz1 = 0.0;
    diff = 0.0;

    x = distribution(generator);
    y = 0.5*yz1 + x - 0.5*xz1;
    diff = std::abs(x-y);

    in = 1L;
    for (i=0; i<N; i++){
        x = distribution(generator);
        y = 0.5*yz1 + x - 0.5*xz1;
        diff = diff > std::abs(x-y) ? diff : std::abs(x-y);
        xz1 = x;
        yz1 = y;

        if (i == in) {
            std::cout << "[" << currentDateTime() << "] -- " << std::scientific << diff << "  [" << in << "] " << std::endl;
            in *= 10;
        }
    }

    std::cout.precision(dbl::digits10);
    std::cout << "Maximum difference is: " << std::scientific << diff << std::endl;

    return 0;
}

/* Output:

[2015-02-25.15:00:56] -- 0.000000000000000e+00  [1] 
[2015-02-25.15:00:56] -- 1.387778780781446e-17  [10] 
[2015-02-25.15:00:56] -- 4.440892098500626e-16  [100] 
[2015-02-25.15:00:56] -- 4.440892098500626e-16  [1000] 
[2015-02-25.15:00:56] -- 4.440892098500626e-16  [10000] 
[2015-02-25.15:00:56] -- 4.440892098500626e-16  [100000] 
[2015-02-25.15:00:56] -- 8.881784197001252e-16  [1000000] 
[2015-02-25.15:00:58] -- 8.881784197001252e-16  [10000000] 
[2015-02-25.15:01:18] -- 8.881784197001252e-16  [100000000] 
[2015-02-25.15:04:36] -- 8.881784197001252e-16  [1000000000] 
[2015-02-25.15:37:35] -- 8.881784197001252e-16  [10000000000] 
[2015-02-25.21:13:03] -- 8.881784197001252e-16  [100000000000] 
[2015-02-28.05:09:45] -- 8.881784197001252e-16  [1000000000000] 
Maximum difference is: 8.881784197001252e-16

*/