Riemann's prime number formula, C++ (gcc)

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#include "bits/stdc++.h"
using namespace std;
int factorial(int x) {
    if (x == 1) return x;
    return x * factorial(x - 1);
}
double Ei(double x) {
    double ec = 0.5772156649;
    double a = log(x);
    double b = 0;
    for (int k = 1; k < 10; ++k) {
        b += pow(x, k) / (k * factorial(k));
    }
    return ec + a + b;
}
double Li(double x) {
    return Ei(log(x));
}
int main()
{
    int mebius[] = { 0, 1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1, 0, -1, 0, 1, 1, -1, 0, 0, 1, 0, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, 1, 1, 0, -1, -1, -1, 0, 0, 1, -1, 0, 0, 0, 1, 0, -1, 0, 1, 0, 1, 1, -1, 0, -1, 1, 0, 0, 1, -1, -1, 0, 1, -1, -1, 0, -1, 1, 0, 0, 1 };
    double p[] = { 14.134725142,  21.022039639,  25.010857580,  30.424876126,  32.935061588,  37.586178159,  40.918719012,  43.327073281,  48.005150881,  49.773832478,  52.970321478,  56.446247697,  59.347044003,  60.831778525,  65.112544048,  67.079810529,  69.546401711,  72.067157674,  75.704690699,  77.144840069,  79.337375020,  82.910380854,  84.735492981,  87.425274613,  88.809111208,  92.491899271,  94.651344041,  95.870634228,  98.831194218, 101.317851006, 103.725538040, 105.446623052, 107.168611184, 111.029535543, 111.874659177, 114.320220915, 116.226680321, 118.790782866, 121.370125002, 122.946829294, 124.256818554, 127.516683880, 129.578704200, 131.087688531, 133.497737203, 134.756509753, 138.116042055, 139.736208952, 141.123707404, 143.111845808, 146.000982487, 147.422765343, 150.053520421, 150.925257612, 153.024693811, 156.112909294, 157.597591818, 158.849988171, 161.188964138, 163.030709687, 165.537069188, 167.184439978, 169.094515416, 169.911976479, 173.411536520, 174.754191523, 176.441434298, 178.377407776, 179.916484020, 182.207078484, 184.874467848, 185.598783678, 187.228922584, 189.416158656, 192.026656361, 193.079726604, 195.265396680, 196.876481841, 198.015309676, 201.264751944, 202.493594514, 204.189671803, 205.394697202, 207.906258888, 209.576509717, 211.690862595, 213.347919360, 214.547044783, 216.169538508, 219.067596349, 220.714918839, 221.430705555, 224.007000255, 224.983324670, 227.421444280, 229.337413306, 231.250188700, 231.987235253, 233.693404179, 236.524229666, 237.769820481, 239.555477573, 241.049157796, 242.823271934, 244.070898497, 247.136990075, 248.101990060, 249.573689645, 251.014947795, 253.069986748, 255.306256455, 256.380713694, 258.610439492, 259.874406990, 260.805084505, 263.573893905, 265.557851839, 266.614973782, 267.921915083, 269.970449024, 271.494055642, 273.459609188, 275.587492649, 276.452049503, 278.250743530, 279.229250928, 282.465114765, 283.211185733, 284.835963981, 286.667445363, 287.911920501 };
    int N = 1000;
    int m = log(N);
    double r = 0;
    for (int i = 1; i < m + 1; ++i) {
        r += mebius[i] / i * Li(pow(N,1./i));
    }
    double t = 0;
    for (int k = 0; k < 100; ++k) {
        double b = 0;
        for (int i = 1; i < m + 1; ++i) {
            double z = sqrt(0.25 + pow(p[k], 2));
            b += mebius[i] / m * 2 * sqrt(i) / z * cos(p[k] * log(i) - atan(2*p[k]));
        }
        t -= b;
    }
    
    cout << (r + t) << endl;
    
    return EXIT_SUCCESS;
}

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Compilation time: 1.32 sec, absolute running time: 0.14 sec, cpu time: 0 sec, memory peak: 3 Mb, absolute service time: 1,48 sec