#include <iostream>
#include <cmath>


 //fact
double fact(int n) {
    if (n == 0) return 1;
    return n * fact(n - 1);
}

//taylor series for sin(x)
double myfunc(double x) {
    double sum = 0;

    double previous_result;
    for (int i = 0; i < 10; i++) {
        double result = pow(-1, i) * pow(x, 2 * i + 1) / fact(2 * i + 1);
        if(abs(result - previous_result) < 1e-15) {
            break;
        }
        previous_result = pow(-1, i) * pow(x, 2 * i + 1) / fact(2 * i + 1);
        sum += previous_result;
    }
    return sum;
}
int main() {
    int n = 15;
    // array of arguments x
    double *x = new double[n];
    for (int i = 0; i < n; i++ ) x[i] = 0.1 * (i+1); // x=0.1,0.2,...,0.5
    // setup result arrays for your function
    double *fmy = new double[n];
    double *std = new double[n];
    for (int i = 0; i < n; i++ ) {
        fmy[i] = myfunc(x[i]);
        std[i] = sin (x[i]);
    }
    // output the result of standard deviation
    double dev = 0.0;
    for (int i = 0; i < n; i++ ) {
        double diff = std::abs(fmy[i] - std[i]);
        std::cout << i << ") sin(x=" << x[i] << ")=" << fmy[i]
                  << " C++ sin(x)=" << std[i] << " diff=" << diff
                  << std::endl;
        dev += diff * diff;
    }
    dev = sqrt(dev / n);
    std::cout << "dev = " << dev << std::endl;
    return 0;
}