ParabolaMethod

#include <algorithm>
#include <iostream>
#include <vector>
#include <cmath>
#include <exception>
double parab(double x1, double f1, double x2, double f2, double x3, double f3)
{
    return x2 - ((x2 - x1) * (x2 - x1) * (f2 - f3) - (x2 - x3) * (x2 - x3) * (f2 - f1)) / (2 * ((x2 - x1) * (f2 - f3) - (x2 - x3) * (f2 - f1)));
}

double  parabola(double a, double b, double (*f)(double x), int64_t n, double eps)
{
    if (a > b)
        std::swap(a, b);
    double e = (a + b) * 0.5;
    double x = (a + b) * 0.5;
    double res = x;
    double incor = b + 1;
    double c, d;
    for (int64_t i = 0; i < n; ++i)
    {
        res = parab(a, f(a), e, f(e), b, f(b));
        if (!(res >= a && res <= b))
            throw std::invalid_argument("Can't find min");
        if (abs(res - x) < eps)
            return res;
        x = res;
        c = std::min(e, x);
        d = std::max(e, x);
        if (f(c) < f(d))
        {
            b = d;
            e = c;
        }
        else
        {
            a = c;
            e = d;
        }
    }

    return res;
}