HELL 2 TORTURE EDITION

#include <iostream>
#include <functional>
#include <cmath>

double delta = 0.000001;

double f1(double x) {
    return exp(x) + 2;
}

double f2(double x) {
    return -(5 / x);
}

double f3(double x) {
    return -2 * x + 8;
}

double f1d1(double x) {
    return exp(x);
}

double f2d1(double x) {
    return 5 / (x * x);
}

double f3d1(double x) {
    return -2;
}

double f1d2(double x) {
    return exp(x);
}

double f2d2(double x) {
    return -10 / (x * x * x);
}

double f3d2(double x) {
    return 0;
}

double f1mf2(double x) {
    return f1(x) - f2(x);
}

double f2mf3(double x) {
    return f2(x) - f3(x);
}

double f1mf3(double x) {
    return f1(x) - f3(x);
}

double f1d1mf2d1(double x) {
    return f1d1(x) - f2d1(x);
}

double f2d1mf3d1(double x) {
    return f2d1(x) - f3d1(x);
}

double f1d1mf3d1(double x) {
    return f1d1(x) - f3d1(x);
}

double f1d2mf2d2(double x) {
    return f1d2(x) - f2d2(x);
}

double f2d2mf3d2(double x) {
    return f2d2(x) - f3d2(x);
}

double f1d2mf3d2(double x) {
    return f1d2(x) - f3d2(x);
}

double Root(double a, double b, std::function<double(double)> f, std::function<double(double)> d1, std::function<double(double)> d2) {
    bool to_right = d1((a + b) / 2) * d2((a + b) / 2) > 0;

    for (;;) {
        double c = (std::abs(f(b)) * a + std::abs(f(a)) * b) / (std::abs(f(b)) + std::abs(f(a)));

        double d;
        if (to_right) {
            d = (std::fabs(d1(b)) * b - std::fabs(f(b))) / std::fabs(d1(b));
        }
        else {
            d = (std::fabs(d1(a)) * a + std::fabs(f(a))) / std::fabs(d1(a));
        }
        if (to_right) {
            if (f(c) * f(c + delta) < 0) return c;
            if (f(d) * f(d - delta) < 0) return d;
        }
        else {
            if (f(c) * f(c - delta) < 0) return c;
            if (f(d) * f(d + delta) < 0) return d;
        }

        if (to_right) {
            a = c;
            b = d;
        }
        else {
            b = c;
            a = d;
        }
    }
}

double Area(double a, double b, std::function<double(double)> f) {
    double ans = 0;
    for (double i = a; i < b; i += delta) {
        ans += delta * f(i);
    }
    return ans;
}

double FinalArea(std::function<double(double)> f1, std::function<double(double)> f2, std::function<double(double)> f3,
        std::function<double(double)> f1d1, std::function<double(double)> f2d1, std::function<double(double)> f3d1,
        std::function<double(double)> f1d2, std::function<double(double)> f2d2, std::function<double(double)> f3d2,
        std::function<double(double)> f1d1mf2d1, std::function<double(double)> f2d1mf3d1, std::function<double(double)> f1d1mf3d1,
        std::function<double(double)> f1mf2, std::function<double(double)> f2mf3, std::function<double(double)> f1mf3,
        std::function<double(double)> f1d2mf2d2, std::function<double(double)> f2d2mf3d2, std::function<double(double)> f1d2mf3d2) {
    double a = Root(-2, -0.1, f2mf3, f2d1mf3d1, f2d2mf3d2);
    double b = Root(-4, -2, f1mf2, f1d1mf2d1, f1d2mf2d2);
    double c = Root(0, 2, f1mf3, f1d1mf3d1, f1d2mf3d2);
    return Area(b, a, f2) - Area(b, a, f1) + (Area(a, c, f3) - Area(a, c, f1));
}

int main() {
    std::cout << FinalArea(f1, f2, f3, f1d1, f2d1, f3d1, f1d2, f2d2, f3d2, f1d1mf2d1, f2d1mf3d1, f1d1mf3d1, f1mf2, f2mf3, f1mf3, f1d2mf2d2, f2d2mf3d2, f1d2mf3d2);
}