#include <iostream>
#include <cmath>

double f(double x) {
    return x * x + 2 * sin(x) - 1;
}

double f1(double x) {
    return 2 * (x + cos(x));
}

double f2(double x) {
    return 2 - 2 * sin(x);
}

double phi(double x, double lambda) {
    return f1(x) > 0.0 ? x - lambda * f(x) : x + lambda * f(x);
}

double iterative(double a, double b, double eps, double &delta, unsigned int &iter) {
    double m1 = fabs(f1(a)), M1 = fabs(f1(b));
    if (m1 > M1) {
        double t = m1;
        m1 = M1;
        M1 = t;
    }
    double x0, xk = (a+b)/2, lambda = 1.0/M1, q = 1.0 - m1/M1;
    iter = 0;

    do {
        x0 = xk;
        xk = phi(x0, lambda);
        iter++;
    } while (fabs(xk-x0) > (1-q)/q*eps);
    delta = fabs(xk-x0)*q/(1-q);

    return xk;
}

double tangents(double a, double b, double eps, double &delta, unsigned int &iter) {
    double m1 = fabs(f1(a)), M1 = fabs(f1(b)), xk;
    if (m1 > M1) {
        double t = m1;
        m1 = M1;
        M1 = t;
    }
    xk = f(a)*f2(a) > 0 ? a : b;
    iter = 0;

    do {
        xk = xk - f(xk)/f1(xk);
        iter++;
    } while (fabs(f(xk))/m1 > eps);
    delta = fabs(f(xk))/m1;

    return xk;
}

void Iterative(double a, double b) {
    printf("|  eps  | equation root | accuracy estimation for I |\n");
    for (double eps = 1e-2, delta = 0; eps > 1e-14; eps *= 1e-3) {
        unsigned int iterations;
        double x = iterative(a, b, eps, delta, iterations);
        printf("| %.0e | %13.10f | %25.23f |\n", eps, x, delta);
    }
    printf("\n");
}

void Tangents(double a, double b) {
    printf("|  eps  | equation root | accuracy estimation for T |\n");
    for (double eps = 1e-2, delta; eps > 1e-14; eps *= 1e-3) {
        unsigned int iterations;
        double x = tangents(a, b, eps, delta, iterations);
        printf("| %.0e | %13.10f | %25.23f |\n", eps, x, delta);
    }
    printf("\n");
}

void Compare(double a, double b) {
    printf("|  eps  | iteration count for I | iteration count for T |\n");
    for (double eps = 1e-2, delta; eps > 1e-14; eps *= 1e-3) {
        unsigned int iterations1, iterations2;
        iterative(a, b, eps, delta, iterations1);
        tangents(a, b, eps, delta, iterations2);
        printf("| %.0e | %21d | %21d |\n", eps, iterations1, iterations2);
    }
    printf("\n");
}

int main() {
    Iterative(-2, -1.5);
    Tangents(-2, -1.5);
    Iterative(0, 0.5);
    Tangents(0, 0.5);
    Compare(-2, -1.5);
}