write a C program using full Muller-Brent algorithm to find the roots

Sure, I can help you with that. Here is an example C program that uses the full Muller-Brent algorithm to find the roots:

#include <stdio.h>
#include <math.h>

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

double muller_brent(double a, double b, double c, double tol) {
    double fa = f(a);
    double fb = f(b);
    double fc = f(c);
    double d, e, q, r, p;
    double denom, eps, tol1, xm;
    int iter = 0;

    do {
        denom = (b - a) * (c - b) * (c - a);
        eps = 1e-20;
        tol1 = tol * fabs(b) + eps;
        xm = 0.5 * (a + b);

        if (fabs(fc) < fabs(fb)) {
            a = b; b = c; c = a;
            fa = fb; fb = fc; fc = fa;
        }

        q = (a - xm) * (fb - fc);
        r = (b - xm) * (fa - fc);
        p = (b - a) * (fa - fc);

        d = 2.0 * p - sign(p) * (q - r);
        e = sign(b - a) * sign(fa - fb) * fabs(q - r);

        if (fabs(denom) > eps) {
            d /= denom;
            e /= denom;
        } else {
            d = e = 0;
        }

        if (fabs(e) < tol1 || iter > 100) {
            b += sign(b - a) * tol1;
            return b;
        }

        if (fabs(d) < tol1) {
            xm = b + sign(b - a) * tol1;
        } else if (d > 0) {
            xm = b - e / (d + sqrt(d * d - 4.0 * p * e));
        } else {
            xm = b - 2.0 * p / (d - sqrt(d * d - 4.0 * p * e));
        }

        if (isnan(xm) || isinf(xm)) {
            xm = (a + b) / 2;
        }

        double fxm = f(xm);
        a = b;
        b = xm;
        fa = fb;
        fb = fxm;
        iter++;

    } while (iter <= 100);

    return NAN;
}

int main() {
    double root = muller_brent(0, 2.0, 4.0, 1e-9);
    printf("root = %f\n", root);
    return 0;
}

This program defines a function `f(x)` that takes a single input variable `x` and returns the value of the function `x * sin(x) - 1`. It then uses the Muller-Brent algorithm to find a root of this function in the interval `[0, 2.0, 4.0]` with a tolerance of `1e-9`. The `sign` function used in the algorithm is defined as:

double sign(double x) {
    return (x >= 0.0) ? 1.0 : -1.0;
}