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

complex f(complex z){
    return ((z-2)*z-3)*z+10;
}

int main(){
    complex z;
    complex p0=0,p1=1,p2=2;
  for(int n=0;n<10;n++){
    complex fp0=f(p0),fp1=f(p1),fp2=f(p2);
    complex a = (fp0 * p1 - fp0 * p2 - p0 * fp1 + p2 * fp1 + p0 * fp2 - p1 * fp2) / (p0 * p0 * p1 - p0 * p0 * p2 - p0 * p1 * p1 + p0 * p2 * p2 + p1 * p1 * p2 - p1 * p2 * p2);
    complex b = -(p1 * p1 * fp0 - 2 * fp0 * p1 * p2 + fp0 * p2 * p2 - fp1 * p0 * p0 + 2 * fp1 * p0 * p2 - fp1 * p2 * p2 + fp2 * p0 * p0 - 2 * fp2 * p0 * p2 - p1 * p1 * fp2 + 2 * fp2 * p1 * p2) / (p0 - p2) / (p0 * p1 - p0 * p2 - p1 * p1 + p1 * p2);
    complex c = fp2;
    complex dm = -b-csqrt(b*b-4*a*c);
    complex dp = -b+csqrt(b*b-4*a*c);
    if(cabs(dm)>cabs(dp)){
        z=p2+2*c/dm;        
    } else {
        z=p2+2*c/dp;
    }
 //   printf("a=%g,%g, b=%g,%g, c=%g,%g\n",a,b,c);
    complex fz=f(z);
    printf("z=%g,%g f(z)=%g,%g\n",
        creal(z),cimag(z),creal(fz),cimag(fz));
    if(cabs(p2-z)<1e-13*cabs(z)) break;
    p0=p1; p1=p2; p2=z;
  }
    return 0;
}