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

double P(double x)
{
    return ((6435.0*pow(x,8)-12012.0*pow(x,6)+6930.0*pow(x,4)-1260.0*pow(x,2)+35.0)/128.0);
}

double Pderivative (double x)
{
    return ((8.0*6435.0*pow(x,7)-6.0*12012.0*pow(x,5)+4.0*6930.0*pow(x,3)-2.0*1260.0*x)/128.0);
}

int main()
{
    //NR
    double x0 = 0.4;
    double xN;

    //Bisection
    double xL = 0.4;
    double xR = 0.7;
    double xM;

    double Tol = 0.00000001;
    double Error;

    //printf ("Enter x0: ");
    //scanf("%d%", &x0);
    //printf ("Enter xL: ");
    //scanf("%d%", &xL);
    //printf ("Enter xR: ");
    //scanf ("%d", &xR);
    //printf ("Enter tolerance: ");
    //scanf("%d", &Tol);

    printf("%.10lf\n", x0);
    printf("%.10lf\n", xR);
    printf("%.10lf\n", xL);
    printf("%.10lf\n", Tol);


    int n = 0;
    int b = 0;

    do{
        if ((((x0-xL)*Pderivative(x0)-P(x0))*((x0-xR)*Pderivative(x0)-P(x0)))<0)
        {
            //NEWTON
            xN = x0 -(P(x0)/Pderivative(x0));
            Error=fabs((xN-x0)/xN);

            n++;

        }else{
            //BISECTION
            xM = (xL+xR)/2;
            if((P(xL)*P(xM))>0.0)
            {
                xL=xM;
            }
            else{
                xR=xM;
            }
            Error=fabs((xR-xL)/xM);

            b++;

        }

    } while (Error>Tol);

    printf("%.10lf\n",xN);
    printf("%.10lf\n",xM);
    printf("%d NR iterations\n",n);
    printf("%d Bisection iterations\n",b);

    return 0;
}