Aitken Delta Squared Root Finding

#include<cstdio>
#include<cmath>
#include<iostream>

#define ESP 0.000001
#define F(x) (1-4*x*x)/6

using namespace std;

int main()
{
    double x1, x2, x3, x4, y;
    cin >> x1;

    for (int i=1; ; i=i+3)
    {
        x2 = F(x1);
        x3 = F(x2);

        if(fabs(x3-x2) < ESP)
        {
            cout << x3;
            break;
        }

        else
        {
            y = x3-2*x2+x1;
            x1 = x3-(((x3-x2)*(x3-x2))/y);
        }
    }

}