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

double f(double x) { return x * x - 2; }
double df(double x) { return 2 * x; }

int main() {
  double x = 1.5;
  for (int i = 1; i <= 10; i++) {
    double fx = f(x);
    double d = df(x);
    x = x - fx / d;
    printf("iter %2d: x = %.8f\n", i, x);
  }
  printf("sqrt(2) = %.8f\n", x);
  return 0;
}