// implementing square-root without calling any other functions
// originally from w5 notes from class
// added check for convergence
//
#include <stdio.h>
#include <math.h>

double mysqrt( double a)
{
  double prev, x = a/2; 

  for( int count = 0; count < 50; ++count) 
  {
     prev = x; // save copy of x

     x = (x + a/x)/2; // update x

     printf( "x = %.18g\n", x); //debug

     if( x == prev) break; // converged
  }

  return x;
}

int main( void)
{
  double a = 2; scanf( "%lf", &a);
  double x = mysqrt(a);
  double y = sqrt(a);
  printf( "a = %.18g\n", a);
  printf( "x = %.18g\n", x);
  printf( "y = %.18g\n", y);
  printf( "d = %.18g\n", x - y);
  return 0;
}

/* sample runs:

x = 3.25
x = 3.00961538461538458
x = 3.00001536003932179
x = 3.00000000003932143
x = 3
x = 3
a = 9
x = 3
y = 3
d = 0

x = 251
x = 127.492031872509955
x = 67.6678296579155756
x = 41.2229503947159017
x = 32.7406409948669932
x = 31.6418602354120182
x = 31.6227823564825563
x = 31.6227766016843148
x = 31.6227766016837926
x = 31.6227766016837926
a = 1000
x = 31.6227766016837926
y = 31.6227766016837926
d = 0

*/