// implementing square-root without calling any other functions
//
#include <stdio.h>
#include <math.h>

double mysqrt( double a)
{
  double x = a/2; // initial estimate of square root

  int count; // loop counter

  for( count = 0; count < 5; ++count) // concise while loop
  {
     x = (x + a/x)/2; // Newton says this will improve the estimate

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

  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 = 1.5
x = 1.41666666666666652
x = 1.41421568627450966
x = 1.41421356237468987
x = 1.41421356237309492
a = 2
x = 1.41421356237309492
y = 1.41421356237309515
d = -2.22044604925031308e-16

x = 2.25
x = 2.23611111111111116
x = 2.2360679779158037
x = 2.23606797749978981
x = 2.23606797749978981
a = 5
x = 2.23606797749978981
y = 2.23606797749978981
d = 0

x = 251
x = 127.492031872509955
x = 67.6678296579155756
x = 41.2229503947159017
x = 32.7406409948669932
a = 1000
x = 32.7406409948669932
y = 31.6227766016837926
d = 1.11786439318320063

*/