// test power-series implementation of exp(x)
//
#include <stdio.h>
#include <math.h>

// exp(x) = 1 + (x/1) + (x/2)*(x/1) + (x/3)*(x/2)*(x/1) + ...
//
double myexp( double x)
{
  double t = 1, e1, e2 = 1;

  for( int n = 1; n < 50 ; ++n) {
    e1 = e2; // save previous estimate
    t *= x/n; // update term
    e2 += t; // update estimate
    if( e1 == e2) break; // converged
  }

  return e2;
}

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

/* sample runs:

x = 1
m = 2.71828182845904553
y = 2.71828182845904509
d = 4.44089209850062616e-16

x = 100
m = 3.16781183958094239e+35
y = 2.68811714181613561e+43
d = -2.68811711013801703e+43

x = -100
m = -1.10088686522380657e+35
y = 3.72007597602083612e-44
d = -1.10088686522380657e+35

*/