#include <stdio.h>
#include <math.h>
double est(int nu, double x);
double s(int nu, double x);

int main(void)
{
  double x=15.0,y,ei = -1.9186278921478669771e-8,sol;
  int nu;

  sol = -exp(x) * ei;

  printf("%3s   %18s %10s %10s\n","nu","y      ","error","err est");
  for(nu = 0;nu <= 19;nu++){
    y = s(nu,x);
    printf("%3d   %-18.15g %10.3g %10.3g\n",nu,y,y-sol,est(nu,x));
  }
  printf("%3s   %-18.15g\n","sol",sol);

  return 0;
}


/* sum_{k=0}^{nu} (-1)^k k!/x^{k+1} */
double s(int nu, double x) 
{
  int k,sign = -1;
  long long int fact=1LL;
  double y = 0.0,powx = 1.0;

  for(k = 0;k <= nu;k++){
    powx *= x;
    sign *= -1;
    if (k == 0)
      fact=1LL;
    else
      fact *= (long long int) k;
    y += sign * fact /powx;
  }

  return y;
}

double est(int nu, double x)
{
  int k;
  long long int fact=1LL;
  double powx = 1.0;

  for(k = 0;k <= nu+1;k++){
    powx *= x;
    if (k==0)
      fact=1LL;
    else
      fact *= (long long int) k;
  }

  return 2 * fact /powx;
}