Results of PROMISE with the arclength program

Initial code:

double fun( double x){
  int k, n = 5;
  double t1;
  double d1 = 1.0;
  t1 = x;
  for ( k = 1; k <= n; k++ )
    {
      d1 = 2.0 * d1;
      t1 = t1+ sin(d1 * x)/d1;
    }
    return t1;
}

int main( int argc, char **argv) {
  int i,n = 1000000;
  double h, t1, t2, dppi;
  double s1;
  t1 = -1.0;
  dppi = acos(t1);
  s1 = 0.0;
  t1 = 0.0;
  h = dppi / n;
  for ( i = 1; i <= n; i++)
    {
      t2 = fun(i * h);
      s1 = s1 + sqrt(h*h + (t2 - t1) * (t2 - t1));
      t1 = t2;
    }
  std::cout << s1 << std::endl;
  return 0;
}

Result: 5.79577632241303

Code modified to be used with PROMISE:

double fun(double x){
  int k, n = 5;
  double t1;
  double d1 = 1.0;
  t1 = x;
  for ( k = 1; k <= n; k++ )
    {
      d1 = 2.0 * d1;
      t1 = t1+ sin(d1 * x)/d1;
    }
    return t1;
}

int main( int argc, char **argv) {
  cadna_init(0);
  int i,n = 1000000;
  double h;
  double t1;
  double t2;
  double dppi;
  double s1;
  t1 = -1.0;
  dppi = acos(t1);
  s1 = 0.0;
  t1 = 0.0;
  h = dppi / n;
  for ( i = 1; i <= n; i++)
    {
      t2 = fun(i * h);
      s1 = s1 + sqrt(h*h + (t2 - t1) * (t2 - t1));
      t1 = t2;
    }
  dump(s1);
  std::cout << s1 << std::endl;
  return 0;
}

Code after the use of PROMISE (6 digits requested):

double fun( double x){
  int k, n = 5;
  double t1;
  float d1 = 1.0;
  t1 = x;
  for ( k = 1; k <= n; k++ )
    {
      d1 = 2.0 * d1;
      t1 = t1+ sin(d1 * x)/d1;
    }
    return t1;
}

int main( int argc, char **argv) {
  int i,n = 1000000;
  double h;
  double t1;
  double t2;
  float dppi;
  double s1;
  t1 = -1.0;
  dppi = acos(t1);
  s1 = 0.0;
  t1 = 0.0;
  h = dppi / n;
  for ( i = 1; i <= n; i++)
    {
      t2 = fun(i * h);
      s1 = s1 + sqrt(h*h + (t2 - t1) * (t2 - t1));
      t1 = t2;
    }
  std::cout << s1 << std::endl;
  return 0;
}

If printed without using CADNA,
Result: 5.79577686259398

If printed using CADNA, 
Result: 0.579577E+001 (other digits are affected by round-off errors)		     

Reference