Integration of a normal distribution from 0 to +inf

half.c

#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include <assert.h>
#include <stdint.h>

static double derivative(double x){
  return pow(M_E, -pow(x, 2.0)/2.0)/sqrt(2.0*M_PI);}

int main(int argc, char **argv) {
  assert(argc==2);
  long double delta_t = 0.0000001, u = 0, t = 0;
#pragma omp parallel for reduction (+:u,t)
  for (uint64_t i = 0; i < (uint64_t)((long double)(atof(argv[1])+delta_t)/(long double)delta_t);i++){
    t+=delta_t;
    long double s = (long double)(i+(uint64_t)1)*delta_t;
    u+=delta_t*derivative(s);;

  }
    printf("%0.13Lf %0.13Lf\n", t, u);
  return 0;
}