// the actual functions come from particle physics and are extremely ugly
double f(double x){
  return 2*x+1;
}
//in reality a numerical derivative term
double F(const std::function<double(double)>& f, double x){
  return f(x) - f(x+1);
}
// in reality another higher order numerical derivative
double G(const std::function<double(double)>& f, double x){
  return f(x) + f(x+1);
}
// in reality a function where the index is supposed to control the degree of derivatives of the function
double H(const std::function<double(double)>& f, double x, int switch){
  if(0 == switch){
    return G(f(x));
  } else {
    return F(f(x));
  }
}

double sum=0;
for(int i=0; i<1;++i){
  for(int j=0; j<1;++j){
    sum += H(H(f,i),j);
  }
}