autodiff example 1

ad_example1.cpp

#include "dualmath.hpp"
#include <cmath>
#include <iostream>

template<class T>
T fun(T x) {
  return sin(x) / cos(x); // tan(x)
}

int main() {
  for ( double x = 0; x < 10; x += 0.01 ) {
    // promote x to dual
    Dual xe(x, 1.0); // set y = 1
    // the derivative of tan(x) is 1/cos^2(x)
    std::cout << x << " " << fun(xe).y << " " << 1/(cos(x) * cos(x)) << std::endl;
  }
  return 0;
}