//           Copyright Matthew Pulver 2018 - 2019.
// Distributed under the Boost Software License, Version 1.0.
//      (See accompanying file LICENSE_1_0.txt or copy at
//           https://www.boost.org/LICENSE_1_0.txt)

#include <boost/math/differentiation/autodiff.hpp>
#include <iostream>

template <typename T>
T fourth_power(T const& x) {
  T x4 = x * x;  // retval in operator*() uses x4's memory via NRVO.
  x4 *= x4;      // No copies of x4 are made within operator*=() even when squaring.
  return x4;     // x4 uses y's memory in main() via NRVO.
}

int main() {
  using namespace boost::math::differentiation;

  constexpr unsigned Order = 5;                  // Highest order derivative to be calculated.
  auto const x = make_fvar<double, Order>(2.0);  // Find derivatives at x=2.
  auto const y = fourth_power(x);
  for (unsigned i = 0; i <= Order; ++i)
    std::cout << "y.derivative(" << i << ") = " << y.derivative(i) << std::endl;
  return 0;
}
/*
Output:
y.derivative(0) = 16
y.derivative(1) = 32
y.derivative(2) = 48
y.derivative(3) = 48
y.derivative(4) = 24
y.derivative(5) = 0
**/