//           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/lexical_cast.hpp>
#include <boost/math/differentiation/autodiff.hpp>
#include <boost/mp11/tuple.hpp>
#include <boost/mp11/utility.hpp>
#include <boost/multiprecision/cpp_bin_float.hpp>
#include <iostream>

using namespace boost::math::differentiation;

struct f {
  template <typename W, typename X, typename Y, typename Z>
  promote<W, X, Y, Z> operator()(W const& w, X const& x, Y const& y, Z const& z) const {
    return exp(w * sin(x * log(y) / z) + sqrt(w * z / (x * y))) + w * w / tan(z);
  }
};

// Derivatives calculated from symbolic differentiation by Mathematica for comparison. Script:
// mixed_partials.nb
static constexpr std::array<char const*, 240> answers{
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int main() {
  using float50 = boost::multiprecision::cpp_bin_float_50;
  constexpr std::size_t Nw = 3;  // Max order of derivative to calculate for w
  constexpr std::size_t Nx = 2;  // Max order of derivative to calculate for x
  constexpr std::size_t Ny = 4;  // Max order of derivative to calculate for y
  constexpr std::size_t Nz = 3;  // Max order of derivative to calculate for z
  auto const variables = make_ftuple<float50, Nw, Nx, Ny, Nz>(11, 12, 13, 14);
  auto const v = boost::mp11::tuple_apply(f{}, variables);
  std::size_t ia = 0;
  double max_relative_error = 0;
  for (std::size_t iw = 0; iw <= Nw; ++iw)
    for (std::size_t ix = 0; ix <= Nx; ++ix)
      for (std::size_t iy = 0; iy <= Ny; ++iy)
        for (std::size_t iz = 0; iz <= Nz; ++iz) {
          float50 const value = v.derivative(iw, ix, iy, iz);
          float50 const answer = boost::lexical_cast<float50>(answers[ia++]);
          double const error = static_cast<double>(fabs(value / answer - 1));
          max_relative_error = (std::max)(error, max_relative_error);
        }
  std::cout << "max_relative_error = " << std::setprecision(3) << max_relative_error << " out of " << ia
            << " calculated values." << std::endl;
  return 0;
}
/*
Output:
max_relative_error = 6.82e-13 out of 240 calculated values. (for double)
max_relative_error = 3.36e-47 out of 240 calculated values. (for cpp_bin_float_50)
**/