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@(@\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }@)@
Source: det_grad_33
# ifndef CPPAD_DET_GRAD_33_HPP
# define CPPAD_DET_GRAD_33_HPP
# include <limits>
# include <cppad/utility/near_equal.hpp>
namespace CppAD {
template <class Vector>
     bool det_grad_33(const Vector &x, const Vector &g)
     {     bool ok = true;
          typedef typename Vector::value_type Float;
          Float eps = 10. * Float( std::numeric_limits<double>::epsilon() );

          // use expansion by minors to compute the derivative by hand
          double check[9];
          check[0] = + ( x[4] * x[8] - x[5] * x[7] );
          check[1] = - ( x[3] * x[8] - x[5] * x[6] );
          check[2] = + ( x[3] * x[7] - x[4] * x[6] );
          //
          check[3] = - ( x[1] * x[8] - x[2] * x[7] );
          check[4] = + ( x[0] * x[8] - x[2] * x[6] );
          check[5] = - ( x[0] * x[7] - x[1] * x[6] );
          //
          check[6] = + ( x[1] * x[5] - x[2] * x[4] );
          check[7] = - ( x[0] * x[5] - x[2] * x[3] );
          check[8] = + ( x[0] * x[4] - x[1] * x[3] );
          //
          for(size_t i = 0; i < 3 * 3; i++)
               ok &= CppAD::NearEqual(check[i], g[i], eps, eps);

          return ok;
     }
}
# endif

Input File: omh/det_grad_33_hpp.omh