NAG Library Manual, Mark 28.5
```/* nag::ad::e01bg tangent over adjoint Example Program.
*/

#include <dco.hpp>
#include <iostream>

// Function which calls NAG AD routines.
template <typename T> void func(const T &xint, T &fint, T &dint);

// Driver with the adjoint calls.
//  Evaluates a piecewise cubic Hermite interpolant and computes function value
//  and derivative at point xint.
// Also computes the sum of all Hessian elements d^2(fint, dint)/d(xint)^2.
void driver(const double &xint, double &fint, double &dint, double &d);

int main()
{
std::cout

// Point to interpolate at
double xint = 8.4;
// Interpolated function and derivative value
double fint, dint;

// Sum of Hessian elements
double d;

// Call driver
driver(xint, fint, dint, d);

// Print outputs
std::cout << " Derivatives calculated: Second order adjoints\n";
std::cout << " Computational mode    : algorithmic\n";

std::cout.setf(std::ios::scientific, std::ios::floatfield);
std::cout.precision(6);
std::cout << "\n fint = " << fint << std::endl;
std::cout << " dint = " << dint << std::endl;

// Print derivative
std::cout
<< "\n Sum of all Hessian elements of (fint, dint) w.r.t. interpolation point xint :\n";
std::cout << " sum_i [d^2(fint, dint) / d(xint)^2]_i = " << d << std::endl;

return 0;
}

// Driver with the adjoint calls.
//  Evaluates a piecewise cubic Hermite interpolant and computes function value
//  and derivative at point xint.
// Also computes the sum of all Hessian elements d^2(fint, dint)/d(xint)^2.
void driver(const double &xintv, double &fintv, double &dintv, double &d)
{
using mode = dco::ga1s<dco::gt1s<double>::type>;
using T    = mode::type;

mode::global_tape = mode::tape_t::create();

// Variable to differentiate w.r.t.
T xint = xintv;

// Register variable to differentiate w.r.t.
mode::global_tape->register_variable(xint);
dco::derivative(dco::value(xint)) = 1.0;

// Interpolated function and derivative value
T fint, dint;

// Call the NAG AD Lib functions
func(xint, fint, dint);

// Extract the computed solutions
fintv = dco::passive_value(fint);
dintv = dco::passive_value(dint);
mode::global_tape->register_output_variable(fint);
mode::global_tape->register_output_variable(dint);
dco::derivative(fint) = 1.0;
dco::derivative(dint) = 1.0;

// Interpret the tape

d = dco::derivative(dco::derivative(xint));

// Remove tape
mode::tape_t::remove(mode::global_tape);
}

// function which calls NAG AD Library routines
template <typename T> void func(const T &xint, T &fint, T &dint)
{

// Create AD configuration data object
Integer           ifail = 0;

// Initialize abscissa and ordinate data
std::vector<T> x{7.99, 8.09, 8.19, 8.70, 9.20, 10.00, 12.00, 15.00, 20.00};
std::vector<T> f{0.00000E+0, 0.27643E-4, 0.43750E-1, 0.16918E+0, 0.46943E+0,
0.94374E+0, 0.99864E+0, 0.99992E+0, 0.99999E+0};

// Local output of e01be; approximation of derivatives at points x
std::vector<T> d(x.size());
ifail = 0;