NAG Library Manual, Mark 27.2
```/* nag::ad::c05ay Tangent over Tangent Example Program.
*/

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

// Function which calls NAG AD Library routines.
template <typename T> void func(T r, T &x);

// Driver with the tangent calls.
// Finds the zero point f(xv) = 0 for the function
// f(x) =  exp(-x) - r*x.
// Also, computes the Hessian d2x_dr2 = d2xv/dr2.
void driver(const double &rv, double &xv, double &d2x_dr2);

// The function f
template <typename T>
void NAG_CALL f(void *&ad_handle, const T &x, T &z, Integer iuser[], T ruser[]);

int main()
{
std::cout << " nag::ad::c05ay Tangent over Tangent Example Program Results\n";

// Set problem parameters
double rv = 2.0;
// Solution x
double xv;
// Derivative of x
double d2x_dr2;

// Call driver
driver(rv, xv, d2x_dr2);

// Print outputs
std::cout << "\n Derivatives calculated: Second order tangents\n";

// Print derivatives
std::cout.setf(std::ios::scientific, std::ios::floatfield);
std::cout.precision(12);
std::cout << "\n Solution:\n";
std::cout << " x = " << xv << std::endl;
std::cout << "\n Second derivative of solution x w.r.t. parameter r:\n";
std::cout << " d2x/dr2(x) = " << d2x_dr2 << std::endl;

return 0;
}

// Driver with the tangent calls.
// Finds the zero point f(xv) = 0 for the function
// f(x) =  exp(-x) - r*x.
// Also, computes the Hessian d2x_dr2 = d2xv/dr2.
void driver(const double &rv, double &xv, double &d2x_dr2)
{
using T = dco::gt1s<dco::gt1s<double>::type>::type;

// Function parameter r
T r = rv;
// Variable to differentiate w.r.t.
dco::derivative(dco::value(r)) = 1.0;
dco::value(dco::derivative(r)) = 1.0;

// Variable to differentiate
T x;

// Call the NAG AD Lib functions
func(r, x);

// Extract the computed solution
xv = dco::passive_value(x);
// Extract the 2nd order tangent of x
d2x_dr2 = dco::derivative(dco::derivative(x));
}

// Function which calls NAG AD Library routines.
template <typename T> void func(T r, T &x)
{
// Active variables
T a = 0.0, b = 1.0;
T eps = 1.0e-5, eta = 0.0;
// Create AD configuration data object
Integer ifail     = 0;
// Call routine for computing an approximation to a simple zero of the
// function f
ifail = 0;
nag::ad::c05ay(ad_handle, a, b, eps, eta, f<T>, x, 0, nullptr, 1, &r, ifail);
// Remove computational data object
ifail = 0;