NAG Library Manual, Mark 27.2
```/* D02PU_T1W_F C++ Header Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
*
* Mark 27.2, 2021.
*/

#include <dco.hpp>
#include <iostream>
#include <math.h>
#include <nag.h>
#include <stdio.h>
using namespace std;

#ifdef __cplusplus
extern "C"
{
#endif
static void NAG_CALL f(void *&                  ad_handle,
const Integer &          n,
Integer                  iuser[],
#ifdef __cplusplus
}
#endif

int main(void)
{
const Integer n      = 4;
const Integer liwsav = 130;
const Integer lrwsav = 350 + 32 * n;

Integer exit_status = 0;

nagad_t1w_w_rtype *rwsav = 0, *thresh = 0, *ygot = 0, *ymax = 0;
nagad_t1w_w_rtype *ypgot = 0, *y = 0, ruser[1];
Integer *          iwsav  = 0, iuser[1];

cout << "D02PU_T1W_F C++ Header Example Program Results\n\n";

iwsav  = new Integer[liwsav];

// Set initial conditions for ODE and parameters for the integrator.
Integer           method = 3;
nagad_t1w_w_rtype tol, hstart, tend, tstart, eps;
eps    = 0.7;
tstart = 0.0;
tol    = 1.0e-6;
tend   = 3.0 * nag_math_pi;
hstart = 0.0;
for (int i = 0; i < n; ++i)
{
thresh[i] = 1.0e-10;
}

{
double tolr = dco::value(tol);
cout << "\n  Calculation with tol = " << tolr << endl;
}
cout.setf(ios::fixed);
cout.setf(ios::right);
cout.precision(3);
{
double t = dco::value(tstart);
cout << "\n    t         y1         y2         y3         y4" << endl;
cout.width(6);
cout << t;
}

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

double inc           = 1.0;
dco::derivative(eps) = inc;

y[0] = 1.0 - eps;
y[1] = 0.0;
y[2] = 0.0;
y[3] = sqrt((1.0 + eps) / (1.0 - eps));
for (int k = 0; k < n; k++)
{
double yr = dco::value(y[k]);
cout.width(11);
cout << yr;
}
cout << endl;

// Initialize Runge-Kutta method for integrating ODE
ifail = 0;
iwsav, rwsav, ifail);

twant = tend;

ifail = 2;
while (ifail > 1 && ifail < 5)
{
ifail = -1;
-1, ruser, iwsav, rwsav, ifail);
}

if (ifail == 0)
{
cout.width(6);
cout << dco::value(tgot);
for (int k = 0; k < n; ++k)
{
cout.width(11);
cout << dco::value(ygot[k]);
}
cout << endl;

// Get Error estimates
ifail = 0;

cout.setf(ios::scientific, ios::floatfield);
cout.precision(2);
cout << "\n Componentwise error assessment\n        ";
for (int k = 0; k < n; ++k)
{
cout.width(11);
cout << dco::value(rmserr[k]);
}
cout << endl;
cout.precision(3);
cout << "\n Worst global error observed was ";
cout.width(9);
cout << dco::value(errmax) << endl;
cout << "              it occurred at T = ";
cout.width(8);
cout << dco::value(terrmx) << endl;

Integer           fevals, stepcost, stepsok;
ifail = 0;
rwsav, ifail);
cout << "\n Cost of the integration in evaluations of f is " << fevals;
cout << endl;

cout << "\n Derivatives calculated: First order tangents\n";
cout << " Computational mode    : algorithmic\n";

// Get derivatives
cout << "\n Derivatives: (solution w.r.t. eps)\n";

cout.setf(ios::scientific, ios::floatfield);
cout.precision(4);
double deps;
deps = dco::derivative(ygot[0]);
cout << " dy(t)/deps = ";
cout.width(12);
cout << deps << endl;
}

delete[] thresh;
delete[] ygot;
delete[] y;
delete[] ypgot;
delete[] ymax;
delete[] iwsav;
delete[] rwsav;
delete[] rmserr;
return exit_status;
}

static void NAG_CALL f(void *&                  ad_handle,
const Integer &          n,