NAG Library Manual, Mark 28.5
```/* E04DG_A1W_F C++ Header Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
* Mark 28.5, 2022.
*/

#include <dco.hpp>
#include <iostream>
#include <math.h>
#include <nag.h>
#include <nagx02.h>
#include <stdio.h>
using namespace std;

int main()
{
int               exit_status = 0;
cout << "E04DG_A1W_F C++ Header Example Program Results\n\n";

dco::ga1s<double>::global_tape = dco::ga1s<double>::tape_t::create();

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

// Read problem parameters and register for differentiation
// Skip first line of data file
string mystr;
getline(cin, mystr);

Integer n;
cin >> n;

// AD routine fixed length array arguments
Integer           iwsav[610];
char              cwsav[1];
logical           lwsav[120];
const Charlen     name_l = 6, cwsav_l = 1;

Integer &               mode,
const Integer &         n,
const Integer &         nstate)
{
// dco/c++ used here to perform AD of objfun
nagad_a1w_w_rtype x1, x2, y1, y2, expx1;

x1    = x[0];
x2    = x[1];
expx1 = exp(x1);
y1    = 2.0 * x1;
y1    = y1 + x2;
y2    = x2 + 1.0;
x1    = y1 * y1;
x2    = y2 * y2;
x1    = x1 + x2;
objf  = expx1 * x1;

if (mode == 2)
{
y2        = y1 + y2;
y2        = 2.0 * y2;
y1        = 4.0 * y1;
y1        = expx1 * y1;
objgrd[0] = y1 + objf;
objgrd[1] = expx1 * y2;
}
};

// AD routine variable length arrays
Integer *          iwork = 0;
nagad_a1w_w_rtype *x = 0, *x_in = 0, *objgrd = 0, *work = 0;

if (!(iwork = NAG_ALLOC(n + 1, Integer)) ||
!(work = NAG_ALLOC(13 * n, nagad_a1w_w_rtype)))
{
cout << "Allocation failure\n";
exit_status = -1;
goto END;
}

double xr;
for (int i = 0; i < n; i++)
{
cin >> xr;
x_in[i] = xr;
dco::ga1s<double>::global_tape->register_variable(x_in[i]);
x[i] = x_in[i];
}

// Initialize sav arrays
ifail = 0;
nag::ad::e04wb("E04DGA", cwsav, 1, lwsav, 120, iwsav, 610, rwsav, 475, ifail);

// Options can be set here via E04DJA and/or E04DKA
// Solve the problem
Integer iter;
ifail = 0;
nag::ad::e04dg(ad_handle, n, objfun, iter, objf, objgrd, x, iwork, work, lwsav, iwsav, rwsav, ifail);

// Primal results
cout.setf(ios::scientific, ios::floatfield);
cout.precision(3);
cout << "\n Objective value = ";
cout.width(12);
cout << dco::value(objf);
cout << "\n Solution point  = ";
for (int i = 0; i < n; i++)
{
cout.width(12);
cout << dco::value(x[i]);
}

cout << "\n Estim gradient  = ";
for (int i = 0; i < n; i++)
{
cout.width(12);
cout << dco::value(objgrd[i]);
}

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

// Setup evaluation of derivatives of objf via adjoints.
{
double inc = 1.0;
dco::derivative(objf) += inc;
}
ifail                                              = 0;
dco::ga1s<double>::global_tape->sparse_interpret() = true;

// Get derivatives of solution points
cout << "      dobjf/dx : ";
for (int i = 0; i < n; i++)
{
double d = dco::derivative(x[i]);
cout.width(12);
cout << d;
}
cout << endl;

//  Setup evaluation of derivatives via adjoints
for (int j = 0; j < n; j++)
{
double inc = 1.0;
dco::derivative(objgrd[j]) += inc;
ifail                                              = 0;
dco::ga1s<double>::global_tape->sparse_interpret() = true;
cout << " dobjgrd(";
cout.width(1);
cout << j + 1;
cout << ")/dx : ";
for (int i = 0; i < n; i++)
{
double d = dco::derivative(x[i]);
cout.width(12);
cout << d;
}
cout << endl;
}

END:

dco::ga1s<double>::tape_t::remove(dco::ga1s<double>::global_tape);

NAG_FREE(iwork);
NAG_FREE(x);
NAG_FREE(x_in);
NAG_FREE(objgrd);
NAG_FREE(work);

return exit_status;
}
```