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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}} }@)@This is cppad-20221105 documentation. Here is a link to its current documentation .
Optimize Reverse Activity Analysis: Example and Test
# include <cppad/cppad.hpp>
namespace {
    struct tape_size { size_t n_var; size_t n_op; };

    template <class Vector> void fun(
        const Vector& x, Vector& y, tape_size& before, tape_size& after
    )
    {   typedef typename Vector::value_type scalar;

        // phantom variable with index 0 and independent variables
        // begin operator, independent variable operators and end operator
        before.n_var = 1 + x.size(); before.n_op  = 2 + x.size();
        after.n_var  = 1 + x.size(); after.n_op   = 2 + x.size();

        // initilized product of even and odd variables
        scalar prod_even = x[0];
        scalar prod_odd  = x[1];
        before.n_var += 0; before.n_op  += 0;
        after.n_var  += 0; after.n_op   += 0;
        //
        // compute product of even and odd variables
        for(size_t i = 2; i < size_t( x.size() ); i++)
        {   if( i % 2 == 0 )
            {   // prod_even will affect dependent variable
                prod_even = prod_even * x[i];
                before.n_var += 1; before.n_op += 1;
                after.n_var  += 1; after.n_op  += 1;
            }
            else
            {   // prod_odd will not affect dependent variable
                prod_odd  = prod_odd * x[i];
                before.n_var += 1; before.n_op += 1;
                after.n_var  += 0; after.n_op  += 0;
            }
        }

        // dependent variable for this operation sequence
        y[0] = prod_even;
        before.n_var += 0; before.n_op  += 0;
        after.n_var  += 0; after.n_op   += 0;
    }
}

bool reverse_active(void)
{   bool ok = true;
    using CppAD::AD;
    using CppAD::NearEqual;
    double eps10 = 10.0 * std::numeric_limits<double>::epsilon();

    // domain space vector
    size_t n  = 6;
    CPPAD_TESTVECTOR(AD<double>) ax(n);
    for(size_t i = 0; i < n; i++)
        ax[i] = AD<double>(i + 1);

    // declare independent variables and start tape recording
    CppAD::Independent(ax);

    // range space vector
    size_t m = 1;
    CPPAD_TESTVECTOR(AD<double>) ay(m);
    tape_size before, after;
    fun(ax, ay, before, after);

    // create f: x -> y and stop tape recording
    CppAD::ADFun<double> f(ax, ay);
    ok &= f.size_order() == 1; // this constructor does 0 order forward
    ok &= f.size_var() == before.n_var;
    ok &= f.size_op()  == before.n_op;

    // Optimize the operation sequence
    f.optimize();
    ok &= f.size_order() == 0; // 0 order forward not present
    ok &= f.size_var() == after.n_var;
    ok &= f.size_op()  == after.n_op;

    // check zero order forward with different argument value
    CPPAD_TESTVECTOR(double) x(n), y(m), check(m);
    for(size_t i = 0; i < n; i++)
        x[i] = double(i + 2);
    y    = f.Forward(0, x);
    fun(x, check, before, after);
    ok &= NearEqual(y[0], check[0], eps10, eps10);

    return ok;
}
Input File: example/optimize/reverse_active.cpp