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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 .
First Order Reverse Mode: Example and Test
# include <cppad/cppad.hpp>
namespace { // ----------------------------------------------------------
// define the template function reverse_one_cases<Vector> in empty namespace
template <class Vector>
bool reverse_one_cases(void)
{   bool ok = true;
    using CppAD::AD;
    using CppAD::NearEqual;
    double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

    // domain space vector
    size_t n = 2;
    CPPAD_TESTVECTOR(AD<double>) ax(n);
    ax[0] = 0.;
    ax[1] = 1.;

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

    // range space vector
    size_t m = 1;
    CPPAD_TESTVECTOR(AD<double>) ay(m);
    ay[0] = ax[0] * ax[0] * ax[1];

    // create f : x -> y and stop recording
    CppAD::ADFun<double> f(ax, ay);

    // use first order reverse mode to evaluate derivative of y[0]
    // and use the values in x for the independent variables.
    CPPAD_TESTVECTOR(double) w(m), dw(n);
    w[0] = 1.;
    dw   = f.Reverse(1, w);
    ok  &= NearEqual(dw[0] , 2.*ax[0]*ax[1], eps99, eps99);
    ok  &= NearEqual(dw[1] ,    ax[0]*ax[0], eps99, eps99);

    // use zero order forward mode to evaluate y at x = (3, 4)
    // and use the template parameter Vector for the vector type
    Vector x(n), y(m);
    x[0]    = 3.;
    x[1]    = 4.;
    y       = f.Forward(0, x);
    ok     &= NearEqual(y[0] , x[0]*x[0]*x[1], eps99, eps99);

    // use first order reverse mode to evaluate derivative of y[0]
    // and using the values in x for the independent variables.
    w[0] = 1.;
    dw   = f.Reverse(1, w);
    ok  &= NearEqual(dw[0] , 2.*x[0]*x[1], eps99, eps99);
    ok  &= NearEqual(dw[1] ,    x[0]*x[0], eps99, eps99);

    return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool reverse_one(void)
{   bool ok = true;
    // Run with Vector equal to three different cases
    // all of which are Simple Vectors with elements of type double.
    ok &= reverse_one_cases< CppAD::vector  <double> >();
    ok &= reverse_one_cases< std::vector    <double> >();
    ok &= reverse_one_cases< std::valarray  <double> >();
    return ok;
}
Input File: example/general/reverse_one.cpp