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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 .
Creating Your Own Interface to an ADFun Object

# include <cppad/cppad.hpp>

namespace {

    // This class is an example of a different interface to an AD function object
    template <class Base>
    class my_ad_fun {

    private:
        CppAD::ADFun<Base> f;

    public:
        // default constructor
        my_ad_fun(void)
        { }

        // destructor
        ~ my_ad_fun(void)
        { }

        // Construct an my_ad_fun object with an operation sequence.
        // This is the same as for ADFun<Base> except that no zero
        // order forward sweep is done. Note Hessian and Jacobian do
        // their own zero order forward mode sweep.
        template <class ADvector>
        my_ad_fun(const ADvector& x, const ADvector& y)
        {   f.Dependent(x, y); }

        // same as ADFun<Base>::Jacobian
        template <class BaseVector>
        BaseVector jacobian(const BaseVector& x)
        {   return f.Jacobian(x); }

        // same as ADFun<Base>::Hessian
            template <class BaseVector>
        BaseVector hessian(const BaseVector &x, const BaseVector &w)
        {   return f.Hessian(x, w); }
    };

} // End empty namespace

bool ad_fun(void)
{   // This example is similar to example/jacobian.cpp, except that it
    // uses my_ad_fun instead of ADFun.

    bool ok = true;
    using CppAD::AD;
    using CppAD::NearEqual;
    double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
    using CppAD::exp;
    using CppAD::sin;
    using CppAD::cos;

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

    // declare independent variables and starting recording
    CppAD::Independent(X);

    // a calculation between the domain and range values
    AD<double> Square = X[0] * X[0];

    // range space vector
    size_t m = 3;
    CPPAD_TESTVECTOR(AD<double>)  Y(m);
    Y[0] = Square * exp( X[1] );
    Y[1] = Square * sin( X[1] );
    Y[2] = Square * cos( X[1] );

    // create f: X -> Y and stop tape recording
    my_ad_fun<double> f(X, Y);

    // new value for the independent variable vector
    CPPAD_TESTVECTOR(double) x(n);
    x[0] = 2.;
    x[1] = 1.;

    // compute the derivative at this x
    CPPAD_TESTVECTOR(double) jac( m * n );
    jac = f.jacobian(x);

    /*
    F'(x) = [ 2 * x[0] * exp(x[1]) ,  x[0] * x[0] * exp(x[1]) ]
            [ 2 * x[0] * sin(x[1]) ,  x[0] * x[0] * cos(x[1]) ]
            [ 2 * x[0] * cos(x[1]) , -x[0] * x[0] * sin(x[i]) ]
    */
    ok &=  NearEqual( 2.*x[0]*exp(x[1]), jac[0*n+0], eps99, eps99);
    ok &=  NearEqual( 2.*x[0]*sin(x[1]), jac[1*n+0], eps99, eps99);
    ok &=  NearEqual( 2.*x[0]*cos(x[1]), jac[2*n+0], eps99, eps99);

    ok &=  NearEqual( x[0] * x[0] *exp(x[1]), jac[0*n+1], eps99, eps99);
    ok &=  NearEqual( x[0] * x[0] *cos(x[1]), jac[1*n+1], eps99, eps99);
    ok &=  NearEqual(-x[0] * x[0] *sin(x[1]), jac[2*n+1], eps99, eps99);

    return ok;
}
Input File: example/general/ad_fun.cpp