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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 .
Independent and ADFun Constructor: Example and Test
# include <cppad/cppad.hpp>

namespace { // --------------------------------------------------------
// define the template function Test<ADVector>(void) in empty namespace
template <class ADVector>
bool Test(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;
    ADVector X(n);  // ADVector is the template parameter in call to Test
    X[0] = 0.;
    X[1] = 1.;

    // declare independent variables and start recording
    // use the template parameter ADVector for the vector type
    CppAD::Independent(X);

    AD<double> a = X[0] + X[1];      // first AD operation
    AD<double> b = X[0] * X[1];      // second AD operation

    // range space vector
    size_t m = 2;
    ADVector Y(m);  // ADVector is the template paraemter in call to Test
    Y[0] = a;
    Y[1] = b;

    // create f: X -> Y and stop tape recording
    // use the template parameter ADVector for the vector type
    CppAD::ADFun<double> f(X, Y);

    // check value
    ok &= NearEqual(Y[0] , 1.,  eps99 , eps99);
    ok &= NearEqual(Y[1] , 0.,  eps99 , eps99);

    // compute f(1, 2)
    CPPAD_TESTVECTOR(double) x(n);
    CPPAD_TESTVECTOR(double) y(m);
    x[0] = 1.;
    x[1] = 2.;
    y    = f.Forward(0, x);
    ok &= NearEqual(y[0] , 3.,  eps99 , eps99);
    ok &= NearEqual(y[1] , 2.,  eps99 , eps99);

    // compute partial of f w.r.t x[0] at (1, 2)
    CPPAD_TESTVECTOR(double) dx(n);
    CPPAD_TESTVECTOR(double) dy(m);
    dx[0] = 1.;
    dx[1] = 0.;
    dy    = f.Forward(1, dx);
    ok &= NearEqual(dy[0] ,   1.,  eps99 , eps99);
    ok &= NearEqual(dy[1] , x[1],  eps99 , eps99);

    // compute partial of f w.r.t x[1] at (1, 2)
    dx[0] = 0.;
    dx[1] = 1.;
    dy    = f.Forward(1, dx);
    ok &= NearEqual(dy[0] ,   1.,  eps99 , eps99);
    ok &= NearEqual(dy[1] , x[0],  eps99 , eps99);

    return ok;
}
} // End of empty namespace -------------------------------------------

# include <vector>
# include <valarray>
bool Independent(void)
{   bool ok = true;
    typedef CppAD::AD<double> ADdouble;
    // Run with ADVector equal to three different cases
    // all of which are Simple Vectors with elements of type AD<double>.
    ok &= Test< CppAD::vector  <ADdouble> >();
    ok &= Test< std::vector    <ADdouble> >();
    ok &= Test< std::valarray  <ADdouble> >();
    return ok;
}
Input File: example/general/independent.cpp