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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 .
Controlling Taylor Coefficient Memory Allocation: Example and Test
# include <cppad/cppad.hpp>

namespace {
    bool test(void)
    {   bool ok = true;
        using CppAD::AD;
        using CppAD::NearEqual;
        using CppAD::thread_alloc;

        // domain space vector
        size_t n(1), m(1);
        CPPAD_TESTVECTOR(AD<double>) ax(n), ay(n);

        // declare independent variables and start tape recording
        ax[0]  = 1.0;
        CppAD::Independent(ax);

        // Set y = x^3, use enough variables so more that the minimal amount
        // of memory is allocated for Taylor coefficients
        ay[0] = 0.;
        for( size_t i = 0; i < 10; i++)
            ay[0] += ax[0] * ax[0] * ax[0];
        ay[0] = ay[0] / 10.;

        // create f: x -> y and stop tape recording
        // (without running zero order forward mode).
        CppAD::ADFun<double> f;
        f.Dependent(ax, ay);

        // check that this is master thread
        size_t thread = thread_alloc::thread_num();
        ok           &= thread == 0; // this should be master thread

        // The highest order forward mode calculation below is first order.
        // This corresponds to two Taylor coefficient per variable,direction
        // (orders zero and one). Preallocate memory for speed.
        size_t inuse  = thread_alloc::inuse(thread);
        f.capacity_order(2);
        ok &= thread_alloc::inuse(thread) > inuse;

        // zero order forward mode
        CPPAD_TESTVECTOR(double) x(n), y(m);
        x[0] = 0.5;
        y    = f.Forward(0, x);
        double eps = 10. * CppAD::numeric_limits<double>::epsilon();
        ok  &= NearEqual(y[0], x[0] * x[0] * x[0], eps, eps);

        // forward computation of partials w.r.t. x
        CPPAD_TESTVECTOR(double) dx(n), dy(m);
        dx[0] = 1.;
        dy    = f.Forward(1, dx);
        ok   &= NearEqual(dy[0], 3. * x[0] * x[0], eps, eps);

        // Suppose we no longer need the first order Taylor coefficients.
        inuse = thread_alloc::inuse(thread);
        f.capacity_order(1); // just keep zero order coefficients
        ok   &= thread_alloc::inuse(thread) < inuse;

        // Suppose we no longer need the zero order Taylor coefficients
        // (could have done this first and not used f.capacity_order(1)).
        inuse = thread_alloc::inuse(thread);
        f.capacity_order(0);
        ok   &= thread_alloc::inuse(thread) < inuse;

        // turn off memory holding
        thread_alloc::hold_memory(false);

        return ok;
    }
}
bool capacity_order(void)
{   bool ok = true;
    using CppAD::thread_alloc;

    // original amount of memory inuse
    size_t thread = thread_alloc::thread_num();
    ok           &= thread == 0; // this should be master thread
    size_t inuse  = thread_alloc::inuse(thread);

    // do test in separate routine so all objects are destroyed
    ok &= test();

    // check that the amount of memroy inuse has not changed
    ok &= thread_alloc::inuse(thread) == inuse;

    // Test above uses hold_memory, so return available memory
    thread_alloc::free_available(thread);

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