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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 .
Json Conditional Expressions: Example and Test

Source Code 

# include <cppad/cppad.hpp>

bool cexp_op(void)
{   bool ok = true;
    using CppAD::vector;
    using CppAD::AD;
    double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
    //
    // AD graph example
    // node_1 : p[0]
    // node_2 : x[0]
    // node_3 : c[0]
    // node_4 : cexp_le(p[0], x[0], p[0], x[0])
    // y[0]   = cexp_le(p[0], x[0], p[0], x[0])
    // use single quote to avoid having to escape double quote
    std::string json =
        "{\n"
        "   'function_name'  : 'cexp_op example',\n"
        "   'op_define_vec'  : [ 1, [\n"
        "       { 'op_code':1, 'name':'cexp_le', 'n_arg':4 } ]\n"
        "   ],\n"
        "   'n_dynamic_ind'  : 1,\n"
        "   'n_variable_ind' : 1,\n"
        "   'constant_vec'   : [ 1, [ -0.1 ] ],\n" // c[0]
        "   'op_usage_vec'   : [ 1, [\n"
        "       [ 1, 1, 2, 1, 2 ]      ]\n" // cexp_le(p[0], x[0], p[0], x[0])
        "   ],\n"
        "   'dependent_vec' : [ 1, [4] ] \n"
        "}\n";
    // Convert the single quote to double quote
    for(size_t i = 0; i < json.size(); ++i)
        if( json[i] == '\'' ) json[i] = '"';
    //
    // f(x, p) = cexp_le(p[0], x[0], p[0], x[0])
    CppAD::ADFun<double> f;
    f.from_json(json);
    ok &= f.Domain() == 1;
    ok &= f.Range() == 1;
    ok &= f.size_dyn_ind() == 1;
    //
    // set independent variables and parameters
    vector<double> p(1), x(1);
    p[0] = 0.2;
    x[0] = 0.3;
    //
    // compute y = f(x, p)
    f.new_dynamic(p);
    vector<double> y = f.Forward(0, x);
    //
    // check result
    double check;
    if( p[0] <= x[0] )
        check= p[0];
    else
        check = x[0];
    //
    // check result
    ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
    // ----------------------------------------------------------------------
    // Convert to Json graph and back again
    json = f.to_json();
    f.from_json(json);
    // ----------------------------------------------------------------------
    //
    // compute y = f(x, p)
    f.new_dynamic(p);
    y = f.Forward(0, x);
    //
    // check result
    ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
    //
    return ok;
}
Input File: example/json/cexp_op.cpp