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Example Optimization and Nested Conditional Expressions
See Also
cond_exp.cpp `

    # include <cppad/cppad.hpp>
    namespace {
         struct tape_size { size_t n_var; size_t n_op; };

         template <class Vector> void fun(
              const std::string& options ,
              const Vector& x, Vector& y, tape_size& before, tape_size& after
         )
         {     typedef typename Vector::value_type scalar;

              // phantom variable with index 0 and independent variables
              // begin operator, independent variable operators and end operator
              before.n_var = 1 + x.size(); before.n_op  = 2 + x.size();
              after.n_var  = 1 + x.size(); after.n_op   = 2 + x.size();

              // Create a variable that is is only used in the second comparision
              scalar two = 1. + x[0];
              before.n_var += 1; before.n_op += 1;
              after.n_var  += 1; after.n_op  += 1;

              // Conditional skip for second comparison will be inserted here.
              if( options.find("no_conditional_skip") == std::string::npos )
                   after.n_op += 1; // for conditional skip operation

              // Create a variable that is is only used in the first comparision
              // (can be skipped when second comparison result is false)
              scalar one = 1. / x[0];
              before.n_var += 1; before.n_op += 1;
              after.n_var  += 1; after.n_op  += 1;

              // Conditional skip for first comparison will be inserted here.
              if( options.find("no_conditional_skip") == std::string::npos )
                   after.n_op += 1; // for conditional skip operation

              // value when first comparison if false
              scalar one_false = 5.0;

              // Create a variable that is only used when second comparison is true
              // (can be skipped when it is false)
              scalar one_true = x[0] / 5.0;
              before.n_var += 1; before.n_op += 1;
              after.n_var  += 1; after.n_op  += 1;

              // value when second comparison is false
              scalar two_false = 3.0;

              // First conditional compaison is 1 / x[0] < x[0]
              // is only used when second conditional expression is true
              // (can be skipped when it is false)
              scalar two_true  = CppAD::CondExpLt(one, x[0], one_true, one_false);
              before.n_var += 1; before.n_op += 1;
              after.n_var  += 1; after.n_op  += 1;

              // Second conditional compaison is 1 + x[0] < x[1]
              scalar two_value = CppAD::CondExpLt(two, x[1], two_true, two_false);
              before.n_var += 1; before.n_op += 1;
              after.n_var  += 1; after.n_op  += 1;

              // results for this operation sequence
              y[0] = two_value;
              before.n_var += 0; before.n_op  += 0;
              after.n_var  += 0; after.n_op   += 0;
         }
    }

    bool nest_conditional(void)
    {     bool ok = true;
         using CppAD::AD;
         using CppAD::NearEqual;
         double eps10 = 10.0 * std::numeric_limits<double>::epsilon();

         // domain space vector
         size_t n  = 2;
         CPPAD_TESTVECTOR(AD<double>) ax(n);
         ax[0] = 0.5;
         ax[1] = 0.5;

         // range space vector
         size_t m = 1;
         CPPAD_TESTVECTOR(AD<double>) ay(m);

         for(size_t k = 0; k < 2; k++)
         {     // optimization options
              std::string options = "";
              if( k == 0 )
                   options = "no_conditional_skip";

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

              // compute function computation
              tape_size before, after;
              fun(options, ax, ay, before, after);

              // create f: x -> y and stop tape recording
              CppAD::ADFun<double> f(ax, ay);
              ok &= f.size_var() == before.n_var;
              ok &= f.size_op()  == before.n_op;

              // Optimize the operation sequence
              f.optimize(options);
              ok &= f.size_var() == after.n_var;
              ok &= f.size_op()  == after.n_op;

              // Check case where result of the second comparison is true
              // and first comparison is true
              CPPAD_TESTVECTOR(double) x(n), y(m), check(m);
              x[0] = 1.75;
              x[1] = 4.0;
              y    = f.Forward(0, x);
              fun(options, x, check, before, after);
              ok &= NearEqual(y[0], check[0], eps10, eps10);
              ok  &= f.number_skip() == 0;

              // Check case where result of the second comparison is true
              // and first comparison is false
              x[0] = 0.5;
              x[1] = 4.0;
              y    = f.Forward(0, x);
              fun(options, x, check, before, after);
              ok &= NearEqual(y[0], check[0], eps10, eps10);
              if( options == "" )
                   ok  &= f.number_skip() == 1;
              else
                   ok &= f.number_skip() == 0;

              // Check case where result of the second comparison is false
              // and first comparison is true
              x[0] = 1.75;
              x[1] = 0.0;
              y    = f.Forward(0, x);
              fun(options, x, check, before, after);
              ok &= NearEqual(y[0], check[0], eps10, eps10);
              if( options == "" )
                   ok  &= f.number_skip() == 3;
              else
                   ok &= f.number_skip() == 0;

              // Check case where result of the second comparison is false
              // and first comparison is false
              x[0] = 0.5;
              x[1] = 0.0;
              y    = f.Forward(0, x);
              fun(options, x, check, before, after);
              ok &= NearEqual(y[0], check[0], eps10, eps10);
              if( options == "" )
                   ok  &= f.number_skip() == 3;
              else
                   ok &= f.number_skip() == 0;
         }
         return ok;
    }

`

Input File: example/optimize/nest_conditional.cpp