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$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
exp_2: Verify Zero Order Forward Sweep
# include <cmath>            // for fabs function
bool exp_2_for0(double *v0)  // double v0[6]
{     bool  ok = true;
double x = .5;

v0[1] = x;                                  // v1 = x
ok  &= std::fabs( v0[1] - 0.5) < 1e-10;

v0[2] = 1. + v0[1];                         // v2 = 1 + v1
ok  &= std::fabs( v0[2] - 1.5) < 1e-10;

v0[3] = v0[1] * v0[1];                      // v3 = v1 * v1
ok  &= std::fabs( v0[3] - 0.25) < 1e-10;

v0[4] = v0[3] / 2.;                         // v4 = v3 / 2
ok  &= std::fabs( v0[4] - 0.125) < 1e-10;

v0[5] = v0[2] + v0[4];                      // v5  = v2 + v4
ok  &= std::fabs( v0[5] - 1.625) < 1e-10;

return ok;
}
bool exp_2_for0(void)
{     double v0[6];
return exp_2_for0(v0);
}

Input File: introduction/exp_2_for0.cpp