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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_eps: Verify Zero Order Forward Sweep
# include <cmath>                // for fabs function
bool exp_eps_for0(double *v0)    // double v0[8]
{     bool  ok = true;
double x = .5;

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

v0[2] = 1. * v0[1];                         // temp = term * abs_x;
ok  &= std::fabs( v0[2] - 0.5) < 1e-10;

v0[3] = v0[2] / 1.;                         // term = temp / Type(k);
ok  &= std::fabs( v0[3] - 0.5) < 1e-10;

v0[4] = 1. + v0[3];                         // sum = sum + term;
ok  &= std::fabs( v0[4] - 1.5) < 1e-10;

v0[5] = v0[3] * v0[1];                      // temp = term * abs_x;
ok  &= std::fabs( v0[5] - 0.25) < 1e-10;

v0[6] = v0[5] / 2.;                         // term = temp / Type(k);
ok  &= std::fabs( v0[6] - 0.125) < 1e-10;

v0[7] = v0[4] + v0[6];                      // sum = sum + term;
ok  &= std::fabs( v0[7] - 1.625) < 1e-10;

return ok;
}
bool exp_eps_for0(void)
{     double v0[8];
return exp_eps_for0(v0);
}

Input File: introduction/exp_eps_for0.cpp