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\[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2}\]
\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2}
double f(double x, double eps) {
        double r21591743 = 1.0;
        double r21591744 = eps;
        double r21591745 = r21591743 / r21591744;
        double r21591746 = r21591743 + r21591745;
        double r21591747 = r21591743 - r21591744;
        double r21591748 = x;
        double r21591749 = r21591747 * r21591748;
        double r21591750 = -r21591749;
        double r21591751 = exp(r21591750);
        double r21591752 = r21591746 * r21591751;
        double r21591753 = r21591745 - r21591743;
        double r21591754 = r21591743 + r21591744;
        double r21591755 = r21591754 * r21591748;
        double r21591756 = -r21591755;
        double r21591757 = exp(r21591756);
        double r21591758 = r21591753 * r21591757;
        double r21591759 = r21591752 - r21591758;
        double r21591760 = 2.0;
        double r21591761 = r21591759 / r21591760;
        return r21591761;
}

Reproduce

herbie shell --seed 2019121 +o rules:numerics
(FPCore (x eps)
  :name "NMSE Section 6.1 mentioned, A"
  (/ (- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))) 2))