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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 r14610697 = 1.0;
        double r14610698 = eps;
        double r14610699 = r14610697 / r14610698;
        double r14610700 = r14610697 + r14610699;
        double r14610701 = r14610697 - r14610698;
        double r14610702 = x;
        double r14610703 = r14610701 * r14610702;
        double r14610704 = -r14610703;
        double r14610705 = exp(r14610704);
        double r14610706 = r14610700 * r14610705;
        double r14610707 = r14610699 - r14610697;
        double r14610708 = r14610697 + r14610698;
        double r14610709 = r14610708 * r14610702;
        double r14610710 = -r14610709;
        double r14610711 = exp(r14610710);
        double r14610712 = r14610707 * r14610711;
        double r14610713 = r14610706 - r14610712;
        double r14610714 = 2.0;
        double r14610715 = r14610713 / r14610714;
        return r14610715;
}

Reproduce

herbie shell --seed 2019112 +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))