\[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2}\]

↓

\[\begin{array}{l} \mathbf{if}\;x \le 295.27480666079055:\\ \;\;\;\;\frac{\mathsf{fma}\left({x}^{2}, 0.66666666666666674 \cdot x - 1, 2\right)}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(1, \frac{e^{x \cdot \varepsilon - 1 \cdot x}}{\varepsilon}, 1 \cdot \left(\frac{1}{e^{\mathsf{fma}\left(x, \varepsilon, 1 \cdot x\right)}} + e^{x \cdot \varepsilon - 1 \cdot x}\right) - 1 \cdot \frac{e^{-\left(x \cdot \varepsilon + 1 \cdot x\right)}}{\varepsilon}\right)}{2}\\ \end{array}\]

\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}

↓

\begin{array}{l}
\mathbf{if}\;x \le 295.27480666079055:\\
\;\;\;\;\frac{\mathsf{fma}\left({x}^{2}, 0.66666666666666674 \cdot x - 1, 2\right)}{2}\\

\mathbf{else}:\\
\;\;\;\;\frac{\mathsf{fma}\left(1, \frac{e^{x \cdot \varepsilon - 1 \cdot x}}{\varepsilon}, 1 \cdot \left(\frac{1}{e^{\mathsf{fma}\left(x, \varepsilon, 1 \cdot x\right)}} + e^{x \cdot \varepsilon - 1 \cdot x}\right) - 1 \cdot \frac{e^{-\left(x \cdot \varepsilon + 1 \cdot x\right)}}{\varepsilon}\right)}{2}\\

\end{array}

double f(double x, double eps) {
        double r37148 = 1.0;
        double r37149 = eps;
        double r37150 = r37148 / r37149;
        double r37151 = r37148 + r37150;
        double r37152 = r37148 - r37149;
        double r37153 = x;
        double r37154 = r37152 * r37153;
        double r37155 = -r37154;
        double r37156 = exp(r37155);
        double r37157 = r37151 * r37156;
        double r37158 = r37150 - r37148;
        double r37159 = r37148 + r37149;
        double r37160 = r37159 * r37153;
        double r37161 = -r37160;
        double r37162 = exp(r37161);
        double r37163 = r37158 * r37162;
        double r37164 = r37157 - r37163;
        double r37165 = 2.0;
        double r37166 = r37164 / r37165;
        return r37166;
}

↓

double f(double x, double eps) {
        double r37167 = x;
        double r37168 = 295.27480666079055;
        bool r37169 = r37167 <= r37168;
        double r37170 = 2.0;
        double r37171 = pow(r37167, r37170);
        double r37172 = 0.6666666666666667;
        double r37173 = r37172 * r37167;
        double r37174 = 1.0;
        double r37175 = r37173 - r37174;
        double r37176 = 2.0;
        double r37177 = fma(r37171, r37175, r37176);
        double r37178 = r37177 / r37176;
        double r37179 = eps;
        double r37180 = r37167 * r37179;
        double r37181 = r37174 * r37167;
        double r37182 = r37180 - r37181;
        double r37183 = exp(r37182);
        double r37184 = r37183 / r37179;
        double r37185 = 1.0;
        double r37186 = fma(r37167, r37179, r37181);
        double r37187 = exp(r37186);
        double r37188 = r37185 / r37187;
        double r37189 = r37188 + r37183;
        double r37190 = r37174 * r37189;
        double r37191 = r37180 + r37181;
        double r37192 = -r37191;
        double r37193 = exp(r37192);
        double r37194 = r37193 / r37179;
        double r37195 = r37174 * r37194;
        double r37196 = r37190 - r37195;
        double r37197 = fma(r37174, r37184, r37196);
        double r37198 = r37197 / r37176;
        double r37199 = r37169 ? r37178 : r37198;
        return r37199;
}

Derivation

Split input into 2 regimes
if x < 295.27480666079055
1. Initial program 38.9
  \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2}\]
2. Taylor expanded around 0 1.3
  \[\leadsto \frac{\color{blue}{\left(0.66666666666666674 \cdot {x}^{3} + 2\right) - 1 \cdot {x}^{2}}}{2}\]
3. Simplified1.3
  \[\leadsto \frac{\color{blue}{\mathsf{fma}\left({x}^{3}, 0.66666666666666674, 2 - 1 \cdot {x}^{2}\right)}}{2}\]
4. Taylor expanded around 0 1.3
  \[\leadsto \frac{\color{blue}{\left(0.66666666666666674 \cdot {x}^{3} + 2\right) - 1 \cdot {x}^{2}}}{2}\]
5. Simplified1.3
  \[\leadsto \frac{\color{blue}{\mathsf{fma}\left({x}^{2}, 0.66666666666666674 \cdot x - 1, 2\right)}}{2}\]
if 295.27480666079055 < x
1. Initial program 0.1
  \[\frac{\left(1 + \frac{1}{\varepsilon}\right) \cdot e^{-\left(1 - \varepsilon\right) \cdot x} - \left(\frac{1}{\varepsilon} - 1\right) \cdot e^{-\left(1 + \varepsilon\right) \cdot x}}{2}\]
2. Taylor expanded around inf 0.1
  \[\leadsto \frac{\color{blue}{\left(1 \cdot \frac{e^{x \cdot \varepsilon - 1 \cdot x}}{\varepsilon} + \left(1 \cdot e^{-\left(x \cdot \varepsilon + 1 \cdot x\right)} + 1 \cdot e^{x \cdot \varepsilon - 1 \cdot x}\right)\right) - 1 \cdot \frac{e^{-\left(x \cdot \varepsilon + 1 \cdot x\right)}}{\varepsilon}}}{2}\]
3. Simplified0.1
  \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(1, \frac{e^{x \cdot \varepsilon - 1 \cdot x}}{\varepsilon}, 1 \cdot \left(\frac{1}{e^{\mathsf{fma}\left(x, \varepsilon, 1 \cdot x\right)}} + e^{x \cdot \varepsilon - 1 \cdot x}\right) - 1 \cdot \frac{e^{-\left(x \cdot \varepsilon + 1 \cdot x\right)}}{\varepsilon}\right)}}{2}\]
Recombined 2 regimes into one program.
Final simplification1.0
\[\leadsto \begin{array}{l} \mathbf{if}\;x \le 295.27480666079055:\\ \;\;\;\;\frac{\mathsf{fma}\left({x}^{2}, 0.66666666666666674 \cdot x - 1, 2\right)}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(1, \frac{e^{x \cdot \varepsilon - 1 \cdot x}}{\varepsilon}, 1 \cdot \left(\frac{1}{e^{\mathsf{fma}\left(x, \varepsilon, 1 \cdot x\right)}} + e^{x \cdot \varepsilon - 1 \cdot x}\right) - 1 \cdot \frac{e^{-\left(x \cdot \varepsilon + 1 \cdot x\right)}}{\varepsilon}\right)}{2}\\ \end{array}\]

could not determine a ground truth for program body (more)

Error

Derivation

`if x < 295.27480666079055`

`if 295.27480666079055 < x`

Reproduce