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

↓

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

\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 r37168 = 1.0;
        double r37169 = eps;
        double r37170 = r37168 / r37169;
        double r37171 = r37168 + r37170;
        double r37172 = r37168 - r37169;
        double r37173 = x;
        double r37174 = r37172 * r37173;
        double r37175 = -r37174;
        double r37176 = exp(r37175);
        double r37177 = r37171 * r37176;
        double r37178 = r37170 - r37168;
        double r37179 = r37168 + r37169;
        double r37180 = r37179 * r37173;
        double r37181 = -r37180;
        double r37182 = exp(r37181);
        double r37183 = r37178 * r37182;
        double r37184 = r37177 - r37183;
        double r37185 = 2.0;
        double r37186 = r37184 / r37185;
        return r37186;
}

↓

double f(double x, double eps) {
        double r37187 = x;
        double r37188 = 295.27480666079055;
        bool r37189 = r37187 <= r37188;
        double r37190 = 2.0;
        double r37191 = pow(r37187, r37190);
        double r37192 = 0.6666666666666667;
        double r37193 = r37192 * r37187;
        double r37194 = 1.0;
        double r37195 = r37193 - r37194;
        double r37196 = 2.0;
        double r37197 = fma(r37191, r37195, r37196);
        double r37198 = r37197 / r37196;
        double r37199 = eps;
        double r37200 = r37187 * r37199;
        double r37201 = r37194 * r37187;
        double r37202 = r37200 - r37201;
        double r37203 = exp(r37202);
        double r37204 = r37203 / r37199;
        double r37205 = 1.0;
        double r37206 = fma(r37187, r37199, r37201);
        double r37207 = exp(r37206);
        double r37208 = r37205 / r37207;
        double r37209 = r37208 + r37203;
        double r37210 = r37194 * r37209;
        double r37211 = r37200 + r37201;
        double r37212 = -r37211;
        double r37213 = exp(r37212);
        double r37214 = r37213 / r37199;
        double r37215 = r37194 * r37214;
        double r37216 = r37210 - r37215;
        double r37217 = fma(r37194, r37204, r37216);
        double r37218 = r37217 / r37196;
        double r37219 = r37189 ? r37198 : r37218;
        return r37219;
}

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