\[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}\]

↓

\[\begin{array}{l} \mathbf{if}\;wj \le -8.775235746042734 \cdot 10^{-09}:\\ \;\;\;\;wj - \frac{\left(wj - 1\right) \cdot \frac{e^{wj} \cdot wj - x}{\mathsf{fma}\left(wj, wj, -1\right)}}{e^{wj}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(wj, wj, x\right) - \left(wj + wj\right) \cdot x\\ \end{array}\]

wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}

↓

\begin{array}{l}
\mathbf{if}\;wj \le -8.775235746042734 \cdot 10^{-09}:\\
\;\;\;\;wj - \frac{\left(wj - 1\right) \cdot \frac{e^{wj} \cdot wj - x}{\mathsf{fma}\left(wj, wj, -1\right)}}{e^{wj}}\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(wj, wj, x\right) - \left(wj + wj\right) \cdot x\\

\end{array}

double f(double wj, double x) {
        double r6849313 = wj;
        double r6849314 = exp(r6849313);
        double r6849315 = r6849313 * r6849314;
        double r6849316 = x;
        double r6849317 = r6849315 - r6849316;
        double r6849318 = r6849314 + r6849315;
        double r6849319 = r6849317 / r6849318;
        double r6849320 = r6849313 - r6849319;
        return r6849320;
}

↓

double f(double wj, double x) {
        double r6849321 = wj;
        double r6849322 = -8.775235746042734e-09;
        bool r6849323 = r6849321 <= r6849322;
        double r6849324 = 1.0;
        double r6849325 = r6849321 - r6849324;
        double r6849326 = exp(r6849321);
        double r6849327 = r6849326 * r6849321;
        double r6849328 = x;
        double r6849329 = r6849327 - r6849328;
        double r6849330 = -1.0;
        double r6849331 = fma(r6849321, r6849321, r6849330);
        double r6849332 = r6849329 / r6849331;
        double r6849333 = r6849325 * r6849332;
        double r6849334 = r6849333 / r6849326;
        double r6849335 = r6849321 - r6849334;
        double r6849336 = fma(r6849321, r6849321, r6849328);
        double r6849337 = r6849321 + r6849321;
        double r6849338 = r6849337 * r6849328;
        double r6849339 = r6849336 - r6849338;
        double r6849340 = r6849323 ? r6849335 : r6849339;
        return r6849340;
}

Original	13.7
Target	13.0
Herbie	1.6

Derivation

Split input into 2 regimes
if wj < -8.775235746042734e-09
1. Initial program 5.8
  \[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}\]
2. Using strategy rm
3. Applied distribute-rgt1-in5.8
  \[\leadsto wj - \frac{wj \cdot e^{wj} - x}{\color{blue}{\left(wj + 1\right) \cdot e^{wj}}}\]
4. Applied associate-/r*5.8
  \[\leadsto wj - \color{blue}{\frac{\frac{wj \cdot e^{wj} - x}{wj + 1}}{e^{wj}}}\]
5. Using strategy rm
6. Applied flip-+5.9
  \[\leadsto wj - \frac{\frac{wj \cdot e^{wj} - x}{\color{blue}{\frac{wj \cdot wj - 1 \cdot 1}{wj - 1}}}}{e^{wj}}\]
7. Applied associate-/r/6.1
  \[\leadsto wj - \frac{\color{blue}{\frac{wj \cdot e^{wj} - x}{wj \cdot wj - 1 \cdot 1} \cdot \left(wj - 1\right)}}{e^{wj}}\]
8. Simplified6.1
  \[\leadsto wj - \frac{\color{blue}{\frac{e^{wj} \cdot wj - x}{\mathsf{fma}\left(wj, wj, -1\right)}} \cdot \left(wj - 1\right)}{e^{wj}}\]
if -8.775235746042734e-09 < wj
1. Initial program 13.9
  \[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}\]
2. Taylor expanded around 0 1.5
  \[\leadsto \color{blue}{\left({wj}^{2} + x\right) - 2 \cdot \left(x \cdot wj\right)}\]
3. Simplified1.5
  \[\leadsto \color{blue}{\mathsf{fma}\left(wj, wj, x\right) - x \cdot \left(wj + wj\right)}\]
Recombined 2 regimes into one program.
Final simplification1.6
\[\leadsto \begin{array}{l} \mathbf{if}\;wj \le -8.775235746042734 \cdot 10^{-09}:\\ \;\;\;\;wj - \frac{\left(wj - 1\right) \cdot \frac{e^{wj} \cdot wj - x}{\mathsf{fma}\left(wj, wj, -1\right)}}{e^{wj}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(wj, wj, x\right) - \left(wj + wj\right) \cdot x\\ \end{array}\]

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

Error

Target

Derivation

`if wj < -8.775235746042734e-09`

`if -8.775235746042734e-09 < wj`

Reproduce