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

↓

\[\begin{array}{l} \mathbf{if}\;wj \le 6.715218772498828 \cdot 10^{-07}:\\ \;\;\;\;\mathsf{fma}\left(wj \cdot wj, wj \cdot wj, \mathsf{fma}\left(wj, wj, -\left(wj \cdot wj\right) \cdot wj\right)\right) + \frac{x}{e^{wj} \cdot wj + e^{wj}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{e^{wj} \cdot wj + e^{wj}} + \left(wj - \frac{wj}{1 + wj}\right)\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;wj \le 6.715218772498828 \cdot 10^{-07}:\\
\;\;\;\;\mathsf{fma}\left(wj \cdot wj, wj \cdot wj, \mathsf{fma}\left(wj, wj, -\left(wj \cdot wj\right) \cdot wj\right)\right) + \frac{x}{e^{wj} \cdot wj + e^{wj}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{e^{wj} \cdot wj + e^{wj}} + \left(wj - \frac{wj}{1 + wj}\right)\\

\end{array}

double f(double wj, double x) {
        double r7625989 = wj;
        double r7625990 = exp(r7625989);
        double r7625991 = r7625989 * r7625990;
        double r7625992 = x;
        double r7625993 = r7625991 - r7625992;
        double r7625994 = r7625990 + r7625991;
        double r7625995 = r7625993 / r7625994;
        double r7625996 = r7625989 - r7625995;
        return r7625996;
}

↓

double f(double wj, double x) {
        double r7625997 = wj;
        double r7625998 = 6.715218772498828e-07;
        bool r7625999 = r7625997 <= r7625998;
        double r7626000 = r7625997 * r7625997;
        double r7626001 = r7626000 * r7625997;
        double r7626002 = -r7626001;
        double r7626003 = fma(r7625997, r7625997, r7626002);
        double r7626004 = fma(r7626000, r7626000, r7626003);
        double r7626005 = x;
        double r7626006 = exp(r7625997);
        double r7626007 = r7626006 * r7625997;
        double r7626008 = r7626007 + r7626006;
        double r7626009 = r7626005 / r7626008;
        double r7626010 = r7626004 + r7626009;
        double r7626011 = 1.0;
        double r7626012 = r7626011 + r7625997;
        double r7626013 = r7625997 / r7626012;
        double r7626014 = r7625997 - r7626013;
        double r7626015 = r7626009 + r7626014;
        double r7626016 = r7625999 ? r7626010 : r7626015;
        return r7626016;
}

Original	13.3
Target	12.7
Herbie	0.4

Derivation

Split input into 2 regimes
if wj < 6.715218772498828e-07
1. Initial program 13.0
  \[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}\]
2. Using strategy rm
3. Applied div-sub13.0
  \[\leadsto wj - \color{blue}{\left(\frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}} - \frac{x}{e^{wj} + wj \cdot e^{wj}}\right)}\]
4. Applied associate--r-6.9
  \[\leadsto \color{blue}{\left(wj - \frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}}\right) + \frac{x}{e^{wj} + wj \cdot e^{wj}}}\]
5. Taylor expanded around 0 0.3
  \[\leadsto \color{blue}{\left(\left({wj}^{2} + {wj}^{4}\right) - {wj}^{3}\right)} + \frac{x}{e^{wj} + wj \cdot e^{wj}}\]
6. Simplified0.3
  \[\leadsto \color{blue}{\mathsf{fma}\left(wj \cdot wj, wj \cdot wj, wj \cdot wj - wj \cdot \left(wj \cdot wj\right)\right)} + \frac{x}{e^{wj} + wj \cdot e^{wj}}\]
7. Using strategy rm
8. Applied fma-neg0.3
  \[\leadsto \mathsf{fma}\left(wj \cdot wj, wj \cdot wj, \color{blue}{\mathsf{fma}\left(wj, wj, -wj \cdot \left(wj \cdot wj\right)\right)}\right) + \frac{x}{e^{wj} + wj \cdot e^{wj}}\]
if 6.715218772498828e-07 < wj
1. Initial program 26.6
  \[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}\]
2. Using strategy rm
3. Applied div-sub26.6
  \[\leadsto wj - \color{blue}{\left(\frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}} - \frac{x}{e^{wj} + wj \cdot e^{wj}}\right)}\]
4. Applied associate--r-26.6
  \[\leadsto \color{blue}{\left(wj - \frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}}\right) + \frac{x}{e^{wj} + wj \cdot e^{wj}}}\]
5. Using strategy rm
6. Applied *-un-lft-identity26.6
  \[\leadsto \left(wj - \frac{wj \cdot e^{wj}}{\color{blue}{1 \cdot e^{wj}} + wj \cdot e^{wj}}\right) + \frac{x}{e^{wj} + wj \cdot e^{wj}}\]
7. Applied distribute-rgt-out26.7
  \[\leadsto \left(wj - \frac{wj \cdot e^{wj}}{\color{blue}{e^{wj} \cdot \left(1 + wj\right)}}\right) + \frac{x}{e^{wj} + wj \cdot e^{wj}}\]
8. Applied associate-/r*26.4
  \[\leadsto \left(wj - \color{blue}{\frac{\frac{wj \cdot e^{wj}}{e^{wj}}}{1 + wj}}\right) + \frac{x}{e^{wj} + wj \cdot e^{wj}}\]
9. Simplified2.0
  \[\leadsto \left(wj - \frac{\color{blue}{wj}}{1 + wj}\right) + \frac{x}{e^{wj} + wj \cdot e^{wj}}\]
Recombined 2 regimes into one program.
Final simplification0.4
\[\leadsto \begin{array}{l} \mathbf{if}\;wj \le 6.715218772498828 \cdot 10^{-07}:\\ \;\;\;\;\mathsf{fma}\left(wj \cdot wj, wj \cdot wj, \mathsf{fma}\left(wj, wj, -\left(wj \cdot wj\right) \cdot wj\right)\right) + \frac{x}{e^{wj} \cdot wj + e^{wj}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{e^{wj} \cdot wj + e^{wj}} + \left(wj - \frac{wj}{1 + wj}\right)\\ \end{array}\]

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

Error

Target

Derivation

`if wj < 6.715218772498828e-07`

`if 6.715218772498828e-07 < wj`

Reproduce