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

↓

\[\begin{array}{l} \mathbf{if}\;wj \le 7.575706194898737323694237493331283921083 \cdot 10^{-11}:\\ \;\;\;\;1 \cdot \mathsf{fma}\left(wj, wj, x\right) - 2 \cdot \left(wj \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{wj + 1}}{e^{wj}} + \left(wj - \frac{wj}{wj + 1}\right)\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;wj \le 7.575706194898737323694237493331283921083 \cdot 10^{-11}:\\
\;\;\;\;1 \cdot \mathsf{fma}\left(wj, wj, x\right) - 2 \cdot \left(wj \cdot x\right)\\

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

\end{array}

double f(double wj, double x) {
        double r185699 = wj;
        double r185700 = exp(r185699);
        double r185701 = r185699 * r185700;
        double r185702 = x;
        double r185703 = r185701 - r185702;
        double r185704 = r185700 + r185701;
        double r185705 = r185703 / r185704;
        double r185706 = r185699 - r185705;
        return r185706;
}

↓

double f(double wj, double x) {
        double r185707 = wj;
        double r185708 = 7.575706194898737e-11;
        bool r185709 = r185707 <= r185708;
        double r185710 = 1.0;
        double r185711 = x;
        double r185712 = fma(r185707, r185707, r185711);
        double r185713 = r185710 * r185712;
        double r185714 = 2.0;
        double r185715 = r185707 * r185711;
        double r185716 = r185714 * r185715;
        double r185717 = r185713 - r185716;
        double r185718 = r185707 + r185710;
        double r185719 = r185711 / r185718;
        double r185720 = exp(r185707);
        double r185721 = r185719 / r185720;
        double r185722 = r185707 / r185718;
        double r185723 = r185707 - r185722;
        double r185724 = r185721 + r185723;
        double r185725 = r185709 ? r185717 : r185724;
        return r185725;
}

Original	13.7
Target	13.1
Herbie	1.0

Derivation

Split input into 2 regimes
if wj < 7.575706194898737e-11
1. Initial program 13.4
  \[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}\]
2. Simplified13.4
  \[\leadsto \color{blue}{\left(\frac{\frac{x}{wj + 1}}{e^{wj}} + wj\right) - \frac{wj}{wj + 1}}\]
3. Taylor expanded around 0 0.9
  \[\leadsto \color{blue}{\left(x + {wj}^{2}\right) - 2 \cdot \left(wj \cdot x\right)}\]
4. Using strategy rm
5. Applied *-un-lft-identity0.9
  \[\leadsto \left(x + \color{blue}{1 \cdot {wj}^{2}}\right) - 2 \cdot \left(wj \cdot x\right)\]
6. Applied *-un-lft-identity0.9
  \[\leadsto \left(\color{blue}{1 \cdot x} + 1 \cdot {wj}^{2}\right) - 2 \cdot \left(wj \cdot x\right)\]
7. Applied distribute-lft-out0.9
  \[\leadsto \color{blue}{1 \cdot \left(x + {wj}^{2}\right)} - 2 \cdot \left(wj \cdot x\right)\]
8. Simplified0.9
  \[\leadsto 1 \cdot \color{blue}{\mathsf{fma}\left(wj, wj, x\right)} - 2 \cdot \left(wj \cdot x\right)\]
if 7.575706194898737e-11 < wj
1. Initial program 25.5
  \[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}\]
2. Simplified4.0
  \[\leadsto \color{blue}{\left(\frac{\frac{x}{wj + 1}}{e^{wj}} + wj\right) - \frac{wj}{wj + 1}}\]
3. Using strategy rm
4. Applied associate--l+3.9
  \[\leadsto \color{blue}{\frac{\frac{x}{wj + 1}}{e^{wj}} + \left(wj - \frac{wj}{wj + 1}\right)}\]
Recombined 2 regimes into one program.
Final simplification1.0
\[\leadsto \begin{array}{l} \mathbf{if}\;wj \le 7.575706194898737323694237493331283921083 \cdot 10^{-11}:\\ \;\;\;\;1 \cdot \mathsf{fma}\left(wj, wj, x\right) - 2 \cdot \left(wj \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{wj + 1}}{e^{wj}} + \left(wj - \frac{wj}{wj + 1}\right)\\ \end{array}\]

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

Error

Target

Derivation

`if wj < 7.575706194898737e-11`

`if 7.575706194898737e-11 < wj`

Reproduce