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

↓

\[\begin{array}{l} \mathbf{if}\;wj \le 1.9744252120415485 \cdot 10^{-9}:\\ \;\;\;\;1 \cdot \mathsf{fma}\left(wj, wj, x\right) - 2 \cdot \left(wj \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\frac{x}{{wj}^{3} + 1}}{\sqrt{e^{wj}}} \cdot \frac{wj \cdot wj + \left(1 - wj \cdot 1\right)}{\sqrt{e^{wj}}} + wj\right) - \frac{wj}{wj + 1}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;wj \le 1.9744252120415485 \cdot 10^{-9}:\\
\;\;\;\;1 \cdot \mathsf{fma}\left(wj, wj, x\right) - 2 \cdot \left(wj \cdot x\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{\frac{x}{{wj}^{3} + 1}}{\sqrt{e^{wj}}} \cdot \frac{wj \cdot wj + \left(1 - wj \cdot 1\right)}{\sqrt{e^{wj}}} + wj\right) - \frac{wj}{wj + 1}\\

\end{array}

double f(double wj, double x) {
        double r147619 = wj;
        double r147620 = exp(r147619);
        double r147621 = r147619 * r147620;
        double r147622 = x;
        double r147623 = r147621 - r147622;
        double r147624 = r147620 + r147621;
        double r147625 = r147623 / r147624;
        double r147626 = r147619 - r147625;
        return r147626;
}

↓

double f(double wj, double x) {
        double r147627 = wj;
        double r147628 = 1.9744252120415485e-09;
        bool r147629 = r147627 <= r147628;
        double r147630 = 1.0;
        double r147631 = x;
        double r147632 = fma(r147627, r147627, r147631);
        double r147633 = r147630 * r147632;
        double r147634 = 2.0;
        double r147635 = r147627 * r147631;
        double r147636 = r147634 * r147635;
        double r147637 = r147633 - r147636;
        double r147638 = 3.0;
        double r147639 = pow(r147627, r147638);
        double r147640 = r147639 + r147630;
        double r147641 = r147631 / r147640;
        double r147642 = exp(r147627);
        double r147643 = sqrt(r147642);
        double r147644 = r147641 / r147643;
        double r147645 = r147627 * r147627;
        double r147646 = r147627 * r147630;
        double r147647 = r147630 - r147646;
        double r147648 = r147645 + r147647;
        double r147649 = r147648 / r147643;
        double r147650 = r147644 * r147649;
        double r147651 = r147650 + r147627;
        double r147652 = r147627 + r147630;
        double r147653 = r147627 / r147652;
        double r147654 = r147651 - r147653;
        double r147655 = r147629 ? r147637 : r147654;
        return r147655;
}

Original	13.6
Target	13.0
Herbie	1.0

Derivation

Split input into 2 regimes
if wj < 1.9744252120415485e-09
1. Initial program 13.3
  \[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}\]
2. Simplified13.3
  \[\leadsto \color{blue}{\left(\frac{\frac{x}{wj + 1}}{e^{wj}} + wj\right) - \frac{wj}{wj + 1}}\]
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 1.9744252120415485e-09 < wj
1. Initial program 22.7
  \[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}\]
2. Simplified3.6
  \[\leadsto \color{blue}{\left(\frac{\frac{x}{wj + 1}}{e^{wj}} + wj\right) - \frac{wj}{wj + 1}}\]
3. Using strategy rm
4. Applied add-sqr-sqrt3.7
  \[\leadsto \left(\frac{\frac{x}{wj + 1}}{\color{blue}{\sqrt{e^{wj}} \cdot \sqrt{e^{wj}}}} + wj\right) - \frac{wj}{wj + 1}\]
5. Applied flip3-+3.8
  \[\leadsto \left(\frac{\frac{x}{\color{blue}{\frac{{wj}^{3} + {1}^{3}}{wj \cdot wj + \left(1 \cdot 1 - wj \cdot 1\right)}}}}{\sqrt{e^{wj}} \cdot \sqrt{e^{wj}}} + wj\right) - \frac{wj}{wj + 1}\]
6. Applied associate-/r/3.7
  \[\leadsto \left(\frac{\color{blue}{\frac{x}{{wj}^{3} + {1}^{3}} \cdot \left(wj \cdot wj + \left(1 \cdot 1 - wj \cdot 1\right)\right)}}{\sqrt{e^{wj}} \cdot \sqrt{e^{wj}}} + wj\right) - \frac{wj}{wj + 1}\]
7. Applied times-frac3.7
  \[\leadsto \left(\color{blue}{\frac{\frac{x}{{wj}^{3} + {1}^{3}}}{\sqrt{e^{wj}}} \cdot \frac{wj \cdot wj + \left(1 \cdot 1 - wj \cdot 1\right)}{\sqrt{e^{wj}}}} + wj\right) - \frac{wj}{wj + 1}\]
8. Simplified3.7
  \[\leadsto \left(\color{blue}{\frac{\frac{x}{{wj}^{3} + 1}}{\sqrt{e^{wj}}}} \cdot \frac{wj \cdot wj + \left(1 \cdot 1 - wj \cdot 1\right)}{\sqrt{e^{wj}}} + wj\right) - \frac{wj}{wj + 1}\]
9. Simplified3.7
  \[\leadsto \left(\frac{\frac{x}{{wj}^{3} + 1}}{\sqrt{e^{wj}}} \cdot \color{blue}{\frac{wj \cdot wj + \left(1 - wj \cdot 1\right)}{\sqrt{e^{wj}}}} + wj\right) - \frac{wj}{wj + 1}\]
Recombined 2 regimes into one program.
Final simplification1.0
\[\leadsto \begin{array}{l} \mathbf{if}\;wj \le 1.9744252120415485 \cdot 10^{-9}:\\ \;\;\;\;1 \cdot \mathsf{fma}\left(wj, wj, x\right) - 2 \cdot \left(wj \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\frac{x}{{wj}^{3} + 1}}{\sqrt{e^{wj}}} \cdot \frac{wj \cdot wj + \left(1 - wj \cdot 1\right)}{\sqrt{e^{wj}}} + wj\right) - \frac{wj}{wj + 1}\\ \end{array}\]

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

Error

Target

Derivation

`if wj < 1.9744252120415485e-09`

`if 1.9744252120415485e-09 < wj`

Reproduce