\[x \cdot \log \left(\frac{x}{y}\right) - z\]

↓

\[\begin{array}{l} \mathbf{if}\;y \le -5.435048613210959909118539310961078344525 \cdot 10^{-309}:\\ \;\;\;\;\left(\log \left(\frac{-1}{y}\right) - \log \left(\frac{-1}{x}\right)\right) \cdot x - z\\ \mathbf{else}:\\ \;\;\;\;\left(\left(2 \cdot \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)\right) \cdot x + x \cdot \log \left(\frac{\sqrt[3]{{x}^{\frac{2}{3}}} \cdot \sqrt[3]{\sqrt[3]{x}}}{\sqrt[3]{y}}\right)\right) - z\\ \end{array}\]

x \cdot \log \left(\frac{x}{y}\right) - z

↓

\begin{array}{l}
\mathbf{if}\;y \le -5.435048613210959909118539310961078344525 \cdot 10^{-309}:\\
\;\;\;\;\left(\log \left(\frac{-1}{y}\right) - \log \left(\frac{-1}{x}\right)\right) \cdot x - z\\

\mathbf{else}:\\
\;\;\;\;\left(\left(2 \cdot \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)\right) \cdot x + x \cdot \log \left(\frac{\sqrt[3]{{x}^{\frac{2}{3}}} \cdot \sqrt[3]{\sqrt[3]{x}}}{\sqrt[3]{y}}\right)\right) - z\\

\end{array}

double f(double x, double y, double z) {
        double r306622 = x;
        double r306623 = y;
        double r306624 = r306622 / r306623;
        double r306625 = log(r306624);
        double r306626 = r306622 * r306625;
        double r306627 = z;
        double r306628 = r306626 - r306627;
        return r306628;
}

↓

double f(double x, double y, double z) {
        double r306629 = y;
        double r306630 = -5.43504861321096e-309;
        bool r306631 = r306629 <= r306630;
        double r306632 = -1.0;
        double r306633 = r306632 / r306629;
        double r306634 = log(r306633);
        double r306635 = x;
        double r306636 = r306632 / r306635;
        double r306637 = log(r306636);
        double r306638 = r306634 - r306637;
        double r306639 = r306638 * r306635;
        double r306640 = z;
        double r306641 = r306639 - r306640;
        double r306642 = 2.0;
        double r306643 = cbrt(r306635);
        double r306644 = cbrt(r306629);
        double r306645 = r306643 / r306644;
        double r306646 = log(r306645);
        double r306647 = r306642 * r306646;
        double r306648 = r306647 * r306635;
        double r306649 = 0.6666666666666666;
        double r306650 = pow(r306635, r306649);
        double r306651 = cbrt(r306650);
        double r306652 = cbrt(r306643);
        double r306653 = r306651 * r306652;
        double r306654 = r306653 / r306644;
        double r306655 = log(r306654);
        double r306656 = r306635 * r306655;
        double r306657 = r306648 + r306656;
        double r306658 = r306657 - r306640;
        double r306659 = r306631 ? r306641 : r306658;
        return r306659;
}

Original	15.8
Target	8.2
Herbie	0.3

Derivation

Split input into 2 regimes
if y < -5.43504861321096e-309
1. Initial program 16.3
  \[x \cdot \log \left(\frac{x}{y}\right) - z\]
2. Taylor expanded around -inf 0.3
  \[\leadsto \color{blue}{x \cdot \left(\log \left(\frac{-1}{y}\right) - \log \left(\frac{-1}{x}\right)\right)} - z\]
3. Simplified0.3
  \[\leadsto \color{blue}{\left(\log \left(\frac{-1}{y}\right) - \log \left(\frac{-1}{x}\right)\right) \cdot x} - z\]
if -5.43504861321096e-309 < y
1. Initial program 15.2
  \[x \cdot \log \left(\frac{x}{y}\right) - z\]
2. Using strategy rm
3. Applied add-cube-cbrt15.2
  \[\leadsto x \cdot \log \left(\frac{x}{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}\right) - z\]
4. Applied add-cube-cbrt15.2
  \[\leadsto x \cdot \log \left(\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}\right) - z\]
5. Applied times-frac15.2
  \[\leadsto x \cdot \log \color{blue}{\left(\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)} - z\]
6. Applied log-prod3.7
  \[\leadsto x \cdot \color{blue}{\left(\log \left(\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) + \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)\right)} - z\]
7. Applied distribute-lft-in3.7
  \[\leadsto \color{blue}{\left(x \cdot \log \left(\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) + x \cdot \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)\right)} - z\]
8. Simplified0.2
  \[\leadsto \left(\color{blue}{\left(2 \cdot \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)\right) \cdot x} + x \cdot \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)\right) - z\]
9. Using strategy rm
10. Applied add-cube-cbrt0.2
  \[\leadsto \left(\left(2 \cdot \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)\right) \cdot x + x \cdot \log \left(\frac{\sqrt[3]{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}}{\sqrt[3]{y}}\right)\right) - z\]
11. Applied cbrt-prod0.2
  \[\leadsto \left(\left(2 \cdot \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)\right) \cdot x + x \cdot \log \left(\frac{\color{blue}{\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x}}}}{\sqrt[3]{y}}\right)\right) - z\]
12. Simplified0.2
  \[\leadsto \left(\left(2 \cdot \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)\right) \cdot x + x \cdot \log \left(\frac{\color{blue}{\sqrt[3]{{x}^{\frac{2}{3}}}} \cdot \sqrt[3]{\sqrt[3]{x}}}{\sqrt[3]{y}}\right)\right) - z\]
Recombined 2 regimes into one program.
Final simplification0.3
\[\leadsto \begin{array}{l} \mathbf{if}\;y \le -5.435048613210959909118539310961078344525 \cdot 10^{-309}:\\ \;\;\;\;\left(\log \left(\frac{-1}{y}\right) - \log \left(\frac{-1}{x}\right)\right) \cdot x - z\\ \mathbf{else}:\\ \;\;\;\;\left(\left(2 \cdot \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)\right) \cdot x + x \cdot \log \left(\frac{\sqrt[3]{{x}^{\frac{2}{3}}} \cdot \sqrt[3]{\sqrt[3]{x}}}{\sqrt[3]{y}}\right)\right) - z\\ \end{array}\]

Error

Try it out

Target

Derivation

`if y < -5.43504861321096e-309`

`if -5.43504861321096e-309 < y`

Reproduce

In
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