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

↓

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

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

↓

\begin{array}{l}
\mathbf{if}\;y \le -5.435048613210959909118539310961078344525 \cdot 10^{-309}:\\
\;\;\;\;x \cdot \left(\log \left(\frac{-1}{y}\right) - \log \left(\frac{-1}{x}\right)\right) - 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 r388278 = x;
        double r388279 = y;
        double r388280 = r388278 / r388279;
        double r388281 = log(r388280);
        double r388282 = r388278 * r388281;
        double r388283 = z;
        double r388284 = r388282 - r388283;
        return r388284;
}

↓

double f(double x, double y, double z) {
        double r388285 = y;
        double r388286 = -5.43504861321096e-309;
        bool r388287 = r388285 <= r388286;
        double r388288 = x;
        double r388289 = -1.0;
        double r388290 = r388289 / r388285;
        double r388291 = log(r388290);
        double r388292 = r388289 / r388288;
        double r388293 = log(r388292);
        double r388294 = r388291 - r388293;
        double r388295 = r388288 * r388294;
        double r388296 = z;
        double r388297 = r388295 - r388296;
        double r388298 = 2.0;
        double r388299 = cbrt(r388288);
        double r388300 = cbrt(r388285);
        double r388301 = r388299 / r388300;
        double r388302 = log(r388301);
        double r388303 = r388298 * r388302;
        double r388304 = r388303 * r388288;
        double r388305 = 0.6666666666666666;
        double r388306 = pow(r388288, r388305);
        double r388307 = cbrt(r388306);
        double r388308 = cbrt(r388299);
        double r388309 = r388307 * r388308;
        double r388310 = r388309 / r388300;
        double r388311 = log(r388310);
        double r388312 = r388288 * r388311;
        double r388313 = r388304 + r388312;
        double r388314 = r388313 - r388296;
        double r388315 = r388287 ? r388297 : r388314;
        return r388315;
}

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

Error

Try it out

Target

Derivation

`if y < -5.43504861321096e-309`

`if -5.43504861321096e-309 < y`

Reproduce

In
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