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

↓

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

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 r284141 = x;
        double r284142 = y;
        double r284143 = r284141 / r284142;
        double r284144 = log(r284143);
        double r284145 = r284141 * r284144;
        double r284146 = z;
        double r284147 = r284145 - r284146;
        return r284147;
}

↓

double f(double x, double y, double z) {
        double r284148 = y;
        double r284149 = -5.43504861321096e-309;
        bool r284150 = r284148 <= r284149;
        double r284151 = x;
        double r284152 = -1.0;
        double r284153 = r284152 / r284148;
        double r284154 = log(r284153);
        double r284155 = r284152 / r284151;
        double r284156 = log(r284155);
        double r284157 = r284154 - r284156;
        double r284158 = r284151 * r284157;
        double r284159 = z;
        double r284160 = r284158 - r284159;
        double r284161 = 2.0;
        double r284162 = cbrt(r284151);
        double r284163 = cbrt(r284148);
        double r284164 = r284162 / r284163;
        double r284165 = log(r284164);
        double r284166 = r284161 * r284165;
        double r284167 = r284166 * r284151;
        double r284168 = 0.6666666666666666;
        double r284169 = pow(r284151, r284168);
        double r284170 = cbrt(r284169);
        double r284171 = cbrt(r284162);
        double r284172 = r284170 * r284171;
        double r284173 = r284172 / r284163;
        double r284174 = log(r284173);
        double r284175 = r284151 * r284174;
        double r284176 = r284167 + r284175;
        double r284177 = r284176 - r284159;
        double r284178 = r284150 ? r284160 : r284177;
        return r284178;
}

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
Out