\[\frac{a1 \cdot a2}{b1 \cdot b2}\]

↓

\[\begin{array}{l} \mathbf{if}\;a1 \cdot a2 \le -3.975410788026315 \cdot 10^{+305}:\\ \;\;\;\;\frac{\frac{a1}{b1}}{\sqrt[3]{b2} \cdot \sqrt[3]{b2}} \cdot \frac{a2}{\sqrt[3]{b2}}\\ \mathbf{elif}\;a1 \cdot a2 \le -5.1555799853760176 \cdot 10^{-213}:\\ \;\;\;\;\frac{a1 \cdot a2}{b2 \cdot b1}\\ \mathbf{elif}\;a1 \cdot a2 \le 1.1084891218651217 \cdot 10^{-234}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b1}}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le 1.7118743416701524 \cdot 10^{+99}:\\ \;\;\;\;\frac{a1 \cdot a2}{b2 \cdot b1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a1}{b1}}{\sqrt[3]{b2} \cdot \sqrt[3]{b2}} \cdot \frac{a2}{\sqrt[3]{b2}}\\ \end{array}\]

\frac{a1 \cdot a2}{b1 \cdot b2}

↓

\begin{array}{l}
\mathbf{if}\;a1 \cdot a2 \le -3.975410788026315 \cdot 10^{+305}:\\
\;\;\;\;\frac{\frac{a1}{b1}}{\sqrt[3]{b2} \cdot \sqrt[3]{b2}} \cdot \frac{a2}{\sqrt[3]{b2}}\\

\mathbf{elif}\;a1 \cdot a2 \le -5.1555799853760176 \cdot 10^{-213}:\\
\;\;\;\;\frac{a1 \cdot a2}{b2 \cdot b1}\\

\mathbf{elif}\;a1 \cdot a2 \le 1.1084891218651217 \cdot 10^{-234}:\\
\;\;\;\;a1 \cdot \frac{\frac{a2}{b1}}{b2}\\

\mathbf{elif}\;a1 \cdot a2 \le 1.7118743416701524 \cdot 10^{+99}:\\
\;\;\;\;\frac{a1 \cdot a2}{b2 \cdot b1}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{a1}{b1}}{\sqrt[3]{b2} \cdot \sqrt[3]{b2}} \cdot \frac{a2}{\sqrt[3]{b2}}\\

\end{array}

double f(double a1, double a2, double b1, double b2) {
        double r1320366 = a1;
        double r1320367 = a2;
        double r1320368 = r1320366 * r1320367;
        double r1320369 = b1;
        double r1320370 = b2;
        double r1320371 = r1320369 * r1320370;
        double r1320372 = r1320368 / r1320371;
        return r1320372;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r1320373 = a1;
        double r1320374 = a2;
        double r1320375 = r1320373 * r1320374;
        double r1320376 = -3.975410788026315e+305;
        bool r1320377 = r1320375 <= r1320376;
        double r1320378 = b1;
        double r1320379 = r1320373 / r1320378;
        double r1320380 = b2;
        double r1320381 = cbrt(r1320380);
        double r1320382 = r1320381 * r1320381;
        double r1320383 = r1320379 / r1320382;
        double r1320384 = r1320374 / r1320381;
        double r1320385 = r1320383 * r1320384;
        double r1320386 = -5.1555799853760176e-213;
        bool r1320387 = r1320375 <= r1320386;
        double r1320388 = r1320380 * r1320378;
        double r1320389 = r1320375 / r1320388;
        double r1320390 = 1.1084891218651217e-234;
        bool r1320391 = r1320375 <= r1320390;
        double r1320392 = r1320374 / r1320378;
        double r1320393 = r1320392 / r1320380;
        double r1320394 = r1320373 * r1320393;
        double r1320395 = 1.7118743416701524e+99;
        bool r1320396 = r1320375 <= r1320395;
        double r1320397 = r1320396 ? r1320389 : r1320385;
        double r1320398 = r1320391 ? r1320394 : r1320397;
        double r1320399 = r1320387 ? r1320389 : r1320398;
        double r1320400 = r1320377 ? r1320385 : r1320399;
        return r1320400;
}

Original	10.8
Target	11.0
Herbie	5.0

Derivation

Split input into 3 regimes
if (* a1 a2) < -3.975410788026315e+305 or 1.7118743416701524e+99 < (* a1 a2)
1. Initial program 29.9
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied times-frac10.6
  \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
4. Using strategy rm
5. Applied add-cube-cbrt11.5
  \[\leadsto \frac{a1}{b1} \cdot \frac{a2}{\color{blue}{\left(\sqrt[3]{b2} \cdot \sqrt[3]{b2}\right) \cdot \sqrt[3]{b2}}}\]
6. Applied *-un-lft-identity11.5
  \[\leadsto \frac{a1}{b1} \cdot \frac{\color{blue}{1 \cdot a2}}{\left(\sqrt[3]{b2} \cdot \sqrt[3]{b2}\right) \cdot \sqrt[3]{b2}}\]
7. Applied times-frac11.4
  \[\leadsto \frac{a1}{b1} \cdot \color{blue}{\left(\frac{1}{\sqrt[3]{b2} \cdot \sqrt[3]{b2}} \cdot \frac{a2}{\sqrt[3]{b2}}\right)}\]
8. Applied associate-*r*9.7
  \[\leadsto \color{blue}{\left(\frac{a1}{b1} \cdot \frac{1}{\sqrt[3]{b2} \cdot \sqrt[3]{b2}}\right) \cdot \frac{a2}{\sqrt[3]{b2}}}\]
9. Simplified9.7
  \[\leadsto \color{blue}{\frac{\frac{a1}{b1}}{\sqrt[3]{b2} \cdot \sqrt[3]{b2}}} \cdot \frac{a2}{\sqrt[3]{b2}}\]
if -3.975410788026315e+305 < (* a1 a2) < -5.1555799853760176e-213 or 1.1084891218651217e-234 < (* a1 a2) < 1.7118743416701524e+99
1. Initial program 4.0
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
if -5.1555799853760176e-213 < (* a1 a2) < 1.1084891218651217e-234
1. Initial program 15.4
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied times-frac4.5
  \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
4. Using strategy rm
5. Applied div-inv4.5
  \[\leadsto \color{blue}{\left(a1 \cdot \frac{1}{b1}\right)} \cdot \frac{a2}{b2}\]
6. Applied associate-*l*4.6
  \[\leadsto \color{blue}{a1 \cdot \left(\frac{1}{b1} \cdot \frac{a2}{b2}\right)}\]
7. Simplified4.4
  \[\leadsto a1 \cdot \color{blue}{\frac{\frac{a2}{b1}}{b2}}\]
Recombined 3 regimes into one program.
Final simplification5.0
\[\leadsto \begin{array}{l} \mathbf{if}\;a1 \cdot a2 \le -3.975410788026315 \cdot 10^{+305}:\\ \;\;\;\;\frac{\frac{a1}{b1}}{\sqrt[3]{b2} \cdot \sqrt[3]{b2}} \cdot \frac{a2}{\sqrt[3]{b2}}\\ \mathbf{elif}\;a1 \cdot a2 \le -5.1555799853760176 \cdot 10^{-213}:\\ \;\;\;\;\frac{a1 \cdot a2}{b2 \cdot b1}\\ \mathbf{elif}\;a1 \cdot a2 \le 1.1084891218651217 \cdot 10^{-234}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b1}}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le 1.7118743416701524 \cdot 10^{+99}:\\ \;\;\;\;\frac{a1 \cdot a2}{b2 \cdot b1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a1}{b1}}{\sqrt[3]{b2} \cdot \sqrt[3]{b2}} \cdot \frac{a2}{\sqrt[3]{b2}}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if (* a1 a2) < -3.975410788026315e+305 or 1.7118743416701524e+99 < (* a1 a2)`

`if -3.975410788026315e+305 < (* a1 a2) < -5.1555799853760176e-213 or 1.1084891218651217e-234 < (* a1 a2) < 1.7118743416701524e+99`

`if -5.1555799853760176e-213 < (* a1 a2) < 1.1084891218651217e-234`

Reproduce

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