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

↓

\[\begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -4.9182133109132441 \cdot 10^{88}:\\ \;\;\;\;\frac{a1 \cdot \frac{a2}{b2}}{b1}\\ \mathbf{elif}\;b1 \cdot b2 \le -3.7720840321361484 \cdot 10^{-215}:\\ \;\;\;\;\left(a1 \cdot a2\right) \cdot \frac{1}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \cdot b2 \le 2.02333864 \cdot 10^{-317}:\\ \;\;\;\;\frac{a2 \cdot \frac{a1}{b1}}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le 3.785288238963702 \cdot 10^{229}:\\ \;\;\;\;\left(a1 \cdot a2\right) \cdot \frac{1}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{\frac{a1}{b1}} \cdot \sqrt[3]{\frac{a1}{b1}}\right) \cdot \left(\sqrt[3]{\frac{a1}{b1}} \cdot \frac{a2}{b2}\right)\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;b1 \cdot b2 \le -4.9182133109132441 \cdot 10^{88}:\\
\;\;\;\;\frac{a1 \cdot \frac{a2}{b2}}{b1}\\

\mathbf{elif}\;b1 \cdot b2 \le -3.7720840321361484 \cdot 10^{-215}:\\
\;\;\;\;\left(a1 \cdot a2\right) \cdot \frac{1}{b1 \cdot b2}\\

\mathbf{elif}\;b1 \cdot b2 \le 2.02333864 \cdot 10^{-317}:\\
\;\;\;\;\frac{a2 \cdot \frac{a1}{b1}}{b2}\\

\mathbf{elif}\;b1 \cdot b2 \le 3.785288238963702 \cdot 10^{229}:\\
\;\;\;\;\left(a1 \cdot a2\right) \cdot \frac{1}{b1 \cdot b2}\\

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

\end{array}

double f(double a1, double a2, double b1, double b2) {
        double r94447 = a1;
        double r94448 = a2;
        double r94449 = r94447 * r94448;
        double r94450 = b1;
        double r94451 = b2;
        double r94452 = r94450 * r94451;
        double r94453 = r94449 / r94452;
        return r94453;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r94454 = b1;
        double r94455 = b2;
        double r94456 = r94454 * r94455;
        double r94457 = -4.918213310913244e+88;
        bool r94458 = r94456 <= r94457;
        double r94459 = a1;
        double r94460 = a2;
        double r94461 = r94460 / r94455;
        double r94462 = r94459 * r94461;
        double r94463 = r94462 / r94454;
        double r94464 = -3.7720840321361484e-215;
        bool r94465 = r94456 <= r94464;
        double r94466 = r94459 * r94460;
        double r94467 = 1.0;
        double r94468 = r94467 / r94456;
        double r94469 = r94466 * r94468;
        double r94470 = 2.0233386402977e-317;
        bool r94471 = r94456 <= r94470;
        double r94472 = r94459 / r94454;
        double r94473 = r94460 * r94472;
        double r94474 = r94473 / r94455;
        double r94475 = 3.785288238963702e+229;
        bool r94476 = r94456 <= r94475;
        double r94477 = cbrt(r94472);
        double r94478 = r94477 * r94477;
        double r94479 = r94477 * r94461;
        double r94480 = r94478 * r94479;
        double r94481 = r94476 ? r94469 : r94480;
        double r94482 = r94471 ? r94474 : r94481;
        double r94483 = r94465 ? r94469 : r94482;
        double r94484 = r94458 ? r94463 : r94483;
        return r94484;
}

Original	11.3
Target	11.8
Herbie	5.9

Derivation

Split input into 4 regimes
if (* b1 b2) < -4.918213310913244e+88
1. Initial program 12.1
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied times-frac8.1
  \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
4. Using strategy rm
5. Applied associate-*l/7.9
  \[\leadsto \color{blue}{\frac{a1 \cdot \frac{a2}{b2}}{b1}}\]
if -4.918213310913244e+88 < (* b1 b2) < -3.7720840321361484e-215 or 2.0233386402977e-317 < (* b1 b2) < 3.785288238963702e+229
1. Initial program 4.6
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied div-inv4.8
  \[\leadsto \color{blue}{\left(a1 \cdot a2\right) \cdot \frac{1}{b1 \cdot b2}}\]
if -3.7720840321361484e-215 < (* b1 b2) < 2.0233386402977e-317
1. Initial program 44.2
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied times-frac9.3
  \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
4. Using strategy rm
5. Applied associate-*r/9.8
  \[\leadsto \color{blue}{\frac{\frac{a1}{b1} \cdot a2}{b2}}\]
6. Simplified9.8
  \[\leadsto \frac{\color{blue}{a2 \cdot \frac{a1}{b1}}}{b2}\]
if 3.785288238963702e+229 < (* b1 b2)
1. Initial program 16.9
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied times-frac3.9
  \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
4. Using strategy rm
5. Applied add-cube-cbrt4.3
  \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\frac{a1}{b1}} \cdot \sqrt[3]{\frac{a1}{b1}}\right) \cdot \sqrt[3]{\frac{a1}{b1}}\right)} \cdot \frac{a2}{b2}\]
6. Applied associate-*l*4.3
  \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{a1}{b1}} \cdot \sqrt[3]{\frac{a1}{b1}}\right) \cdot \left(\sqrt[3]{\frac{a1}{b1}} \cdot \frac{a2}{b2}\right)}\]
Recombined 4 regimes into one program.
Final simplification5.9
\[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -4.9182133109132441 \cdot 10^{88}:\\ \;\;\;\;\frac{a1 \cdot \frac{a2}{b2}}{b1}\\ \mathbf{elif}\;b1 \cdot b2 \le -3.7720840321361484 \cdot 10^{-215}:\\ \;\;\;\;\left(a1 \cdot a2\right) \cdot \frac{1}{b1 \cdot b2}\\ \mathbf{elif}\;b1 \cdot b2 \le 2.02333864 \cdot 10^{-317}:\\ \;\;\;\;\frac{a2 \cdot \frac{a1}{b1}}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le 3.785288238963702 \cdot 10^{229}:\\ \;\;\;\;\left(a1 \cdot a2\right) \cdot \frac{1}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{\frac{a1}{b1}} \cdot \sqrt[3]{\frac{a1}{b1}}\right) \cdot \left(\sqrt[3]{\frac{a1}{b1}} \cdot \frac{a2}{b2}\right)\\ \end{array}\]

Error

Try it out

Target

Derivation

`if (* b1 b2) < -4.918213310913244e+88`

`if -4.918213310913244e+88 < (* b1 b2) < -3.7720840321361484e-215 or 2.0233386402977e-317 < (* b1 b2) < 3.785288238963702e+229`

`if -3.7720840321361484e-215 < (* b1 b2) < 2.0233386402977e-317`

`if 3.785288238963702e+229 < (* b1 b2)`

Reproduce

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