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

↓

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

\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{\frac{a1}{b1} \cdot a2}{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 r116619 = a1;
        double r116620 = a2;
        double r116621 = r116619 * r116620;
        double r116622 = b1;
        double r116623 = b2;
        double r116624 = r116622 * r116623;
        double r116625 = r116621 / r116624;
        return r116625;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r116626 = b1;
        double r116627 = b2;
        double r116628 = r116626 * r116627;
        double r116629 = -4.918213310913244e+88;
        bool r116630 = r116628 <= r116629;
        double r116631 = a1;
        double r116632 = a2;
        double r116633 = r116632 / r116627;
        double r116634 = r116631 * r116633;
        double r116635 = r116634 / r116626;
        double r116636 = -3.7720840321361484e-215;
        bool r116637 = r116628 <= r116636;
        double r116638 = r116631 * r116632;
        double r116639 = 1.0;
        double r116640 = r116639 / r116628;
        double r116641 = r116638 * r116640;
        double r116642 = 2.0233386402977e-317;
        bool r116643 = r116628 <= r116642;
        double r116644 = r116631 / r116626;
        double r116645 = r116644 * r116632;
        double r116646 = r116645 / r116627;
        double r116647 = 3.785288238963702e+229;
        bool r116648 = r116628 <= r116647;
        double r116649 = cbrt(r116644);
        double r116650 = r116649 * r116649;
        double r116651 = r116649 * r116633;
        double r116652 = r116650 * r116651;
        double r116653 = r116648 ? r116641 : r116652;
        double r116654 = r116643 ? r116646 : r116653;
        double r116655 = r116637 ? r116641 : r116654;
        double r116656 = r116630 ? r116635 : r116655;
        return r116656;
}

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

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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