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

↓

\[\begin{array}{l} \mathbf{if}\;a1 \cdot a2 = -\infty:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le -4.369619197843261223988403902442698260098 \cdot 10^{-287}:\\ \;\;\;\;\frac{1}{\frac{b2 \cdot b1}{a1 \cdot a2}}\\ \mathbf{elif}\;a1 \cdot a2 \le 2.983618642889101104598899002423951855124 \cdot 10^{-209}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le 5.979773594632940735324722698003690676961 \cdot 10^{199}:\\ \;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{a1} \cdot \sqrt[3]{a1}\right) \cdot \left(\frac{a2}{b2} \cdot \frac{\sqrt[3]{a1}}{b1}\right)\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;a1 \cdot a2 = -\infty:\\
\;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\

\mathbf{elif}\;a1 \cdot a2 \le -4.369619197843261223988403902442698260098 \cdot 10^{-287}:\\
\;\;\;\;\frac{1}{\frac{b2 \cdot b1}{a1 \cdot a2}}\\

\mathbf{elif}\;a1 \cdot a2 \le 2.983618642889101104598899002423951855124 \cdot 10^{-209}:\\
\;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\

\mathbf{elif}\;a1 \cdot a2 \le 5.979773594632940735324722698003690676961 \cdot 10^{199}:\\
\;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\

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

\end{array}

double f(double a1, double a2, double b1, double b2) {
        double r6583813 = a1;
        double r6583814 = a2;
        double r6583815 = r6583813 * r6583814;
        double r6583816 = b1;
        double r6583817 = b2;
        double r6583818 = r6583816 * r6583817;
        double r6583819 = r6583815 / r6583818;
        return r6583819;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r6583820 = a1;
        double r6583821 = a2;
        double r6583822 = r6583820 * r6583821;
        double r6583823 = -inf.0;
        bool r6583824 = r6583822 <= r6583823;
        double r6583825 = b1;
        double r6583826 = r6583820 / r6583825;
        double r6583827 = b2;
        double r6583828 = r6583821 / r6583827;
        double r6583829 = r6583826 * r6583828;
        double r6583830 = -4.369619197843261e-287;
        bool r6583831 = r6583822 <= r6583830;
        double r6583832 = 1.0;
        double r6583833 = r6583827 * r6583825;
        double r6583834 = r6583833 / r6583822;
        double r6583835 = r6583832 / r6583834;
        double r6583836 = 2.983618642889101e-209;
        bool r6583837 = r6583822 <= r6583836;
        double r6583838 = 5.979773594632941e+199;
        bool r6583839 = r6583822 <= r6583838;
        double r6583840 = r6583822 / r6583825;
        double r6583841 = r6583840 / r6583827;
        double r6583842 = cbrt(r6583820);
        double r6583843 = r6583842 * r6583842;
        double r6583844 = r6583842 / r6583825;
        double r6583845 = r6583828 * r6583844;
        double r6583846 = r6583843 * r6583845;
        double r6583847 = r6583839 ? r6583841 : r6583846;
        double r6583848 = r6583837 ? r6583829 : r6583847;
        double r6583849 = r6583831 ? r6583835 : r6583848;
        double r6583850 = r6583824 ? r6583829 : r6583849;
        return r6583850;
}

Original	11.5
Target	11.1
Herbie	5.3

Derivation

Split input into 4 regimes
if (* a1 a2) < -inf.0 or -4.369619197843261e-287 < (* a1 a2) < 2.983618642889101e-209
1. Initial program 21.8
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied times-frac4.0
  \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
if -inf.0 < (* a1 a2) < -4.369619197843261e-287
1. Initial program 5.9
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied clear-num6.2
  \[\leadsto \color{blue}{\frac{1}{\frac{b1 \cdot b2}{a1 \cdot a2}}}\]
if 2.983618642889101e-209 < (* a1 a2) < 5.979773594632941e+199
1. Initial program 4.5
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/r*4.3
  \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b1}}{b2}}\]
if 5.979773594632941e+199 < (* a1 a2)
1. Initial program 34.1
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied times-frac11.5
  \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
4. Using strategy rm
5. Applied *-un-lft-identity11.5
  \[\leadsto \frac{a1}{\color{blue}{1 \cdot b1}} \cdot \frac{a2}{b2}\]
6. Applied add-cube-cbrt12.3
  \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{a1} \cdot \sqrt[3]{a1}\right) \cdot \sqrt[3]{a1}}}{1 \cdot b1} \cdot \frac{a2}{b2}\]
7. Applied times-frac12.3
  \[\leadsto \color{blue}{\left(\frac{\sqrt[3]{a1} \cdot \sqrt[3]{a1}}{1} \cdot \frac{\sqrt[3]{a1}}{b1}\right)} \cdot \frac{a2}{b2}\]
8. Applied associate-*l*10.0
  \[\leadsto \color{blue}{\frac{\sqrt[3]{a1} \cdot \sqrt[3]{a1}}{1} \cdot \left(\frac{\sqrt[3]{a1}}{b1} \cdot \frac{a2}{b2}\right)}\]
Recombined 4 regimes into one program.
Final simplification5.3
\[\leadsto \begin{array}{l} \mathbf{if}\;a1 \cdot a2 = -\infty:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le -4.369619197843261223988403902442698260098 \cdot 10^{-287}:\\ \;\;\;\;\frac{1}{\frac{b2 \cdot b1}{a1 \cdot a2}}\\ \mathbf{elif}\;a1 \cdot a2 \le 2.983618642889101104598899002423951855124 \cdot 10^{-209}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le 5.979773594632940735324722698003690676961 \cdot 10^{199}:\\ \;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{a1} \cdot \sqrt[3]{a1}\right) \cdot \left(\frac{a2}{b2} \cdot \frac{\sqrt[3]{a1}}{b1}\right)\\ \end{array}\]

Error

Try it out

Target

Derivation

`if (* a1 a2) < -inf.0 or -4.369619197843261e-287 < (* a1 a2) < 2.983618642889101e-209`

`if -inf.0 < (* a1 a2) < -4.369619197843261e-287`

`if 2.983618642889101e-209 < (* a1 a2) < 5.979773594632941e+199`

`if 5.979773594632941e+199 < (* a1 a2)`

Reproduce

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