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

↓

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

\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 r6419405 = a1;
        double r6419406 = a2;
        double r6419407 = r6419405 * r6419406;
        double r6419408 = b1;
        double r6419409 = b2;
        double r6419410 = r6419408 * r6419409;
        double r6419411 = r6419407 / r6419410;
        return r6419411;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r6419412 = a1;
        double r6419413 = a2;
        double r6419414 = r6419412 * r6419413;
        double r6419415 = -inf.0;
        bool r6419416 = r6419414 <= r6419415;
        double r6419417 = b1;
        double r6419418 = r6419412 / r6419417;
        double r6419419 = b2;
        double r6419420 = r6419413 / r6419419;
        double r6419421 = r6419418 * r6419420;
        double r6419422 = -4.369619197843261e-287;
        bool r6419423 = r6419414 <= r6419422;
        double r6419424 = 1.0;
        double r6419425 = r6419419 * r6419417;
        double r6419426 = r6419425 / r6419414;
        double r6419427 = r6419424 / r6419426;
        double r6419428 = 2.983618642889101e-209;
        bool r6419429 = r6419414 <= r6419428;
        double r6419430 = 5.979773594632941e+199;
        bool r6419431 = r6419414 <= r6419430;
        double r6419432 = r6419414 / r6419417;
        double r6419433 = r6419432 / r6419419;
        double r6419434 = cbrt(r6419412);
        double r6419435 = r6419434 * r6419434;
        double r6419436 = r6419434 / r6419417;
        double r6419437 = r6419420 * r6419436;
        double r6419438 = r6419435 * r6419437;
        double r6419439 = r6419431 ? r6419433 : r6419438;
        double r6419440 = r6419429 ? r6419421 : r6419439;
        double r6419441 = r6419423 ? r6419427 : r6419440;
        double r6419442 = r6419416 ? r6419421 : r6419441;
        return r6419442;
}

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

In
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