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

↓

\[\begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -1.8654071526797647 \cdot 10^{+191}:\\ \;\;\;\;\left(a2 \cdot \frac{a1}{b1}\right) \cdot \frac{1}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le -1.0176507098003041 \cdot 10^{-184}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \le 2.105160204145219 \cdot 10^{-202}:\\ \;\;\;\;\left(\frac{a1}{b1} \cdot \left(\sqrt[3]{a2} \cdot \sqrt[3]{a2}\right)\right) \cdot \frac{\sqrt[3]{a2}}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le 3.692200814826821 \cdot 10^{+161}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{else}:\\ \;\;\;\;\left(a2 \cdot \frac{a1}{b1}\right) \cdot \frac{1}{b2}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;b1 \cdot b2 \le -1.8654071526797647 \cdot 10^{+191}:\\
\;\;\;\;\left(a2 \cdot \frac{a1}{b1}\right) \cdot \frac{1}{b2}\\

\mathbf{elif}\;b1 \cdot b2 \le -1.0176507098003041 \cdot 10^{-184}:\\
\;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\

\mathbf{elif}\;b1 \cdot b2 \le 2.105160204145219 \cdot 10^{-202}:\\
\;\;\;\;\left(\frac{a1}{b1} \cdot \left(\sqrt[3]{a2} \cdot \sqrt[3]{a2}\right)\right) \cdot \frac{\sqrt[3]{a2}}{b2}\\

\mathbf{elif}\;b1 \cdot b2 \le 3.692200814826821 \cdot 10^{+161}:\\
\;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\

\mathbf{else}:\\
\;\;\;\;\left(a2 \cdot \frac{a1}{b1}\right) \cdot \frac{1}{b2}\\

\end{array}

double f(double a1, double a2, double b1, double b2) {
        double r17993607 = a1;
        double r17993608 = a2;
        double r17993609 = r17993607 * r17993608;
        double r17993610 = b1;
        double r17993611 = b2;
        double r17993612 = r17993610 * r17993611;
        double r17993613 = r17993609 / r17993612;
        return r17993613;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r17993614 = b1;
        double r17993615 = b2;
        double r17993616 = r17993614 * r17993615;
        double r17993617 = -1.8654071526797647e+191;
        bool r17993618 = r17993616 <= r17993617;
        double r17993619 = a2;
        double r17993620 = a1;
        double r17993621 = r17993620 / r17993614;
        double r17993622 = r17993619 * r17993621;
        double r17993623 = 1.0;
        double r17993624 = r17993623 / r17993615;
        double r17993625 = r17993622 * r17993624;
        double r17993626 = -1.0176507098003041e-184;
        bool r17993627 = r17993616 <= r17993626;
        double r17993628 = r17993616 / r17993619;
        double r17993629 = r17993620 / r17993628;
        double r17993630 = 2.105160204145219e-202;
        bool r17993631 = r17993616 <= r17993630;
        double r17993632 = cbrt(r17993619);
        double r17993633 = r17993632 * r17993632;
        double r17993634 = r17993621 * r17993633;
        double r17993635 = r17993632 / r17993615;
        double r17993636 = r17993634 * r17993635;
        double r17993637 = 3.692200814826821e+161;
        bool r17993638 = r17993616 <= r17993637;
        double r17993639 = r17993638 ? r17993629 : r17993625;
        double r17993640 = r17993631 ? r17993636 : r17993639;
        double r17993641 = r17993627 ? r17993629 : r17993640;
        double r17993642 = r17993618 ? r17993625 : r17993641;
        return r17993642;
}

Original	11.2
Target	11.1
Herbie	5.0

Derivation

Split input into 3 regimes
if (* b1 b2) < -1.8654071526797647e+191 or 3.692200814826821e+161 < (* b1 b2)
1. Initial program 14.2
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied times-frac4.9
  \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
4. Using strategy rm
5. Applied div-inv5.0
  \[\leadsto \frac{a1}{b1} \cdot \color{blue}{\left(a2 \cdot \frac{1}{b2}\right)}\]
6. Applied associate-*r*5.1
  \[\leadsto \color{blue}{\left(\frac{a1}{b1} \cdot a2\right) \cdot \frac{1}{b2}}\]
if -1.8654071526797647e+191 < (* b1 b2) < -1.0176507098003041e-184 or 2.105160204145219e-202 < (* b1 b2) < 3.692200814826821e+161
1. Initial program 4.2
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/l*4.1
  \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]
if -1.0176507098003041e-184 < (* b1 b2) < 2.105160204145219e-202
1. Initial program 31.8
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied times-frac8.8
  \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
4. Using strategy rm
5. Applied *-un-lft-identity8.8
  \[\leadsto \frac{a1}{b1} \cdot \frac{a2}{\color{blue}{1 \cdot b2}}\]
6. Applied add-cube-cbrt9.8
  \[\leadsto \frac{a1}{b1} \cdot \frac{\color{blue}{\left(\sqrt[3]{a2} \cdot \sqrt[3]{a2}\right) \cdot \sqrt[3]{a2}}}{1 \cdot b2}\]
7. Applied times-frac9.8
  \[\leadsto \frac{a1}{b1} \cdot \color{blue}{\left(\frac{\sqrt[3]{a2} \cdot \sqrt[3]{a2}}{1} \cdot \frac{\sqrt[3]{a2}}{b2}\right)}\]
8. Applied associate-*r*8.5
  \[\leadsto \color{blue}{\left(\frac{a1}{b1} \cdot \frac{\sqrt[3]{a2} \cdot \sqrt[3]{a2}}{1}\right) \cdot \frac{\sqrt[3]{a2}}{b2}}\]
Recombined 3 regimes into one program.
Final simplification5.0
\[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -1.8654071526797647 \cdot 10^{+191}:\\ \;\;\;\;\left(a2 \cdot \frac{a1}{b1}\right) \cdot \frac{1}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le -1.0176507098003041 \cdot 10^{-184}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \le 2.105160204145219 \cdot 10^{-202}:\\ \;\;\;\;\left(\frac{a1}{b1} \cdot \left(\sqrt[3]{a2} \cdot \sqrt[3]{a2}\right)\right) \cdot \frac{\sqrt[3]{a2}}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le 3.692200814826821 \cdot 10^{+161}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{else}:\\ \;\;\;\;\left(a2 \cdot \frac{a1}{b1}\right) \cdot \frac{1}{b2}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if (* b1 b2) < -1.8654071526797647e+191 or 3.692200814826821e+161 < (* b1 b2)`

`if -1.8654071526797647e+191 < (* b1 b2) < -1.0176507098003041e-184 or 2.105160204145219e-202 < (* b1 b2) < 3.692200814826821e+161`

`if -1.0176507098003041e-184 < (* b1 b2) < 2.105160204145219e-202`

Reproduce

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