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

↓

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

\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 r22479787 = a1;
        double r22479788 = a2;
        double r22479789 = r22479787 * r22479788;
        double r22479790 = b1;
        double r22479791 = b2;
        double r22479792 = r22479790 * r22479791;
        double r22479793 = r22479789 / r22479792;
        return r22479793;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r22479794 = b1;
        double r22479795 = b2;
        double r22479796 = r22479794 * r22479795;
        double r22479797 = -1.8654071526797647e+191;
        bool r22479798 = r22479796 <= r22479797;
        double r22479799 = a2;
        double r22479800 = a1;
        double r22479801 = r22479800 / r22479794;
        double r22479802 = r22479799 * r22479801;
        double r22479803 = 1.0;
        double r22479804 = r22479803 / r22479795;
        double r22479805 = r22479802 * r22479804;
        double r22479806 = -1.0176507098003041e-184;
        bool r22479807 = r22479796 <= r22479806;
        double r22479808 = r22479796 / r22479799;
        double r22479809 = r22479800 / r22479808;
        double r22479810 = 2.105160204145219e-202;
        bool r22479811 = r22479796 <= r22479810;
        double r22479812 = cbrt(r22479799);
        double r22479813 = r22479812 * r22479812;
        double r22479814 = r22479801 * r22479813;
        double r22479815 = r22479812 / r22479795;
        double r22479816 = r22479814 * r22479815;
        double r22479817 = 3.692200814826821e+161;
        bool r22479818 = r22479796 <= r22479817;
        double r22479819 = r22479818 ? r22479809 : r22479805;
        double r22479820 = r22479811 ? r22479816 : r22479819;
        double r22479821 = r22479807 ? r22479809 : r22479820;
        double r22479822 = r22479798 ? r22479805 : r22479821;
        return r22479822;
}

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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