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

↓

\[\begin{array}{l} \mathbf{if}\;a1 \cdot a2 \le -2.11620674526193 \cdot 10^{+207}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \mathbf{elif}\;a1 \cdot a2 \le -1.65549822385213 \cdot 10^{-190}:\\ \;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le 2.2374340498592432 \cdot 10^{-200}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \mathbf{elif}\;a1 \cdot a2 \le 3.054460206803236 \cdot 10^{+166}:\\ \;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a2}{\sqrt[3]{b1}}}{b2} \cdot \frac{a1}{\sqrt[3]{b1} \cdot \sqrt[3]{b1}}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;a1 \cdot a2 \le -2.11620674526193 \cdot 10^{+207}:\\
\;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\

\mathbf{elif}\;a1 \cdot a2 \le -1.65549822385213 \cdot 10^{-190}:\\
\;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\

\mathbf{elif}\;a1 \cdot a2 \le 2.2374340498592432 \cdot 10^{-200}:\\
\;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\

\mathbf{elif}\;a1 \cdot a2 \le 3.054460206803236 \cdot 10^{+166}:\\
\;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\

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

\end{array}

double f(double a1, double a2, double b1, double b2) {
        double r2517749 = a1;
        double r2517750 = a2;
        double r2517751 = r2517749 * r2517750;
        double r2517752 = b1;
        double r2517753 = b2;
        double r2517754 = r2517752 * r2517753;
        double r2517755 = r2517751 / r2517754;
        return r2517755;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r2517756 = a1;
        double r2517757 = a2;
        double r2517758 = r2517756 * r2517757;
        double r2517759 = -2.11620674526193e+207;
        bool r2517760 = r2517758 <= r2517759;
        double r2517761 = b2;
        double r2517762 = b1;
        double r2517763 = r2517757 / r2517762;
        double r2517764 = r2517761 / r2517763;
        double r2517765 = r2517756 / r2517764;
        double r2517766 = -1.65549822385213e-190;
        bool r2517767 = r2517758 <= r2517766;
        double r2517768 = r2517758 / r2517762;
        double r2517769 = r2517768 / r2517761;
        double r2517770 = 2.2374340498592432e-200;
        bool r2517771 = r2517758 <= r2517770;
        double r2517772 = 3.054460206803236e+166;
        bool r2517773 = r2517758 <= r2517772;
        double r2517774 = cbrt(r2517762);
        double r2517775 = r2517757 / r2517774;
        double r2517776 = r2517775 / r2517761;
        double r2517777 = r2517774 * r2517774;
        double r2517778 = r2517756 / r2517777;
        double r2517779 = r2517776 * r2517778;
        double r2517780 = r2517773 ? r2517769 : r2517779;
        double r2517781 = r2517771 ? r2517765 : r2517780;
        double r2517782 = r2517767 ? r2517769 : r2517781;
        double r2517783 = r2517760 ? r2517765 : r2517782;
        return r2517783;
}

Original	11.1
Target	11.2
Herbie	4.9

Derivation

Split input into 3 regimes
if (* a1 a2) < -2.11620674526193e+207 or -1.65549822385213e-190 < (* a1 a2) < 2.2374340498592432e-200
1. Initial program 18.4
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/r*18.4
  \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b1}}{b2}}\]
4. Using strategy rm
5. Applied *-un-lft-identity18.4
  \[\leadsto \frac{\frac{a1 \cdot a2}{\color{blue}{1 \cdot b1}}}{b2}\]
6. Applied times-frac9.6
  \[\leadsto \frac{\color{blue}{\frac{a1}{1} \cdot \frac{a2}{b1}}}{b2}\]
7. Applied associate-/l*5.0
  \[\leadsto \color{blue}{\frac{\frac{a1}{1}}{\frac{b2}{\frac{a2}{b1}}}}\]
if -2.11620674526193e+207 < (* a1 a2) < -1.65549822385213e-190 or 2.2374340498592432e-200 < (* a1 a2) < 3.054460206803236e+166
1. Initial program 4.2
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/r*4.3
  \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b1}}{b2}}\]
if 3.054460206803236e+166 < (* a1 a2)
1. Initial program 29.0
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/r*28.8
  \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b1}}{b2}}\]
4. Using strategy rm
5. Applied *-un-lft-identity28.8
  \[\leadsto \frac{\frac{a1 \cdot a2}{b1}}{\color{blue}{1 \cdot b2}}\]
6. Applied add-cube-cbrt29.3
  \[\leadsto \frac{\frac{a1 \cdot a2}{\color{blue}{\left(\sqrt[3]{b1} \cdot \sqrt[3]{b1}\right) \cdot \sqrt[3]{b1}}}}{1 \cdot b2}\]
7. Applied times-frac17.3
  \[\leadsto \frac{\color{blue}{\frac{a1}{\sqrt[3]{b1} \cdot \sqrt[3]{b1}} \cdot \frac{a2}{\sqrt[3]{b1}}}}{1 \cdot b2}\]
8. Applied times-frac9.4
  \[\leadsto \color{blue}{\frac{\frac{a1}{\sqrt[3]{b1} \cdot \sqrt[3]{b1}}}{1} \cdot \frac{\frac{a2}{\sqrt[3]{b1}}}{b2}}\]
9. Simplified9.4
  \[\leadsto \color{blue}{\frac{a1}{\sqrt[3]{b1} \cdot \sqrt[3]{b1}}} \cdot \frac{\frac{a2}{\sqrt[3]{b1}}}{b2}\]
Recombined 3 regimes into one program.
Final simplification4.9
\[\leadsto \begin{array}{l} \mathbf{if}\;a1 \cdot a2 \le -2.11620674526193 \cdot 10^{+207}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \mathbf{elif}\;a1 \cdot a2 \le -1.65549822385213 \cdot 10^{-190}:\\ \;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le 2.2374340498592432 \cdot 10^{-200}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \mathbf{elif}\;a1 \cdot a2 \le 3.054460206803236 \cdot 10^{+166}:\\ \;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a2}{\sqrt[3]{b1}}}{b2} \cdot \frac{a1}{\sqrt[3]{b1} \cdot \sqrt[3]{b1}}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if (* a1 a2) < -2.11620674526193e+207 or -1.65549822385213e-190 < (* a1 a2) < 2.2374340498592432e-200`

`if -2.11620674526193e+207 < (* a1 a2) < -1.65549822385213e-190 or 2.2374340498592432e-200 < (* a1 a2) < 3.054460206803236e+166`

`if 3.054460206803236e+166 < (* a1 a2)`

Reproduce

In
Out