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

↓

\[\begin{array}{l} \mathbf{if}\;b2 \cdot b1 \le -5.027198331468452971083277390987079564256 \cdot 10^{271}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{elif}\;b2 \cdot b1 \le -1.708279358278811067826228393370497973053 \cdot 10^{-240}:\\ \;\;\;\;\frac{a1}{b2 \cdot b1} \cdot a2\\ \mathbf{elif}\;b2 \cdot b1 \le 2.491183802213925616452581733594161045108 \cdot 10^{-239}:\\ \;\;\;\;\frac{1}{b1} \cdot \frac{a1}{\frac{b2}{a2}}\\ \mathbf{elif}\;b2 \cdot b1 \le 3.274003468956291087635927220582233224264 \cdot 10^{201}:\\ \;\;\;\;\frac{a1}{b2 \cdot b1} \cdot a2\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;b2 \cdot b1 \le -5.027198331468452971083277390987079564256 \cdot 10^{271}:\\
\;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\

\mathbf{elif}\;b2 \cdot b1 \le -1.708279358278811067826228393370497973053 \cdot 10^{-240}:\\
\;\;\;\;\frac{a1}{b2 \cdot b1} \cdot a2\\

\mathbf{elif}\;b2 \cdot b1 \le 2.491183802213925616452581733594161045108 \cdot 10^{-239}:\\
\;\;\;\;\frac{1}{b1} \cdot \frac{a1}{\frac{b2}{a2}}\\

\mathbf{elif}\;b2 \cdot b1 \le 3.274003468956291087635927220582233224264 \cdot 10^{201}:\\
\;\;\;\;\frac{a1}{b2 \cdot b1} \cdot a2\\

\mathbf{else}:\\
\;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\

\end{array}

double f(double a1, double a2, double b1, double b2) {
        double r4521112 = a1;
        double r4521113 = a2;
        double r4521114 = r4521112 * r4521113;
        double r4521115 = b1;
        double r4521116 = b2;
        double r4521117 = r4521115 * r4521116;
        double r4521118 = r4521114 / r4521117;
        return r4521118;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r4521119 = b2;
        double r4521120 = b1;
        double r4521121 = r4521119 * r4521120;
        double r4521122 = -5.027198331468453e+271;
        bool r4521123 = r4521121 <= r4521122;
        double r4521124 = a2;
        double r4521125 = r4521124 / r4521119;
        double r4521126 = a1;
        double r4521127 = r4521126 / r4521120;
        double r4521128 = r4521125 * r4521127;
        double r4521129 = -1.708279358278811e-240;
        bool r4521130 = r4521121 <= r4521129;
        double r4521131 = r4521126 / r4521121;
        double r4521132 = r4521131 * r4521124;
        double r4521133 = 2.4911838022139256e-239;
        bool r4521134 = r4521121 <= r4521133;
        double r4521135 = 1.0;
        double r4521136 = r4521135 / r4521120;
        double r4521137 = r4521119 / r4521124;
        double r4521138 = r4521126 / r4521137;
        double r4521139 = r4521136 * r4521138;
        double r4521140 = 3.274003468956291e+201;
        bool r4521141 = r4521121 <= r4521140;
        double r4521142 = r4521141 ? r4521132 : r4521128;
        double r4521143 = r4521134 ? r4521139 : r4521142;
        double r4521144 = r4521130 ? r4521132 : r4521143;
        double r4521145 = r4521123 ? r4521128 : r4521144;
        return r4521145;
}

Original	11.5
Target	11.2
Herbie	5.0

Derivation

Split input into 3 regimes
if (* b1 b2) < -5.027198331468453e+271 or 3.274003468956291e+201 < (* b1 b2)
1. Initial program 17.4
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied times-frac3.7
  \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
if -5.027198331468453e+271 < (* b1 b2) < -1.708279358278811e-240 or 2.4911838022139256e-239 < (* b1 b2) < 3.274003468956291e+201
1. Initial program 4.9
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/l*4.6
  \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]
4. Using strategy rm
5. Applied associate-/r/4.9
  \[\leadsto \color{blue}{\frac{a1}{b1 \cdot b2} \cdot a2}\]
if -1.708279358278811e-240 < (* b1 b2) < 2.4911838022139256e-239
1. Initial program 40.3
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/l*39.4
  \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]
4. Using strategy rm
5. Applied *-un-lft-identity39.4
  \[\leadsto \frac{a1}{\frac{b1 \cdot b2}{\color{blue}{1 \cdot a2}}}\]
6. Applied times-frac17.8
  \[\leadsto \frac{a1}{\color{blue}{\frac{b1}{1} \cdot \frac{b2}{a2}}}\]
7. Applied *-un-lft-identity17.8
  \[\leadsto \frac{\color{blue}{1 \cdot a1}}{\frac{b1}{1} \cdot \frac{b2}{a2}}\]
8. Applied times-frac8.9
  \[\leadsto \color{blue}{\frac{1}{\frac{b1}{1}} \cdot \frac{a1}{\frac{b2}{a2}}}\]
9. Simplified8.9
  \[\leadsto \color{blue}{\frac{1}{b1}} \cdot \frac{a1}{\frac{b2}{a2}}\]
Recombined 3 regimes into one program.
Final simplification5.0
\[\leadsto \begin{array}{l} \mathbf{if}\;b2 \cdot b1 \le -5.027198331468452971083277390987079564256 \cdot 10^{271}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{elif}\;b2 \cdot b1 \le -1.708279358278811067826228393370497973053 \cdot 10^{-240}:\\ \;\;\;\;\frac{a1}{b2 \cdot b1} \cdot a2\\ \mathbf{elif}\;b2 \cdot b1 \le 2.491183802213925616452581733594161045108 \cdot 10^{-239}:\\ \;\;\;\;\frac{1}{b1} \cdot \frac{a1}{\frac{b2}{a2}}\\ \mathbf{elif}\;b2 \cdot b1 \le 3.274003468956291087635927220582233224264 \cdot 10^{201}:\\ \;\;\;\;\frac{a1}{b2 \cdot b1} \cdot a2\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if (* b1 b2) < -5.027198331468453e+271 or 3.274003468956291e+201 < (* b1 b2)`

`if -5.027198331468453e+271 < (* b1 b2) < -1.708279358278811e-240 or 2.4911838022139256e-239 < (* b1 b2) < 3.274003468956291e+201`

`if -1.708279358278811e-240 < (* b1 b2) < 2.4911838022139256e-239`

Reproduce

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