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

↓

\[\begin{array}{l} \mathbf{if}\;a1 \cdot a2 \le -1.100721826907999911467992266722832772944 \cdot 10^{269}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le -3.49050163230014819970050953927807740633 \cdot 10^{-197}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1} \cdot \frac{1}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le 4.475784744408438094636863798469716860556 \cdot 10^{-83}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \mathbf{elif}\;a1 \cdot a2 \le 6.099192957207017609535814106210005852322 \cdot 10^{243}:\\ \;\;\;\;\frac{a1 \cdot a2}{b2 \cdot b1}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;a1 \cdot a2 \le -1.100721826907999911467992266722832772944 \cdot 10^{269}:\\
\;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\

\mathbf{elif}\;a1 \cdot a2 \le -3.49050163230014819970050953927807740633 \cdot 10^{-197}:\\
\;\;\;\;\frac{a1 \cdot a2}{b1} \cdot \frac{1}{b2}\\

\mathbf{elif}\;a1 \cdot a2 \le 4.475784744408438094636863798469716860556 \cdot 10^{-83}:\\
\;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\

\mathbf{elif}\;a1 \cdot a2 \le 6.099192957207017609535814106210005852322 \cdot 10^{243}:\\
\;\;\;\;\frac{a1 \cdot a2}{b2 \cdot b1}\\

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

\end{array}

double f(double a1, double a2, double b1, double b2) {
        double r5654041 = a1;
        double r5654042 = a2;
        double r5654043 = r5654041 * r5654042;
        double r5654044 = b1;
        double r5654045 = b2;
        double r5654046 = r5654044 * r5654045;
        double r5654047 = r5654043 / r5654046;
        return r5654047;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r5654048 = a1;
        double r5654049 = a2;
        double r5654050 = r5654048 * r5654049;
        double r5654051 = -1.1007218269079999e+269;
        bool r5654052 = r5654050 <= r5654051;
        double r5654053 = b1;
        double r5654054 = r5654048 / r5654053;
        double r5654055 = b2;
        double r5654056 = r5654049 / r5654055;
        double r5654057 = r5654054 * r5654056;
        double r5654058 = -3.490501632300148e-197;
        bool r5654059 = r5654050 <= r5654058;
        double r5654060 = r5654050 / r5654053;
        double r5654061 = 1.0;
        double r5654062 = r5654061 / r5654055;
        double r5654063 = r5654060 * r5654062;
        double r5654064 = 4.475784744408438e-83;
        bool r5654065 = r5654050 <= r5654064;
        double r5654066 = r5654049 / r5654053;
        double r5654067 = r5654055 / r5654066;
        double r5654068 = r5654048 / r5654067;
        double r5654069 = 6.0991929572070176e+243;
        bool r5654070 = r5654050 <= r5654069;
        double r5654071 = r5654055 * r5654053;
        double r5654072 = r5654050 / r5654071;
        double r5654073 = r5654070 ? r5654072 : r5654057;
        double r5654074 = r5654065 ? r5654068 : r5654073;
        double r5654075 = r5654059 ? r5654063 : r5654074;
        double r5654076 = r5654052 ? r5654057 : r5654075;
        return r5654076;
}

Original	11.5
Target	11.3
Herbie	5.7

Derivation

Split input into 4 regimes
if (* a1 a2) < -1.1007218269079999e+269 or 6.0991929572070176e+243 < (* a1 a2)
1. Initial program 46.1
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied times-frac10.3
  \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
if -1.1007218269079999e+269 < (* a1 a2) < -3.490501632300148e-197
1. Initial program 4.9
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/r*4.7
  \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b1}}{b2}}\]
4. Using strategy rm
5. Applied div-inv4.8
  \[\leadsto \color{blue}{\frac{a1 \cdot a2}{b1} \cdot \frac{1}{b2}}\]
if -3.490501632300148e-197 < (* a1 a2) < 4.475784744408438e-83
1. Initial program 12.9
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/r*12.5
  \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b1}}{b2}}\]
4. Using strategy rm
5. Applied *-un-lft-identity12.5
  \[\leadsto \frac{\frac{a1 \cdot a2}{\color{blue}{1 \cdot b1}}}{b2}\]
6. Applied times-frac8.0
  \[\leadsto \frac{\color{blue}{\frac{a1}{1} \cdot \frac{a2}{b1}}}{b2}\]
7. Applied associate-/l*6.0
  \[\leadsto \color{blue}{\frac{\frac{a1}{1}}{\frac{b2}{\frac{a2}{b1}}}}\]
if 4.475784744408438e-83 < (* a1 a2) < 6.0991929572070176e+243
1. Initial program 4.9
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/r*4.5
  \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b1}}{b2}}\]
4. Using strategy rm
5. Applied clear-num4.8
  \[\leadsto \frac{\color{blue}{\frac{1}{\frac{b1}{a1 \cdot a2}}}}{b2}\]
6. Taylor expanded around 0 4.9
  \[\leadsto \color{blue}{\frac{a1 \cdot a2}{b2 \cdot b1}}\]
Recombined 4 regimes into one program.
Final simplification5.7
\[\leadsto \begin{array}{l} \mathbf{if}\;a1 \cdot a2 \le -1.100721826907999911467992266722832772944 \cdot 10^{269}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le -3.49050163230014819970050953927807740633 \cdot 10^{-197}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1} \cdot \frac{1}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le 4.475784744408438094636863798469716860556 \cdot 10^{-83}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \mathbf{elif}\;a1 \cdot a2 \le 6.099192957207017609535814106210005852322 \cdot 10^{243}:\\ \;\;\;\;\frac{a1 \cdot a2}{b2 \cdot b1}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if (* a1 a2) < -1.1007218269079999e+269 or 6.0991929572070176e+243 < (* a1 a2)`

`if -1.1007218269079999e+269 < (* a1 a2) < -3.490501632300148e-197`

`if -3.490501632300148e-197 < (* a1 a2) < 4.475784744408438e-83`

`if 4.475784744408438e-83 < (* a1 a2) < 6.0991929572070176e+243`

Reproduce

In
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