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

↓

\[\begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -3.78185687302351595353600927911780875218 \cdot 10^{144}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le -4.150210671513833606732172966148884455885 \cdot 10^{-228}:\\ \;\;\;\;\frac{a1}{\frac{1}{\frac{a2}{b1 \cdot b2}}}\\ \mathbf{elif}\;b1 \cdot b2 \le 4.343720045836759282443581250746346844563 \cdot 10^{-182} \lor \neg \left(b1 \cdot b2 \le 4.542196225721951094431610617285657897859 \cdot 10^{280}\right):\\ \;\;\;\;\frac{1}{b1} \cdot \left(\frac{a1}{b2} \cdot a2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1 \cdot b2} \cdot a2\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;b1 \cdot b2 \le -3.78185687302351595353600927911780875218 \cdot 10^{144}:\\
\;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\

\mathbf{elif}\;b1 \cdot b2 \le -4.150210671513833606732172966148884455885 \cdot 10^{-228}:\\
\;\;\;\;\frac{a1}{\frac{1}{\frac{a2}{b1 \cdot b2}}}\\

\mathbf{elif}\;b1 \cdot b2 \le 4.343720045836759282443581250746346844563 \cdot 10^{-182} \lor \neg \left(b1 \cdot b2 \le 4.542196225721951094431610617285657897859 \cdot 10^{280}\right):\\
\;\;\;\;\frac{1}{b1} \cdot \left(\frac{a1}{b2} \cdot a2\right)\\

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

\end{array}

double f(double a1, double a2, double b1, double b2) {
        double r134331 = a1;
        double r134332 = a2;
        double r134333 = r134331 * r134332;
        double r134334 = b1;
        double r134335 = b2;
        double r134336 = r134334 * r134335;
        double r134337 = r134333 / r134336;
        return r134337;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r134338 = b1;
        double r134339 = b2;
        double r134340 = r134338 * r134339;
        double r134341 = -3.781856873023516e+144;
        bool r134342 = r134340 <= r134341;
        double r134343 = a1;
        double r134344 = r134343 / r134338;
        double r134345 = a2;
        double r134346 = r134345 / r134339;
        double r134347 = r134344 * r134346;
        double r134348 = -4.1502106715138336e-228;
        bool r134349 = r134340 <= r134348;
        double r134350 = 1.0;
        double r134351 = r134345 / r134340;
        double r134352 = r134350 / r134351;
        double r134353 = r134343 / r134352;
        double r134354 = 4.343720045836759e-182;
        bool r134355 = r134340 <= r134354;
        double r134356 = 4.542196225721951e+280;
        bool r134357 = r134340 <= r134356;
        double r134358 = !r134357;
        bool r134359 = r134355 || r134358;
        double r134360 = r134350 / r134338;
        double r134361 = r134343 / r134339;
        double r134362 = r134361 * r134345;
        double r134363 = r134360 * r134362;
        double r134364 = r134343 / r134340;
        double r134365 = r134364 * r134345;
        double r134366 = r134359 ? r134363 : r134365;
        double r134367 = r134349 ? r134353 : r134366;
        double r134368 = r134342 ? r134347 : r134367;
        return r134368;
}

Original	11.5
Target	11.2
Herbie	5.1

Derivation

Split input into 4 regimes
if (* b1 b2) < -3.781856873023516e+144
1. Initial program 14.7
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied times-frac5.7
  \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
if -3.781856873023516e+144 < (* b1 b2) < -4.1502106715138336e-228
1. Initial program 4.4
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/l*4.1
  \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]
4. Using strategy rm
5. Applied clear-num4.4
  \[\leadsto \frac{a1}{\color{blue}{\frac{1}{\frac{a2}{b1 \cdot b2}}}}\]
if -4.1502106715138336e-228 < (* b1 b2) < 4.343720045836759e-182 or 4.542196225721951e+280 < (* b1 b2)
1. Initial program 26.9
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/l*27.3
  \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]
4. Using strategy rm
5. Applied associate-/r/27.2
  \[\leadsto \color{blue}{\frac{a1}{b1 \cdot b2} \cdot a2}\]
6. Using strategy rm
7. Applied *-un-lft-identity27.2
  \[\leadsto \frac{\color{blue}{1 \cdot a1}}{b1 \cdot b2} \cdot a2\]
8. Applied times-frac13.2
  \[\leadsto \color{blue}{\left(\frac{1}{b1} \cdot \frac{a1}{b2}\right)} \cdot a2\]
9. Applied associate-*l*6.6
  \[\leadsto \color{blue}{\frac{1}{b1} \cdot \left(\frac{a1}{b2} \cdot a2\right)}\]
if 4.343720045836759e-182 < (* b1 b2) < 4.542196225721951e+280
1. Initial program 5.3
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
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/4.4
  \[\leadsto \color{blue}{\frac{a1}{b1 \cdot b2} \cdot a2}\]
Recombined 4 regimes into one program.
Final simplification5.1
\[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -3.78185687302351595353600927911780875218 \cdot 10^{144}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le -4.150210671513833606732172966148884455885 \cdot 10^{-228}:\\ \;\;\;\;\frac{a1}{\frac{1}{\frac{a2}{b1 \cdot b2}}}\\ \mathbf{elif}\;b1 \cdot b2 \le 4.343720045836759282443581250746346844563 \cdot 10^{-182} \lor \neg \left(b1 \cdot b2 \le 4.542196225721951094431610617285657897859 \cdot 10^{280}\right):\\ \;\;\;\;\frac{1}{b1} \cdot \left(\frac{a1}{b2} \cdot a2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1 \cdot b2} \cdot a2\\ \end{array}\]

Error

Try it out

Target

Derivation

`if (* b1 b2) < -3.781856873023516e+144`

`if -3.781856873023516e+144 < (* b1 b2) < -4.1502106715138336e-228`

`if -4.1502106715138336e-228 < (* b1 b2) < 4.343720045836759e-182 or 4.542196225721951e+280 < (* b1 b2)`

`if 4.343720045836759e-182 < (* b1 b2) < 4.542196225721951e+280`

Reproduce

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