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

↓

\[\begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -9.675631413915364 \cdot 10^{120}:\\ \;\;\;\;\frac{\frac{a2}{b1}}{\frac{b2}{a1}}\\ \mathbf{elif}\;b1 \cdot b2 \le -3.0079329750767313 \cdot 10^{-303}:\\ \;\;\;\;\frac{a2}{\frac{b1 \cdot b2}{a1}}\\ \mathbf{elif}\;b1 \cdot b2 \le 2.21214754521356796 \cdot 10^{-306}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le 3.5769750751020911 \cdot 10^{186}:\\ \;\;\;\;\frac{a2}{\frac{b1 \cdot b2}{a1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a2}{b1}}{\frac{b2}{a1}}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;b1 \cdot b2 \le -9.675631413915364 \cdot 10^{120}:\\
\;\;\;\;\frac{\frac{a2}{b1}}{\frac{b2}{a1}}\\

\mathbf{elif}\;b1 \cdot b2 \le -3.0079329750767313 \cdot 10^{-303}:\\
\;\;\;\;\frac{a2}{\frac{b1 \cdot b2}{a1}}\\

\mathbf{elif}\;b1 \cdot b2 \le 2.21214754521356796 \cdot 10^{-306}:\\
\;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\

\mathbf{elif}\;b1 \cdot b2 \le 3.5769750751020911 \cdot 10^{186}:\\
\;\;\;\;\frac{a2}{\frac{b1 \cdot b2}{a1}}\\

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

\end{array}

double f(double a1, double a2, double b1, double b2) {
        double r155329 = a1;
        double r155330 = a2;
        double r155331 = r155329 * r155330;
        double r155332 = b1;
        double r155333 = b2;
        double r155334 = r155332 * r155333;
        double r155335 = r155331 / r155334;
        return r155335;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r155336 = b1;
        double r155337 = b2;
        double r155338 = r155336 * r155337;
        double r155339 = -9.675631413915364e+120;
        bool r155340 = r155338 <= r155339;
        double r155341 = a2;
        double r155342 = r155341 / r155336;
        double r155343 = a1;
        double r155344 = r155337 / r155343;
        double r155345 = r155342 / r155344;
        double r155346 = -3.007932975076731e-303;
        bool r155347 = r155338 <= r155346;
        double r155348 = r155338 / r155343;
        double r155349 = r155341 / r155348;
        double r155350 = 2.212147545213568e-306;
        bool r155351 = r155338 <= r155350;
        double r155352 = r155343 / r155336;
        double r155353 = r155341 / r155337;
        double r155354 = r155352 * r155353;
        double r155355 = 3.576975075102091e+186;
        bool r155356 = r155338 <= r155355;
        double r155357 = r155356 ? r155349 : r155345;
        double r155358 = r155351 ? r155354 : r155357;
        double r155359 = r155347 ? r155349 : r155358;
        double r155360 = r155340 ? r155345 : r155359;
        return r155360;
}

Original	11.0
Target	11.6
Herbie	5.6

Derivation

Split input into 3 regimes
if (* b1 b2) < -9.675631413915364e+120 or 3.576975075102091e+186 < (* b1 b2)
1. Initial program 13.6
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied clear-num13.9
  \[\leadsto \color{blue}{\frac{1}{\frac{b1 \cdot b2}{a1 \cdot a2}}}\]
4. Using strategy rm
5. Applied associate-/r*13.9
  \[\leadsto \frac{1}{\color{blue}{\frac{\frac{b1 \cdot b2}{a1}}{a2}}}\]
6. Taylor expanded around 0 13.6
  \[\leadsto \color{blue}{\frac{a1 \cdot a2}{b1 \cdot b2}}\]
7. Simplified13.7
  \[\leadsto \color{blue}{\frac{a2}{\frac{b1 \cdot b2}{a1}}}\]
8. Using strategy rm
9. Applied *-un-lft-identity13.7
  \[\leadsto \frac{a2}{\frac{b1 \cdot b2}{\color{blue}{1 \cdot a1}}}\]
10. Applied times-frac8.0
  \[\leadsto \frac{a2}{\color{blue}{\frac{b1}{1} \cdot \frac{b2}{a1}}}\]
11. Applied associate-/r*5.5
  \[\leadsto \color{blue}{\frac{\frac{a2}{\frac{b1}{1}}}{\frac{b2}{a1}}}\]
12. Simplified5.5
  \[\leadsto \frac{\color{blue}{\frac{a2}{b1}}}{\frac{b2}{a1}}\]
if -9.675631413915364e+120 < (* b1 b2) < -3.007932975076731e-303 or 2.212147545213568e-306 < (* b1 b2) < 3.576975075102091e+186
1. Initial program 4.9
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied clear-num5.1
  \[\leadsto \color{blue}{\frac{1}{\frac{b1 \cdot b2}{a1 \cdot a2}}}\]
4. Using strategy rm
5. Applied associate-/r*5.8
  \[\leadsto \frac{1}{\color{blue}{\frac{\frac{b1 \cdot b2}{a1}}{a2}}}\]
6. Taylor expanded around 0 4.9
  \[\leadsto \color{blue}{\frac{a1 \cdot a2}{b1 \cdot b2}}\]
7. Simplified5.4
  \[\leadsto \color{blue}{\frac{a2}{\frac{b1 \cdot b2}{a1}}}\]
if -3.007932975076731e-303 < (* b1 b2) < 2.212147545213568e-306
1. Initial program 58.2
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied times-frac8.7
  \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
Recombined 3 regimes into one program.
Final simplification5.6
\[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -9.675631413915364 \cdot 10^{120}:\\ \;\;\;\;\frac{\frac{a2}{b1}}{\frac{b2}{a1}}\\ \mathbf{elif}\;b1 \cdot b2 \le -3.0079329750767313 \cdot 10^{-303}:\\ \;\;\;\;\frac{a2}{\frac{b1 \cdot b2}{a1}}\\ \mathbf{elif}\;b1 \cdot b2 \le 2.21214754521356796 \cdot 10^{-306}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le 3.5769750751020911 \cdot 10^{186}:\\ \;\;\;\;\frac{a2}{\frac{b1 \cdot b2}{a1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a2}{b1}}{\frac{b2}{a1}}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if (* b1 b2) < -9.675631413915364e+120 or 3.576975075102091e+186 < (* b1 b2)`

`if -9.675631413915364e+120 < (* b1 b2) < -3.007932975076731e-303 or 2.212147545213568e-306 < (* b1 b2) < 3.576975075102091e+186`

`if -3.007932975076731e-303 < (* b1 b2) < 2.212147545213568e-306`

Reproduce

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