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

↓

\[\begin{array}{l} \mathbf{if}\;a2 \cdot a1 \le -1.2876487305313636 \cdot 10^{+181}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b1}}{b2}\\ \mathbf{elif}\;a2 \cdot a1 \le -6.385030884325899 \cdot 10^{-218}:\\ \;\;\;\;\frac{a2 \cdot a1}{b1} \cdot \frac{1}{b2}\\ \mathbf{elif}\;a2 \cdot a1 \le 4.775209065579154 \cdot 10^{-193}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \mathbf{elif}\;a2 \cdot a1 \le 1.1827835492321197 \cdot 10^{+164}:\\ \;\;\;\;\frac{a2 \cdot a1}{b1} \cdot \frac{1}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;a2 \cdot a1 \le -1.2876487305313636 \cdot 10^{+181}:\\
\;\;\;\;a1 \cdot \frac{\frac{a2}{b1}}{b2}\\

\mathbf{elif}\;a2 \cdot a1 \le -6.385030884325899 \cdot 10^{-218}:\\
\;\;\;\;\frac{a2 \cdot a1}{b1} \cdot \frac{1}{b2}\\

\mathbf{elif}\;a2 \cdot a1 \le 4.775209065579154 \cdot 10^{-193}:\\
\;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\

\mathbf{elif}\;a2 \cdot a1 \le 1.1827835492321197 \cdot 10^{+164}:\\
\;\;\;\;\frac{a2 \cdot a1}{b1} \cdot \frac{1}{b2}\\

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

\end{array}

double f(double a1, double a2, double b1, double b2) {
        double r5983460 = a1;
        double r5983461 = a2;
        double r5983462 = r5983460 * r5983461;
        double r5983463 = b1;
        double r5983464 = b2;
        double r5983465 = r5983463 * r5983464;
        double r5983466 = r5983462 / r5983465;
        return r5983466;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r5983467 = a2;
        double r5983468 = a1;
        double r5983469 = r5983467 * r5983468;
        double r5983470 = -1.2876487305313636e+181;
        bool r5983471 = r5983469 <= r5983470;
        double r5983472 = b1;
        double r5983473 = r5983467 / r5983472;
        double r5983474 = b2;
        double r5983475 = r5983473 / r5983474;
        double r5983476 = r5983468 * r5983475;
        double r5983477 = -6.385030884325899e-218;
        bool r5983478 = r5983469 <= r5983477;
        double r5983479 = r5983469 / r5983472;
        double r5983480 = 1.0;
        double r5983481 = r5983480 / r5983474;
        double r5983482 = r5983479 * r5983481;
        double r5983483 = 4.775209065579154e-193;
        bool r5983484 = r5983469 <= r5983483;
        double r5983485 = r5983474 / r5983473;
        double r5983486 = r5983468 / r5983485;
        double r5983487 = 1.1827835492321197e+164;
        bool r5983488 = r5983469 <= r5983487;
        double r5983489 = r5983488 ? r5983482 : r5983486;
        double r5983490 = r5983484 ? r5983486 : r5983489;
        double r5983491 = r5983478 ? r5983482 : r5983490;
        double r5983492 = r5983471 ? r5983476 : r5983491;
        return r5983492;
}

Original	10.9
Target	10.9
Herbie	5.4

Derivation

Split input into 3 regimes
if (* a1 a2) < -1.2876487305313636e+181
1. Initial program 29.7
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/r*31.7
  \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b1}}{b2}}\]
4. Using strategy rm
5. Applied *-un-lft-identity31.7
  \[\leadsto \frac{\frac{a1 \cdot a2}{b1}}{\color{blue}{1 \cdot b2}}\]
6. Applied *-un-lft-identity31.7
  \[\leadsto \frac{\frac{a1 \cdot a2}{\color{blue}{1 \cdot b1}}}{1 \cdot b2}\]
7. Applied times-frac19.8
  \[\leadsto \frac{\color{blue}{\frac{a1}{1} \cdot \frac{a2}{b1}}}{1 \cdot b2}\]
8. Applied times-frac10.9
  \[\leadsto \color{blue}{\frac{\frac{a1}{1}}{1} \cdot \frac{\frac{a2}{b1}}{b2}}\]
9. Simplified10.9
  \[\leadsto \color{blue}{a1} \cdot \frac{\frac{a2}{b1}}{b2}\]
if -1.2876487305313636e+181 < (* a1 a2) < -6.385030884325899e-218 or 4.775209065579154e-193 < (* a1 a2) < 1.1827835492321197e+164
1. Initial program 4.1
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/r*4.2
  \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b1}}{b2}}\]
4. Using strategy rm
5. Applied *-un-lft-identity4.2
  \[\leadsto \frac{\frac{a1 \cdot a2}{b1}}{\color{blue}{1 \cdot b2}}\]
6. Applied associate-/r*4.2
  \[\leadsto \color{blue}{\frac{\frac{\frac{a1 \cdot a2}{b1}}{1}}{b2}}\]
7. Simplified11.3
  \[\leadsto \frac{\color{blue}{\frac{a1}{b1} \cdot a2}}{b2}\]
8. Using strategy rm
9. Applied associate-*l/4.2
  \[\leadsto \frac{\color{blue}{\frac{a1 \cdot a2}{b1}}}{b2}\]
10. Using strategy rm
11. Applied div-inv4.3
  \[\leadsto \color{blue}{\frac{a1 \cdot a2}{b1} \cdot \frac{1}{b2}}\]
if -6.385030884325899e-218 < (* a1 a2) < 4.775209065579154e-193 or 1.1827835492321197e+164 < (* a1 a2)
1. Initial program 18.0
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/r*17.3
  \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b1}}{b2}}\]
4. Using strategy rm
5. Applied *-un-lft-identity17.3
  \[\leadsto \frac{\frac{a1 \cdot a2}{\color{blue}{1 \cdot b1}}}{b2}\]
6. Applied times-frac9.7
  \[\leadsto \frac{\color{blue}{\frac{a1}{1} \cdot \frac{a2}{b1}}}{b2}\]
7. Applied associate-/l*6.1
  \[\leadsto \color{blue}{\frac{\frac{a1}{1}}{\frac{b2}{\frac{a2}{b1}}}}\]
Recombined 3 regimes into one program.
Final simplification5.4
\[\leadsto \begin{array}{l} \mathbf{if}\;a2 \cdot a1 \le -1.2876487305313636 \cdot 10^{+181}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b1}}{b2}\\ \mathbf{elif}\;a2 \cdot a1 \le -6.385030884325899 \cdot 10^{-218}:\\ \;\;\;\;\frac{a2 \cdot a1}{b1} \cdot \frac{1}{b2}\\ \mathbf{elif}\;a2 \cdot a1 \le 4.775209065579154 \cdot 10^{-193}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \mathbf{elif}\;a2 \cdot a1 \le 1.1827835492321197 \cdot 10^{+164}:\\ \;\;\;\;\frac{a2 \cdot a1}{b1} \cdot \frac{1}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{\frac{b2}{\frac{a2}{b1}}}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if (* a1 a2) < -1.2876487305313636e+181`

`if -1.2876487305313636e+181 < (* a1 a2) < -6.385030884325899e-218 or 4.775209065579154e-193 < (* a1 a2) < 1.1827835492321197e+164`

`if -6.385030884325899e-218 < (* a1 a2) < 4.775209065579154e-193 or 1.1827835492321197e+164 < (* a1 a2)`

Reproduce

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