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

↓

\[\begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -9.384563571355019 \cdot 10^{+255}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le -1.0490423713698057 \cdot 10^{-109}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \le 5.934410328828728 \cdot 10^{-246}:\\ \;\;\;\;\frac{a2 \cdot \frac{a1}{b1}}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le 2.6156936580694473 \cdot 10^{+78}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a1}{\frac{b1}{a2}}}{b2}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;b1 \cdot b2 \le -9.384563571355019 \cdot 10^{+255}:\\
\;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\

\mathbf{elif}\;b1 \cdot b2 \le -1.0490423713698057 \cdot 10^{-109}:\\
\;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\

\mathbf{elif}\;b1 \cdot b2 \le 5.934410328828728 \cdot 10^{-246}:\\
\;\;\;\;\frac{a2 \cdot \frac{a1}{b1}}{b2}\\

\mathbf{elif}\;b1 \cdot b2 \le 2.6156936580694473 \cdot 10^{+78}:\\
\;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\

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

\end{array}

double f(double a1, double a2, double b1, double b2) {
        double r20680414 = a1;
        double r20680415 = a2;
        double r20680416 = r20680414 * r20680415;
        double r20680417 = b1;
        double r20680418 = b2;
        double r20680419 = r20680417 * r20680418;
        double r20680420 = r20680416 / r20680419;
        return r20680420;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r20680421 = b1;
        double r20680422 = b2;
        double r20680423 = r20680421 * r20680422;
        double r20680424 = -9.384563571355019e+255;
        bool r20680425 = r20680423 <= r20680424;
        double r20680426 = a1;
        double r20680427 = r20680426 / r20680421;
        double r20680428 = a2;
        double r20680429 = r20680428 / r20680422;
        double r20680430 = r20680427 * r20680429;
        double r20680431 = -1.0490423713698057e-109;
        bool r20680432 = r20680423 <= r20680431;
        double r20680433 = r20680423 / r20680428;
        double r20680434 = r20680426 / r20680433;
        double r20680435 = 5.934410328828728e-246;
        bool r20680436 = r20680423 <= r20680435;
        double r20680437 = r20680428 * r20680427;
        double r20680438 = r20680437 / r20680422;
        double r20680439 = 2.6156936580694473e+78;
        bool r20680440 = r20680423 <= r20680439;
        double r20680441 = r20680421 / r20680428;
        double r20680442 = r20680426 / r20680441;
        double r20680443 = r20680442 / r20680422;
        double r20680444 = r20680440 ? r20680434 : r20680443;
        double r20680445 = r20680436 ? r20680438 : r20680444;
        double r20680446 = r20680432 ? r20680434 : r20680445;
        double r20680447 = r20680425 ? r20680430 : r20680446;
        return r20680447;
}

Original	11.1
Target	11.0
Herbie	5.6

Derivation

Split input into 4 regimes
if (* b1 b2) < -9.384563571355019e+255
1. Initial program 17.9
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/r*8.4
  \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b1}}{b2}}\]
4. Using strategy rm
5. Applied associate-/l*3.7
  \[\leadsto \frac{\color{blue}{\frac{a1}{\frac{b1}{a2}}}}{b2}\]
6. Using strategy rm
7. Applied *-un-lft-identity3.7
  \[\leadsto \frac{\frac{a1}{\frac{b1}{a2}}}{\color{blue}{1 \cdot b2}}\]
8. Applied associate-/r/3.7
  \[\leadsto \frac{\color{blue}{\frac{a1}{b1} \cdot a2}}{1 \cdot b2}\]
9. Applied times-frac2.9
  \[\leadsto \color{blue}{\frac{\frac{a1}{b1}}{1} \cdot \frac{a2}{b2}}\]
10. Simplified2.9
  \[\leadsto \color{blue}{\frac{a1}{b1}} \cdot \frac{a2}{b2}\]
if -9.384563571355019e+255 < (* b1 b2) < -1.0490423713698057e-109 or 5.934410328828728e-246 < (* b1 b2) < 2.6156936580694473e+78
1. Initial program 4.8
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/l*4.1
  \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]
if -1.0490423713698057e-109 < (* b1 b2) < 5.934410328828728e-246
1. Initial program 25.8
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/r*15.0
  \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b1}}{b2}}\]
4. Using strategy rm
5. Applied associate-/l*11.0
  \[\leadsto \frac{\color{blue}{\frac{a1}{\frac{b1}{a2}}}}{b2}\]
6. Using strategy rm
7. Applied associate-/r/9.8
  \[\leadsto \frac{\color{blue}{\frac{a1}{b1} \cdot a2}}{b2}\]
if 2.6156936580694473e+78 < (* b1 b2)
1. Initial program 11.4
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/r*8.5
  \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b1}}{b2}}\]
4. Using strategy rm
5. Applied associate-/l*6.9
  \[\leadsto \frac{\color{blue}{\frac{a1}{\frac{b1}{a2}}}}{b2}\]
Recombined 4 regimes into one program.
Final simplification5.6
\[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -9.384563571355019 \cdot 10^{+255}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le -1.0490423713698057 \cdot 10^{-109}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \le 5.934410328828728 \cdot 10^{-246}:\\ \;\;\;\;\frac{a2 \cdot \frac{a1}{b1}}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le 2.6156936580694473 \cdot 10^{+78}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a1}{\frac{b1}{a2}}}{b2}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if (* b1 b2) < -9.384563571355019e+255`

`if -9.384563571355019e+255 < (* b1 b2) < -1.0490423713698057e-109 or 5.934410328828728e-246 < (* b1 b2) < 2.6156936580694473e+78`

`if -1.0490423713698057e-109 < (* b1 b2) < 5.934410328828728e-246`

`if 2.6156936580694473e+78 < (* b1 b2)`

Reproduce

In
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