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

↓

\[\begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -3.2418970626461063 \cdot 10^{+149}:\\ \;\;\;\;\frac{\frac{1}{b1}}{\frac{\frac{b2}{a1}}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \le -1.0084599578011689 \cdot 10^{-263}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \le 3.019673003289364 \cdot 10^{-116}:\\ \;\;\;\;\frac{\frac{a2}{\frac{b1}{a1}}}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le 2.5857146802439288 \cdot 10^{+182}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{b1}}{\frac{\frac{b2}{a1}}{a2}}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;b1 \cdot b2 \le -3.2418970626461063 \cdot 10^{+149}:\\
\;\;\;\;\frac{\frac{1}{b1}}{\frac{\frac{b2}{a1}}{a2}}\\

\mathbf{elif}\;b1 \cdot b2 \le -1.0084599578011689 \cdot 10^{-263}:\\
\;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\

\mathbf{elif}\;b1 \cdot b2 \le 3.019673003289364 \cdot 10^{-116}:\\
\;\;\;\;\frac{\frac{a2}{\frac{b1}{a1}}}{b2}\\

\mathbf{elif}\;b1 \cdot b2 \le 2.5857146802439288 \cdot 10^{+182}:\\
\;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{1}{b1}}{\frac{\frac{b2}{a1}}{a2}}\\

\end{array}

double f(double a1, double a2, double b1, double b2) {
        double r5309537 = a1;
        double r5309538 = a2;
        double r5309539 = r5309537 * r5309538;
        double r5309540 = b1;
        double r5309541 = b2;
        double r5309542 = r5309540 * r5309541;
        double r5309543 = r5309539 / r5309542;
        return r5309543;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r5309544 = b1;
        double r5309545 = b2;
        double r5309546 = r5309544 * r5309545;
        double r5309547 = -3.2418970626461063e+149;
        bool r5309548 = r5309546 <= r5309547;
        double r5309549 = 1.0;
        double r5309550 = r5309549 / r5309544;
        double r5309551 = a1;
        double r5309552 = r5309545 / r5309551;
        double r5309553 = a2;
        double r5309554 = r5309552 / r5309553;
        double r5309555 = r5309550 / r5309554;
        double r5309556 = -1.0084599578011689e-263;
        bool r5309557 = r5309546 <= r5309556;
        double r5309558 = r5309546 / r5309553;
        double r5309559 = r5309551 / r5309558;
        double r5309560 = 3.019673003289364e-116;
        bool r5309561 = r5309546 <= r5309560;
        double r5309562 = r5309544 / r5309551;
        double r5309563 = r5309553 / r5309562;
        double r5309564 = r5309563 / r5309545;
        double r5309565 = 2.5857146802439288e+182;
        bool r5309566 = r5309546 <= r5309565;
        double r5309567 = r5309566 ? r5309559 : r5309555;
        double r5309568 = r5309561 ? r5309564 : r5309567;
        double r5309569 = r5309557 ? r5309559 : r5309568;
        double r5309570 = r5309548 ? r5309555 : r5309569;
        return r5309570;
}

Original	11.1
Target	10.9
Herbie	5.4

Derivation

Split input into 3 regimes
if (* b1 b2) < -3.2418970626461063e+149 or 2.5857146802439288e+182 < (* b1 b2)
1. Initial program 14.6
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/r*7.9
  \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b1}}{b2}}\]
4. Using strategy rm
5. Applied *-un-lft-identity7.9
  \[\leadsto \frac{\frac{a1 \cdot a2}{b1}}{\color{blue}{1 \cdot b2}}\]
6. Applied associate-/r*7.9
  \[\leadsto \color{blue}{\frac{\frac{\frac{a1 \cdot a2}{b1}}{1}}{b2}}\]
7. Simplified5.5
  \[\leadsto \frac{\color{blue}{\frac{a2}{\frac{b1}{a1}}}}{b2}\]
8. Using strategy rm
9. Applied div-inv5.5
  \[\leadsto \frac{\frac{a2}{\color{blue}{b1 \cdot \frac{1}{a1}}}}{b2}\]
10. Applied *-un-lft-identity5.5
  \[\leadsto \frac{\frac{\color{blue}{1 \cdot a2}}{b1 \cdot \frac{1}{a1}}}{b2}\]
11. Applied times-frac7.9
  \[\leadsto \frac{\color{blue}{\frac{1}{b1} \cdot \frac{a2}{\frac{1}{a1}}}}{b2}\]
12. Applied associate-/l*8.2
  \[\leadsto \color{blue}{\frac{\frac{1}{b1}}{\frac{b2}{\frac{a2}{\frac{1}{a1}}}}}\]
13. Simplified5.5
  \[\leadsto \frac{\frac{1}{b1}}{\color{blue}{\frac{\frac{b2}{a1}}{a2}}}\]
if -3.2418970626461063e+149 < (* b1 b2) < -1.0084599578011689e-263 or 3.019673003289364e-116 < (* b1 b2) < 2.5857146802439288e+182
1. Initial program 3.8
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/l*3.8
  \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]
if -1.0084599578011689e-263 < (* b1 b2) < 3.019673003289364e-116
1. Initial program 28.0
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/r*15.4
  \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b1}}{b2}}\]
4. Using strategy rm
5. Applied *-un-lft-identity15.4
  \[\leadsto \frac{\frac{a1 \cdot a2}{b1}}{\color{blue}{1 \cdot b2}}\]
6. Applied associate-/r*15.4
  \[\leadsto \color{blue}{\frac{\frac{\frac{a1 \cdot a2}{b1}}{1}}{b2}}\]
7. Simplified10.0
  \[\leadsto \frac{\color{blue}{\frac{a2}{\frac{b1}{a1}}}}{b2}\]
Recombined 3 regimes into one program.
Final simplification5.4
\[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -3.2418970626461063 \cdot 10^{+149}:\\ \;\;\;\;\frac{\frac{1}{b1}}{\frac{\frac{b2}{a1}}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \le -1.0084599578011689 \cdot 10^{-263}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \le 3.019673003289364 \cdot 10^{-116}:\\ \;\;\;\;\frac{\frac{a2}{\frac{b1}{a1}}}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le 2.5857146802439288 \cdot 10^{+182}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{b1}}{\frac{\frac{b2}{a1}}{a2}}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if (* b1 b2) < -3.2418970626461063e+149 or 2.5857146802439288e+182 < (* b1 b2)`

`if -3.2418970626461063e+149 < (* b1 b2) < -1.0084599578011689e-263 or 3.019673003289364e-116 < (* b1 b2) < 2.5857146802439288e+182`

`if -1.0084599578011689e-263 < (* b1 b2) < 3.019673003289364e-116`

Reproduce

In
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