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

↓

\[\begin{array}{l} \mathbf{if}\;a1 \cdot a2 \le -4.103031774251489582409915525348219347136 \cdot 10^{241}:\\ \;\;\;\;\frac{a1}{\frac{b1}{\frac{a2}{b2}}}\\ \mathbf{elif}\;a1 \cdot a2 \le -1.940973758331948228787265542772159085713 \cdot 10^{-276}:\\ \;\;\;\;\frac{1}{\frac{b1 \cdot b2}{a1 \cdot a2}}\\ \mathbf{elif}\;a1 \cdot a2 \le 2.471768101920643639195818820332840731202 \cdot 10^{-213}:\\ \;\;\;\;\frac{a1}{\frac{b1}{\frac{a2}{b2}}}\\ \mathbf{elif}\;a1 \cdot a2 \le 1.222017195284376264633152553789587622996 \cdot 10^{102}:\\ \;\;\;\;\frac{1}{\frac{b1 \cdot b2}{a1 \cdot a2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;a1 \cdot a2 \le -4.103031774251489582409915525348219347136 \cdot 10^{241}:\\
\;\;\;\;\frac{a1}{\frac{b1}{\frac{a2}{b2}}}\\

\mathbf{elif}\;a1 \cdot a2 \le -1.940973758331948228787265542772159085713 \cdot 10^{-276}:\\
\;\;\;\;\frac{1}{\frac{b1 \cdot b2}{a1 \cdot a2}}\\

\mathbf{elif}\;a1 \cdot a2 \le 2.471768101920643639195818820332840731202 \cdot 10^{-213}:\\
\;\;\;\;\frac{a1}{\frac{b1}{\frac{a2}{b2}}}\\

\mathbf{elif}\;a1 \cdot a2 \le 1.222017195284376264633152553789587622996 \cdot 10^{102}:\\
\;\;\;\;\frac{1}{\frac{b1 \cdot b2}{a1 \cdot a2}}\\

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

\end{array}

double f(double a1, double a2, double b1, double b2) {
        double r115555 = a1;
        double r115556 = a2;
        double r115557 = r115555 * r115556;
        double r115558 = b1;
        double r115559 = b2;
        double r115560 = r115558 * r115559;
        double r115561 = r115557 / r115560;
        return r115561;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r115562 = a1;
        double r115563 = a2;
        double r115564 = r115562 * r115563;
        double r115565 = -4.1030317742514896e+241;
        bool r115566 = r115564 <= r115565;
        double r115567 = b1;
        double r115568 = b2;
        double r115569 = r115563 / r115568;
        double r115570 = r115567 / r115569;
        double r115571 = r115562 / r115570;
        double r115572 = -1.9409737583319482e-276;
        bool r115573 = r115564 <= r115572;
        double r115574 = 1.0;
        double r115575 = r115567 * r115568;
        double r115576 = r115575 / r115564;
        double r115577 = r115574 / r115576;
        double r115578 = 2.4717681019206436e-213;
        bool r115579 = r115564 <= r115578;
        double r115580 = 1.2220171952843763e+102;
        bool r115581 = r115564 <= r115580;
        double r115582 = r115562 / r115567;
        double r115583 = r115582 * r115569;
        double r115584 = r115581 ? r115577 : r115583;
        double r115585 = r115579 ? r115571 : r115584;
        double r115586 = r115573 ? r115577 : r115585;
        double r115587 = r115566 ? r115571 : r115586;
        return r115587;
}

Original	11.5
Target	11.8
Herbie	6.1

Derivation

Split input into 3 regimes
if (* a1 a2) < -4.1030317742514896e+241 or -1.9409737583319482e-276 < (* a1 a2) < 2.4717681019206436e-213
1. Initial program 21.8
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied clear-num22.0
  \[\leadsto \color{blue}{\frac{1}{\frac{b1 \cdot b2}{a1 \cdot a2}}}\]
4. Using strategy rm
5. Applied *-un-lft-identity22.0
  \[\leadsto \frac{1}{\color{blue}{1 \cdot \frac{b1 \cdot b2}{a1 \cdot a2}}}\]
6. Applied add-cube-cbrt22.0
  \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{1 \cdot \frac{b1 \cdot b2}{a1 \cdot a2}}\]
7. Applied times-frac22.0
  \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{1} \cdot \frac{\sqrt[3]{1}}{\frac{b1 \cdot b2}{a1 \cdot a2}}}\]
8. Simplified22.0
  \[\leadsto \color{blue}{1} \cdot \frac{\sqrt[3]{1}}{\frac{b1 \cdot b2}{a1 \cdot a2}}\]
9. Simplified21.8
  \[\leadsto 1 \cdot \color{blue}{\left(\frac{a1 \cdot a2}{b1 \cdot b2} \cdot 1\right)}\]
10. Using strategy rm
11. Applied associate-/l*9.7
  \[\leadsto 1 \cdot \left(\color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}} \cdot 1\right)\]
12. Using strategy rm
13. Applied associate-/l*4.8
  \[\leadsto 1 \cdot \left(\frac{a1}{\color{blue}{\frac{b1}{\frac{a2}{b2}}}} \cdot 1\right)\]
if -4.1030317742514896e+241 < (* a1 a2) < -1.9409737583319482e-276 or 2.4717681019206436e-213 < (* a1 a2) < 1.2220171952843763e+102
1. Initial program 4.7
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied clear-num5.0
  \[\leadsto \color{blue}{\frac{1}{\frac{b1 \cdot b2}{a1 \cdot a2}}}\]
if 1.2220171952843763e+102 < (* a1 a2)
1. Initial program 21.8
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied times-frac14.3
  \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
Recombined 3 regimes into one program.
Final simplification6.1
\[\leadsto \begin{array}{l} \mathbf{if}\;a1 \cdot a2 \le -4.103031774251489582409915525348219347136 \cdot 10^{241}:\\ \;\;\;\;\frac{a1}{\frac{b1}{\frac{a2}{b2}}}\\ \mathbf{elif}\;a1 \cdot a2 \le -1.940973758331948228787265542772159085713 \cdot 10^{-276}:\\ \;\;\;\;\frac{1}{\frac{b1 \cdot b2}{a1 \cdot a2}}\\ \mathbf{elif}\;a1 \cdot a2 \le 2.471768101920643639195818820332840731202 \cdot 10^{-213}:\\ \;\;\;\;\frac{a1}{\frac{b1}{\frac{a2}{b2}}}\\ \mathbf{elif}\;a1 \cdot a2 \le 1.222017195284376264633152553789587622996 \cdot 10^{102}:\\ \;\;\;\;\frac{1}{\frac{b1 \cdot b2}{a1 \cdot a2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if (* a1 a2) < -4.1030317742514896e+241 or -1.9409737583319482e-276 < (* a1 a2) < 2.4717681019206436e-213`

`if -4.1030317742514896e+241 < (* a1 a2) < -1.9409737583319482e-276 or 2.4717681019206436e-213 < (* a1 a2) < 1.2220171952843763e+102`

`if 1.2220171952843763e+102 < (* a1 a2)`

Reproduce

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Out