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

↓

\[\begin{array}{l} \mathbf{if}\;b2 \cdot b1 \le -5.027198331468452971083277390987079564256 \cdot 10^{271}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{elif}\;b2 \cdot b1 \le -1.708279358278811067826228393370497973053 \cdot 10^{-240}:\\ \;\;\;\;\frac{a1}{b2 \cdot b1} \cdot a2\\ \mathbf{elif}\;b2 \cdot b1 \le 2.491183802213925616452581733594161045108 \cdot 10^{-239}:\\ \;\;\;\;\frac{1}{b1} \cdot \frac{a1}{\frac{b2}{a2}}\\ \mathbf{elif}\;b2 \cdot b1 \le 3.274003468956291087635927220582233224264 \cdot 10^{201}:\\ \;\;\;\;\frac{a1}{b2 \cdot b1} \cdot a2\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;b2 \cdot b1 \le -5.027198331468452971083277390987079564256 \cdot 10^{271}:\\
\;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\

\mathbf{elif}\;b2 \cdot b1 \le -1.708279358278811067826228393370497973053 \cdot 10^{-240}:\\
\;\;\;\;\frac{a1}{b2 \cdot b1} \cdot a2\\

\mathbf{elif}\;b2 \cdot b1 \le 2.491183802213925616452581733594161045108 \cdot 10^{-239}:\\
\;\;\;\;\frac{1}{b1} \cdot \frac{a1}{\frac{b2}{a2}}\\

\mathbf{elif}\;b2 \cdot b1 \le 3.274003468956291087635927220582233224264 \cdot 10^{201}:\\
\;\;\;\;\frac{a1}{b2 \cdot b1} \cdot a2\\

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

\end{array}

double f(double a1, double a2, double b1, double b2) {
        double r3822286 = a1;
        double r3822287 = a2;
        double r3822288 = r3822286 * r3822287;
        double r3822289 = b1;
        double r3822290 = b2;
        double r3822291 = r3822289 * r3822290;
        double r3822292 = r3822288 / r3822291;
        return r3822292;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r3822293 = b2;
        double r3822294 = b1;
        double r3822295 = r3822293 * r3822294;
        double r3822296 = -5.027198331468453e+271;
        bool r3822297 = r3822295 <= r3822296;
        double r3822298 = a2;
        double r3822299 = r3822298 / r3822293;
        double r3822300 = a1;
        double r3822301 = r3822300 / r3822294;
        double r3822302 = r3822299 * r3822301;
        double r3822303 = -1.708279358278811e-240;
        bool r3822304 = r3822295 <= r3822303;
        double r3822305 = r3822300 / r3822295;
        double r3822306 = r3822305 * r3822298;
        double r3822307 = 2.4911838022139256e-239;
        bool r3822308 = r3822295 <= r3822307;
        double r3822309 = 1.0;
        double r3822310 = r3822309 / r3822294;
        double r3822311 = r3822293 / r3822298;
        double r3822312 = r3822300 / r3822311;
        double r3822313 = r3822310 * r3822312;
        double r3822314 = 3.274003468956291e+201;
        bool r3822315 = r3822295 <= r3822314;
        double r3822316 = r3822315 ? r3822306 : r3822302;
        double r3822317 = r3822308 ? r3822313 : r3822316;
        double r3822318 = r3822304 ? r3822306 : r3822317;
        double r3822319 = r3822297 ? r3822302 : r3822318;
        return r3822319;
}

Original	11.5
Target	11.2
Herbie	5.0

Derivation

Split input into 3 regimes
if (* b1 b2) < -5.027198331468453e+271 or 3.274003468956291e+201 < (* b1 b2)
1. Initial program 17.4
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied times-frac3.7
  \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
if -5.027198331468453e+271 < (* b1 b2) < -1.708279358278811e-240 or 2.4911838022139256e-239 < (* b1 b2) < 3.274003468956291e+201
1. Initial program 4.9
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/l*4.6
  \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]
4. Using strategy rm
5. Applied associate-/r/4.9
  \[\leadsto \color{blue}{\frac{a1}{b1 \cdot b2} \cdot a2}\]
if -1.708279358278811e-240 < (* b1 b2) < 2.4911838022139256e-239
1. Initial program 40.3
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/l*39.4
  \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]
4. Using strategy rm
5. Applied *-un-lft-identity39.4
  \[\leadsto \frac{a1}{\frac{b1 \cdot b2}{\color{blue}{1 \cdot a2}}}\]
6. Applied times-frac17.8
  \[\leadsto \frac{a1}{\color{blue}{\frac{b1}{1} \cdot \frac{b2}{a2}}}\]
7. Applied *-un-lft-identity17.8
  \[\leadsto \frac{\color{blue}{1 \cdot a1}}{\frac{b1}{1} \cdot \frac{b2}{a2}}\]
8. Applied times-frac8.9
  \[\leadsto \color{blue}{\frac{1}{\frac{b1}{1}} \cdot \frac{a1}{\frac{b2}{a2}}}\]
9. Simplified8.9
  \[\leadsto \color{blue}{\frac{1}{b1}} \cdot \frac{a1}{\frac{b2}{a2}}\]
Recombined 3 regimes into one program.
Final simplification5.0
\[\leadsto \begin{array}{l} \mathbf{if}\;b2 \cdot b1 \le -5.027198331468452971083277390987079564256 \cdot 10^{271}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \mathbf{elif}\;b2 \cdot b1 \le -1.708279358278811067826228393370497973053 \cdot 10^{-240}:\\ \;\;\;\;\frac{a1}{b2 \cdot b1} \cdot a2\\ \mathbf{elif}\;b2 \cdot b1 \le 2.491183802213925616452581733594161045108 \cdot 10^{-239}:\\ \;\;\;\;\frac{1}{b1} \cdot \frac{a1}{\frac{b2}{a2}}\\ \mathbf{elif}\;b2 \cdot b1 \le 3.274003468956291087635927220582233224264 \cdot 10^{201}:\\ \;\;\;\;\frac{a1}{b2 \cdot b1} \cdot a2\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if (* b1 b2) < -5.027198331468453e+271 or 3.274003468956291e+201 < (* b1 b2)`

`if -5.027198331468453e+271 < (* b1 b2) < -1.708279358278811e-240 or 2.4911838022139256e-239 < (* b1 b2) < 3.274003468956291e+201`

`if -1.708279358278811e-240 < (* b1 b2) < 2.4911838022139256e-239`

Reproduce

In
Out