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

↓

\[\begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -2.32021152475378652 \cdot 10^{210}:\\ \;\;\;\;\left(\frac{a1}{b1} \cdot a2\right) \cdot \frac{1}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le -4.173350324846027 \cdot 10^{-151}:\\ \;\;\;\;a1 \cdot \frac{a2}{b2 \cdot b1}\\ \mathbf{elif}\;b1 \cdot b2 \le -0.0 \lor \neg \left(b1 \cdot b2 \le 7.6189236997402214 \cdot 10^{265}\right):\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{b1 \cdot b2}{a1 \cdot a2}}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;b1 \cdot b2 \le -2.32021152475378652 \cdot 10^{210}:\\
\;\;\;\;\left(\frac{a1}{b1} \cdot a2\right) \cdot \frac{1}{b2}\\

\mathbf{elif}\;b1 \cdot b2 \le -4.173350324846027 \cdot 10^{-151}:\\
\;\;\;\;a1 \cdot \frac{a2}{b2 \cdot b1}\\

\mathbf{elif}\;b1 \cdot b2 \le -0.0 \lor \neg \left(b1 \cdot b2 \le 7.6189236997402214 \cdot 10^{265}\right):\\
\;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\

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

\end{array}

double f(double a1, double a2, double b1, double b2) {
        double r129093 = a1;
        double r129094 = a2;
        double r129095 = r129093 * r129094;
        double r129096 = b1;
        double r129097 = b2;
        double r129098 = r129096 * r129097;
        double r129099 = r129095 / r129098;
        return r129099;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r129100 = b1;
        double r129101 = b2;
        double r129102 = r129100 * r129101;
        double r129103 = -2.3202115247537865e+210;
        bool r129104 = r129102 <= r129103;
        double r129105 = a1;
        double r129106 = r129105 / r129100;
        double r129107 = a2;
        double r129108 = r129106 * r129107;
        double r129109 = 1.0;
        double r129110 = r129109 / r129101;
        double r129111 = r129108 * r129110;
        double r129112 = -4.173350324846027e-151;
        bool r129113 = r129102 <= r129112;
        double r129114 = r129101 * r129100;
        double r129115 = r129107 / r129114;
        double r129116 = r129105 * r129115;
        double r129117 = -0.0;
        bool r129118 = r129102 <= r129117;
        double r129119 = 7.618923699740221e+265;
        bool r129120 = r129102 <= r129119;
        double r129121 = !r129120;
        bool r129122 = r129118 || r129121;
        double r129123 = r129107 / r129101;
        double r129124 = r129106 * r129123;
        double r129125 = r129105 * r129107;
        double r129126 = r129102 / r129125;
        double r129127 = r129109 / r129126;
        double r129128 = r129122 ? r129124 : r129127;
        double r129129 = r129113 ? r129116 : r129128;
        double r129130 = r129104 ? r129111 : r129129;
        return r129130;
}

Original	10.7
Target	11.2
Herbie	5.5

Derivation

Split input into 4 regimes
if (* b1 b2) < -2.3202115247537865e+210
1. Initial program 15.4
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied div-inv15.4
  \[\leadsto \color{blue}{\left(a1 \cdot a2\right) \cdot \frac{1}{b1 \cdot b2}}\]
4. Using strategy rm
5. Applied *-un-lft-identity15.4
  \[\leadsto \left(a1 \cdot a2\right) \cdot \frac{\color{blue}{1 \cdot 1}}{b1 \cdot b2}\]
6. Applied times-frac14.8
  \[\leadsto \left(a1 \cdot a2\right) \cdot \color{blue}{\left(\frac{1}{b1} \cdot \frac{1}{b2}\right)}\]
7. Applied associate-*r*7.7
  \[\leadsto \color{blue}{\left(\left(a1 \cdot a2\right) \cdot \frac{1}{b1}\right) \cdot \frac{1}{b2}}\]
8. Simplified4.1
  \[\leadsto \color{blue}{\left(\frac{a1}{b1} \cdot a2\right)} \cdot \frac{1}{b2}\]
if -2.3202115247537865e+210 < (* b1 b2) < -4.173350324846027e-151
1. Initial program 3.7
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied div-inv3.7
  \[\leadsto \color{blue}{\left(a1 \cdot a2\right) \cdot \frac{1}{b1 \cdot b2}}\]
4. Using strategy rm
5. Applied div-inv3.7
  \[\leadsto \left(a1 \cdot a2\right) \cdot \color{blue}{\left(1 \cdot \frac{1}{b1 \cdot b2}\right)}\]
6. Simplified3.7
  \[\leadsto \left(a1 \cdot a2\right) \cdot \left(1 \cdot \color{blue}{\frac{\frac{1}{b1}}{b2}}\right)\]
7. Using strategy rm
8. Applied associate-*l*4.3
  \[\leadsto \color{blue}{a1 \cdot \left(a2 \cdot \left(1 \cdot \frac{\frac{1}{b1}}{b2}\right)\right)}\]
9. Simplified4.3
  \[\leadsto a1 \cdot \color{blue}{\frac{a2}{b2 \cdot b1}}\]
if -4.173350324846027e-151 < (* b1 b2) < -0.0 or 7.618923699740221e+265 < (* b1 b2)
1. Initial program 25.9
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied times-frac7.4
  \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
if -0.0 < (* b1 b2) < 7.618923699740221e+265
1. Initial program 5.6
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied clear-num5.9
  \[\leadsto \color{blue}{\frac{1}{\frac{b1 \cdot b2}{a1 \cdot a2}}}\]
Recombined 4 regimes into one program.
Final simplification5.5
\[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -2.32021152475378652 \cdot 10^{210}:\\ \;\;\;\;\left(\frac{a1}{b1} \cdot a2\right) \cdot \frac{1}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le -4.173350324846027 \cdot 10^{-151}:\\ \;\;\;\;a1 \cdot \frac{a2}{b2 \cdot b1}\\ \mathbf{elif}\;b1 \cdot b2 \le -0.0 \lor \neg \left(b1 \cdot b2 \le 7.6189236997402214 \cdot 10^{265}\right):\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{b1 \cdot b2}{a1 \cdot a2}}\\ \end{array}\]

Falling back on racket egraph because egg-herbie package not installed (more)

Error

Try it out

Target

Derivation

`if (* b1 b2) < -2.3202115247537865e+210`

`if -2.3202115247537865e+210 < (* b1 b2) < -4.173350324846027e-151`

`if -4.173350324846027e-151 < (* b1 b2) < -0.0 or 7.618923699740221e+265 < (* b1 b2)`

`if -0.0 < (* b1 b2) < 7.618923699740221e+265`

Reproduce

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