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

↓

\[\begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -7.49674299200361345 \cdot 10^{288}:\\ \;\;\;\;\frac{\frac{a1}{b2}}{\frac{b1}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \le -1.5748794443415678 \cdot 10^{-93}:\\ \;\;\;\;\frac{a1}{b2 \cdot b1} \cdot a2\\ \mathbf{elif}\;b1 \cdot b2 \le 7.07595946555220674 \cdot 10^{-255} \lor \neg \left(b1 \cdot b2 \le 2.41792096653949384 \cdot 10^{269}\right):\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;b1 \cdot b2 \le -7.49674299200361345 \cdot 10^{288}:\\
\;\;\;\;\frac{\frac{a1}{b2}}{\frac{b1}{a2}}\\

\mathbf{elif}\;b1 \cdot b2 \le -1.5748794443415678 \cdot 10^{-93}:\\
\;\;\;\;\frac{a1}{b2 \cdot b1} \cdot a2\\

\mathbf{elif}\;b1 \cdot b2 \le 7.07595946555220674 \cdot 10^{-255} \lor \neg \left(b1 \cdot b2 \le 2.41792096653949384 \cdot 10^{269}\right):\\
\;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\

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

\end{array}

double f(double a1, double a2, double b1, double b2) {
        double r133936 = a1;
        double r133937 = a2;
        double r133938 = r133936 * r133937;
        double r133939 = b1;
        double r133940 = b2;
        double r133941 = r133939 * r133940;
        double r133942 = r133938 / r133941;
        return r133942;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r133943 = b1;
        double r133944 = b2;
        double r133945 = r133943 * r133944;
        double r133946 = -7.496742992003613e+288;
        bool r133947 = r133945 <= r133946;
        double r133948 = a1;
        double r133949 = r133948 / r133944;
        double r133950 = a2;
        double r133951 = r133943 / r133950;
        double r133952 = r133949 / r133951;
        double r133953 = -1.5748794443415678e-93;
        bool r133954 = r133945 <= r133953;
        double r133955 = r133944 * r133943;
        double r133956 = r133948 / r133955;
        double r133957 = r133956 * r133950;
        double r133958 = 7.075959465552207e-255;
        bool r133959 = r133945 <= r133958;
        double r133960 = 2.4179209665394938e+269;
        bool r133961 = r133945 <= r133960;
        double r133962 = !r133961;
        bool r133963 = r133959 || r133962;
        double r133964 = r133948 / r133943;
        double r133965 = r133950 / r133944;
        double r133966 = r133964 * r133965;
        double r133967 = r133950 / r133945;
        double r133968 = r133948 * r133967;
        double r133969 = r133963 ? r133966 : r133968;
        double r133970 = r133954 ? r133957 : r133969;
        double r133971 = r133947 ? r133952 : r133970;
        return r133971;
}

Original	11.1
Target	11.6
Herbie	5.8

Derivation

Split input into 4 regimes
if (* b1 b2) < -7.496742992003613e+288
1. Initial program 18.6
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/l*18.4
  \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]
4. Simplified6.9
  \[\leadsto \frac{a1}{\color{blue}{b2 \cdot \frac{b1}{a2}}}\]
5. Using strategy rm
6. Applied associate-/r*3.1
  \[\leadsto \color{blue}{\frac{\frac{a1}{b2}}{\frac{b1}{a2}}}\]
if -7.496742992003613e+288 < (* b1 b2) < -1.5748794443415678e-93
1. Initial program 4.8
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/l*4.2
  \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]
4. Simplified11.0
  \[\leadsto \frac{a1}{\color{blue}{b2 \cdot \frac{b1}{a2}}}\]
5. Using strategy rm
6. Applied associate-*r/4.2
  \[\leadsto \frac{a1}{\color{blue}{\frac{b2 \cdot b1}{a2}}}\]
7. Applied associate-/r/4.1
  \[\leadsto \color{blue}{\frac{a1}{b2 \cdot b1} \cdot a2}\]
if -1.5748794443415678e-93 < (* b1 b2) < 7.075959465552207e-255 or 2.4179209665394938e+269 < (* b1 b2)
1. Initial program 23.4
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied times-frac8.5
  \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
if 7.075959465552207e-255 < (* b1 b2) < 2.4179209665394938e+269
1. Initial program 5.0
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/l*5.6
  \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]
4. Simplified11.5
  \[\leadsto \frac{a1}{\color{blue}{b2 \cdot \frac{b1}{a2}}}\]
5. Using strategy rm
6. Applied associate-*r/5.6
  \[\leadsto \frac{a1}{\color{blue}{\frac{b2 \cdot b1}{a2}}}\]
7. Simplified5.6
  \[\leadsto \frac{a1}{\frac{\color{blue}{b1 \cdot b2}}{a2}}\]
8. Using strategy rm
9. Applied div-inv5.9
  \[\leadsto \color{blue}{a1 \cdot \frac{1}{\frac{b1 \cdot b2}{a2}}}\]
10. Simplified5.7
  \[\leadsto a1 \cdot \color{blue}{\frac{a2}{b1 \cdot b2}}\]
Recombined 4 regimes into one program.
Final simplification5.8
\[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -7.49674299200361345 \cdot 10^{288}:\\ \;\;\;\;\frac{\frac{a1}{b2}}{\frac{b1}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \le -1.5748794443415678 \cdot 10^{-93}:\\ \;\;\;\;\frac{a1}{b2 \cdot b1} \cdot a2\\ \mathbf{elif}\;b1 \cdot b2 \le 7.07595946555220674 \cdot 10^{-255} \lor \neg \left(b1 \cdot b2 \le 2.41792096653949384 \cdot 10^{269}\right):\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \end{array}\]

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

Error

Try it out

Target

Derivation

`if (* b1 b2) < -7.496742992003613e+288`

`if -7.496742992003613e+288 < (* b1 b2) < -1.5748794443415678e-93`

`if -1.5748794443415678e-93 < (* b1 b2) < 7.075959465552207e-255 or 2.4179209665394938e+269 < (* b1 b2)`

`if 7.075959465552207e-255 < (* b1 b2) < 2.4179209665394938e+269`

Reproduce

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