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

↓

\[\begin{array}{l} \mathbf{if}\;a1 \cdot a2 \le -2.12735229765193038 \cdot 10^{182}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \mathbf{elif}\;a1 \cdot a2 \le -1.0024754663520561 \cdot 10^{-263}:\\ \;\;\;\;\left(a1 \cdot a2\right) \cdot \frac{\frac{1}{b1}}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le 2.0414339865440529 \cdot 10^{-241}:\\ \;\;\;\;\frac{a1}{b2 \cdot \frac{b1}{a2}}\\ \mathbf{elif}\;a1 \cdot a2 \le 5.0133543486933235 \cdot 10^{213}:\\ \;\;\;\;\left(a1 \cdot a2\right) \cdot \frac{\frac{1}{b1}}{b2}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;a1 \cdot a2 \le -2.12735229765193038 \cdot 10^{182}:\\
\;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\

\mathbf{elif}\;a1 \cdot a2 \le -1.0024754663520561 \cdot 10^{-263}:\\
\;\;\;\;\left(a1 \cdot a2\right) \cdot \frac{\frac{1}{b1}}{b2}\\

\mathbf{elif}\;a1 \cdot a2 \le 2.0414339865440529 \cdot 10^{-241}:\\
\;\;\;\;\frac{a1}{b2 \cdot \frac{b1}{a2}}\\

\mathbf{elif}\;a1 \cdot a2 \le 5.0133543486933235 \cdot 10^{213}:\\
\;\;\;\;\left(a1 \cdot a2\right) \cdot \frac{\frac{1}{b1}}{b2}\\

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

\end{array}

double f(double a1, double a2, double b1, double b2) {
        double r197933 = a1;
        double r197934 = a2;
        double r197935 = r197933 * r197934;
        double r197936 = b1;
        double r197937 = b2;
        double r197938 = r197936 * r197937;
        double r197939 = r197935 / r197938;
        return r197939;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r197940 = a1;
        double r197941 = a2;
        double r197942 = r197940 * r197941;
        double r197943 = -2.1273522976519304e+182;
        bool r197944 = r197942 <= r197943;
        double r197945 = b2;
        double r197946 = r197941 / r197945;
        double r197947 = b1;
        double r197948 = r197946 / r197947;
        double r197949 = r197940 * r197948;
        double r197950 = -1.002475466352056e-263;
        bool r197951 = r197942 <= r197950;
        double r197952 = 1.0;
        double r197953 = r197952 / r197947;
        double r197954 = r197953 / r197945;
        double r197955 = r197942 * r197954;
        double r197956 = 2.041433986544053e-241;
        bool r197957 = r197942 <= r197956;
        double r197958 = r197947 / r197941;
        double r197959 = r197945 * r197958;
        double r197960 = r197940 / r197959;
        double r197961 = 5.0133543486933235e+213;
        bool r197962 = r197942 <= r197961;
        double r197963 = r197962 ? r197955 : r197949;
        double r197964 = r197957 ? r197960 : r197963;
        double r197965 = r197951 ? r197955 : r197964;
        double r197966 = r197944 ? r197949 : r197965;
        return r197966;
}

Original	11.4
Target	11.0
Herbie	5.2

Derivation

Split input into 3 regimes
if (* a1 a2) < -2.1273522976519304e+182 or 5.0133543486933235e+213 < (* a1 a2)
1. Initial program 33.5
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied times-frac10.6
  \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
4. Using strategy rm
5. Applied div-inv10.6
  \[\leadsto \color{blue}{\left(a1 \cdot \frac{1}{b1}\right)} \cdot \frac{a2}{b2}\]
6. Applied associate-*l*9.7
  \[\leadsto \color{blue}{a1 \cdot \left(\frac{1}{b1} \cdot \frac{a2}{b2}\right)}\]
7. Simplified9.6
  \[\leadsto a1 \cdot \color{blue}{\frac{\frac{a2}{b2}}{b1}}\]
if -2.1273522976519304e+182 < (* a1 a2) < -1.002475466352056e-263 or 2.041433986544053e-241 < (* a1 a2) < 5.0133543486933235e+213
1. Initial program 5.0
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied div-inv5.3
  \[\leadsto \color{blue}{\left(a1 \cdot a2\right) \cdot \frac{1}{b1 \cdot b2}}\]
4. Using strategy rm
5. Applied associate-/r*5.0
  \[\leadsto \left(a1 \cdot a2\right) \cdot \color{blue}{\frac{\frac{1}{b1}}{b2}}\]
if -1.002475466352056e-263 < (* a1 a2) < 2.041433986544053e-241
1. Initial program 17.1
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/l*7.4
  \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]
4. Simplified3.2
  \[\leadsto \frac{a1}{\color{blue}{b2 \cdot \frac{b1}{a2}}}\]
Recombined 3 regimes into one program.
Final simplification5.2
\[\leadsto \begin{array}{l} \mathbf{if}\;a1 \cdot a2 \le -2.12735229765193038 \cdot 10^{182}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \mathbf{elif}\;a1 \cdot a2 \le -1.0024754663520561 \cdot 10^{-263}:\\ \;\;\;\;\left(a1 \cdot a2\right) \cdot \frac{\frac{1}{b1}}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le 2.0414339865440529 \cdot 10^{-241}:\\ \;\;\;\;\frac{a1}{b2 \cdot \frac{b1}{a2}}\\ \mathbf{elif}\;a1 \cdot a2 \le 5.0133543486933235 \cdot 10^{213}:\\ \;\;\;\;\left(a1 \cdot a2\right) \cdot \frac{\frac{1}{b1}}{b2}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b2}}{b1}\\ \end{array}\]

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

Error

Try it out

Target

Derivation

`if (* a1 a2) < -2.1273522976519304e+182 or 5.0133543486933235e+213 < (* a1 a2)`

`if -2.1273522976519304e+182 < (* a1 a2) < -1.002475466352056e-263 or 2.041433986544053e-241 < (* a1 a2) < 5.0133543486933235e+213`

`if -1.002475466352056e-263 < (* a1 a2) < 2.041433986544053e-241`

Reproduce

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