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

↓

\[\begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -9.384563571355019 \cdot 10^{+255}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le -1.0490423713698057 \cdot 10^{-109}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \le 5.934410328828728 \cdot 10^{-246}:\\ \;\;\;\;\frac{a2 \cdot \frac{a1}{b1}}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le 2.6156936580694473 \cdot 10^{+78}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a1}{\frac{b1}{a2}}}{b2}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;b1 \cdot b2 \le -9.384563571355019 \cdot 10^{+255}:\\
\;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\

\mathbf{elif}\;b1 \cdot b2 \le -1.0490423713698057 \cdot 10^{-109}:\\
\;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\

\mathbf{elif}\;b1 \cdot b2 \le 5.934410328828728 \cdot 10^{-246}:\\
\;\;\;\;\frac{a2 \cdot \frac{a1}{b1}}{b2}\\

\mathbf{elif}\;b1 \cdot b2 \le 2.6156936580694473 \cdot 10^{+78}:\\
\;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\

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

\end{array}

double f(double a1, double a2, double b1, double b2) {
        double r32326861 = a1;
        double r32326862 = a2;
        double r32326863 = r32326861 * r32326862;
        double r32326864 = b1;
        double r32326865 = b2;
        double r32326866 = r32326864 * r32326865;
        double r32326867 = r32326863 / r32326866;
        return r32326867;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r32326868 = b1;
        double r32326869 = b2;
        double r32326870 = r32326868 * r32326869;
        double r32326871 = -9.384563571355019e+255;
        bool r32326872 = r32326870 <= r32326871;
        double r32326873 = a1;
        double r32326874 = r32326873 / r32326868;
        double r32326875 = a2;
        double r32326876 = r32326875 / r32326869;
        double r32326877 = r32326874 * r32326876;
        double r32326878 = -1.0490423713698057e-109;
        bool r32326879 = r32326870 <= r32326878;
        double r32326880 = r32326870 / r32326875;
        double r32326881 = r32326873 / r32326880;
        double r32326882 = 5.934410328828728e-246;
        bool r32326883 = r32326870 <= r32326882;
        double r32326884 = r32326875 * r32326874;
        double r32326885 = r32326884 / r32326869;
        double r32326886 = 2.6156936580694473e+78;
        bool r32326887 = r32326870 <= r32326886;
        double r32326888 = r32326868 / r32326875;
        double r32326889 = r32326873 / r32326888;
        double r32326890 = r32326889 / r32326869;
        double r32326891 = r32326887 ? r32326881 : r32326890;
        double r32326892 = r32326883 ? r32326885 : r32326891;
        double r32326893 = r32326879 ? r32326881 : r32326892;
        double r32326894 = r32326872 ? r32326877 : r32326893;
        return r32326894;
}

Original	11.1
Target	11.0
Herbie	5.6

Derivation

Split input into 4 regimes
if (* b1 b2) < -9.384563571355019e+255
1. Initial program 17.9
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/r*8.4
  \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b1}}{b2}}\]
4. Using strategy rm
5. Applied associate-/l*3.7
  \[\leadsto \frac{\color{blue}{\frac{a1}{\frac{b1}{a2}}}}{b2}\]
6. Using strategy rm
7. Applied *-un-lft-identity3.7
  \[\leadsto \frac{\frac{a1}{\frac{b1}{a2}}}{\color{blue}{1 \cdot b2}}\]
8. Applied associate-/r/3.7
  \[\leadsto \frac{\color{blue}{\frac{a1}{b1} \cdot a2}}{1 \cdot b2}\]
9. Applied times-frac2.9
  \[\leadsto \color{blue}{\frac{\frac{a1}{b1}}{1} \cdot \frac{a2}{b2}}\]
10. Simplified2.9
  \[\leadsto \color{blue}{\frac{a1}{b1}} \cdot \frac{a2}{b2}\]
if -9.384563571355019e+255 < (* b1 b2) < -1.0490423713698057e-109 or 5.934410328828728e-246 < (* b1 b2) < 2.6156936580694473e+78
1. Initial program 4.8
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/l*4.1
  \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]
if -1.0490423713698057e-109 < (* b1 b2) < 5.934410328828728e-246
1. Initial program 25.8
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/r*15.0
  \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b1}}{b2}}\]
4. Using strategy rm
5. Applied associate-/l*11.0
  \[\leadsto \frac{\color{blue}{\frac{a1}{\frac{b1}{a2}}}}{b2}\]
6. Using strategy rm
7. Applied associate-/r/9.8
  \[\leadsto \frac{\color{blue}{\frac{a1}{b1} \cdot a2}}{b2}\]
if 2.6156936580694473e+78 < (* b1 b2)
1. Initial program 11.4
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/r*8.5
  \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b1}}{b2}}\]
4. Using strategy rm
5. Applied associate-/l*6.9
  \[\leadsto \frac{\color{blue}{\frac{a1}{\frac{b1}{a2}}}}{b2}\]
Recombined 4 regimes into one program.
Final simplification5.6
\[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -9.384563571355019 \cdot 10^{+255}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le -1.0490423713698057 \cdot 10^{-109}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \le 5.934410328828728 \cdot 10^{-246}:\\ \;\;\;\;\frac{a2 \cdot \frac{a1}{b1}}{b2}\\ \mathbf{elif}\;b1 \cdot b2 \le 2.6156936580694473 \cdot 10^{+78}:\\ \;\;\;\;\frac{a1}{\frac{b1 \cdot b2}{a2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a1}{\frac{b1}{a2}}}{b2}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if (* b1 b2) < -9.384563571355019e+255`

`if -9.384563571355019e+255 < (* b1 b2) < -1.0490423713698057e-109 or 5.934410328828728e-246 < (* b1 b2) < 2.6156936580694473e+78`

`if -1.0490423713698057e-109 < (* b1 b2) < 5.934410328828728e-246`

`if 2.6156936580694473e+78 < (* b1 b2)`

Reproduce

In
Out