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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -1.68280036335944034 \cdot 10^{301}:\\ \;\;\;\;\left(a1 \cdot \frac{a2}{b1}\right) \cdot \frac{1}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -4.5204447990899316 \cdot 10^{-307}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 0.0:\\ \;\;\;\;\frac{a1}{\frac{b1}{\frac{a2}{b2}}}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 4.51733405101081216 \cdot 10^{288}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\left(a1 \cdot \frac{a2}{b1}\right) \cdot \frac{1}{b2}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -1.68280036335944034 \cdot 10^{301}:\\
\;\;\;\;\left(a1 \cdot \frac{a2}{b1}\right) \cdot \frac{1}{b2}\\

\mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -4.5204447990899316 \cdot 10^{-307}:\\
\;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\

\mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 0.0:\\
\;\;\;\;\frac{a1}{\frac{b1}{\frac{a2}{b2}}}\\

\mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 4.51733405101081216 \cdot 10^{288}:\\
\;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\

\mathbf{else}:\\
\;\;\;\;\left(a1 \cdot \frac{a2}{b1}\right) \cdot \frac{1}{b2}\\

\end{array}

double f(double a1, double a2, double b1, double b2) {
        double r165801 = a1;
        double r165802 = a2;
        double r165803 = r165801 * r165802;
        double r165804 = b1;
        double r165805 = b2;
        double r165806 = r165804 * r165805;
        double r165807 = r165803 / r165806;
        return r165807;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r165808 = a1;
        double r165809 = a2;
        double r165810 = r165808 * r165809;
        double r165811 = b1;
        double r165812 = b2;
        double r165813 = r165811 * r165812;
        double r165814 = r165810 / r165813;
        double r165815 = -1.6828003633594403e+301;
        bool r165816 = r165814 <= r165815;
        double r165817 = r165809 / r165811;
        double r165818 = r165808 * r165817;
        double r165819 = 1.0;
        double r165820 = r165819 / r165812;
        double r165821 = r165818 * r165820;
        double r165822 = -4.520444799089932e-307;
        bool r165823 = r165814 <= r165822;
        double r165824 = 0.0;
        bool r165825 = r165814 <= r165824;
        double r165826 = r165809 / r165812;
        double r165827 = r165811 / r165826;
        double r165828 = r165808 / r165827;
        double r165829 = 4.517334051010812e+288;
        bool r165830 = r165814 <= r165829;
        double r165831 = r165830 ? r165814 : r165821;
        double r165832 = r165825 ? r165828 : r165831;
        double r165833 = r165823 ? r165814 : r165832;
        double r165834 = r165816 ? r165821 : r165833;
        return r165834;
}

Original	11.4
Target	11.5
Herbie	3.4

Derivation

Split input into 3 regimes
if (/ (* a1 a2) (* b1 b2)) < -1.6828003633594403e+301 or 4.517334051010812e+288 < (/ (* a1 a2) (* b1 b2))
1. Initial program 59.3
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/l*39.8
  \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]
4. Using strategy rm
5. Applied div-inv39.9
  \[\leadsto \color{blue}{a1 \cdot \frac{1}{\frac{b1 \cdot b2}{a2}}}\]
6. Simplified39.8
  \[\leadsto a1 \cdot \color{blue}{\frac{a2}{b1 \cdot b2}}\]
7. Using strategy rm
8. Applied associate-/r*15.2
  \[\leadsto a1 \cdot \color{blue}{\frac{\frac{a2}{b1}}{b2}}\]
9. Using strategy rm
10. Applied div-inv15.3
  \[\leadsto a1 \cdot \color{blue}{\left(\frac{a2}{b1} \cdot \frac{1}{b2}\right)}\]
11. Applied associate-*r*14.9
  \[\leadsto \color{blue}{\left(a1 \cdot \frac{a2}{b1}\right) \cdot \frac{1}{b2}}\]
if -1.6828003633594403e+301 < (/ (* a1 a2) (* b1 b2)) < -4.520444799089932e-307 or 0.0 < (/ (* a1 a2) (* b1 b2)) < 4.517334051010812e+288
1. Initial program 0.8
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/l*7.3
  \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]
4. Using strategy rm
5. Applied div-inv7.6
  \[\leadsto \color{blue}{a1 \cdot \frac{1}{\frac{b1 \cdot b2}{a2}}}\]
6. Simplified7.3
  \[\leadsto a1 \cdot \color{blue}{\frac{a2}{b1 \cdot b2}}\]
7. Using strategy rm
8. Applied associate-*r/0.8
  \[\leadsto \color{blue}{\frac{a1 \cdot a2}{b1 \cdot b2}}\]
if -4.520444799089932e-307 < (/ (* a1 a2) (* b1 b2)) < 0.0
1. Initial program 13.1
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/l*7.1
  \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]
4. Using strategy rm
5. Applied associate-/l*3.8
  \[\leadsto \frac{a1}{\color{blue}{\frac{b1}{\frac{a2}{b2}}}}\]
Recombined 3 regimes into one program.
Final simplification3.4
\[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -1.68280036335944034 \cdot 10^{301}:\\ \;\;\;\;\left(a1 \cdot \frac{a2}{b1}\right) \cdot \frac{1}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le -4.5204447990899316 \cdot 10^{-307}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 0.0:\\ \;\;\;\;\frac{a1}{\frac{b1}{\frac{a2}{b2}}}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \le 4.51733405101081216 \cdot 10^{288}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\left(a1 \cdot \frac{a2}{b1}\right) \cdot \frac{1}{b2}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if (/ (* a1 a2) (* b1 b2)) < -1.6828003633594403e+301 or 4.517334051010812e+288 < (/ (* a1 a2) (* b1 b2))`

`if -1.6828003633594403e+301 < (/ (* a1 a2) (* b1 b2)) < -4.520444799089932e-307 or 0.0 < (/ (* a1 a2) (* b1 b2)) < 4.517334051010812e+288`

`if -4.520444799089932e-307 < (/ (* a1 a2) (* b1 b2)) < 0.0`

Reproduce

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