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

↓

\[\begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -2.776996541214902 \cdot 10^{+242}:\\ \;\;\;\;\frac{\frac{a1}{b1}}{\frac{b2}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \le -1.2620149532156769 \cdot 10^{-221}:\\ \;\;\;\;\frac{a1}{\frac{1}{\frac{a2}{b1 \cdot b2}}}\\ \mathbf{elif}\;b1 \cdot b2 \le -0.0:\\ \;\;\;\;\frac{\frac{a1}{b1}}{\frac{b2}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \le 5.0652006343350663 \cdot 10^{+179}:\\ \;\;\;\;\frac{1}{\frac{\frac{b1 \cdot b2}{a2}}{a1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a1}{b1}}{\frac{b2}{a2}}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;b1 \cdot b2 \le -2.776996541214902 \cdot 10^{+242}:\\
\;\;\;\;\frac{\frac{a1}{b1}}{\frac{b2}{a2}}\\

\mathbf{elif}\;b1 \cdot b2 \le -1.2620149532156769 \cdot 10^{-221}:\\
\;\;\;\;\frac{a1}{\frac{1}{\frac{a2}{b1 \cdot b2}}}\\

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

\mathbf{elif}\;b1 \cdot b2 \le 5.0652006343350663 \cdot 10^{+179}:\\
\;\;\;\;\frac{1}{\frac{\frac{b1 \cdot b2}{a2}}{a1}}\\

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

\end{array}

double f(double a1, double a2, double b1, double b2) {
        double r6338005 = a1;
        double r6338006 = a2;
        double r6338007 = r6338005 * r6338006;
        double r6338008 = b1;
        double r6338009 = b2;
        double r6338010 = r6338008 * r6338009;
        double r6338011 = r6338007 / r6338010;
        return r6338011;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r6338012 = b1;
        double r6338013 = b2;
        double r6338014 = r6338012 * r6338013;
        double r6338015 = -2.776996541214902e+242;
        bool r6338016 = r6338014 <= r6338015;
        double r6338017 = a1;
        double r6338018 = r6338017 / r6338012;
        double r6338019 = a2;
        double r6338020 = r6338013 / r6338019;
        double r6338021 = r6338018 / r6338020;
        double r6338022 = -1.2620149532156769e-221;
        bool r6338023 = r6338014 <= r6338022;
        double r6338024 = 1.0;
        double r6338025 = r6338019 / r6338014;
        double r6338026 = r6338024 / r6338025;
        double r6338027 = r6338017 / r6338026;
        double r6338028 = -0.0;
        bool r6338029 = r6338014 <= r6338028;
        double r6338030 = 5.0652006343350663e+179;
        bool r6338031 = r6338014 <= r6338030;
        double r6338032 = r6338014 / r6338019;
        double r6338033 = r6338032 / r6338017;
        double r6338034 = r6338024 / r6338033;
        double r6338035 = r6338031 ? r6338034 : r6338021;
        double r6338036 = r6338029 ? r6338021 : r6338035;
        double r6338037 = r6338023 ? r6338027 : r6338036;
        double r6338038 = r6338016 ? r6338021 : r6338037;
        return r6338038;
}

Original	10.7
Target	10.8
Herbie	5.0

Derivation

Split input into 3 regimes
if (* b1 b2) < -2.776996541214902e+242 or -1.2620149532156769e-221 < (* b1 b2) < -0.0 or 5.0652006343350663e+179 < (* b1 b2)
1. Initial program 21.5
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/l*21.8
  \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]
4. Using strategy rm
5. Applied *-un-lft-identity21.8
  \[\leadsto \frac{a1}{\frac{b1 \cdot b2}{\color{blue}{1 \cdot a2}}}\]
6. Applied times-frac9.3
  \[\leadsto \frac{a1}{\color{blue}{\frac{b1}{1} \cdot \frac{b2}{a2}}}\]
7. Simplified9.3
  \[\leadsto \frac{a1}{\color{blue}{b1} \cdot \frac{b2}{a2}}\]
8. Using strategy rm
9. Applied associate-/r*4.9
  \[\leadsto \color{blue}{\frac{\frac{a1}{b1}}{\frac{b2}{a2}}}\]
if -2.776996541214902e+242 < (* b1 b2) < -1.2620149532156769e-221
1. Initial program 4.6
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/l*4.1
  \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]
4. Using strategy rm
5. Applied clear-num4.4
  \[\leadsto \frac{a1}{\color{blue}{\frac{1}{\frac{a2}{b1 \cdot b2}}}}\]
if -0.0 < (* b1 b2) < 5.0652006343350663e+179
1. Initial program 5.1
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/l*5.3
  \[\leadsto \color{blue}{\frac{a1}{\frac{b1 \cdot b2}{a2}}}\]
4. Using strategy rm
5. Applied *-un-lft-identity5.3
  \[\leadsto \frac{\color{blue}{1 \cdot a1}}{\frac{b1 \cdot b2}{a2}}\]
6. Applied associate-/l*5.7
  \[\leadsto \color{blue}{\frac{1}{\frac{\frac{b1 \cdot b2}{a2}}{a1}}}\]
Recombined 3 regimes into one program.
Final simplification5.0
\[\leadsto \begin{array}{l} \mathbf{if}\;b1 \cdot b2 \le -2.776996541214902 \cdot 10^{+242}:\\ \;\;\;\;\frac{\frac{a1}{b1}}{\frac{b2}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \le -1.2620149532156769 \cdot 10^{-221}:\\ \;\;\;\;\frac{a1}{\frac{1}{\frac{a2}{b1 \cdot b2}}}\\ \mathbf{elif}\;b1 \cdot b2 \le -0.0:\\ \;\;\;\;\frac{\frac{a1}{b1}}{\frac{b2}{a2}}\\ \mathbf{elif}\;b1 \cdot b2 \le 5.0652006343350663 \cdot 10^{+179}:\\ \;\;\;\;\frac{1}{\frac{\frac{b1 \cdot b2}{a2}}{a1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a1}{b1}}{\frac{b2}{a2}}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if (* b1 b2) < -2.776996541214902e+242 or -1.2620149532156769e-221 < (* b1 b2) < -0.0 or 5.0652006343350663e+179 < (* b1 b2)`

`if -2.776996541214902e+242 < (* b1 b2) < -1.2620149532156769e-221`

`if -0.0 < (* b1 b2) < 5.0652006343350663e+179`

Reproduce

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