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

↓

\[\begin{array}{l} \mathbf{if}\;a1 \cdot a2 \le -8.1576239880029206 \cdot 10^{195}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b1}}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le -7.6760268479022844 \cdot 10^{-278}:\\ \;\;\;\;\frac{a1 \cdot a2}{\sqrt[3]{b2} \cdot \sqrt[3]{b2}} \cdot \frac{\frac{1}{b1}}{\sqrt[3]{b2}}\\ \mathbf{elif}\;a1 \cdot a2 \le 1.3851302523781732 \cdot 10^{-273}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le 2.0507310125992406 \cdot 10^{162}:\\ \;\;\;\;\frac{a1 \cdot a2}{\sqrt[3]{b2} \cdot \sqrt[3]{b2}} \cdot \frac{\frac{1}{b1}}{\sqrt[3]{b2}}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b1}}{b2}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;a1 \cdot a2 \le -8.1576239880029206 \cdot 10^{195}:\\
\;\;\;\;a1 \cdot \frac{\frac{a2}{b1}}{b2}\\

\mathbf{elif}\;a1 \cdot a2 \le -7.6760268479022844 \cdot 10^{-278}:\\
\;\;\;\;\frac{a1 \cdot a2}{\sqrt[3]{b2} \cdot \sqrt[3]{b2}} \cdot \frac{\frac{1}{b1}}{\sqrt[3]{b2}}\\

\mathbf{elif}\;a1 \cdot a2 \le 1.3851302523781732 \cdot 10^{-273}:\\
\;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\

\mathbf{elif}\;a1 \cdot a2 \le 2.0507310125992406 \cdot 10^{162}:\\
\;\;\;\;\frac{a1 \cdot a2}{\sqrt[3]{b2} \cdot \sqrt[3]{b2}} \cdot \frac{\frac{1}{b1}}{\sqrt[3]{b2}}\\

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

\end{array}

double f(double a1, double a2, double b1, double b2) {
        double r291201 = a1;
        double r291202 = a2;
        double r291203 = r291201 * r291202;
        double r291204 = b1;
        double r291205 = b2;
        double r291206 = r291204 * r291205;
        double r291207 = r291203 / r291206;
        return r291207;
}

↓

double f(double a1, double a2, double b1, double b2) {
        double r291208 = a1;
        double r291209 = a2;
        double r291210 = r291208 * r291209;
        double r291211 = -8.157623988002921e+195;
        bool r291212 = r291210 <= r291211;
        double r291213 = b1;
        double r291214 = r291209 / r291213;
        double r291215 = b2;
        double r291216 = r291214 / r291215;
        double r291217 = r291208 * r291216;
        double r291218 = -7.676026847902284e-278;
        bool r291219 = r291210 <= r291218;
        double r291220 = cbrt(r291215);
        double r291221 = r291220 * r291220;
        double r291222 = r291210 / r291221;
        double r291223 = 1.0;
        double r291224 = r291223 / r291213;
        double r291225 = r291224 / r291220;
        double r291226 = r291222 * r291225;
        double r291227 = 1.3851302523781732e-273;
        bool r291228 = r291210 <= r291227;
        double r291229 = r291208 / r291213;
        double r291230 = r291209 / r291215;
        double r291231 = r291229 * r291230;
        double r291232 = 2.0507310125992406e+162;
        bool r291233 = r291210 <= r291232;
        double r291234 = r291233 ? r291226 : r291217;
        double r291235 = r291228 ? r291231 : r291234;
        double r291236 = r291219 ? r291226 : r291235;
        double r291237 = r291212 ? r291217 : r291236;
        return r291237;
}

Original	11.5
Target	11.3
Herbie	4.7

Derivation

Split input into 3 regimes
if (* a1 a2) < -8.157623988002921e+195 or 2.0507310125992406e+162 < (* a1 a2)
1. Initial program 30.8
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/r*31.9
  \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b1}}{b2}}\]
4. Using strategy rm
5. Applied *-un-lft-identity31.9
  \[\leadsto \frac{\frac{a1 \cdot a2}{b1}}{\color{blue}{1 \cdot b2}}\]
6. Applied *-un-lft-identity31.9
  \[\leadsto \frac{\frac{a1 \cdot a2}{\color{blue}{1 \cdot b1}}}{1 \cdot b2}\]
7. Applied times-frac18.2
  \[\leadsto \frac{\color{blue}{\frac{a1}{1} \cdot \frac{a2}{b1}}}{1 \cdot b2}\]
8. Applied times-frac11.8
  \[\leadsto \color{blue}{\frac{\frac{a1}{1}}{1} \cdot \frac{\frac{a2}{b1}}{b2}}\]
9. Simplified11.8
  \[\leadsto \color{blue}{a1} \cdot \frac{\frac{a2}{b1}}{b2}\]
if -8.157623988002921e+195 < (* a1 a2) < -7.676026847902284e-278 or 1.3851302523781732e-273 < (* a1 a2) < 2.0507310125992406e+162
1. Initial program 5.0
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied associate-/r*4.6
  \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b1}}{b2}}\]
4. Using strategy rm
5. Applied add-cube-cbrt5.4
  \[\leadsto \frac{\frac{a1 \cdot a2}{b1}}{\color{blue}{\left(\sqrt[3]{b2} \cdot \sqrt[3]{b2}\right) \cdot \sqrt[3]{b2}}}\]
6. Applied div-inv5.4
  \[\leadsto \frac{\color{blue}{\left(a1 \cdot a2\right) \cdot \frac{1}{b1}}}{\left(\sqrt[3]{b2} \cdot \sqrt[3]{b2}\right) \cdot \sqrt[3]{b2}}\]
7. Applied times-frac3.5
  \[\leadsto \color{blue}{\frac{a1 \cdot a2}{\sqrt[3]{b2} \cdot \sqrt[3]{b2}} \cdot \frac{\frac{1}{b1}}{\sqrt[3]{b2}}}\]
if -7.676026847902284e-278 < (* a1 a2) < 1.3851302523781732e-273
1. Initial program 18.1
  \[\frac{a1 \cdot a2}{b1 \cdot b2}\]
2. Using strategy rm
3. Applied times-frac3.2
  \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}}\]
Recombined 3 regimes into one program.
Final simplification4.7
\[\leadsto \begin{array}{l} \mathbf{if}\;a1 \cdot a2 \le -8.1576239880029206 \cdot 10^{195}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b1}}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le -7.6760268479022844 \cdot 10^{-278}:\\ \;\;\;\;\frac{a1 \cdot a2}{\sqrt[3]{b2} \cdot \sqrt[3]{b2}} \cdot \frac{\frac{1}{b1}}{\sqrt[3]{b2}}\\ \mathbf{elif}\;a1 \cdot a2 \le 1.3851302523781732 \cdot 10^{-273}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \le 2.0507310125992406 \cdot 10^{162}:\\ \;\;\;\;\frac{a1 \cdot a2}{\sqrt[3]{b2} \cdot \sqrt[3]{b2}} \cdot \frac{\frac{1}{b1}}{\sqrt[3]{b2}}\\ \mathbf{else}:\\ \;\;\;\;a1 \cdot \frac{\frac{a2}{b1}}{b2}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if (* a1 a2) < -8.157623988002921e+195 or 2.0507310125992406e+162 < (* a1 a2)`

`if -8.157623988002921e+195 < (* a1 a2) < -7.676026847902284e-278 or 1.3851302523781732e-273 < (* a1 a2) < 2.0507310125992406e+162`

`if -7.676026847902284e-278 < (* a1 a2) < 1.3851302523781732e-273`

Reproduce

In
Out