\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.2665860626305797 \cdot 10^{-139}:\\ \;\;\;\;\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot \frac{x}{\frac{\sqrt[3]{z}}{\sqrt[3]{y}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{y}}}\\ \mathbf{elif}\;\frac{y}{z} \le 8.578702620784637 \cdot 10^{-293}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot \frac{x}{\frac{\sqrt[3]{z}}{\sqrt[3]{y}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{y}}}\\ \end{array}\]

double f(double x, double y, double z, double t) {
        double r17467983 = x;
        double r17467984 = y;
        double r17467985 = z;
        double r17467986 = r17467984 / r17467985;
        double r17467987 = t;
        double r17467988 = r17467986 * r17467987;
        double r17467989 = r17467988 / r17467987;
        double r17467990 = r17467983 * r17467989;
        return r17467990;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r17467991 = y;
        double r17467992 = z;
        double r17467993 = r17467991 / r17467992;
        double r17467994 = -2.2665860626305797e-139;
        bool r17467995 = r17467993 <= r17467994;
        double r17467996 = cbrt(r17467991);
        double r17467997 = cbrt(r17467992);
        double r17467998 = r17467996 / r17467997;
        double r17467999 = x;
        double r17468000 = r17467997 / r17467996;
        double r17468001 = r17468000 * r17468000;
        double r17468002 = r17467999 / r17468001;
        double r17468003 = r17467998 * r17468002;
        double r17468004 = 8.578702620784637e-293;
        bool r17468005 = r17467993 <= r17468004;
        double r17468006 = r17467999 * r17467991;
        double r17468007 = r17468006 / r17467992;
        double r17468008 = r17468005 ? r17468007 : r17468003;
        double r17468009 = r17467995 ? r17468003 : r17468008;
        return r17468009;
}

x \cdot \frac{\frac{y}{z} \cdot t}{t}

↓

\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -2.2665860626305797 \cdot 10^{-139}:\\
\;\;\;\;\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot \frac{x}{\frac{\sqrt[3]{z}}{\sqrt[3]{y}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{y}}}\\

\mathbf{elif}\;\frac{y}{z} \le 8.578702620784637 \cdot 10^{-293}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot \frac{x}{\frac{\sqrt[3]{z}}{\sqrt[3]{y}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{y}}}\\

\end{array}

Derivation

Split input into 2 regimes
if (/ y z) < -2.2665860626305797e-139 or 8.578702620784637e-293 < (/ y z)
1. Initial program 13.3
  \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
2. Simplified4.3
  \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
3. Using strategy rm
4. Applied add-cube-cbrt5.2
  \[\leadsto x \cdot \frac{y}{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}\]
5. Applied add-cube-cbrt5.5
  \[\leadsto x \cdot \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}\]
6. Applied times-frac5.5
  \[\leadsto x \cdot \color{blue}{\left(\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\right)}\]
7. Applied associate-*r*2.0
  \[\leadsto \color{blue}{\left(x \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}}\]
8. Using strategy rm
9. Applied pow12.0
  \[\leadsto \left(x \cdot \color{blue}{{\left(\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right)}^{1}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\]
10. Applied pow12.0
  \[\leadsto \left(\color{blue}{{x}^{1}} \cdot {\left(\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right)}^{1}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\]
11. Applied pow-prod-down2.0
  \[\leadsto \color{blue}{{\left(x \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right)}^{1}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\]
12. Simplified1.9
  \[\leadsto {\color{blue}{\left(\frac{x}{\frac{\sqrt[3]{z}}{\sqrt[3]{y}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{y}}}\right)}}^{1} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\]
if -2.2665860626305797e-139 < (/ y z) < 8.578702620784637e-293
1. Initial program 18.1
  \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
2. Simplified11.0
  \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
3. Taylor expanded around -inf 1.2
  \[\leadsto \color{blue}{\frac{x \cdot y}{z}}\]
Recombined 2 regimes into one program.
Final simplification1.7
\[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.2665860626305797 \cdot 10^{-139}:\\ \;\;\;\;\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot \frac{x}{\frac{\sqrt[3]{z}}{\sqrt[3]{y}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{y}}}\\ \mathbf{elif}\;\frac{y}{z} \le 8.578702620784637 \cdot 10^{-293}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{y}}{\sqrt[3]{z}} \cdot \frac{x}{\frac{\sqrt[3]{z}}{\sqrt[3]{y}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{y}}}\\ \end{array}\]

Error

Derivation

`if (/ y z) < -2.2665860626305797e-139 or 8.578702620784637e-293 < (/ y z)`

`if -2.2665860626305797e-139 < (/ y z) < 8.578702620784637e-293`

Reproduce