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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -5.662799451522715 \cdot 10^{-101}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 5.661789367158313 \cdot 10^{-215}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \frac{\sqrt[3]{y}}{z}\\ \end{array}\]

double f(double x, double y, double z, double t) {
        double r13264867 = x;
        double r13264868 = y;
        double r13264869 = z;
        double r13264870 = r13264868 / r13264869;
        double r13264871 = t;
        double r13264872 = r13264870 * r13264871;
        double r13264873 = r13264872 / r13264871;
        double r13264874 = r13264867 * r13264873;
        return r13264874;
}

↓

double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r13264875 = y;
        double r13264876 = z;
        double r13264877 = r13264875 / r13264876;
        double r13264878 = -inf.0;
        bool r13264879 = r13264877 <= r13264878;
        double r13264880 = x;
        double r13264881 = r13264880 * r13264875;
        double r13264882 = r13264881 / r13264876;
        double r13264883 = -5.662799451522715e-101;
        bool r13264884 = r13264877 <= r13264883;
        double r13264885 = r13264877 * r13264880;
        double r13264886 = 5.661789367158313e-215;
        bool r13264887 = r13264877 <= r13264886;
        double r13264888 = r13264876 / r13264880;
        double r13264889 = r13264875 / r13264888;
        double r13264890 = cbrt(r13264875);
        double r13264891 = r13264890 * r13264890;
        double r13264892 = r13264880 * r13264891;
        double r13264893 = r13264890 / r13264876;
        double r13264894 = r13264892 * r13264893;
        double r13264895 = r13264887 ? r13264889 : r13264894;
        double r13264896 = r13264884 ? r13264885 : r13264895;
        double r13264897 = r13264879 ? r13264882 : r13264896;
        return r13264897;
}

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

↓

\begin{array}{l}
\mathbf{if}\;\frac{y}{z} = -\infty:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -5.662799451522715 \cdot 10^{-101}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le 5.661789367158313 \cdot 10^{-215}:\\
\;\;\;\;\frac{y}{\frac{z}{x}}\\

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

\end{array}

Derivation

Split input into 4 regimes
if (/ y z) < -inf.0
1. Initial program 60.0
  \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
2. Simplified60.0
  \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
3. Using strategy rm
4. Applied *-un-lft-identity60.0
  \[\leadsto x \cdot \frac{y}{\color{blue}{1 \cdot z}}\]
5. Applied add-cube-cbrt60.0
  \[\leadsto x \cdot \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{1 \cdot z}\]
6. Applied times-frac60.0
  \[\leadsto x \cdot \color{blue}{\left(\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1} \cdot \frac{\sqrt[3]{y}}{z}\right)}\]
7. Applied associate-*r*13.5
  \[\leadsto \color{blue}{\left(x \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1}\right) \cdot \frac{\sqrt[3]{y}}{z}}\]
8. Taylor expanded around 0 0.3
  \[\leadsto \color{blue}{\frac{x \cdot y}{z}}\]
if -inf.0 < (/ y z) < -5.662799451522715e-101
1. Initial program 9.7
  \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
2. Simplified0.3
  \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
if -5.662799451522715e-101 < (/ y z) < 5.661789367158313e-215
1. Initial program 15.5
  \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
2. Simplified8.5
  \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
3. Using strategy rm
4. Applied *-un-lft-identity8.5
  \[\leadsto x \cdot \frac{y}{\color{blue}{1 \cdot z}}\]
5. Applied add-cube-cbrt8.9
  \[\leadsto x \cdot \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{1 \cdot z}\]
6. Applied times-frac8.9
  \[\leadsto x \cdot \color{blue}{\left(\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1} \cdot \frac{\sqrt[3]{y}}{z}\right)}\]
7. Applied associate-*r*2.9
  \[\leadsto \color{blue}{\left(x \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1}\right) \cdot \frac{\sqrt[3]{y}}{z}}\]
8. Using strategy rm
9. Applied associate-*r/2.9
  \[\leadsto \color{blue}{\frac{x \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)}{1}} \cdot \frac{\sqrt[3]{y}}{z}\]
10. Applied associate-*l/2.9
  \[\leadsto \color{blue}{\frac{\left(x \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \frac{\sqrt[3]{y}}{z}}{1}}\]
11. Simplified1.6
  \[\leadsto \frac{\color{blue}{\frac{y}{\frac{z}{x}}}}{1}\]
if 5.661789367158313e-215 < (/ y z)
1. Initial program 13.4
  \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
2. Simplified4.3
  \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
3. Using strategy rm
4. Applied *-un-lft-identity4.3
  \[\leadsto x \cdot \frac{y}{\color{blue}{1 \cdot z}}\]
5. Applied add-cube-cbrt5.3
  \[\leadsto x \cdot \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{1 \cdot z}\]
6. Applied times-frac5.3
  \[\leadsto x \cdot \color{blue}{\left(\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1} \cdot \frac{\sqrt[3]{y}}{z}\right)}\]
7. Applied associate-*r*6.3
  \[\leadsto \color{blue}{\left(x \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1}\right) \cdot \frac{\sqrt[3]{y}}{z}}\]
Recombined 4 regimes into one program.
Final simplification2.9
\[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -5.662799451522715 \cdot 10^{-101}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 5.661789367158313 \cdot 10^{-215}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \frac{\sqrt[3]{y}}{z}\\ \end{array}\]

Error

Derivation

`if (/ y z) < -inf.0`

`if -inf.0 < (/ y z) < -5.662799451522715e-101`

`if -5.662799451522715e-101 < (/ y z) < 5.661789367158313e-215`

`if 5.661789367158313e-215 < (/ y z)`

Reproduce