\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]

↓

\[\begin{array}{l} \mathbf{if}\;y \le -3.8614843403324857 \cdot 10^{+90}:\\ \;\;\;\;\left|\frac{4 + x}{y} - \frac{\frac{z}{y}}{\frac{1}{x}}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - \frac{z \cdot x}{y}\right|\\ \end{array}\]

double f(double x, double y, double z) {
        double r17682913 = x;
        double r17682914 = 4.0;
        double r17682915 = r17682913 + r17682914;
        double r17682916 = y;
        double r17682917 = r17682915 / r17682916;
        double r17682918 = r17682913 / r17682916;
        double r17682919 = z;
        double r17682920 = r17682918 * r17682919;
        double r17682921 = r17682917 - r17682920;
        double r17682922 = fabs(r17682921);
        return r17682922;
}

↓

double f(double x, double y, double z) {
        double r17682923 = y;
        double r17682924 = -3.8614843403324857e+90;
        bool r17682925 = r17682923 <= r17682924;
        double r17682926 = 4.0;
        double r17682927 = x;
        double r17682928 = r17682926 + r17682927;
        double r17682929 = r17682928 / r17682923;
        double r17682930 = z;
        double r17682931 = r17682930 / r17682923;
        double r17682932 = 1.0;
        double r17682933 = r17682932 / r17682927;
        double r17682934 = r17682931 / r17682933;
        double r17682935 = r17682929 - r17682934;
        double r17682936 = fabs(r17682935);
        double r17682937 = r17682930 * r17682927;
        double r17682938 = r17682937 / r17682923;
        double r17682939 = r17682929 - r17682938;
        double r17682940 = fabs(r17682939);
        double r17682941 = r17682925 ? r17682936 : r17682940;
        return r17682941;
}

\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|

↓

\begin{array}{l}
\mathbf{if}\;y \le -3.8614843403324857 \cdot 10^{+90}:\\
\;\;\;\;\left|\frac{4 + x}{y} - \frac{\frac{z}{y}}{\frac{1}{x}}\right|\\

\mathbf{else}:\\
\;\;\;\;\left|\frac{4 + x}{y} - \frac{z \cdot x}{y}\right|\\

\end{array}

Derivation

Split input into 2 regimes
if y < -3.8614843403324857e+90
1. Initial program 2.9
  \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
2. Using strategy rm
3. Applied *-un-lft-identity2.9
  \[\leadsto \left|\frac{x + 4}{\color{blue}{1 \cdot y}} - \frac{x}{y} \cdot z\right|\]
4. Applied add-cube-cbrt3.7
  \[\leadsto \left|\frac{\color{blue}{\left(\sqrt[3]{x + 4} \cdot \sqrt[3]{x + 4}\right) \cdot \sqrt[3]{x + 4}}}{1 \cdot y} - \frac{x}{y} \cdot z\right|\]
5. Applied times-frac3.7
  \[\leadsto \left|\color{blue}{\frac{\sqrt[3]{x + 4} \cdot \sqrt[3]{x + 4}}{1} \cdot \frac{\sqrt[3]{x + 4}}{y}} - \frac{x}{y} \cdot z\right|\]
6. Applied prod-diff3.7
  \[\leadsto \left|\color{blue}{(\left(\frac{\sqrt[3]{x + 4} \cdot \sqrt[3]{x + 4}}{1}\right) \cdot \left(\frac{\sqrt[3]{x + 4}}{y}\right) + \left(-z \cdot \frac{x}{y}\right))_* + (\left(-z\right) \cdot \left(\frac{x}{y}\right) + \left(z \cdot \frac{x}{y}\right))_*}\right|\]
7. Simplified3.1
  \[\leadsto \left|\color{blue}{\left(\frac{4 + x}{y} - \frac{z}{\frac{y}{x}}\right)} + (\left(-z\right) \cdot \left(\frac{x}{y}\right) + \left(z \cdot \frac{x}{y}\right))_*\right|\]
8. Simplified3.1
  \[\leadsto \left|\left(\frac{4 + x}{y} - \frac{z}{\frac{y}{x}}\right) + \color{blue}{0}\right|\]
9. Using strategy rm
10. Applied div-inv3.1
  \[\leadsto \left|\left(\frac{4 + x}{y} - \frac{z}{\color{blue}{y \cdot \frac{1}{x}}}\right) + 0\right|\]
11. Applied associate-/r*0.1
  \[\leadsto \left|\left(\frac{4 + x}{y} - \color{blue}{\frac{\frac{z}{y}}{\frac{1}{x}}}\right) + 0\right|\]
if -3.8614843403324857e+90 < y
1. Initial program 1.1
  \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
2. Using strategy rm
3. Applied associate-*l/2.2
  \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right|\]
Recombined 2 regimes into one program.
Final simplification1.8
\[\leadsto \begin{array}{l} \mathbf{if}\;y \le -3.8614843403324857 \cdot 10^{+90}:\\ \;\;\;\;\left|\frac{4 + x}{y} - \frac{\frac{z}{y}}{\frac{1}{x}}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - \frac{z \cdot x}{y}\right|\\ \end{array}\]

Error

Derivation

`if y < -3.8614843403324857e+90`

`if -3.8614843403324857e+90 < y`

Reproduce