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

↓

\[\begin{array}{l} \mathbf{if}\;x \le -1.109110258294614752055774941493075991437 \cdot 10^{97}:\\ \;\;\;\;\left|\frac{1}{\frac{y}{x + 4}} - \frac{z}{\frac{y}{x}}\right|\\ \mathbf{elif}\;x \le 4.00953015364486885541650984422639355434 \cdot 10^{48}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\left(x + 4\right) \cdot \frac{1}{y} - \frac{x}{y} \cdot z\right|\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;x \le -1.109110258294614752055774941493075991437 \cdot 10^{97}:\\
\;\;\;\;\left|\frac{1}{\frac{y}{x + 4}} - \frac{z}{\frac{y}{x}}\right|\\

\mathbf{elif}\;x \le 4.00953015364486885541650984422639355434 \cdot 10^{48}:\\
\;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\

\mathbf{else}:\\
\;\;\;\;\left|\left(x + 4\right) \cdot \frac{1}{y} - \frac{x}{y} \cdot z\right|\\

\end{array}

double f(double x, double y, double z) {
        double r32867 = x;
        double r32868 = 4.0;
        double r32869 = r32867 + r32868;
        double r32870 = y;
        double r32871 = r32869 / r32870;
        double r32872 = r32867 / r32870;
        double r32873 = z;
        double r32874 = r32872 * r32873;
        double r32875 = r32871 - r32874;
        double r32876 = fabs(r32875);
        return r32876;
}

↓

double f(double x, double y, double z) {
        double r32877 = x;
        double r32878 = -1.1091102582946148e+97;
        bool r32879 = r32877 <= r32878;
        double r32880 = 1.0;
        double r32881 = y;
        double r32882 = 4.0;
        double r32883 = r32877 + r32882;
        double r32884 = r32881 / r32883;
        double r32885 = r32880 / r32884;
        double r32886 = z;
        double r32887 = r32881 / r32877;
        double r32888 = r32886 / r32887;
        double r32889 = r32885 - r32888;
        double r32890 = fabs(r32889);
        double r32891 = 4.009530153644869e+48;
        bool r32892 = r32877 <= r32891;
        double r32893 = r32877 * r32886;
        double r32894 = r32883 - r32893;
        double r32895 = r32894 / r32881;
        double r32896 = fabs(r32895);
        double r32897 = r32880 / r32881;
        double r32898 = r32883 * r32897;
        double r32899 = r32877 / r32881;
        double r32900 = r32899 * r32886;
        double r32901 = r32898 - r32900;
        double r32902 = fabs(r32901);
        double r32903 = r32892 ? r32896 : r32902;
        double r32904 = r32879 ? r32890 : r32903;
        return r32904;
}

Derivation

Split input into 3 regimes
if x < -1.1091102582946148e+97
1. Initial program 0.1
  \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
2. Using strategy rm
3. Applied clear-num0.3
  \[\leadsto \left|\color{blue}{\frac{1}{\frac{y}{x + 4}}} - \frac{x}{y} \cdot z\right|\]
4. Using strategy rm
5. Applied pow10.3
  \[\leadsto \left|\frac{1}{\frac{y}{x + 4}} - \frac{x}{y} \cdot \color{blue}{{z}^{1}}\right|\]
6. Applied pow10.3
  \[\leadsto \left|\frac{1}{\frac{y}{x + 4}} - \color{blue}{{\left(\frac{x}{y}\right)}^{1}} \cdot {z}^{1}\right|\]
7. Applied pow-prod-down0.3
  \[\leadsto \left|\frac{1}{\frac{y}{x + 4}} - \color{blue}{{\left(\frac{x}{y} \cdot z\right)}^{1}}\right|\]
8. Simplified0.3
  \[\leadsto \left|\frac{1}{\frac{y}{x + 4}} - {\color{blue}{\left(\frac{z}{\frac{y}{x}}\right)}}^{1}\right|\]
if -1.1091102582946148e+97 < x < 4.009530153644869e+48
1. Initial program 2.0
  \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
2. Using strategy rm
3. Applied associate-*l/0.5
  \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right|\]
4. Applied sub-div0.5
  \[\leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right|\]
if 4.009530153644869e+48 < x
1. Initial program 0.1
  \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
2. Using strategy rm
3. Applied div-inv0.3
  \[\leadsto \left|\color{blue}{\left(x + 4\right) \cdot \frac{1}{y}} - \frac{x}{y} \cdot z\right|\]
Recombined 3 regimes into one program.
Final simplification0.4
\[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.109110258294614752055774941493075991437 \cdot 10^{97}:\\ \;\;\;\;\left|\frac{1}{\frac{y}{x + 4}} - \frac{z}{\frac{y}{x}}\right|\\ \mathbf{elif}\;x \le 4.00953015364486885541650984422639355434 \cdot 10^{48}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\left(x + 4\right) \cdot \frac{1}{y} - \frac{x}{y} \cdot z\right|\\ \end{array}\]

Error

Try it out

Derivation

`if x < -1.1091102582946148e+97`

`if -1.1091102582946148e+97 < x < 4.009530153644869e+48`

`if 4.009530153644869e+48 < x`

Reproduce

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