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

↓

\[\begin{array}{l} \mathbf{if}\;x \le -1.38469845285193904 \cdot 10^{-17} \lor \neg \left(x \le 4.17631854478254968 \cdot 10^{-35}\right):\\ \;\;\;\;\left|\left(\frac{4}{y} + \frac{x}{y}\right) - x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;x \le -1.38469845285193904 \cdot 10^{-17} \lor \neg \left(x \le 4.17631854478254968 \cdot 10^{-35}\right):\\
\;\;\;\;\left|\left(\frac{4}{y} + \frac{x}{y}\right) - x \cdot \frac{z}{y}\right|\\

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

\end{array}

double f(double x, double y, double z) {
        double r26265 = x;
        double r26266 = 4.0;
        double r26267 = r26265 + r26266;
        double r26268 = y;
        double r26269 = r26267 / r26268;
        double r26270 = r26265 / r26268;
        double r26271 = z;
        double r26272 = r26270 * r26271;
        double r26273 = r26269 - r26272;
        double r26274 = fabs(r26273);
        return r26274;
}

↓

double f(double x, double y, double z) {
        double r26275 = x;
        double r26276 = -1.384698452851939e-17;
        bool r26277 = r26275 <= r26276;
        double r26278 = 4.1763185447825497e-35;
        bool r26279 = r26275 <= r26278;
        double r26280 = !r26279;
        bool r26281 = r26277 || r26280;
        double r26282 = 4.0;
        double r26283 = y;
        double r26284 = r26282 / r26283;
        double r26285 = r26275 / r26283;
        double r26286 = r26284 + r26285;
        double r26287 = z;
        double r26288 = r26287 / r26283;
        double r26289 = r26275 * r26288;
        double r26290 = r26286 - r26289;
        double r26291 = fabs(r26290);
        double r26292 = r26275 + r26282;
        double r26293 = r26275 * r26287;
        double r26294 = r26292 - r26293;
        double r26295 = r26294 / r26283;
        double r26296 = fabs(r26295);
        double r26297 = r26281 ? r26291 : r26296;
        return r26297;
}

Derivation

Split input into 2 regimes
if x < -1.384698452851939e-17 or 4.1763185447825497e-35 < x
1. Initial program 0.2
  \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
2. Taylor expanded around 0 0.2
  \[\leadsto \left|\color{blue}{\left(4 \cdot \frac{1}{y} + \frac{x}{y}\right)} - \frac{x}{y} \cdot z\right|\]
3. Simplified0.2
  \[\leadsto \left|\color{blue}{\left(\frac{4}{y} + \frac{x}{y}\right)} - \frac{x}{y} \cdot z\right|\]
4. Using strategy rm
5. Applied div-inv0.2
  \[\leadsto \left|\left(\frac{4}{y} + \frac{x}{y}\right) - \color{blue}{\left(x \cdot \frac{1}{y}\right)} \cdot z\right|\]
6. Applied associate-*l*0.3
  \[\leadsto \left|\left(\frac{4}{y} + \frac{x}{y}\right) - \color{blue}{x \cdot \left(\frac{1}{y} \cdot z\right)}\right|\]
7. Simplified0.3
  \[\leadsto \left|\left(\frac{4}{y} + \frac{x}{y}\right) - x \cdot \color{blue}{\frac{z}{y}}\right|\]
if -1.384698452851939e-17 < x < 4.1763185447825497e-35
1. Initial program 2.8
  \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
2. Using strategy rm
3. Applied associate-*l/0.1
  \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right|\]
4. Applied sub-div0.1
  \[\leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right|\]
Recombined 2 regimes into one program.
Final simplification0.1
\[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.38469845285193904 \cdot 10^{-17} \lor \neg \left(x \le 4.17631854478254968 \cdot 10^{-35}\right):\\ \;\;\;\;\left|\left(\frac{4}{y} + \frac{x}{y}\right) - x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \end{array}\]

Falling back on racket egraph because egg-herbie package not installed (more)

Error

Try it out

Derivation

`if x < -1.384698452851939e-17 or 4.1763185447825497e-35 < x`

`if -1.384698452851939e-17 < x < 4.1763185447825497e-35`

Reproduce

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