Average Error: 1.6 → 0.6
Time: 3.0s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -3.23303180311761695 \cdot 10^{88} \lor \neg \left(x \le 4.01567555002013953 \cdot 10^{-110}\right):\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \left(x \cdot z\right) \cdot \frac{1}{y}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -3.23303180311761695 \cdot 10^{88} \lor \neg \left(x \le 4.01567555002013953 \cdot 10^{-110}\right):\\
\;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\

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

\end{array}
double f(double x, double y, double z) {
        double r26341 = x;
        double r26342 = 4.0;
        double r26343 = r26341 + r26342;
        double r26344 = y;
        double r26345 = r26343 / r26344;
        double r26346 = r26341 / r26344;
        double r26347 = z;
        double r26348 = r26346 * r26347;
        double r26349 = r26345 - r26348;
        double r26350 = fabs(r26349);
        return r26350;
}
↓
double f(double x, double y, double z) {
        double r26351 = x;
        double r26352 = -3.233031803117617e+88;
        bool r26353 = r26351 <= r26352;
        double r26354 = 4.0156755500201395e-110;
        bool r26355 = r26351 <= r26354;
        double r26356 = !r26355;
        bool r26357 = r26353 || r26356;
        double r26358 = 4.0;
        double r26359 = r26351 + r26358;
        double r26360 = y;
        double r26361 = r26359 / r26360;
        double r26362 = z;
        double r26363 = r26362 / r26360;
        double r26364 = r26351 * r26363;
        double r26365 = r26361 - r26364;
        double r26366 = fabs(r26365);
        double r26367 = r26351 * r26362;
        double r26368 = 1.0;
        double r26369 = r26368 / r26360;
        double r26370 = r26367 * r26369;
        double r26371 = r26361 - r26370;
        double r26372 = fabs(r26371);
        double r26373 = r26357 ? r26366 : r26372;
        return r26373;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if x < -3.233031803117617e+88 or 4.0156755500201395e-110 < x

    1. Initial program 0.6

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
    2. Using strategy rm

    3. Applied div-inv0.6

      \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\left(x \cdot \frac{1}{y}\right)} \cdot z\right|\]

    4. Applied associate-*l*0.8

      \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{x \cdot \left(\frac{1}{y} \cdot z\right)}\right|\]

    5. Simplified0.7

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

    if -3.233031803117617e+88 < x < 4.0156755500201395e-110

    1. Initial program 2.4

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
    2. Using strategy rm

    3. Applied div-inv2.4

      \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\left(x \cdot \frac{1}{y}\right)} \cdot z\right|\]

    4. Applied associate-*l*5.2

      \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{x \cdot \left(\frac{1}{y} \cdot z\right)}\right|\]

    5. Simplified5.2

      \[\leadsto \left|\frac{x + 4}{y} - x \cdot \color{blue}{\frac{z}{y}}\right|\]
    6. Using strategy rm

    7. Applied div-inv5.2

      \[\leadsto \left|\frac{x + 4}{y} - x \cdot \color{blue}{\left(z \cdot \frac{1}{y}\right)}\right|\]

    8. Applied associate-*r*0.4

      \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\left(x \cdot z\right) \cdot \frac{1}{y}}\right|\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.23303180311761695 \cdot 10^{88} \lor \neg \left(x \le 4.01567555002013953 \cdot 10^{-110}\right):\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \left(x \cdot z\right) \cdot \frac{1}{y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2020003 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))