Average Error: 1.8 → 0.7
Time: 6.2s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -4.21510854934102217 \cdot 10^{93}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\\ \mathbf{elif}\;x \le 7.43806599639702096 \cdot 10^{-140}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -4.21510854934102217 \cdot 10^{93}:\\
\;\;\;\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\\

\mathbf{elif}\;x \le 7.43806599639702096 \cdot 10^{-140}:\\
\;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\

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

\end{array}
double f(double x, double y, double z) {
        double r26342 = x;
        double r26343 = 4.0;
        double r26344 = r26342 + r26343;
        double r26345 = y;
        double r26346 = r26344 / r26345;
        double r26347 = r26342 / r26345;
        double r26348 = z;
        double r26349 = r26347 * r26348;
        double r26350 = r26346 - r26349;
        double r26351 = fabs(r26350);
        return r26351;
}
↓
double f(double x, double y, double z) {
        double r26352 = x;
        double r26353 = -4.215108549341022e+93;
        bool r26354 = r26352 <= r26353;
        double r26355 = 4.0;
        double r26356 = r26352 + r26355;
        double r26357 = y;
        double r26358 = r26356 / r26357;
        double r26359 = r26352 / r26357;
        double r26360 = z;
        double r26361 = r26359 * r26360;
        double r26362 = r26358 - r26361;
        double r26363 = fabs(r26362);
        double r26364 = 7.438065996397021e-140;
        bool r26365 = r26352 <= r26364;
        double r26366 = r26352 * r26360;
        double r26367 = r26356 - r26366;
        double r26368 = r26367 / r26357;
        double r26369 = fabs(r26368);
        double r26370 = r26360 / r26357;
        double r26371 = r26352 * r26370;
        double r26372 = r26358 - r26371;
        double r26373 = fabs(r26372);
        double r26374 = r26365 ? r26369 : r26373;
        double r26375 = r26354 ? r26363 : r26374;
        return r26375;
}

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 3 regimes

  2. if x < -4.215108549341022e+93

    1. Initial program 0.1

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

    if -4.215108549341022e+93 < x < 7.438065996397021e-140

    1. Initial program 2.7

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
    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 7.438065996397021e-140 < x

    1. Initial program 1.1

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

    3. Applied div-inv1.1

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

    4. Applied associate-*l*1.3

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

    5. Simplified1.2

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -4.21510854934102217 \cdot 10^{93}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\\ \mathbf{elif}\;x \le 7.43806599639702096 \cdot 10^{-140}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))