Average Error: 1.7 → 0.4
Time: 17.5s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.6359444841938246 \cdot 10^{+35}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \le 4.712266768697627 \cdot 10^{-112}:\\ \;\;\;\;\left|\frac{\left(4 + x\right) - z \cdot x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.6359444841938246 \cdot 10^{+35}:\\
\;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\

\mathbf{elif}\;x \le 4.712266768697627 \cdot 10^{-112}:\\
\;\;\;\;\left|\frac{\left(4 + x\right) - z \cdot x}{y}\right|\\

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

\end{array}
double f(double x, double y, double z) {
        double r1194510 = x;
        double r1194511 = 4.0;
        double r1194512 = r1194510 + r1194511;
        double r1194513 = y;
        double r1194514 = r1194512 / r1194513;
        double r1194515 = r1194510 / r1194513;
        double r1194516 = z;
        double r1194517 = r1194515 * r1194516;
        double r1194518 = r1194514 - r1194517;
        double r1194519 = fabs(r1194518);
        return r1194519;
}
↓
double f(double x, double y, double z) {
        double r1194520 = x;
        double r1194521 = -1.6359444841938246e+35;
        bool r1194522 = r1194520 <= r1194521;
        double r1194523 = 4.0;
        double r1194524 = r1194523 + r1194520;
        double r1194525 = y;
        double r1194526 = r1194524 / r1194525;
        double r1194527 = z;
        double r1194528 = r1194527 / r1194525;
        double r1194529 = r1194520 * r1194528;
        double r1194530 = r1194526 - r1194529;
        double r1194531 = fabs(r1194530);
        double r1194532 = 4.712266768697627e-112;
        bool r1194533 = r1194520 <= r1194532;
        double r1194534 = r1194527 * r1194520;
        double r1194535 = r1194524 - r1194534;
        double r1194536 = r1194535 / r1194525;
        double r1194537 = fabs(r1194536);
        double r1194538 = r1194533 ? r1194537 : r1194531;
        double r1194539 = r1194522 ? r1194531 : r1194538;
        return r1194539;
}

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 < -1.6359444841938246e+35 or 4.712266768697627e-112 < x

    1. Initial program 0.7

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

    3. Applied div-inv0.7

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

    4. Applied associate-*l*0.9

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

    5. Simplified0.8

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

    if -1.6359444841938246e+35 < x < 4.712266768697627e-112

    1. Initial program 2.6

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

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.6359444841938246 \cdot 10^{+35}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \le 4.712266768697627 \cdot 10^{-112}:\\ \;\;\;\;\left|\frac{\left(4 + x\right) - z \cdot x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2019139 +o rules:numerics
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))