Average Error: 1.4 → 0.2
Time: 2.7s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -7.609461543067301 \cdot 10^{55} \lor \neg \left(x \le 2083989822.488266\right):\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -7.609461543067301 \cdot 10^{55} \lor \neg \left(x \le 2083989822.488266\right):\\
\;\;\;\;\left|\frac{x + 4}{y} - 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 r28530 = x;
        double r28531 = 4.0;
        double r28532 = r28530 + r28531;
        double r28533 = y;
        double r28534 = r28532 / r28533;
        double r28535 = r28530 / r28533;
        double r28536 = z;
        double r28537 = r28535 * r28536;
        double r28538 = r28534 - r28537;
        double r28539 = fabs(r28538);
        return r28539;
}
↓
double f(double x, double y, double z) {
        double r28540 = x;
        double r28541 = -7.609461543067301e+55;
        bool r28542 = r28540 <= r28541;
        double r28543 = 2083989822.488266;
        bool r28544 = r28540 <= r28543;
        double r28545 = !r28544;
        bool r28546 = r28542 || r28545;
        double r28547 = 4.0;
        double r28548 = r28540 + r28547;
        double r28549 = y;
        double r28550 = r28548 / r28549;
        double r28551 = z;
        double r28552 = r28551 / r28549;
        double r28553 = r28540 * r28552;
        double r28554 = r28550 - r28553;
        double r28555 = fabs(r28554);
        double r28556 = r28540 * r28551;
        double r28557 = r28548 - r28556;
        double r28558 = r28557 / r28549;
        double r28559 = fabs(r28558);
        double r28560 = r28546 ? r28555 : r28559;
        return r28560;
}

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 < -7.609461543067301e+55 or 2083989822.488266 < x

    1. Initial program 0.1

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

    3. Applied div-inv0.2

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

    4. Applied associate-*l*0.2

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

    5. Simplified0.1

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

    if -7.609461543067301e+55 < x < 2083989822.488266

    1. Initial program 2.1

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

    3. Applied associate-*l/0.2

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

    4. Applied sub-div0.2

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -7.609461543067301 \cdot 10^{55} \lor \neg \left(x \le 2083989822.488266\right):\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))