Average Error: 1.7 → 0.3
Time: 3.2s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -5.613880646235681 \cdot 10^{87} \lor \neg \left(x \le 5.30749059840940589 \cdot 10^{-20}\right):\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -5.613880646235681 \cdot 10^{87} \lor \neg \left(x \le 5.30749059840940589 \cdot 10^{-20}\right):\\
\;\;\;\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\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 r27525 = x;
        double r27526 = 4.0;
        double r27527 = r27525 + r27526;
        double r27528 = y;
        double r27529 = r27527 / r27528;
        double r27530 = r27525 / r27528;
        double r27531 = z;
        double r27532 = r27530 * r27531;
        double r27533 = r27529 - r27532;
        double r27534 = fabs(r27533);
        return r27534;
}
↓
double f(double x, double y, double z) {
        double r27535 = x;
        double r27536 = -5.613880646235681e+87;
        bool r27537 = r27535 <= r27536;
        double r27538 = 5.307490598409406e-20;
        bool r27539 = r27535 <= r27538;
        double r27540 = !r27539;
        bool r27541 = r27537 || r27540;
        double r27542 = 4.0;
        double r27543 = r27535 + r27542;
        double r27544 = y;
        double r27545 = r27543 / r27544;
        double r27546 = r27535 / r27544;
        double r27547 = z;
        double r27548 = r27546 * r27547;
        double r27549 = r27545 - r27548;
        double r27550 = fabs(r27549);
        double r27551 = r27535 * r27547;
        double r27552 = r27543 - r27551;
        double r27553 = r27552 / r27544;
        double r27554 = fabs(r27553);
        double r27555 = r27541 ? r27550 : r27554;
        return r27555;
}

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 < -5.613880646235681e+87 or 5.307490598409406e-20 < x

    1. Initial program 0.1

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

    if -5.613880646235681e+87 < x < 5.307490598409406e-20

    1. Initial program 2.6

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

    3. Applied associate-*l/0.3

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

    4. Applied sub-div0.3

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -5.613880646235681 \cdot 10^{87} \lor \neg \left(x \le 5.30749059840940589 \cdot 10^{-20}\right):\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2020059 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))