Average Error: 1.5 → 0.1
Time: 13.3s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1329896688031834:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{z}{y} \cdot x\right|\\ \mathbf{elif}\;y \le 4.832848088860469210716999004498436556972 \cdot 10^{-23}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{z}{y} \cdot x\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;y \le -1329896688031834:\\
\;\;\;\;\left|\frac{x + 4}{y} - \frac{z}{y} \cdot x\right|\\

\mathbf{elif}\;y \le 4.832848088860469210716999004498436556972 \cdot 10^{-23}:\\
\;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\

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

\end{array}
double f(double x, double y, double z) {
        double r1078513 = x;
        double r1078514 = 4.0;
        double r1078515 = r1078513 + r1078514;
        double r1078516 = y;
        double r1078517 = r1078515 / r1078516;
        double r1078518 = r1078513 / r1078516;
        double r1078519 = z;
        double r1078520 = r1078518 * r1078519;
        double r1078521 = r1078517 - r1078520;
        double r1078522 = fabs(r1078521);
        return r1078522;
}
↓
double f(double x, double y, double z) {
        double r1078523 = y;
        double r1078524 = -1329896688031834.0;
        bool r1078525 = r1078523 <= r1078524;
        double r1078526 = x;
        double r1078527 = 4.0;
        double r1078528 = r1078526 + r1078527;
        double r1078529 = r1078528 / r1078523;
        double r1078530 = z;
        double r1078531 = r1078530 / r1078523;
        double r1078532 = r1078531 * r1078526;
        double r1078533 = r1078529 - r1078532;
        double r1078534 = fabs(r1078533);
        double r1078535 = 4.832848088860469e-23;
        bool r1078536 = r1078523 <= r1078535;
        double r1078537 = r1078526 * r1078530;
        double r1078538 = r1078528 - r1078537;
        double r1078539 = r1078538 / r1078523;
        double r1078540 = fabs(r1078539);
        double r1078541 = r1078536 ? r1078540 : r1078534;
        double r1078542 = r1078525 ? r1078534 : r1078541;
        return r1078542;
}

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 y < -1329896688031834.0 or 4.832848088860469e-23 < y

    1. Initial program 2.5

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

    3. Applied div-inv2.5

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

    4. Applied associate-*l*0.1

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

    5. Simplified0.1

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

    if -1329896688031834.0 < y < 4.832848088860469e-23

    1. Initial program 0.1

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
    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 simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1329896688031834:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{z}{y} \cdot x\right|\\ \mathbf{elif}\;y \le 4.832848088860469210716999004498436556972 \cdot 10^{-23}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{z}{y} \cdot x\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))))