Average Error: 1.7 → 0.3
Time: 35.8s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -6.478942710526426 \cdot 10^{+104}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \left(z \cdot \frac{1}{y}\right) \cdot x\right|\\ \mathbf{elif}\;y \le 1.232811460582678 \cdot 10^{-41}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \left(z \cdot \frac{1}{y}\right) \cdot x\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;y \le -6.478942710526426 \cdot 10^{+104}:\\
\;\;\;\;\left|\frac{x + 4}{y} - \left(z \cdot \frac{1}{y}\right) \cdot x\right|\\

\mathbf{elif}\;y \le 1.232811460582678 \cdot 10^{-41}:\\
\;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\

\mathbf{else}:\\
\;\;\;\;\left|\frac{x + 4}{y} - \left(z \cdot \frac{1}{y}\right) \cdot x\right|\\

\end{array}
double f(double x, double y, double z) {
        double r3976577 = x;
        double r3976578 = 4.0;
        double r3976579 = r3976577 + r3976578;
        double r3976580 = y;
        double r3976581 = r3976579 / r3976580;
        double r3976582 = r3976577 / r3976580;
        double r3976583 = z;
        double r3976584 = r3976582 * r3976583;
        double r3976585 = r3976581 - r3976584;
        double r3976586 = fabs(r3976585);
        return r3976586;
}
↓
double f(double x, double y, double z) {
        double r3976587 = y;
        double r3976588 = -6.478942710526426e+104;
        bool r3976589 = r3976587 <= r3976588;
        double r3976590 = x;
        double r3976591 = 4.0;
        double r3976592 = r3976590 + r3976591;
        double r3976593 = r3976592 / r3976587;
        double r3976594 = z;
        double r3976595 = 1.0;
        double r3976596 = r3976595 / r3976587;
        double r3976597 = r3976594 * r3976596;
        double r3976598 = r3976597 * r3976590;
        double r3976599 = r3976593 - r3976598;
        double r3976600 = fabs(r3976599);
        double r3976601 = 1.232811460582678e-41;
        bool r3976602 = r3976587 <= r3976601;
        double r3976603 = r3976590 * r3976594;
        double r3976604 = r3976592 - r3976603;
        double r3976605 = r3976604 / r3976587;
        double r3976606 = fabs(r3976605);
        double r3976607 = r3976602 ? r3976606 : r3976600;
        double r3976608 = r3976589 ? r3976600 : r3976607;
        return r3976608;
}

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 < -6.478942710526426e+104 or 1.232811460582678e-41 < y

    1. Initial program 3.0

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

    3. Applied div-inv3.1

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

    4. Applied associate-*l*0.2

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

    if -6.478942710526426e+104 < y < 1.232811460582678e-41

    1. Initial program 0.2

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

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -6.478942710526426 \cdot 10^{+104}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \left(z \cdot \frac{1}{y}\right) \cdot x\right|\\ \mathbf{elif}\;y \le 1.232811460582678 \cdot 10^{-41}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \left(z \cdot \frac{1}{y}\right) \cdot x\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2019107 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))