Average Error: 1.7 → 0.3
Time: 32.7s
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 r1243419 = x;
        double r1243420 = 4.0;
        double r1243421 = r1243419 + r1243420;
        double r1243422 = y;
        double r1243423 = r1243421 / r1243422;
        double r1243424 = r1243419 / r1243422;
        double r1243425 = z;
        double r1243426 = r1243424 * r1243425;
        double r1243427 = r1243423 - r1243426;
        double r1243428 = fabs(r1243427);
        return r1243428;
}
↓
double f(double x, double y, double z) {
        double r1243429 = y;
        double r1243430 = -6.478942710526426e+104;
        bool r1243431 = r1243429 <= r1243430;
        double r1243432 = x;
        double r1243433 = 4.0;
        double r1243434 = r1243432 + r1243433;
        double r1243435 = r1243434 / r1243429;
        double r1243436 = z;
        double r1243437 = 1.0;
        double r1243438 = r1243437 / r1243429;
        double r1243439 = r1243436 * r1243438;
        double r1243440 = r1243439 * r1243432;
        double r1243441 = r1243435 - r1243440;
        double r1243442 = fabs(r1243441);
        double r1243443 = 1.232811460582678e-41;
        bool r1243444 = r1243429 <= r1243443;
        double r1243445 = r1243432 * r1243436;
        double r1243446 = r1243434 - r1243445;
        double r1243447 = r1243446 / r1243429;
        double r1243448 = fabs(r1243447);
        double r1243449 = r1243444 ? r1243448 : r1243442;
        double r1243450 = r1243431 ? r1243442 : r1243449;
        return r1243450;
}

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