Average Error: 1.8 → 0.7
Time: 8.4s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -4.21510854934102217 \cdot 10^{93}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\\ \mathbf{elif}\;x \le 7.43806599639702096 \cdot 10^{-140}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -4.21510854934102217 \cdot 10^{93}:\\
\;\;\;\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\\

\mathbf{elif}\;x \le 7.43806599639702096 \cdot 10^{-140}:\\
\;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\

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

\end{array}
double f(double x, double y, double z) {
        double r28658 = x;
        double r28659 = 4.0;
        double r28660 = r28658 + r28659;
        double r28661 = y;
        double r28662 = r28660 / r28661;
        double r28663 = r28658 / r28661;
        double r28664 = z;
        double r28665 = r28663 * r28664;
        double r28666 = r28662 - r28665;
        double r28667 = fabs(r28666);
        return r28667;
}
↓
double f(double x, double y, double z) {
        double r28668 = x;
        double r28669 = -4.215108549341022e+93;
        bool r28670 = r28668 <= r28669;
        double r28671 = 4.0;
        double r28672 = r28668 + r28671;
        double r28673 = y;
        double r28674 = r28672 / r28673;
        double r28675 = r28668 / r28673;
        double r28676 = z;
        double r28677 = r28675 * r28676;
        double r28678 = r28674 - r28677;
        double r28679 = fabs(r28678);
        double r28680 = 7.438065996397021e-140;
        bool r28681 = r28668 <= r28680;
        double r28682 = r28668 * r28676;
        double r28683 = r28672 - r28682;
        double r28684 = r28683 / r28673;
        double r28685 = fabs(r28684);
        double r28686 = r28676 / r28673;
        double r28687 = r28668 * r28686;
        double r28688 = r28674 - r28687;
        double r28689 = fabs(r28688);
        double r28690 = r28681 ? r28685 : r28689;
        double r28691 = r28670 ? r28679 : r28690;
        return r28691;
}

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 3 regimes

  2. if x < -4.215108549341022e+93

    1. Initial program 0.1

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

    if -4.215108549341022e+93 < x < 7.438065996397021e-140

    1. Initial program 2.7

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

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

    if 7.438065996397021e-140 < x

    1. Initial program 1.1

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

    3. Applied div-inv1.1

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

    4. Applied associate-*l*1.3

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

    5. Simplified1.2

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -4.21510854934102217 \cdot 10^{93}:\\ \;\;\;\;\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\\ \mathbf{elif}\;x \le 7.43806599639702096 \cdot 10^{-140}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))