Average Error: 1.5 → 0.2
Time: 20.5s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -4.566012676414608 \cdot 10^{-11}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \le 1.7329015777673845 \cdot 10^{+52}:\\ \;\;\;\;\left|\frac{\left(4 + x\right) - z \cdot x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - z \cdot \frac{x}{y}\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -4.566012676414608 \cdot 10^{-11}:\\
\;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\

\mathbf{elif}\;x \le 1.7329015777673845 \cdot 10^{+52}:\\
\;\;\;\;\left|\frac{\left(4 + x\right) - z \cdot x}{y}\right|\\

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

\end{array}
double f(double x, double y, double z) {
        double r1116745 = x;
        double r1116746 = 4.0;
        double r1116747 = r1116745 + r1116746;
        double r1116748 = y;
        double r1116749 = r1116747 / r1116748;
        double r1116750 = r1116745 / r1116748;
        double r1116751 = z;
        double r1116752 = r1116750 * r1116751;
        double r1116753 = r1116749 - r1116752;
        double r1116754 = fabs(r1116753);
        return r1116754;
}
↓
double f(double x, double y, double z) {
        double r1116755 = x;
        double r1116756 = -4.566012676414608e-11;
        bool r1116757 = r1116755 <= r1116756;
        double r1116758 = 4.0;
        double r1116759 = r1116758 + r1116755;
        double r1116760 = y;
        double r1116761 = r1116759 / r1116760;
        double r1116762 = z;
        double r1116763 = r1116762 / r1116760;
        double r1116764 = r1116755 * r1116763;
        double r1116765 = r1116761 - r1116764;
        double r1116766 = fabs(r1116765);
        double r1116767 = 1.7329015777673845e+52;
        bool r1116768 = r1116755 <= r1116767;
        double r1116769 = r1116762 * r1116755;
        double r1116770 = r1116759 - r1116769;
        double r1116771 = r1116770 / r1116760;
        double r1116772 = fabs(r1116771);
        double r1116773 = r1116755 / r1116760;
        double r1116774 = r1116762 * r1116773;
        double r1116775 = r1116761 - r1116774;
        double r1116776 = fabs(r1116775);
        double r1116777 = r1116768 ? r1116772 : r1116776;
        double r1116778 = r1116757 ? r1116766 : r1116777;
        return r1116778;
}

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 < -4.566012676414608e-11

    1. Initial program 0.1

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

    3. Applied div-inv0.2

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

    4. Applied associate-*l*0.2

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

    5. Simplified0.2

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

    if -4.566012676414608e-11 < x < 1.7329015777673845e+52

    1. Initial program 2.3

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

    3. Applied associate-*l/0.2

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

    4. Applied sub-div0.2

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

    if 1.7329015777673845e+52 < x

    1. Initial program 0.1

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -4.566012676414608 \cdot 10^{-11}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \frac{z}{y}\right|\\ \mathbf{elif}\;x \le 1.7329015777673845 \cdot 10^{+52}:\\ \;\;\;\;\left|\frac{\left(4 + x\right) - z \cdot x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - z \cdot \frac{x}{y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2019132 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))