Average Error: 1.7 → 0.4
Time: 27.4s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -8.312384016693071 \cdot 10^{+68}:\\ \;\;\;\;\left|\frac{4 + x}{y} - \frac{x}{y} \cdot z\right|\\ \mathbf{elif}\;x \le 1.600822711776517 \cdot 10^{+81}:\\ \;\;\;\;\left|\frac{\left(4 + x\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - \frac{x}{y} \cdot z\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -8.312384016693071 \cdot 10^{+68}:\\
\;\;\;\;\left|\frac{4 + x}{y} - \frac{x}{y} \cdot z\right|\\

\mathbf{elif}\;x \le 1.600822711776517 \cdot 10^{+81}:\\
\;\;\;\;\left|\frac{\left(4 + x\right) - x \cdot z}{y}\right|\\

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

\end{array}
double f(double x, double y, double z) {
        double r1459096 = x;
        double r1459097 = 4.0;
        double r1459098 = r1459096 + r1459097;
        double r1459099 = y;
        double r1459100 = r1459098 / r1459099;
        double r1459101 = r1459096 / r1459099;
        double r1459102 = z;
        double r1459103 = r1459101 * r1459102;
        double r1459104 = r1459100 - r1459103;
        double r1459105 = fabs(r1459104);
        return r1459105;
}
↓
double f(double x, double y, double z) {
        double r1459106 = x;
        double r1459107 = -8.312384016693071e+68;
        bool r1459108 = r1459106 <= r1459107;
        double r1459109 = 4.0;
        double r1459110 = r1459109 + r1459106;
        double r1459111 = y;
        double r1459112 = r1459110 / r1459111;
        double r1459113 = r1459106 / r1459111;
        double r1459114 = z;
        double r1459115 = r1459113 * r1459114;
        double r1459116 = r1459112 - r1459115;
        double r1459117 = fabs(r1459116);
        double r1459118 = 1.600822711776517e+81;
        bool r1459119 = r1459106 <= r1459118;
        double r1459120 = r1459106 * r1459114;
        double r1459121 = r1459110 - r1459120;
        double r1459122 = r1459121 / r1459111;
        double r1459123 = fabs(r1459122);
        double r1459124 = r1459119 ? r1459123 : r1459117;
        double r1459125 = r1459108 ? r1459117 : r1459124;
        return r1459125;
}

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 x < -8.312384016693071e+68 or 1.600822711776517e+81 < x

    1. Initial program 0.1

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

    if -8.312384016693071e+68 < x < 1.600822711776517e+81

    1. Initial program 2.2

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

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -8.312384016693071 \cdot 10^{+68}:\\ \;\;\;\;\left|\frac{4 + x}{y} - \frac{x}{y} \cdot z\right|\\ \mathbf{elif}\;x \le 1.600822711776517 \cdot 10^{+81}:\\ \;\;\;\;\left|\frac{\left(4 + x\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - \frac{x}{y} \cdot z\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2019104 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))