Average Error: 1.5 → 0.7
Time: 25.4s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -3.3838648223904146 \cdot 10^{+193}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \left(z \cdot \frac{1}{y}\right)\right|\\ \mathbf{elif}\;x \le 5.423759248273869 \cdot 10^{-22}:\\ \;\;\;\;\left|\frac{\left(4 + x\right) - z \cdot x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \left(z \cdot \frac{1}{y}\right)\right|\\ \end{array}\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\begin{array}{l}
\mathbf{if}\;x \le -3.3838648223904146 \cdot 10^{+193}:\\
\;\;\;\;\left|\frac{4 + x}{y} - x \cdot \left(z \cdot \frac{1}{y}\right)\right|\\

\mathbf{elif}\;x \le 5.423759248273869 \cdot 10^{-22}:\\
\;\;\;\;\left|\frac{\left(4 + x\right) - z \cdot x}{y}\right|\\

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

\end{array}
double f(double x, double y, double z) {
        double r1485759 = x;
        double r1485760 = 4.0;
        double r1485761 = r1485759 + r1485760;
        double r1485762 = y;
        double r1485763 = r1485761 / r1485762;
        double r1485764 = r1485759 / r1485762;
        double r1485765 = z;
        double r1485766 = r1485764 * r1485765;
        double r1485767 = r1485763 - r1485766;
        double r1485768 = fabs(r1485767);
        return r1485768;
}
↓
double f(double x, double y, double z) {
        double r1485769 = x;
        double r1485770 = -3.3838648223904146e+193;
        bool r1485771 = r1485769 <= r1485770;
        double r1485772 = 4.0;
        double r1485773 = r1485772 + r1485769;
        double r1485774 = y;
        double r1485775 = r1485773 / r1485774;
        double r1485776 = z;
        double r1485777 = 1.0;
        double r1485778 = r1485777 / r1485774;
        double r1485779 = r1485776 * r1485778;
        double r1485780 = r1485769 * r1485779;
        double r1485781 = r1485775 - r1485780;
        double r1485782 = fabs(r1485781);
        double r1485783 = 5.423759248273869e-22;
        bool r1485784 = r1485769 <= r1485783;
        double r1485785 = r1485776 * r1485769;
        double r1485786 = r1485773 - r1485785;
        double r1485787 = r1485786 / r1485774;
        double r1485788 = fabs(r1485787);
        double r1485789 = r1485784 ? r1485788 : r1485782;
        double r1485790 = r1485771 ? r1485782 : r1485789;
        return r1485790;
}

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 < -3.3838648223904146e+193 or 5.423759248273869e-22 < x

    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

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

    if -3.3838648223904146e+193 < x < 5.423759248273869e-22

    1. Initial program 2.0

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

    3. Applied associate-*l/0.9

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

    4. Applied sub-div0.8

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.3838648223904146 \cdot 10^{+193}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \left(z \cdot \frac{1}{y}\right)\right|\\ \mathbf{elif}\;x \le 5.423759248273869 \cdot 10^{-22}:\\ \;\;\;\;\left|\frac{\left(4 + x\right) - z \cdot x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - x \cdot \left(z \cdot \frac{1}{y}\right)\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2019119 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))