Average Error: 1.6 → 1.6
Time: 7.6s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|\left(-\frac{x}{y}\right) \cdot z + \frac{4 + x}{y}\right|\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\left|\left(-\frac{x}{y}\right) \cdot z + \frac{4 + x}{y}\right|
double f(double x, double y, double z) {
        double r830770 = x;
        double r830771 = 4.0;
        double r830772 = r830770 + r830771;
        double r830773 = y;
        double r830774 = r830772 / r830773;
        double r830775 = r830770 / r830773;
        double r830776 = z;
        double r830777 = r830775 * r830776;
        double r830778 = r830774 - r830777;
        double r830779 = fabs(r830778);
        return r830779;
}
↓
double f(double x, double y, double z) {
        double r830780 = x;
        double r830781 = y;
        double r830782 = r830780 / r830781;
        double r830783 = -r830782;
        double r830784 = z;
        double r830785 = r830783 * r830784;
        double r830786 = 4.0;
        double r830787 = r830786 + r830780;
        double r830788 = r830787 / r830781;
        double r830789 = r830785 + r830788;
        double r830790 = fabs(r830789);
        return r830790;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.6

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

  3. Applied sub-neg1.6

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

  4. Final simplification1.6

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

Reproduce

herbie shell --seed 2019156 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))