Average Error: 1.5 → 3.7
Time: 3.1s
Precision: 64
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\]
\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|
↓
\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|
double f(double x, double y, double z) {
        double r27855 = x;
        double r27856 = 4.0;
        double r27857 = r27855 + r27856;
        double r27858 = y;
        double r27859 = r27857 / r27858;
        double r27860 = r27855 / r27858;
        double r27861 = z;
        double r27862 = r27860 * r27861;
        double r27863 = r27859 - r27862;
        double r27864 = fabs(r27863);
        return r27864;
}
↓
double f(double x, double y, double z) {
        double r27865 = x;
        double r27866 = 4.0;
        double r27867 = r27865 + r27866;
        double r27868 = z;
        double r27869 = r27865 * r27868;
        double r27870 = r27867 - r27869;
        double r27871 = y;
        double r27872 = r27870 / r27871;
        double r27873 = fabs(r27872);
        return r27873;
}

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. Initial program 1.5

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

  3. Applied associate-*l/3.7

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

  4. Applied sub-div3.7

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

  5. Final simplification3.7

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

Reproduce

herbie shell --seed 2020081 +o rules:numerics
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))