Average Error: 0.4 → 0.2
Time: 15.0s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)
double f(double x, double y, double z) {
        double r226920 = x;
        double r226921 = y;
        double r226922 = r226921 - r226920;
        double r226923 = 6.0;
        double r226924 = r226922 * r226923;
        double r226925 = 2.0;
        double r226926 = 3.0;
        double r226927 = r226925 / r226926;
        double r226928 = z;
        double r226929 = r226927 - r226928;
        double r226930 = r226924 * r226929;
        double r226931 = r226920 + r226930;
        return r226931;
}
↓
double f(double x, double y, double z) {
        double r226932 = x;
        double r226933 = y;
        double r226934 = r226933 - r226932;
        double r226935 = 6.0;
        double r226936 = 2.0;
        double r226937 = 3.0;
        double r226938 = r226936 / r226937;
        double r226939 = z;
        double r226940 = r226938 - r226939;
        double r226941 = r226935 * r226940;
        double r226942 = r226934 * r226941;
        double r226943 = r226932 + r226942;
        return r226943;
}

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 0.4

    \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.2

    \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\]

  4. Final simplification0.2

    \[\leadsto x + \left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)\]

Reproduce

herbie shell --seed 2019294 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6) (- (/ 2 3) z))))