Average Error: 0.4 → 0.2
Time: 2.9s
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 r135706 = x;
        double r135707 = y;
        double r135708 = r135707 - r135706;
        double r135709 = 6.0;
        double r135710 = r135708 * r135709;
        double r135711 = 2.0;
        double r135712 = 3.0;
        double r135713 = r135711 / r135712;
        double r135714 = z;
        double r135715 = r135713 - r135714;
        double r135716 = r135710 * r135715;
        double r135717 = r135706 + r135716;
        return r135717;
}
↓
double f(double x, double y, double z) {
        double r135718 = x;
        double r135719 = y;
        double r135720 = r135719 - r135718;
        double r135721 = 6.0;
        double r135722 = 2.0;
        double r135723 = 3.0;
        double r135724 = r135722 / r135723;
        double r135725 = z;
        double r135726 = r135724 - r135725;
        double r135727 = r135721 * r135726;
        double r135728 = r135720 * r135727;
        double r135729 = r135718 + r135728;
        return r135729;
}

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 2020003 
(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))))