Average Error: 0.4 → 0.2
Time: 16.5s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(y - x\right) \cdot \left(\left(\frac{2}{3} - z\right) \cdot 6\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(y - x\right) \cdot \left(\left(\frac{2}{3} - z\right) \cdot 6\right)
double f(double x, double y, double z) {
        double r202738 = x;
        double r202739 = y;
        double r202740 = r202739 - r202738;
        double r202741 = 6.0;
        double r202742 = r202740 * r202741;
        double r202743 = 2.0;
        double r202744 = 3.0;
        double r202745 = r202743 / r202744;
        double r202746 = z;
        double r202747 = r202745 - r202746;
        double r202748 = r202742 * r202747;
        double r202749 = r202738 + r202748;
        return r202749;
}
↓
double f(double x, double y, double z) {
        double r202750 = x;
        double r202751 = y;
        double r202752 = r202751 - r202750;
        double r202753 = 2.0;
        double r202754 = 3.0;
        double r202755 = r202753 / r202754;
        double r202756 = z;
        double r202757 = r202755 - r202756;
        double r202758 = 6.0;
        double r202759 = r202757 * r202758;
        double r202760 = r202752 * r202759;
        double r202761 = r202750 + r202760;
        return r202761;
}

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. Simplified0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019212 
(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))))