Average Error: 0.4 → 0.4
Time: 3.3s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.66666666666666663 - z\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.66666666666666663 - z\right)
double code(double x, double y, double z) {
	return (x + (((y - x) * 6.0) * ((2.0 / 3.0) - z)));
}
↓
double code(double x, double y, double z) {
	return (x + (((y - x) * 6.0) * (0.6666666666666666 - z)));
}

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. Taylor expanded around 0 0.4

    \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(0.66666666666666663 - z\right)}\]

  3. Final simplification0.4

    \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.66666666666666663 - z\right)\]

Reproduce

herbie shell --seed 2020066 
(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))))