Average Error: 0.4 → 0.2
Time: 2.6s
Precision: binary64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[\left(x + \left(y - x\right) \cdot 4\right) - \left(\left(y - x\right) \cdot 6\right) \cdot z\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
\left(x + \left(y - x\right) \cdot 4\right) - \left(\left(y - x\right) \cdot 6\right) \cdot z
(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))
↓
(FPCore (x y z)
 :precision binary64
 (- (+ x (* (- y x) 4.0)) (* (* (- y x) 6.0) z)))
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) * 4.0)) - (((y - x) * 6.0) * 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. Simplified0.4

    \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}\]
  3. Using strategy rm

  4. Applied sub-neg_binary640.4

    \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\]

  5. Applied distribute-lft-in_binary640.4

    \[\leadsto x + \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot 0.6666666666666666 + \left(\left(y - x\right) \cdot 6\right) \cdot \left(-z\right)\right)}\]

  6. Applied associate-+r+_binary640.4

    \[\leadsto \color{blue}{\left(x + \left(\left(y - x\right) \cdot 6\right) \cdot 0.6666666666666666\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(-z\right)}\]

  7. Simplified0.2

    \[\leadsto \color{blue}{\left(x + \left(y - x\right) \cdot 4\right)} + \left(\left(y - x\right) \cdot 6\right) \cdot \left(-z\right)\]

  8. Final simplification0.2

    \[\leadsto \left(x + \left(y - x\right) \cdot 4\right) - \left(\left(y - x\right) \cdot 6\right) \cdot z\]

Reproduce

herbie shell --seed 2020220 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))