Average Error: 0.4 → 0.2
Time: 9.5s
Precision: binary64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[\left(x + \left(y - x\right) \cdot 4\right) - z \cdot \left(\left(y - x\right) \cdot 6\right)\]
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) - z \cdot \left(\left(y - x\right) \cdot 6\right)
(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)) (* z (* (- y x) 6.0))))
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)) - (z * ((y - x) * 6.0));
}

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_binary64_111910.4

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

  5. Applied distribute-rgt-in_binary64_111500.4

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

  6. Applied associate-+r+_binary64_111320.4

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2020281 
(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))))