Average Error: 0.4 → 0.2
Time: 4.7s
Precision: binary64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(\left(y - x\right) \cdot 4 + \left(\left(y - x\right) \cdot z\right) \cdot -6\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(\left(y - x\right) \cdot 4 + \left(\left(y - x\right) \cdot z\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) (* (* (- y x) z) -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) + (((y - x) * z) * -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. Using strategy rm

  3. Applied sub-neg_binary64_93600.4

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

  4. Applied distribute-rgt-in_binary64_93170.4

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

  5. Simplified0.2

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

  6. Simplified0.2

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

  8. Applied associate-*r*_binary64_93070.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020277 
(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))))