Average Error: 0.4 → 0.2
Time: 5.4s
Precision: binary64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(4 \cdot \left(y - x\right) + \left(y - x\right) \cdot \left(z \cdot -6\right)\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(4 \cdot \left(y - x\right) + \left(y - x\right) \cdot \left(z \cdot -6\right)\right)
(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))
↓
(FPCore (x y z)
 :precision binary64
 (+ x (+ (* 4.0 (- y x)) (* (- 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 + ((4.0 * (y - x)) + ((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. 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 associate-*l*_binary640.2

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

  5. Simplified0.2

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

  7. Applied sub-neg_binary640.2

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

  8. Applied distribute-rgt-in_binary640.2

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

  9. Final simplification0.2

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

Alternatives

Reproduce

herbie shell --seed 2021118 
(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))))