Average Error: 0.4 → 0.2
Time: 2.8s
Precision: binary64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(\left(y - x\right) \cdot 4 + 6 \cdot \left(z \cdot \left(x - y\right)\right)\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(\left(y - x\right) \cdot 4 + 6 \cdot \left(z \cdot \left(x - y\right)\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 (+ (* (- y x) 4.0) (* 6.0 (* z (- x y))))))
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) + (6.0 * (z * (x - y))));
}

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-rgt-in_binary640.4

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

  6. Simplified0.2

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

  7. Simplified0.2

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

  9. Applied associate-*l*_binary640.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2020233 
(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))))