Average Error: 0.4 → 0.2
Time: 13.6s
Precision: binary64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[z \cdot \left(6 \cdot \left(x - y\right)\right) + \left(y \cdot 4 - x \cdot 3\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
z \cdot \left(6 \cdot \left(x - y\right)\right) + \left(y \cdot 4 - x \cdot 3\right)
(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))
↓
(FPCore (x y z)
 :precision binary64
 (+ (* z (* 6.0 (- x y))) (- (* y 4.0) (* x 3.0))))
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 (z * (6.0 * (x - y))) + ((y * 4.0) - (x * 3.0));
}

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. Simplified0.2

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

  3. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{\left(6 \cdot \left(x \cdot z\right) + 4 \cdot y\right) - \left(3 \cdot x + 6 \cdot \left(z \cdot y\right)\right)}\]

  4. Simplified0.2

    \[\leadsto \color{blue}{z \cdot \left(6 \cdot \left(x - y\right)\right) - \left(x \cdot 3 - 4 \cdot y\right)}\]

  5. Final simplification0.2

    \[\leadsto z \cdot \left(6 \cdot \left(x - y\right)\right) + \left(y \cdot 4 - x \cdot 3\right)\]

Reproduce

herbie shell --seed 2021176 
(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))))