Average Error: 0.4 → 0.1
Time: 3.8s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[4 \cdot y - \mathsf{fma}\left(x, 3, \left(\left(y - x\right) \cdot 6\right) \cdot z\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
4 \cdot y - \mathsf{fma}\left(x, 3, \left(\left(y - x\right) \cdot 6\right) \cdot z\right)
double code(double x, double y, double z) {
	return ((double) (x + ((double) (((double) (((double) (y - x)) * 6.0)) * ((double) (((double) (2.0 / 3.0)) - z))))));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) (4.0 * y)) - ((double) fma(x, 3.0, ((double) (((double) (((double) (y - x)) * 6.0)) * z))))));
}

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-neg0.4

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

  4. Applied distribute-lft-in0.4

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

  5. Applied associate-+r+0.4

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

  6. Simplified0.4

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

  7. Taylor expanded around 0 0.2

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

  9. Applied associate-+l-0.2

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

  10. Simplified0.1

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

  11. Final simplification0.1

    \[\leadsto 4 \cdot y - \mathsf{fma}\left(x, 3, \left(\left(y - x\right) \cdot 6\right) \cdot z\right)\]

Reproduce

herbie shell --seed 2020122 +o rules:numerics
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6) (- (/ 2 3) z))))