Data.Colour.CIE:cieLAB from colour-2.3.3, A

Average Error: 0.3 → 0.3

Time: 6.1s

Precision: binary64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]

↓

\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]

C

double code(double x, double y) {
	return ((double) (((double) (((double) (x - (16.0 / 116.0))) * 3.0)) * y));
}

↓

double code(double x, double y) {
	return ((double) (((double) (((double) (x - (16.0 / 116.0))) * 3.0)) * y));
}

Error

Bits error versus x

Bits error versus y

Target

Original	0.3
Target	0.2
Herbie	0.3

\[y \cdot \left(x \cdot 3 - 0.413793103448275856\right)\]

Derivation

1. Initial program 0.3

   \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]

2. Final simplification 0.3

   \[\leadsto \left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]

Reproduce

herbie shell --seed 2020182 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3.0) 0.41379310344827586))

  (* (* (- x (/ 16.0 116.0)) 3.0) y))