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

Average Error: 0.2 → 0.2

Time: 3.6s

Precision: binary64

Cost: 448

Math

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

↓

\[y \cdot \left(3 \cdot \left(x - 0.13793103448275862\right)\right)\]

FPCore

(FPCore (x y) :precision binary64 (* (* (- x (/ 16.0 116.0)) 3.0) y))

↓

(FPCore (x y) :precision binary64 (* y (* 3.0 (- x 0.13793103448275862))))

C

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

↓

double code(double x, double y) {
	return y * (3.0 * (x - 0.13793103448275862));
}

Error

Bits error versus x

Bits error versus y

Target

Original	0.2
Target	0.2
Herbie	0.2

\[y \cdot \left(x \cdot 3 - 0.41379310344827586\right)\]

Alternatives

Alternative 1
Error	1.6
Cost	962

\[\begin{array}{l} \mathbf{if}\;x \leq -0.13662751078619076:\\ \;\;\;\;x \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;x \leq 0.1407298311331217:\\ \;\;\;\;y \cdot -0.41379310344827586\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(3 \cdot x\right)\\ \end{array}\]

Alternative 2
Error	1.6
Cost	648

\[\begin{array}{l} \mathbf{if}\;x \leq -0.13662751078619076 \lor \neg \left(x \leq 0.1407298311331217\right):\\ \;\;\;\;y \cdot \left(3 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.41379310344827586\\ \end{array}\]

Alternative 3
Error	26.8
Cost	192

\[y \cdot -0.41379310344827586\]

Alternative 4
Error	61.7
Cost	64

\[1\]

Derivation

1. Initial program 0.2

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

2. Simplified 0.2

   \[\leadsto \color{blue}{y \cdot \left(3 \cdot \left(x - 0.13793103448275862\right)\right)}\]

3. Final simplification 0.2

   \[\leadsto y \cdot \left(3 \cdot \left(x - 0.13793103448275862\right)\right)\]

Reproduce

herbie shell --seed 2021044 
(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))