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

Average Error: 0.2 → 0.2

Time: 53.9s

Precision: 64

Math

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

↓

\[\left(x \cdot 3 - 0.4137931034482758563264326312491903081536\right) \cdot y\]

C

double f(double x, double y) {
        double r38468666 = x;
        double r38468667 = 16.0;
        double r38468668 = 116.0;
        double r38468669 = r38468667 / r38468668;
        double r38468670 = r38468666 - r38468669;
        double r38468671 = 3.0;
        double r38468672 = r38468670 * r38468671;
        double r38468673 = y;
        double r38468674 = r38468672 * r38468673;
        return r38468674;
}

↓

double f(double x, double y) {
        double r38468675 = x;
        double r38468676 = 3.0;
        double r38468677 = r38468675 * r38468676;
        double r38468678 = 0.41379310344827586;
        double r38468679 = r38468677 - r38468678;
        double r38468680 = y;
        double r38468681 = r38468679 * r38468680;
        return r38468681;
}

Error

Bits error versus x

Bits error versus y

Target

Original	0.2
Target	0.2
Herbie	0.2

\[y \cdot \left(x \cdot 3 - 0.4137931034482758563264326312491903081536\right)\]

Derivation

1. Initial program 0.2

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

2. Taylor expanded around 0 0.2

   \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right) - 0.4137931034482758563264326312491903081536 \cdot y}\]

3. Simplified 0.2

   \[\leadsto \color{blue}{y \cdot \left(3 \cdot x - 0.4137931034482758563264326312491903081536\right)}\]

4. Final simplification 0.2

   \[\leadsto \left(x \cdot 3 - 0.4137931034482758563264326312491903081536\right) \cdot y\]

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"

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

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