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

Average Error: 0.2 → 0.2

Time: 8.9s

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 r738775 = x;
        double r738776 = 16.0;
        double r738777 = 116.0;
        double r738778 = r738776 / r738777;
        double r738779 = r738775 - r738778;
        double r738780 = 3.0;
        double r738781 = r738779 * r738780;
        double r738782 = y;
        double r738783 = r738781 * r738782;
        return r738783;
}

↓

double f(double x, double y) {
        double r738784 = x;
        double r738785 = 3.0;
        double r738786 = r738784 * r738785;
        double r738787 = 0.41379310344827586;
        double r738788 = r738786 - r738787;
        double r738789 = y;
        double r738790 = r738788 * r738789;
        return r738790;
}

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. Using strategy rm

3. Applied associate-*l* 0.3

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

4. Taylor expanded around 0 0.2

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

5. Simplified 0.2

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

6. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019179 
(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))