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

Average Error: 0.2 → 0.2

Time: 15.1s

Precision: 64

Math

\[\left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right) \cdot y\]

↓

\[y \cdot \left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right)\]

C

double f(double x, double y) {
        double r42769710 = x;
        double r42769711 = 16.0;
        double r42769712 = 116.0;
        double r42769713 = r42769711 / r42769712;
        double r42769714 = r42769710 - r42769713;
        double r42769715 = 3.0;
        double r42769716 = r42769714 * r42769715;
        double r42769717 = y;
        double r42769718 = r42769716 * r42769717;
        return r42769718;
}

↓

double f(double x, double y) {
        double r42769719 = y;
        double r42769720 = x;
        double r42769721 = 16.0;
        double r42769722 = 116.0;
        double r42769723 = r42769721 / r42769722;
        double r42769724 = r42769720 - r42769723;
        double r42769725 = 3.0;
        double r42769726 = r42769724 * r42769725;
        double r42769727 = r42769719 * r42769726;
        return r42769727;
}

Error

Bits error versus x

Bits error versus y

Target

Original	0.2
Target	0.2
Herbie	0.2

\[y \cdot \left(x \cdot 3.0 - 0.41379310344827586\right)\]

Derivation

1. Initial program 0.2

   \[\left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right) \cdot y\]

2. Final simplification 0.2

   \[\leadsto y \cdot \left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right)\]

Reproduce

herbie shell --seed 2019158 
(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))