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

Average Error: 0.2 → 0.2

Time: 10.2s

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 r15580055 = x;
        double r15580056 = 16.0;
        double r15580057 = 116.0;
        double r15580058 = r15580056 / r15580057;
        double r15580059 = r15580055 - r15580058;
        double r15580060 = 3.0;
        double r15580061 = r15580059 * r15580060;
        double r15580062 = y;
        double r15580063 = r15580061 * r15580062;
        return r15580063;
}

↓

double f(double x, double y) {
        double r15580064 = y;
        double r15580065 = x;
        double r15580066 = 16.0;
        double r15580067 = 116.0;
        double r15580068 = r15580066 / r15580067;
        double r15580069 = r15580065 - r15580068;
        double r15580070 = 3.0;
        double r15580071 = r15580069 * r15580070;
        double r15580072 = r15580064 * r15580071;
        return r15580072;
}

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 2019156 +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))