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

Average Error: 0.2 → 0.2

Time: 3.9s

Precision: 64

Math

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

↓

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

C

double f(double x, double y) {
        double r864641 = x;
        double r864642 = 16.0;
        double r864643 = 116.0;
        double r864644 = r864642 / r864643;
        double r864645 = r864641 - r864644;
        double r864646 = 3.0;
        double r864647 = r864645 * r864646;
        double r864648 = y;
        double r864649 = r864647 * r864648;
        return r864649;
}

↓

double f(double x, double y) {
        double r864650 = x;
        double r864651 = 16.0;
        double r864652 = 116.0;
        double r864653 = r864651 / r864652;
        double r864654 = r864650 - r864653;
        double r864655 = 3.0;
        double r864656 = r864654 * r864655;
        double r864657 = y;
        double r864658 = r864656 * r864657;
        return r864658;
}

Error

Bits error versus x

Bits error versus y

Target

Original	0.2
Target	0.2
Herbie	0.2

\[y \cdot \left(x \cdot 3 - 0.413793103448275856\right)\]

Derivation

1. Initial program 0.2

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

2. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020021 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3) 0.41379310344827586))

  (* (* (- x (/ 16 116)) 3) y))