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

Average Error: 0.2 → 0.2

Time: 5.5s

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 r989102 = x;
        double r989103 = 16.0;
        double r989104 = 116.0;
        double r989105 = r989103 / r989104;
        double r989106 = r989102 - r989105;
        double r989107 = 3.0;
        double r989108 = r989106 * r989107;
        double r989109 = y;
        double r989110 = r989108 * r989109;
        return r989110;
}

↓

double f(double x, double y) {
        double r989111 = x;
        double r989112 = 16.0;
        double r989113 = 116.0;
        double r989114 = r989112 / r989113;
        double r989115 = r989111 - r989114;
        double r989116 = 3.0;
        double r989117 = r989115 * r989116;
        double r989118 = y;
        double r989119 = r989117 * r989118;
        return r989119;
}

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. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019353 +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))