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

Average Error: 0.2 → 0.2

Time: 36.4s

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 r36984202 = x;
        double r36984203 = 16.0;
        double r36984204 = 116.0;
        double r36984205 = r36984203 / r36984204;
        double r36984206 = r36984202 - r36984205;
        double r36984207 = 3.0;
        double r36984208 = r36984206 * r36984207;
        double r36984209 = y;
        double r36984210 = r36984208 * r36984209;
        return r36984210;
}

↓

double f(double x, double y) {
        double r36984211 = x;
        double r36984212 = 3.0;
        double r36984213 = r36984211 * r36984212;
        double r36984214 = 0.41379310344827586;
        double r36984215 = r36984213 - r36984214;
        double r36984216 = y;
        double r36984217 = r36984215 * r36984216;
        return r36984217;
}

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. Taylor expanded around 0 0.2

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

3. Simplified 0.2

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

4. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019200 +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))