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

Average Error: 0.2 → 0.2

Time: 3.2s

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 r780155 = x;
        double r780156 = 16.0;
        double r780157 = 116.0;
        double r780158 = r780156 / r780157;
        double r780159 = r780155 - r780158;
        double r780160 = 3.0;
        double r780161 = r780159 * r780160;
        double r780162 = y;
        double r780163 = r780161 * r780162;
        return r780163;
}

↓

double f(double x, double y) {
        double r780164 = x;
        double r780165 = 16.0;
        double r780166 = 116.0;
        double r780167 = r780165 / r780166;
        double r780168 = r780164 - r780167;
        double r780169 = 3.0;
        double r780170 = r780168 * r780169;
        double r780171 = y;
        double r780172 = r780170 * r780171;
        return r780172;
}

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 2020020 
(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))