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

Average Error: 0.2 → 0.2

Time: 3.5s

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 r787394 = x;
        double r787395 = 16.0;
        double r787396 = 116.0;
        double r787397 = r787395 / r787396;
        double r787398 = r787394 - r787397;
        double r787399 = 3.0;
        double r787400 = r787398 * r787399;
        double r787401 = y;
        double r787402 = r787400 * r787401;
        return r787402;
}

↓

double f(double x, double y) {
        double r787403 = x;
        double r787404 = 16.0;
        double r787405 = 116.0;
        double r787406 = r787404 / r787405;
        double r787407 = r787403 - r787406;
        double r787408 = 3.0;
        double r787409 = r787407 * r787408;
        double r787410 = y;
        double r787411 = r787409 * r787410;
        return r787411;
}

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 2020049 
(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))