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

Average Error: 0.2 → 0.2

Time: 11.5s

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 r613560 = x;
        double r613561 = 16.0;
        double r613562 = 116.0;
        double r613563 = r613561 / r613562;
        double r613564 = r613560 - r613563;
        double r613565 = 3.0;
        double r613566 = r613564 * r613565;
        double r613567 = y;
        double r613568 = r613566 * r613567;
        return r613568;
}

↓

double f(double x, double y) {
        double r613569 = x;
        double r613570 = 16.0;
        double r613571 = 116.0;
        double r613572 = r613570 / r613571;
        double r613573 = r613569 - r613572;
        double r613574 = 3.0;
        double r613575 = r613573 * r613574;
        double r613576 = y;
        double r613577 = r613575 * r613576;
        return r613577;
}

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 2019305 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3) 0.413793103448275856))

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