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

Average Error: 0.2 → 0.2

Time: 3.4s

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 r887683 = x;
        double r887684 = 16.0;
        double r887685 = 116.0;
        double r887686 = r887684 / r887685;
        double r887687 = r887683 - r887686;
        double r887688 = 3.0;
        double r887689 = r887687 * r887688;
        double r887690 = y;
        double r887691 = r887689 * r887690;
        return r887691;
}

↓

double f(double x, double y) {
        double r887692 = x;
        double r887693 = 16.0;
        double r887694 = 116.0;
        double r887695 = r887693 / r887694;
        double r887696 = r887692 - r887695;
        double r887697 = 3.0;
        double r887698 = r887696 * r887697;
        double r887699 = y;
        double r887700 = r887698 * r887699;
        return r887700;
}

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 2020033 +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))