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

Average Error: 0.2 → 0.2

Time: 4.1s

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 r905544 = x;
        double r905545 = 16.0;
        double r905546 = 116.0;
        double r905547 = r905545 / r905546;
        double r905548 = r905544 - r905547;
        double r905549 = 3.0;
        double r905550 = r905548 * r905549;
        double r905551 = y;
        double r905552 = r905550 * r905551;
        return r905552;
}

↓

double f(double x, double y) {
        double r905553 = x;
        double r905554 = 16.0;
        double r905555 = 116.0;
        double r905556 = r905554 / r905555;
        double r905557 = r905553 - r905556;
        double r905558 = 3.0;
        double r905559 = r905557 * r905558;
        double r905560 = y;
        double r905561 = r905559 * r905560;
        return r905561;
}

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 2020046 +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))