Data.Colour.CIE:lightness from colour-2.3.3

Average Error: 0.0 → 0

Time: 1.3s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[x \cdot 116 - 16\]

↓

\[\mathsf{fma}\left(x, 116, -16\right)\]

C

double f(double x) {
        double r279535 = x;
        double r279536 = 116.0;
        double r279537 = r279535 * r279536;
        double r279538 = 16.0;
        double r279539 = r279537 - r279538;
        return r279539;
}

↓

double f(double x) {
        double r279540 = x;
        double r279541 = 116.0;
        double r279542 = 16.0;
        double r279543 = -r279542;
        double r279544 = fma(r279540, r279541, r279543);
        return r279544;
}

Error

Bits error versus x

Derivation

1. Initial program 0.0

   \[x \cdot 116 - 16\]
2. Using strategy rm

3. Applied fma-neg 0

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 116, -16\right)}\]

4. Final simplification 0

   \[\leadsto \mathsf{fma}\left(x, 116, -16\right)\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  :precision binary64
  (- (* x 116) 16))