Data.Colour.CIE:lightness from colour-2.3.3

Average Error: 0.0 → 0

Time: 3.1s

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 r236733 = x;
        double r236734 = 116.0;
        double r236735 = r236733 * r236734;
        double r236736 = 16.0;
        double r236737 = r236735 - r236736;
        return r236737;
}

↓

double f(double x) {
        double r236738 = x;
        double r236739 = 116.0;
        double r236740 = 16.0;
        double r236741 = -r236740;
        double r236742 = fma(r236738, r236739, r236741);
        return r236742;
}

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 2019351 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  :precision binary64
  (- (* x 116) 16))