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

Average Error: 0.1 → 0.1

Time: 8.7s

Precision: 64

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

Math

\[\frac{841}{108} \cdot x + \frac{4}{29}\]

↓

\[\mathsf{fma}\left(\frac{841}{108}, x, \frac{4}{29}\right)\]

C

double f(double x) {
        double r274229 = 841.0;
        double r274230 = 108.0;
        double r274231 = r274229 / r274230;
        double r274232 = x;
        double r274233 = r274231 * r274232;
        double r274234 = 4.0;
        double r274235 = 29.0;
        double r274236 = r274234 / r274235;
        double r274237 = r274233 + r274236;
        return r274237;
}

↓

double f(double x) {
        double r274238 = 841.0;
        double r274239 = 108.0;
        double r274240 = r274238 / r274239;
        double r274241 = x;
        double r274242 = 4.0;
        double r274243 = 29.0;
        double r274244 = r274242 / r274243;
        double r274245 = fma(r274240, r274241, r274244);
        return r274245;
}

Error

Bits error versus x

Derivation

1. Initial program 0.1

   \[\frac{841}{108} \cdot x + \frac{4}{29}\]

2. Simplified 0.1

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{841}{108}, x, \frac{4}{29}\right)}\]

3. Final simplification 0.1

   \[\leadsto \mathsf{fma}\left(\frac{841}{108}, x, \frac{4}{29}\right)\]

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))