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

Average Error: 0.1 → 0.1

Time: 8.4s

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 r322915 = 841.0;
        double r322916 = 108.0;
        double r322917 = r322915 / r322916;
        double r322918 = x;
        double r322919 = r322917 * r322918;
        double r322920 = 4.0;
        double r322921 = 29.0;
        double r322922 = r322920 / r322921;
        double r322923 = r322919 + r322922;
        return r322923;
}

↓

double f(double x) {
        double r322924 = 841.0;
        double r322925 = 108.0;
        double r322926 = r322924 / r322925;
        double r322927 = x;
        double r322928 = 4.0;
        double r322929 = 29.0;
        double r322930 = r322928 / r322929;
        double r322931 = fma(r322926, r322927, r322930);
        return r322931;
}

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 2020042 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))