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

Average Error: 0.1 → 0.1

Time: 5.9s

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 r308298 = 841.0;
        double r308299 = 108.0;
        double r308300 = r308298 / r308299;
        double r308301 = x;
        double r308302 = r308300 * r308301;
        double r308303 = 4.0;
        double r308304 = 29.0;
        double r308305 = r308303 / r308304;
        double r308306 = r308302 + r308305;
        return r308306;
}

↓

double f(double x) {
        double r308307 = 841.0;
        double r308308 = 108.0;
        double r308309 = r308307 / r308308;
        double r308310 = x;
        double r308311 = 4.0;
        double r308312 = 29.0;
        double r308313 = r308311 / r308312;
        double r308314 = fma(r308309, r308310, r308313);
        return r308314;
}

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 2020047 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))