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

Average Error: 0.1 → 0.1

Time: 8.0s

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 r360032 = 841.0;
        double r360033 = 108.0;
        double r360034 = r360032 / r360033;
        double r360035 = x;
        double r360036 = r360034 * r360035;
        double r360037 = 4.0;
        double r360038 = 29.0;
        double r360039 = r360037 / r360038;
        double r360040 = r360036 + r360039;
        return r360040;
}

↓

double f(double x) {
        double r360041 = 841.0;
        double r360042 = 108.0;
        double r360043 = r360041 / r360042;
        double r360044 = x;
        double r360045 = 4.0;
        double r360046 = 29.0;
        double r360047 = r360045 / r360046;
        double r360048 = fma(r360043, r360044, r360047);
        return r360048;
}

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)))