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

Average Error: 0.1 → 0.1

Time: 10.0s

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 r176539 = 841.0;
        double r176540 = 108.0;
        double r176541 = r176539 / r176540;
        double r176542 = x;
        double r176543 = r176541 * r176542;
        double r176544 = 4.0;
        double r176545 = 29.0;
        double r176546 = r176544 / r176545;
        double r176547 = r176543 + r176546;
        return r176547;
}

↓

double f(double x) {
        double r176548 = 841.0;
        double r176549 = 108.0;
        double r176550 = r176548 / r176549;
        double r176551 = x;
        double r176552 = 4.0;
        double r176553 = 29.0;
        double r176554 = r176552 / r176553;
        double r176555 = fma(r176550, r176551, r176554);
        return r176555;
}

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 2019350 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))