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

Average Error: 0.1 → 0.1

Time: 5.8s

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 r334569 = 841.0;
        double r334570 = 108.0;
        double r334571 = r334569 / r334570;
        double r334572 = x;
        double r334573 = r334571 * r334572;
        double r334574 = 4.0;
        double r334575 = 29.0;
        double r334576 = r334574 / r334575;
        double r334577 = r334573 + r334576;
        return r334577;
}

↓

double f(double x) {
        double r334578 = 841.0;
        double r334579 = 108.0;
        double r334580 = r334578 / r334579;
        double r334581 = x;
        double r334582 = 4.0;
        double r334583 = 29.0;
        double r334584 = r334582 / r334583;
        double r334585 = fma(r334580, r334581, r334584);
        return r334585;
}

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 2020046 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))