Average Error: 0.1 → 0.1
Time: 15.0s
Precision: 64
\[\frac{841}{108} \cdot x + \frac{4}{29}\]
↓
\[\mathsf{fma}\left(\frac{841}{108}, x, \frac{4}{29}\right)\]
\frac{841}{108} \cdot x + \frac{4}{29}
↓
\mathsf{fma}\left(\frac{841}{108}, x, \frac{4}{29}\right)
double f(double x) {
        double r22013995 = 841.0;
        double r22013996 = 108.0;
        double r22013997 = r22013995 / r22013996;
        double r22013998 = x;
        double r22013999 = r22013997 * r22013998;
        double r22014000 = 4.0;
        double r22014001 = 29.0;
        double r22014002 = r22014000 / r22014001;
        double r22014003 = r22013999 + r22014002;
        return r22014003;
}
↓
double f(double x) {
        double r22014004 = 841.0;
        double r22014005 = 108.0;
        double r22014006 = r22014004 / r22014005;
        double r22014007 = x;
        double r22014008 = 4.0;
        double r22014009 = 29.0;
        double r22014010 = r22014008 / r22014009;
        double r22014011 = fma(r22014006, r22014007, r22014010);
        return r22014011;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.1

    \[\frac{841}{108} \cdot x + \frac{4}{29}\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{841}{108}, x, \frac{4}{29}\right)}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(\frac{841}{108}, x, \frac{4}{29}\right)\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0)))