Average Error: 0.1 → 0.1
Time: 3.9s
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 r283821 = 841.0;
        double r283822 = 108.0;
        double r283823 = r283821 / r283822;
        double r283824 = x;
        double r283825 = r283823 * r283824;
        double r283826 = 4.0;
        double r283827 = 29.0;
        double r283828 = r283826 / r283827;
        double r283829 = r283825 + r283828;
        return r283829;
}
↓
double f(double x) {
        double r283830 = 841.0;
        double r283831 = 108.0;
        double r283832 = r283830 / r283831;
        double r283833 = x;
        double r283834 = 4.0;
        double r283835 = 29.0;
        double r283836 = r283834 / r283835;
        double r283837 = fma(r283832, r283833, r283836);
        return r283837;
}

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 2019354 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))