Average Error: 0.1 → 0.1
Time: 9.8s
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 r226998 = 841.0;
        double r226999 = 108.0;
        double r227000 = r226998 / r226999;
        double r227001 = x;
        double r227002 = r227000 * r227001;
        double r227003 = 4.0;
        double r227004 = 29.0;
        double r227005 = r227003 / r227004;
        double r227006 = r227002 + r227005;
        return r227006;
}
↓
double f(double x) {
        double r227007 = 841.0;
        double r227008 = 108.0;
        double r227009 = r227007 / r227008;
        double r227010 = x;
        double r227011 = 4.0;
        double r227012 = 29.0;
        double r227013 = r227011 / r227012;
        double r227014 = fma(r227009, r227010, r227013);
        return r227014;
}

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 2019209 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))