Average Error: 0.1 → 0.1
Time: 14.5s
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 r196111 = 841.0;
        double r196112 = 108.0;
        double r196113 = r196111 / r196112;
        double r196114 = x;
        double r196115 = r196113 * r196114;
        double r196116 = 4.0;
        double r196117 = 29.0;
        double r196118 = r196116 / r196117;
        double r196119 = r196115 + r196118;
        return r196119;
}
↓
double f(double x) {
        double r196120 = 841.0;
        double r196121 = 108.0;
        double r196122 = r196120 / r196121;
        double r196123 = x;
        double r196124 = 4.0;
        double r196125 = 29.0;
        double r196126 = r196124 / r196125;
        double r196127 = fma(r196122, r196123, r196126);
        return r196127;
}

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 2019323 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))