Average Error: 0.1 → 0.1
Time: 1.8s
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 r294185 = 841.0;
        double r294186 = 108.0;
        double r294187 = r294185 / r294186;
        double r294188 = x;
        double r294189 = r294187 * r294188;
        double r294190 = 4.0;
        double r294191 = 29.0;
        double r294192 = r294190 / r294191;
        double r294193 = r294189 + r294192;
        return r294193;
}
↓
double f(double x) {
        double r294194 = 841.0;
        double r294195 = 108.0;
        double r294196 = r294194 / r294195;
        double r294197 = x;
        double r294198 = 4.0;
        double r294199 = 29.0;
        double r294200 = r294198 / r294199;
        double r294201 = fma(r294196, r294197, r294200);
        return r294201;
}

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 2020027 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))