Average Error: 0.1 → 0.1
Time: 14.2s
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 r169961 = 841.0;
        double r169962 = 108.0;
        double r169963 = r169961 / r169962;
        double r169964 = x;
        double r169965 = r169963 * r169964;
        double r169966 = 4.0;
        double r169967 = 29.0;
        double r169968 = r169966 / r169967;
        double r169969 = r169965 + r169968;
        return r169969;
}
↓
double f(double x) {
        double r169970 = 841.0;
        double r169971 = 108.0;
        double r169972 = r169970 / r169971;
        double r169973 = x;
        double r169974 = 4.0;
        double r169975 = 29.0;
        double r169976 = r169974 / r169975;
        double r169977 = fma(r169972, r169973, r169976);
        return r169977;
}

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)))