Average Error: 0.0 → 0
Time: 6.3s
Precision: 64
\[x \cdot 116.0 - 16.0\]
↓
\[\mathsf{fma}\left(x, 116.0, -16.0\right)\]
x \cdot 116.0 - 16.0
↓
\mathsf{fma}\left(x, 116.0, -16.0\right)
double f(double x) {
        double r9521878 = x;
        double r9521879 = 116.0;
        double r9521880 = r9521878 * r9521879;
        double r9521881 = 16.0;
        double r9521882 = r9521880 - r9521881;
        return r9521882;
}
↓
double f(double x) {
        double r9521883 = x;
        double r9521884 = 116.0;
        double r9521885 = 16.0;
        double r9521886 = -r9521885;
        double r9521887 = fma(r9521883, r9521884, r9521886);
        return r9521887;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.0

    \[x \cdot 116.0 - 16.0\]
  2. Using strategy rm

  3. Applied fma-neg0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, 116.0, -16.0\right)}\]

  4. Final simplification0

    \[\leadsto \mathsf{fma}\left(x, 116.0, -16.0\right)\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  (- (* x 116.0) 16.0))