Average Error: 0.0 → 0
Time: 9.2s
Precision: 64
\[x \cdot 116 - 16\]
↓
\[\mathsf{fma}\left(x, 116, -16\right)\]
x \cdot 116 - 16
↓
\mathsf{fma}\left(x, 116, -16\right)
double f(double x) {
        double r159793 = x;
        double r159794 = 116.0;
        double r159795 = r159793 * r159794;
        double r159796 = 16.0;
        double r159797 = r159795 - r159796;
        return r159797;
}
↓
double f(double x) {
        double r159798 = x;
        double r159799 = 116.0;
        double r159800 = 16.0;
        double r159801 = -r159800;
        double r159802 = fma(r159798, r159799, r159801);
        return r159802;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.0

    \[x \cdot 116 - 16\]
  2. Using strategy rm

  3. Applied fma-neg0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, 116, -16\right)}\]

  4. Final simplification0

    \[\leadsto \mathsf{fma}\left(x, 116, -16\right)\]

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  (- (* x 116.0) 16.0))