Average Error: 0.0 → 0
Time: 551.0ms
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 r251990 = x;
        double r251991 = 116.0;
        double r251992 = r251990 * r251991;
        double r251993 = 16.0;
        double r251994 = r251992 - r251993;
        return r251994;
}
↓
double f(double x) {
        double r251995 = x;
        double r251996 = 116.0;
        double r251997 = 16.0;
        double r251998 = -r251997;
        double r251999 = fma(r251995, r251996, r251998);
        return r251999;
}

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 2020057 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  :precision binary64
  (- (* x 116) 16))