Average Error: 0.0 → 0
Time: 7.3s
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 r193334 = x;
        double r193335 = 116.0;
        double r193336 = r193334 * r193335;
        double r193337 = 16.0;
        double r193338 = r193336 - r193337;
        return r193338;
}
↓
double f(double x) {
        double r193339 = x;
        double r193340 = 116.0;
        double r193341 = 16.0;
        double r193342 = -r193341;
        double r193343 = fma(r193339, r193340, r193342);
        return r193343;
}

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 2019323 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  :precision binary64
  (- (* x 116) 16))