Average Error: 0.0 → 0
Time: 5.6s
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 r163803 = x;
        double r163804 = 116.0;
        double r163805 = r163803 * r163804;
        double r163806 = 16.0;
        double r163807 = r163805 - r163806;
        return r163807;
}
↓
double f(double x) {
        double r163808 = x;
        double r163809 = 116.0;
        double r163810 = 16.0;
        double r163811 = -r163810;
        double r163812 = fma(r163808, r163809, r163811);
        return r163812;
}

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 2019208 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  :precision binary64
  (- (* x 116) 16))