Average Error: 0.0 → 0
Time: 7.7s
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 r186157 = x;
        double r186158 = 116.0;
        double r186159 = r186157 * r186158;
        double r186160 = 16.0;
        double r186161 = r186159 - r186160;
        return r186161;
}
↓
double f(double x) {
        double r186162 = x;
        double r186163 = 116.0;
        double r186164 = 16.0;
        double r186165 = -r186164;
        double r186166 = fma(r186162, r186163, r186165);
        return r186166;
}

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))