Average Error: 0.0 → 0
Time: 516.0ms
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 r220683 = x;
        double r220684 = 116.0;
        double r220685 = r220683 * r220684;
        double r220686 = 16.0;
        double r220687 = r220685 - r220686;
        return r220687;
}
↓
double f(double x) {
        double r220688 = x;
        double r220689 = 116.0;
        double r220690 = 16.0;
        double r220691 = -r220690;
        double r220692 = fma(r220688, r220689, r220691);
        return r220692;
}

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 2020065 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  :precision binary64
  (- (* x 116) 16))