Average Error: 0.0 → 0
Time: 539.0ms
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 r215652 = x;
        double r215653 = 116.0;
        double r215654 = r215652 * r215653;
        double r215655 = 16.0;
        double r215656 = r215654 - r215655;
        return r215656;
}
↓
double f(double x) {
        double r215657 = x;
        double r215658 = 116.0;
        double r215659 = 16.0;
        double r215660 = -r215659;
        double r215661 = fma(r215657, r215658, r215660);
        return r215661;
}

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 2020024 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  :precision binary64
  (- (* x 116) 16))