Average Error: 0.0 → 0
Time: 392.0ms
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 r238765 = x;
        double r238766 = 116.0;
        double r238767 = r238765 * r238766;
        double r238768 = 16.0;
        double r238769 = r238767 - r238768;
        return r238769;
}
↓
double f(double x) {
        double r238770 = x;
        double r238771 = 116.0;
        double r238772 = 16.0;
        double r238773 = -r238772;
        double r238774 = fma(r238770, r238771, r238773);
        return r238774;
}

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 2020056 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  :precision binary64
  (- (* x 116) 16))