Average Error: 0.0 → 0
Time: 6.6s
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 r225765 = x;
        double r225766 = 116.0;
        double r225767 = r225765 * r225766;
        double r225768 = 16.0;
        double r225769 = r225767 - r225768;
        return r225769;
}
↓
double f(double x) {
        double r225770 = x;
        double r225771 = 116.0;
        double r225772 = 16.0;
        double r225773 = -r225772;
        double r225774 = fma(r225770, r225771, r225773);
        return r225774;
}

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))