Average Error: 0.0 → 0
Time: 553.0ms
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 r223897 = x;
        double r223898 = 116.0;
        double r223899 = r223897 * r223898;
        double r223900 = 16.0;
        double r223901 = r223899 - r223900;
        return r223901;
}
↓
double f(double x) {
        double r223902 = x;
        double r223903 = 116.0;
        double r223904 = 16.0;
        double r223905 = -r223904;
        double r223906 = fma(r223902, r223903, r223905);
        return r223906;
}

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 2020021 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  :precision binary64
  (- (* x 116) 16))