Average Error: 0.0 → 0
Time: 8.6s
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 r161955 = x;
        double r161956 = 116.0;
        double r161957 = r161955 * r161956;
        double r161958 = 16.0;
        double r161959 = r161957 - r161958;
        return r161959;
}
↓
double f(double x) {
        double r161960 = x;
        double r161961 = 116.0;
        double r161962 = 16.0;
        double r161963 = -r161962;
        double r161964 = fma(r161960, r161961, r161963);
        return r161964;
}

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))