Average Error: 0.0 → 0
Time: 4.7s
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 r8945928 = x;
        double r8945929 = 116.0;
        double r8945930 = r8945928 * r8945929;
        double r8945931 = 16.0;
        double r8945932 = r8945930 - r8945931;
        return r8945932;
}
↓
double f(double x) {
        double r8945933 = x;
        double r8945934 = 116.0;
        double r8945935 = 16.0;
        double r8945936 = -r8945935;
        double r8945937 = fma(r8945933, r8945934, r8945936);
        return r8945937;
}

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 2019171 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  (- (* x 116.0) 16.0))