Average Error: 0.0 → 0
Time: 2.5s
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 r172057 = x;
        double r172058 = 116.0;
        double r172059 = r172057 * r172058;
        double r172060 = 16.0;
        double r172061 = r172059 - r172060;
        return r172061;
}
↓
double f(double x) {
        double r172062 = x;
        double r172063 = 116.0;
        double r172064 = 16.0;
        double r172065 = -r172064;
        double r172066 = fma(r172062, r172063, r172065);
        return r172066;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.0

    \[x \cdot 116 - 16\]

  2. Simplified0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, 116, -16\right)}\]

  3. Final simplification0

    \[\leadsto \mathsf{fma}\left(x, 116, -16\right)\]

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  (- (* x 116.0) 16.0))