Average Error: 0.0 → 0
Time: 3.7s
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 r217960 = x;
        double r217961 = 116.0;
        double r217962 = r217960 * r217961;
        double r217963 = 16.0;
        double r217964 = r217962 - r217963;
        return r217964;
}
↓
double f(double x) {
        double r217965 = x;
        double r217966 = 116.0;
        double r217967 = 16.0;
        double r217968 = -r217967;
        double r217969 = fma(r217965, r217966, r217968);
        return r217969;
}

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 2019347 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  :precision binary64
  (- (* x 116) 16))