Average Error: 0.0 → 0
Time: 7.1s
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 r242129 = x;
        double r242130 = 116.0;
        double r242131 = r242129 * r242130;
        double r242132 = 16.0;
        double r242133 = r242131 - r242132;
        return r242133;
}
↓
double f(double x) {
        double r242134 = x;
        double r242135 = 116.0;
        double r242136 = 16.0;
        double r242137 = -r242136;
        double r242138 = fma(r242134, r242135, r242137);
        return r242138;
}

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 2019326 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  :precision binary64
  (- (* x 116) 16))