Average Error: 0.0 → 0
Time: 530.0ms
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 r221119 = x;
        double r221120 = 116.0;
        double r221121 = r221119 * r221120;
        double r221122 = 16.0;
        double r221123 = r221121 - r221122;
        return r221123;
}
↓
double f(double x) {
        double r221124 = x;
        double r221125 = 116.0;
        double r221126 = 16.0;
        double r221127 = -r221126;
        double r221128 = fma(r221124, r221125, r221127);
        return r221128;
}

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 2020039 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  :precision binary64
  (- (* x 116) 16))