Average Error: 0.0 → 0
Time: 2.7s
Precision: 64
\[x \cdot 116.0 - 16.0\]
↓
\[\mathsf{fma}\left(x, 116.0, -16.0\right)\]
x \cdot 116.0 - 16.0
↓
\mathsf{fma}\left(x, 116.0, -16.0\right)
double f(double x) {
        double r3738239 = x;
        double r3738240 = 116.0;
        double r3738241 = r3738239 * r3738240;
        double r3738242 = 16.0;
        double r3738243 = r3738241 - r3738242;
        return r3738243;
}
↓
double f(double x) {
        double r3738244 = x;
        double r3738245 = 116.0;
        double r3738246 = 16.0;
        double r3738247 = -r3738246;
        double r3738248 = fma(r3738244, r3738245, r3738247);
        return r3738248;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.0

    \[x \cdot 116.0 - 16.0\]
  2. Using strategy rm

  3. Applied fma-neg0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, 116.0, -16.0\right)}\]

  4. Final simplification0

    \[\leadsto \mathsf{fma}\left(x, 116.0, -16.0\right)\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  (- (* x 116.0) 16.0))