Average Error: 0.0 → 0
Time: 5.0s
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 r10256272 = x;
        double r10256273 = 116.0;
        double r10256274 = r10256272 * r10256273;
        double r10256275 = 16.0;
        double r10256276 = r10256274 - r10256275;
        return r10256276;
}
↓
double f(double x) {
        double r10256277 = x;
        double r10256278 = 116.0;
        double r10256279 = 16.0;
        double r10256280 = -r10256279;
        double r10256281 = fma(r10256277, r10256278, r10256280);
        return r10256281;
}

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 2019192 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  (- (* x 116.0) 16.0))