Average Error: 0.0 → 0
Time: 529.0ms
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 r277523 = x;
        double r277524 = 116.0;
        double r277525 = r277523 * r277524;
        double r277526 = 16.0;
        double r277527 = r277525 - r277526;
        return r277527;
}
↓
double f(double x) {
        double r277528 = x;
        double r277529 = 116.0;
        double r277530 = 16.0;
        double r277531 = -r277530;
        double r277532 = fma(r277528, r277529, r277531);
        return r277532;
}

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 2020064 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  :precision binary64
  (- (* x 116) 16))