Average Error: 0.0 → 0
Time: 3.6s
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 r136670 = x;
        double r136671 = 116.0;
        double r136672 = r136670 * r136671;
        double r136673 = 16.0;
        double r136674 = r136672 - r136673;
        return r136674;
}
↓
double f(double x) {
        double r136675 = x;
        double r136676 = 116.0;
        double r136677 = 16.0;
        double r136678 = -r136677;
        double r136679 = fma(r136675, r136676, r136678);
        return r136679;
}

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 2019322 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  :precision binary64
  (- (* x 116) 16))