Average Error: 0.0 → 0
Time: 538.0ms
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 r197210 = x;
        double r197211 = 116.0;
        double r197212 = r197210 * r197211;
        double r197213 = 16.0;
        double r197214 = r197212 - r197213;
        return r197214;
}
↓
double f(double x) {
        double r197215 = x;
        double r197216 = 116.0;
        double r197217 = 16.0;
        double r197218 = -r197217;
        double r197219 = fma(r197215, r197216, r197218);
        return r197219;
}

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 2020027 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  :precision binary64
  (- (* x 116) 16))