Average Error: 0.0 → 0
Time: 448.0ms
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 r184677 = x;
        double r184678 = 116.0;
        double r184679 = r184677 * r184678;
        double r184680 = 16.0;
        double r184681 = r184679 - r184680;
        return r184681;
}
↓
double f(double x) {
        double r184682 = x;
        double r184683 = 116.0;
        double r184684 = 16.0;
        double r184685 = -r184684;
        double r184686 = fma(r184682, r184683, r184685);
        return r184686;
}

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 2020047 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  :precision binary64
  (- (* x 116) 16))