Average Error: 0.0 → 0
Time: 6.8s
Precision: 64
\[x \cdot 116.0 - 16.0\]
↓
\[\mathsf{fma}\left(x, 116.0, -16.0\right)\]
x \cdot 116.0 - 16.0
↓
\mathsf{fma}\left(x, 116.0, -16.0\right)
double f(double x) {
        double r11880043 = x;
        double r11880044 = 116.0;
        double r11880045 = r11880043 * r11880044;
        double r11880046 = 16.0;
        double r11880047 = r11880045 - r11880046;
        return r11880047;
}
↓
double f(double x) {
        double r11880048 = x;
        double r11880049 = 116.0;
        double r11880050 = 16.0;
        double r11880051 = -r11880050;
        double r11880052 = fma(r11880048, r11880049, r11880051);
        return r11880052;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.0

    \[x \cdot 116.0 - 16.0\]
  2. Using strategy rm

  3. Applied fma-neg0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, 116.0, -16.0\right)}\]

  4. Final simplification0

    \[\leadsto \mathsf{fma}\left(x, 116.0, -16.0\right)\]

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  (- (* x 116.0) 16.0))