Average Error: 0.0 → 0
Time: 2.9s
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 r175555 = x;
        double r175556 = 116.0;
        double r175557 = r175555 * r175556;
        double r175558 = 16.0;
        double r175559 = r175557 - r175558;
        return r175559;
}
↓
double f(double x) {
        double r175560 = x;
        double r175561 = 116.0;
        double r175562 = 16.0;
        double r175563 = -r175562;
        double r175564 = fma(r175560, r175561, r175563);
        return r175564;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.0

    \[x \cdot 116 - 16\]

  2. Simplified0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, 116, -16\right)}\]

  3. Final simplification0

    \[\leadsto \mathsf{fma}\left(x, 116, -16\right)\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  (- (* x 116.0) 16.0))