Average Error: 0.0 → 0.0
Time: 3.1s
Precision: 64
\[0.5 \cdot \left(x \cdot x - y\right)\]
↓
\[0.5 \cdot \mathsf{fma}\left(x, x, -y\right)\]
0.5 \cdot \left(x \cdot x - y\right)
↓
0.5 \cdot \mathsf{fma}\left(x, x, -y\right)
double f(double x, double y) {
        double r649 = 0.5;
        double r650 = x;
        double r651 = r650 * r650;
        double r652 = y;
        double r653 = r651 - r652;
        double r654 = r649 * r653;
        return r654;
}
↓
double f(double x, double y) {
        double r655 = 0.5;
        double r656 = x;
        double r657 = y;
        double r658 = -r657;
        double r659 = fma(r656, r656, r658);
        double r660 = r655 * r659;
        return r660;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[0.5 \cdot \left(x \cdot x - y\right)\]
  2. Using strategy rm

  3. Applied fma-neg0.0

    \[\leadsto 0.5 \cdot \color{blue}{\mathsf{fma}\left(x, x, -y\right)}\]

  4. Final simplification0.0

    \[\leadsto 0.5 \cdot \mathsf{fma}\left(x, x, -y\right)\]

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(FPCore (x y)
  :name "System.Random.MWC.Distributions:standard from mwc-random-0.13.3.2"
  :precision binary64
  (* 0.5 (- (* x x) y)))