Average Error: 0.0 → 0.0
Time: 3.5s
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 r645 = 0.5;
        double r646 = x;
        double r647 = r646 * r646;
        double r648 = y;
        double r649 = r647 - r648;
        double r650 = r645 * r649;
        return r650;
}
↓
double f(double x, double y) {
        double r651 = 0.5;
        double r652 = x;
        double r653 = y;
        double r654 = -r653;
        double r655 = fma(r652, r652, r654);
        double r656 = r651 * r655;
        return r656;
}

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 2020043 +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)))