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 r638 = 0.5;
        double r639 = x;
        double r640 = r639 * r639;
        double r641 = y;
        double r642 = r640 - r641;
        double r643 = r638 * r642;
        return r643;
}
↓
double f(double x, double y) {
        double r644 = 0.5;
        double r645 = x;
        double r646 = y;
        double r647 = -r646;
        double r648 = fma(r645, r645, r647);
        double r649 = r644 * r648;
        return r649;
}

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 2020045 +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)))