Average Error: 0.0 → 0.0
Time: 5.7s
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 r8612 = 0.5;
        double r8613 = x;
        double r8614 = r8613 * r8613;
        double r8615 = y;
        double r8616 = r8614 - r8615;
        double r8617 = r8612 * r8616;
        return r8617;
}
↓
double f(double x, double y) {
        double r8618 = 0.5;
        double r8619 = x;
        double r8620 = y;
        double r8621 = -r8620;
        double r8622 = fma(r8619, r8619, r8621);
        double r8623 = r8618 * r8622;
        return r8623;
}

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 2019306 +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)))