Average Error: 0.0 → 0.0
Time: 4.9s
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 r8857 = 0.5;
        double r8858 = x;
        double r8859 = r8858 * r8858;
        double r8860 = y;
        double r8861 = r8859 - r8860;
        double r8862 = r8857 * r8861;
        return r8862;
}
↓
double f(double x, double y) {
        double r8863 = 0.5;
        double r8864 = x;
        double r8865 = y;
        double r8866 = -r8865;
        double r8867 = fma(r8864, r8864, r8866);
        double r8868 = r8863 * r8867;
        return r8868;
}

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 2019347 +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)))