Average Error: 0.0 → 0.0
Time: 5.4s
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 r8638 = 0.5;
        double r8639 = x;
        double r8640 = r8639 * r8639;
        double r8641 = y;
        double r8642 = r8640 - r8641;
        double r8643 = r8638 * r8642;
        return r8643;
}
↓
double f(double x, double y) {
        double r8644 = 0.5;
        double r8645 = x;
        double r8646 = y;
        double r8647 = -r8646;
        double r8648 = fma(r8645, r8645, r8647);
        double r8649 = r8644 * r8648;
        return r8649;
}

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 2019326 +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)))