Average Error: 0.0 → 0.0
Time: 1.8s
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 r782 = 0.5;
        double r783 = x;
        double r784 = r783 * r783;
        double r785 = y;
        double r786 = r784 - r785;
        double r787 = r782 * r786;
        return r787;
}
↓
double f(double x, double y) {
        double r788 = 0.5;
        double r789 = x;
        double r790 = y;
        double r791 = -r790;
        double r792 = fma(r789, r789, r791);
        double r793 = r788 * r792;
        return r793;
}

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 2020046 +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)))