Average Error: 0.0 → 0.0
Time: 38.2s
Precision: 64
\[0.5 \cdot \left(x \cdot x - y\right)\]
↓
\[\mathsf{fma}\left(x, x, -y\right) \cdot 0.5\]
0.5 \cdot \left(x \cdot x - y\right)
↓
\mathsf{fma}\left(x, x, -y\right) \cdot 0.5
double f(double x, double y) {
        double r144215 = 0.5;
        double r144216 = x;
        double r144217 = r144216 * r144216;
        double r144218 = y;
        double r144219 = r144217 - r144218;
        double r144220 = r144215 * r144219;
        return r144220;
}
↓
double f(double x, double y) {
        double r144221 = x;
        double r144222 = y;
        double r144223 = -r144222;
        double r144224 = fma(r144221, r144221, r144223);
        double r144225 = 0.5;
        double r144226 = r144224 * r144225;
        return r144226;
}

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

    \[\leadsto \mathsf{fma}\left(x, x, -y\right) \cdot 0.5\]

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(FPCore (x y)
  :name "System.Random.MWC.Distributions:standard from mwc-random-0.13.3.2"
  (* 0.5 (- (* x x) y)))