Average Error: 0.0 → 0.0
Time: 1.0s
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 r518 = 0.5;
        double r519 = x;
        double r520 = r519 * r519;
        double r521 = y;
        double r522 = r520 - r521;
        double r523 = r518 * r522;
        return r523;
}
↓
double f(double x, double y) {
        double r524 = 0.5;
        double r525 = x;
        double r526 = y;
        double r527 = -r526;
        double r528 = fma(r525, r525, r527);
        double r529 = r524 * r528;
        return r529;
}

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 2019354 +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)))