Average Error: 0.0 → 0.0
Time: 3.9s
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 r88302 = 0.5;
        double r88303 = x;
        double r88304 = r88303 * r88303;
        double r88305 = y;
        double r88306 = r88304 - r88305;
        double r88307 = r88302 * r88306;
        return r88307;
}
↓
double f(double x, double y) {
        double r88308 = x;
        double r88309 = y;
        double r88310 = -r88309;
        double r88311 = fma(r88308, r88308, r88310);
        double r88312 = 0.5;
        double r88313 = r88311 * r88312;
        return r88313;
}

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 2019163 +o rules:numerics
(FPCore (x y)
  :name "System.Random.MWC.Distributions:standard from mwc-random-0.13.3.2"
  (* 0.5 (- (* x x) y)))