Average Error: 0.0 → 0.0
Time: 5.0s
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 r8608 = 0.5;
        double r8609 = x;
        double r8610 = r8609 * r8609;
        double r8611 = y;
        double r8612 = r8610 - r8611;
        double r8613 = r8608 * r8612;
        return r8613;
}
↓
double f(double x, double y) {
        double r8614 = 0.5;
        double r8615 = x;
        double r8616 = y;
        double r8617 = -r8616;
        double r8618 = fma(r8615, r8615, r8617);
        double r8619 = r8614 * r8618;
        return r8619;
}

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 2019325 +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)))