Average Error: 0.0 → 0.0
Time: 1.2s
Precision: binary64
\[0.5 \cdot \left(x \cdot x - y\right) \]
↓
\[0.5 \cdot \mathsf{fma}\left(x, x, -y\right) \]
0.5 \cdot \left(x \cdot x - y\right)
↓
0.5 \cdot \mathsf{fma}\left(x, x, -y\right)

(FPCore (x y) :precision binary64 (* 0.5 (- (* x x) y)))
↓
(FPCore (x y) :precision binary64 (* 0.5 (fma x x (- y))))
double code(double x, double y) {
	return 0.5 * ((x * x) - y);
}
↓
double code(double x, double y) {
	return 0.5 * fma(x, x, -y);
}

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. Applied fma-neg_binary640.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2022067 
(FPCore (x y)
  :name "System.Random.MWC.Distributions:standard from mwc-random-0.13.3.2"
  :precision binary64
  (* 0.5 (- (* x x) y)))