Average Error: 0.0 → 0.0
Time: 1.5s
Precision: binary64
\[500 \cdot \left(x - y\right) \]
↓
\[\mathsf{fma}\left(500, x, -500 \cdot y\right) \]
500 \cdot \left(x - y\right)
↓
\mathsf{fma}\left(500, x, -500 \cdot y\right)

(FPCore (x y) :precision binary64 (* 500.0 (- x y)))
↓
(FPCore (x y) :precision binary64 (fma 500.0 x (* -500.0 y)))
double code(double x, double y) {
	return 500.0 * (x - y);
}
↓
double code(double x, double y) {
	return fma(500.0, x, (-500.0 * y));
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[500 \cdot \left(x - y\right) \]

  2. Taylor expanded in x around 0 0.0

    \[\leadsto \color{blue}{500 \cdot x - 500 \cdot y} \]

  3. Applied fma-neg_binary640.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(500, x, -500 \cdot y\right)} \]

  4. Simplified0.0

    \[\leadsto \mathsf{fma}\left(500, x, \color{blue}{-500 \cdot y}\right) \]

  5. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(500, x, -500 \cdot y\right) \]

Reproduce

herbie shell --seed 2021307 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))