Average Error: 0.0 → 0.0
Time: 919.0ms
Precision: 64
\[500 \cdot \left(x - y\right)\]
↓
\[\mathsf{fma}\left(500 \cdot 1, x, 500 \cdot \left(-y\right)\right)\]
500 \cdot \left(x - y\right)
↓
\mathsf{fma}\left(500 \cdot 1, x, 500 \cdot \left(-y\right)\right)
double code(double x, double y) {
	return (500.0 * (x - y));
}
↓
double code(double x, double y) {
	return fma((500.0 * 1.0), x, (500.0 * -y));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[500 \cdot \left(x - y\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.0

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

  4. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{500 \cdot x + 500 \cdot \left(-y\right)}\]
  5. Using strategy rm

  6. Applied *-un-lft-identity0.0

    \[\leadsto 500 \cdot \color{blue}{\left(1 \cdot x\right)} + 500 \cdot \left(-y\right)\]

  7. Applied associate-*r*0.0

    \[\leadsto \color{blue}{\left(500 \cdot 1\right) \cdot x} + 500 \cdot \left(-y\right)\]

  8. Applied fma-def0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(500 \cdot 1, x, 500 \cdot \left(-y\right)\right)}\]

  9. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(500 \cdot 1, x, 500 \cdot \left(-y\right)\right)\]

Reproduce

herbie shell --seed 2020066 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500 (- x y)))