Average Error: 0.0 → 0.0
Time: 704.0ms
Precision: 64
\[\left(x \cdot y + x\right) + y\]
↓
\[x + \mathsf{fma}\left(x, y, y\right)\]
\left(x \cdot y + x\right) + y
↓
x + \mathsf{fma}\left(x, y, y\right)
double code(double x, double y) {
	return (((x * y) + x) + y);
}
↓
double code(double x, double y) {
	return (x + fma(x, y, 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

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

  3. Applied +-commutative0.0

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

  4. Applied associate-+l+0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

    \[\leadsto x + \mathsf{fma}\left(x, y, y\right)\]

Reproduce

herbie shell --seed 2020071 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))