Average Error: 0.0 → 0.0
Time: 780.0ms
Precision: 64
\[\left(x \cdot y + x\right) + y\]
↓
\[\mathsf{fma}\left(x + 1, y, x\right)\]
\left(x \cdot y + x\right) + y
↓
\mathsf{fma}\left(x + 1, y, x\right)
double code(double x, double y) {
	return ((double) (((double) (((double) (x * y)) + x)) + y));
}
↓
double code(double x, double y) {
	return ((double) fma(((double) (x + 1.0)), y, x));
}

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. Simplified0.0

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

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020120 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))