Average Error: 0.0 → 0.0
Time: 559.0ms
Precision: binary64
\[\left(x \cdot y + x\right) + y\]
↓
\[y + \left(x + x \cdot y\right)\]
\left(x \cdot y + x\right) + y
↓
y + \left(x + x \cdot y\right)
(FPCore (x y) :precision binary64 (+ (+ (* x y) x) y))
↓
(FPCore (x y) :precision binary64 (+ y (+ x (* x y))))
double code(double x, double y) {
	return ((double) (((double) (((double) (x * y)) + x)) + y));
}
↓
double code(double x, double y) {
	return ((double) (y + ((double) (x + ((double) (x * 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. Final simplification0.0

    \[\leadsto y + \left(x + x \cdot y\right)\]

Reproduce

herbie shell --seed 2020198 
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))