Average Error: 0.0 → 0.0
Time: 1.8s
Precision: binary64
\[\left(x \cdot y + x\right) + y\]
↓
\[y + \left(y + 1\right) \cdot x\]
\left(x \cdot y + x\right) + y
↓
y + \left(y + 1\right) \cdot x
(FPCore (x y) :precision binary64 (+ (+ (* x y) x) y))
↓
(FPCore (x y) :precision binary64 (+ y (* (+ y 1.0) x)))
double code(double x, double y) {
	return ((x * y) + x) + y;
}
↓
double code(double x, double y) {
	return y + ((y + 1.0) * 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. Taylor expanded around 0 0.0

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

  3. Final simplification0.0

    \[\leadsto y + \left(y + 1\right) \cdot x\]

Alternatives

Reproduce

herbie shell --seed 2021118 
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  :precision binary64
  (+ (+ (* x y) x) y))