(- (+ (* x y) y) (* x y))

Average Error: 29.8 → 0

Time: 870.0ms

Precision: binary64

Math

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

↓

\[y\]

C

double code(double x, double y) {
	return ((double) (((double) (((double) (x * y)) + y)) - ((double) (x * y))));
}

↓

double code(double x, double y) {
	return y;
}

Error

Bits error versus x

Bits error versus y

Derivation

1. Initial program 29.8

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

2. Simplified 0

   \[\leadsto \color{blue}{y}\]

3. Final simplification 0

   \[\leadsto y\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x y)
  :name "(- (+ (* x y) y) (* x y))"
  :precision binary64
  (- (+ (* x y) y) (* x y)))