"Gotten some shuteye" is a colloquial expression used to indicate that someone has slept or taken a nap. There are a multitude of synonyms that can be used to convey the same message. Some of these synonyms include, but are not limited to: caught some Z's, took a snooze, had a catnap, dozed off, grabbed some shut-eye, hit the hay, slept like a log, caught forty winks, and took a siesta. Depending on the context of the situation, these synonyms can be used interchangeably to convey the same meaning. Regardless of which synonym is chosen, each effectively communicates that someone has taken a brief break to rest and recharge.