"Burn at stake" is a phrase that refers to executing someone by tying them to a post and setting them on fire. However, there are several other phrases which can be used as synonyms for "burn at stake." Some of these include "burned alive," "burned to death," "immolated," "flamed to death," "consumed by fire," "put to the torch," and "set ablaze." Other phrases could be "martyred by fire" or "perished in flames." All of these alternative phrases convey the same idea of death by fire, and may be used interchangeably depending on the context and intended tone of the writer or speaker.