The phrase "hast on carpet" can be interpreted to mean "moving quickly on a carpeted surface." Some synonyms for this phrase might include "stride on carpet," "rush on carpet," or "hurry on carpet." Other options could include "sprint on carpet," "dash on carpet," or "race on carpet." For a more elegant or refined connotation, one might opt for phrases like "glide on carpet," "sashay on carpet," or "flit on carpet." Ultimately, the choice of synonym will depend on the context and tone of the writing, as well as the desired impression on the reader.