Post-haste means very quickly — at once, without delay. It has an old, slightly bookish flavour now, the sort of word you might put in a story, or say with a little humour when you really mean hurry up. It does not belong in a lab report. Though actually, the post here is not the prefix that means “after,” as in post-war. It comes from an old instruction on letters: “haste, post, haste” — hurry, rider, hurry — because post was the rider who carried the mail. Later people heard it as one word, post-haste, and kept the meaning: as fast as a letter can go.

火速