to process in a faster than normal, accelerated way
"The company implemented a speedy protocol that allowed it to process customer refunds in just minutes rather than days."
In plain English: To be speedy means to move very quickly, but it is not used as an action verb so you cannot say someone speedied across the room.
"Speedy is not used as a verb in standard English; it functions only as an adjective (e.g., "a speedy delivery"). You may have been thinking of verbs like hasten, rush, or accelerate. If you intended to use the word correctly, here is an example with its actual meaning: The driver had a very speedy recovery after surgery."
Usage: This verb is primarily used in technical contexts regarding data processing or manufacturing; avoid using it casually as an adjective meaning "fast." When describing speed in general conversation, prefer the adjective "quick" instead.
rapid; swift
"The courier delivered the package in a speedy manner, arriving before lunchtime."
Speedy comes from Middle English spedy, which originally meant not just moving fast but also being lucky, prosperous, or wealthy. The word traveled into modern English with its current meaning of "moving quickly," while retaining traces of its older sense of abundance and success in its Germanic roots.