The phrase "without counting the cost" implies that something is done without taking into account the expense or consequences of the action. It may also suggest a disregard for the potential drawbacks or risks involved. Synonyms for this phrase might include "recklessly," "carelessly," "heedlessly," "impulsively," "rashly," or "hastily." It may also be described as an act of abandon, disregard, or indifference. Regardless of the choice of words used, the message conveyed is one of action taken without consideration for the potential outcomes, which can be dangerous or beneficial, depending on the circumstances and context in which the phrase is used.