'rationally-determined' originates from the combination of 'rationally' and 'determined'. 'Rationally' comes from the Latin 'rationalis', meaning 'reasonable', and 'determined' from the Latin 'determinare', meaning 'to set bounds'.

'Rationally-determined' evolved from the combination of 'rational' and 'determine', which were used separately in Middle English and later combined in modern English.

Initially, it meant 'decided by reason', and this meaning has largely remained the same in modern usage.