'autoschediaze' originates from Modern Latin/New Latin formation, ultimately from Greek elements: Greek 'autos' meaning 'self' and Greek element 'schedios' (from 'schedē' / 'σχέδιον' family) meaning 'offhand' or 'extempore'.

'autoschediaze' was formed in English (19th century usage attested) from New Latin/Modern Latin coinages (such as 'autoschediare'), which themselves were built from Greek 'autós' + 'schedios'; conceptually related medieval/Modern-Latin formations yielded English nouns like 'autoschediasm' and agent noun 'autoschediast'.

Initially it signified 'to act or make something offhand, by oneself', and over time it has retained that basic sense but narrowed in English usage to specifically mean 'to improvise' (often in art, speech, or performance).