'accidentally' originates from Latin, specifically the word 'accidentalis,' where 'accidens' meant 'happening by chance.' 'Performed' originates from Old French, specifically the word 'parformer,' where 'par-' meant 'through' and 'former' meant 'to form or shape.'

'accidentalis' transformed into the Middle English word 'accidental,' and eventually became the modern English word 'accidentally.' 'Parformer' transformed into the Middle English word 'performen,' and eventually became the modern English word 'perform.'

Initially, 'accidentally' meant 'happening by chance,' and this meaning has largely remained the same in modern usage. 'Perform' initially meant 'to carry out or accomplish,' and this meaning has largely remained the same in modern usage.