'formulaically' originates from English adjective 'formulaic', ultimately from Latin 'formula', where 'forma' meant 'shape, form' and the diminutive '-ula' indicated a small form or pattern.

'formulaically' developed from the Modern English adjective 'formulaic' (formed in the 20th century) by adding the adverbial suffix '-ally'; 'formulaic' itself comes from Latin 'formula' (via Medieval/Modern Latin and French influence) and ultimately from Latin 'forma'.

Initially related to 'a little form' or a fixed 'method' (from Latin 'formula'); over time the sense shifted to describe things that follow a set pattern, and in modern usage it also often carries a negative sense of being unoriginal or predictable.