early 15c., "prepare by boiling," from Latin decoctus, past participle of decoquere "to boil down," from de "down" (see de-) + coquere "to cook" (from PIE root *pekw- "to cook, ripen"). Related: Decocted; decocting.
active word-forming element in English and in many verbs inherited from French and Latin, from Latin de "down, down from, from, off; concerning" (see de), also used as a prefix in Latin, usually meaning "down, off, away, from among, down from," but also "down to the bottom, totally" hence "completely" (intensive or completive), which is its sense in many English words.
As a Latin prefix it also had the function of undoing or reversing a verb's action, and hence it came to be used as a pure privative — "not, do the opposite of, undo" — which is its primary function as a living prefix in English, as in defrost (1895), defuse (1943), de-escalate (1964), etc. In some cases, a reduced form of dis-.
It is the hypothetical source of/evidence for its existence is provided by: Sanskrit pakvah "cooked, ripe;" Avestan -paka- "cooked;" Greek peptein "to cook, ripen, digest," pepon "ripe;" Latin coquere "to cook, prepare food, ripen, digest, turn over in the mind," Oscan popina "kitchen;" Lithuanian kepti "to bake, roast;" Old Church Slavonic pecenu "roasted;" Welsh poeth "cooked, baked, hot."
<a href="https://www.etymonline.com/word/decoct">Etymology of decoct by etymonline</a>
Harper, D. (n.d.). Etymology of decoct. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/decoct