it's this sense of the prefix de-
3. Down to the bottom, completely; hence thoroughly on and on, away; also methodically, formally: as declamare to shout away, DECLAIM; declarare to make quite clear, DECLARE; denudare to strip quite bare, DENUDE; deplorare to weep as lost, DEPLORE; derelinquare to abandon completely, DERELICT; dspoliare to spoil utterly, DESPOIL. b. To exhaustion, to the dregs: as decoquere to boil down or away, DECOCT; deliquescere to melt away, DELIQUESCE. (please excuse lack of markings.. just too dang many of them!)

so, de- can be another example of an intensifier(?).