Lucas left her to press Lestrade, who was awkwardly composing a narrative in which he was a marginal figure, brought in arsy-varsy. He found the old guide waiting impatiently, in fear that his clientele would evaporate amid disorder.
-- Robert Stone, Damascus Gate, 1998
...a gob, a prayer, a lesson, a little of each, a prayer got by rote in case of emergency before the soul resigns and bubbling up all arsy-varsy in the old mouth bereft of words, in the old head done with listening, there I am old, it doesn't take long...
-- Samuel Beckett, Stories and Texts for Nothing, 1967
This term first came to English in the 1530s. It is probably an alteration of the Latin vice versa with arse substituted to make a facetious rhyming compound.