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Longman Dictionary of Contemporary English
vanishingly
adverb
COLLOCATIONS FROM CORPUS
■ ADJECTIVE
small
▪ But even if this conclusion is not justified, we can say that infallible beliefs must have vanishingly small content.
▪ Statistically, however, the chance of avoiding synonyms altogether is vanishingly small.
▪ If the object is very distant, linear magnification becomes vanishingly small.
▪ On average, the chances of weediness emerging by accident are vanishingly small.
EXAMPLES FROM CORPUS
▪ But even if this conclusion is not justified, we can say that infallible beliefs must have vanishingly small content.
▪ Cells work to keep calcium at vanishingly low internal concentrations, in order to use it for signalling.
▪ For just the same reason, it is vanishingly improbable that exactly the same evolutionary pathway should ever be travelled twice.
▪ If the object is very distant, linear magnification becomes vanishingly small.
▪ It would need a gigantic and vanishingly improbable leap across genetic hyperspace.
▪ On average, the chances of weediness emerging by accident are vanishingly small.
▪ Statistically, however, the chance of avoiding synonyms altogether is vanishingly small.
Wiktionary
vanishingly

adv. So as to vanish, or appear to vanish, especially very small, very rare.

WordNet
vanishingly

adv. so as to disappear or approach zero; "errors are vanishingly rare"

Usage examples of "vanishingly".

In the presence of a replicase 'machine tool', fragments of RNA will evolve, repeatedly and convergently, towards the same endpoint, an endpoint whose 'probability' seems vanishingly small until you reflect on the power of cumulative selection.

Theropod skeletons, like the Deinonychus, were rare enough to be noteworthy, but fully-articulated skeletons—skeletons that had remained pretty much connected as they had been in life—were vanishingly rare.

Theropod skeletons, like the Deinonychus , were rare enough to be noteworthy, but fully-articulated skeletons—skeletons that had remained pretty much connected as they had been in life—were vanishingly rare.

And in the vanishingly small percentage of instances when there was a germ of truth to the rumors, the rebel militia turned out to be a ragbag gang of roamers, outlaw wanderers of the outlands, justifying their robberies and murders by paying lip service to a political cause.

If vanishingly small changes may have immense and undivinable effects, still, a system has its attractors, its underlying order, and a broken balance may well be redressed.