What is the opposite of case-sensitive and does "case-insensitively" exist?

I thought it was "case-insensitive" but there are very few sources. If it's correct, what is it's adverb? As a non-native english speaker i would say it's "case-insensitively" but that sounds odd and i haven't found any sources but my own post on stackoverflow:

This will compare case insensitively:

bool equals = x.Equals(y , StringComparison.OrdinalIgnoreCase);

Solution 1:

Case-insensitive is indeed the correct antonym. That's the normal tech term. Evidently, it can be used with or without the hyphen.

Example:

To cause a case-sensitive comparison of nonbinary strings to be case insensitive, use COLLATE to name a case-insensitive collation.

Or:

This example shows that VERSION() returns a string that has a case-insensitive collation, so comparisons are case insensitive:

(https://dev.mysql.com/doc/refman/5.0/en/case-sensitivity.html)

As for the adverb, to me case-insensitively sound a bit awkward, so I would prefer in a case-insensitive manner:

You can configure the property value comparisons in query search conditions to be performed in a case-insensitive manner.

(http://www-01.ibm.com/support/knowledgecenter/SSGLW6_5.2.1/com.ibm.p8.ce.admin.tasks.doc/p8pcc406.htm)

Or, you can simply do without an adverb or adverbial phrase and write something like:

This will perform a case-insensitive comparison.