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What's the right way to say it?

Without compromising on either efficiency nor accuracy,...

or

Without compromising on neither efficiency nor accuracy,...
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In standard English (of whichever part of the English speaking world), explicitly negative words and phrases such as no, none,never, nowhere, neither, and nor cannot be used within the scope of another negative (such as not or without), but only when they themselves are the primary carrier of negative meaning. (In many non-standard Englishes, this is not true).

So without compromising on either efficiency or accuracy,...

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If I have understood what your statement implies, rightly, you should write it as- Without compromising on either efficiency or accuracy. Compromising neither on efficiency nor accuracy.

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    To give a general rule that you can use going forward, you always pair either with or, and neither with nor. The best way to remember is that one of the pairs uses words starting with the same letter, and the other set both start with vowels. – John Clifford Nov 16 '16 at 13:04

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