Learn English – How to write ‘first and second order’ properly

The hyphen is not required in the first pair. As you say, high is simply an adjective and performance is simply a noun which high modifies.

In the second pair, high is again an adjective and performance is a noun functioning as an adjective and together they modify computing. The question to ask is whether the absence of a hyphen between high and performance creates ambiguity. Is it possible that a reader might somehow think that computing is modified independently by both high and performance? Probably not. Nevertheless, as the late R L Trask wrote in ‘The Penguin Guide to Punctuation’:

The hyphen is . . . used in writing compound words which, without the hyphen, would be ambiguous, hard to read or overly long. Here, more than anywhere else in the whole field of punctuation, there is room for individual taste and judgement;

The absence of a hyphen might cause the reader a brief moment’s uncertainty over whether high and computing are to be taken separately or as a whole. If you think that might make the piece ‘hard to read’, then you would be well advised to use the hyphen.

1. Use whatever style guide is appropriate for your organization or audience.

2. If there is no appropriate style guide, then here is a general guideline (and it is only a general guideline):

   • Use a hyphen if the term is used as an adjective: XYZ is a decision-maker tool.

   • Do not use a hyphen if the term is used as a noun phrase: She is a decision maker.

3. Beyond that, @FumbleFingers's comment applies: it's pretty much up to you.