Allow me to clear the situation. I was talking with my professor about a piece of software that I had developed. While we were discussing, I wanted to say something like
I don't want to sound too cocky, but my code is way much more efficient
than what we have right now.
But I didn't because I thought "I don't want to sound too cocky" is too informal.
What is a formal way of stating such a phrase?
Best Answer
To say the same thing, you can say
Synonyms that you can substitute here for presumptuous are
impertinent, overconfident, arrogant, bold, insolent, impudent, and of course the less formal sounding "cocky".
To sound deferential, but not say precisely the same thing, you could say
Wording it either way would leave you open to discussing the possibility that your code or your testing may be flawed, while making your point about its apparent improvement.