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I have an old and slow computer and long LaTeX files. When typing I prefer to use \frac 1{x} instead of \frac{1}{x} or x_i instead of x_{i}.

Does the presence or omission of curly braces in these instances affect the compilation time in any way? If so in which way?

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    Well to begin with, x_mn is not the same as x_{mn} but with regards to the compilation I cannot say much.
    – azetina
    Jan 21, 2014 at 15:32
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    A simple experiment using time with and without braces for 60 simple expressions shows that the real and user times increase with braces (from 0.195s to 0.210s and from 0.176s to 0.188s). The sys time remains equal (0.020s).
    – Gonzalo Medina
    Jan 21, 2014 at 15:36
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    I would guess the answer is "yes they do, but not by any appreciable amount". One way to test would be using the PGF benchmarking library.
    – Hammerite
    Jan 21, 2014 at 15:36
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    The version without the braces are an (unreported) syntax error, so you shouldn't use those. The time differences are likely to be orders of magnitute less than the time taken to post the question:-) See tex.stackexchange.com/questions/82329/…
    – David Carlisle
    Jan 21, 2014 at 16:30
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    I tried typesetting $\frac12$ one million times getting a user time of 8.69 seconds, while $\frac{1}{2}$ the same number of times takes 8.81 seconds. This is what I call a negligible difference; the latter syntax is clearer.
    – egreg
    Jan 23, 2014 at 11:37

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The version without the braces is processed a tiny bit faster than the version with braces. Typesetting one million times $\frac12$ required 8.69 seconds, while a million $\frac{1}{2}$ took 8.81 seconds. This is what I call a negligible difference; the latter syntax is clearer.

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