An example where this matters -- a new Mario 64 trick on the Virtual Console version because summing round-towards-zero numbers over a sine wave cycle produces a small delta which builds up over a couple of days to make a jump possible
For anyone else interested in similar tricks, here is an in-depth video where someone talks about getting a star with half a button press. It starts out straightforward enough, but eventually gets really interesting when they start talking about parallell worlds that you can only access by abusing bugs to reach unrealistic speeds.
Strongly recommended watching, in my opinion: very clearly describes some quite complicated manipulations, the circumstances in which they work and how to move between those circumstances, to achieve what should be impossible.
If you're going to watch one commentated "tool-assisted" run, this is it.
A small clarification: this trick is not new. It was discovered very early on in the investigation of the Wii VC release of Super Mario 64. It was rediscovered by a group of people who were interested in an application of it (which enables one to beat SM64 without the A button) a couple of years ago, and the discovery that the glitch is a result of inaccurate rounding mode emulation followed a couple weeks later.
https://www.youtube.com/watch?v=kpk2tdsPh0A&t=77s