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High performance compute techniques are basically used whenever you have code that runs for 20+ hours at a time. Things like Raytracers, supercomputers, database-analysis, physics simulations, chemical simulations, weather simulations, etc. etc.

And I'm not talking about Webservers (which stay up for days, but the compute problem only happens over the course of ~1 second or so). Consider that when 3d movies are made, they hit the "Render" button and then wait 1 or 2 weeks for the movie to be made. Even if they have an entire cluster of computers calculating the scene... it takes a LOT of compute power to make movies.

If you eek out a 10% improvement, your render-time drops from 10-days to 9-days. Alternatively, you can have 10% fewer computers to get the same job done. Or in the case of scientists (ex: a Car engineer who is running a FEA computer-simulated car crash), your models can be more detailed. (Ex: Instead of modeling the engine as a perfectly elastic sphere, maybe you can model the engine as a more appropriate shape in the simulated car-crash)

There are a few exceptions. High-frequency traders also count milliseconds for their speed of execution. I see some HPC work coming out of HFT companies. But for the most part, highly-optimized code is specialized to the communities who still wait days (or even weeks) for the results from modern computers.

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