I come from a DBA world and performance has always been an obsession. I am turning to development and I always think about performance, constantly, all the time.
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I am working on building a search engine. Optimization is what makes the the difference between a user continuing to search or leaving the website. I think It is true for many applications, and unfortunately many of them do not care enough about it. Sometimes it is much cheaper that throwing more hardware at the problem. Unfortunately the latter is easier. To summarize, I'd say you have to optimize whenever you either have to process a LOT of data and/or process it very quickly.