How much does an engineer making $200k a year have to reduce X by before he pays for himself? Not much, and simply finding a hotspot and doubling the performance by aligning a data structure or whatnot could pay for his salary for a decade.
The old adage that computers are cheap and engineers are expensive is about 15 years out of date for a large portion of the software being written today. That is when companies stopped being able to generally externalize the costs of shitty code. Plus, as microcontrollers ate the world, the ability to ship a $1 micro controller instead of a $10 one on a product run of 100k units can mean the difference between a competitive growing company and a dying one.
But I'm an EE, so maybe I misunderstood some finer points?
Amdahl:
A fairly obvious conclusion which can be drawn at this
point is that the effort expended on achieving high
parallel processing rates is wasted unless it is
accompanied by achievements in sequential processing
rates of very nearly the same magnitude.
http://www-inst.eecs.berkeley.edu/~n252/paper/Amdahl.pdfA point made when we read the paper was that Seymour Cray always made sure that his computers were also the fastest scalar computers even though they were sold as vector processors.
I think mathematicians consider an upper limit a positive bound - positive, in the sense of being well defined; you're using negative in the other sense? I actually like that quite a bit.
As a real world example, if an operation involves a network call and you see the RTT dominating the time. You may want to think of ways to avoid the call (caching etc..) if possible to get really good gains.