We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil.
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As Madars says, I consider only the performance of a single call to LinearFibonacci.
For example, if I did a call to LinearFib(1000) and LinearFib(2000), from the analysis algorithm I would expect that LinearFib(2000) would take twice as much time as LinearFib(1000). But in practice it takes four times as much time. The caching would not help here, as you would still have to iterate from 1000 to 2000 without caching!
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