logs and fractional exponents often require deeper analysis. If n=1,000,000 then log n = 6, so n log n would actually be faster than 7n on that size data set.
Certain special cases also require further analysis. Some algorithms run extremely fast, or extremely slow, on specific types of data. For example, with data that's expected to be nearly sorted, some sorting algorithms will run faster than expected while others can choke.
Operations that run at very different speeds also require deeper analysis (or testing). If an algorithm requires O(n) disk reads, O(n^2) memory allocation, and O(n^4) calculations, it's possible for any one of those factors to dominate on real-life data sets.
Certain special cases also require further analysis. Some algorithms run extremely fast, or extremely slow, on specific types of data. For example, with data that's expected to be nearly sorted, some sorting algorithms will run faster than expected while others can choke.
Operations that run at very different speeds also require deeper analysis (or testing). If an algorithm requires O(n) disk reads, O(n^2) memory allocation, and O(n^4) calculations, it's possible for any one of those factors to dominate on real-life data sets.