Alias analysis is a good example. A JIT compiler may speculatively add dynamic disambiguation guards (p1 != p2 ==> p1[i] cannot alias p2[i]). If the assumption turns out to be wrong, the JIT compiler dynamically attaches a side branch to the guard using the new assumption (p1 == p2 ==> p1[i] == p2[i], which is an even more powerful result).
Doing this in a static compiler is hard, because it would have to compile both paths for every such disambiguation possibility. This quickly leads to a code explosion. You'd need very, very smart static PGO to cover this case: there are no branch probabilities to measure, since the compiler doesn't know that inserting such a branch might be beneficial. It may only derive this by running PGO on code which has these branches, which leads to the code explosion again.
Auto-vectorization is another example: a static compiler may have to cover all possible alignments for N input vectors and M output vectors. This can get very expensive, so most static compilers simply don't do it and generate slower, generic code. A JIT compiler can specialize to the runtime alignment and even compile secondary branches in case the alignment changes later on (e.g. a filter fed with different kernel lengths at runtime).
Doing this in a static compiler is hard, because it would have to compile both paths for every such disambiguation possibility. This quickly leads to a code explosion. You'd need very, very smart static PGO to cover this case: there are no branch probabilities to measure, since the compiler doesn't know that inserting such a branch might be beneficial. It may only derive this by running PGO on code which has these branches, which leads to the code explosion again.
Auto-vectorization is another example: a static compiler may have to cover all possible alignments for N input vectors and M output vectors. This can get very expensive, so most static compilers simply don't do it and generate slower, generic code. A JIT compiler can specialize to the runtime alignment and even compile secondary branches in case the alignment changes later on (e.g. a filter fed with different kernel lengths at runtime).