There are quite a few (value, operation) pairs that we cannot specialize.
For those operations, we can spend a significant amount of time repeatedly attempting to specialize, and repeatedly failing.

There is a well known fix for this, which is "exponential backoff".
The idea is that each time you fail to specialize (or otherwise fail to optimize) the countdown counter is set to twice its previous starting value.
Currently, we attempt to specialize every 64 executions, with exponential backoff we would start at 31, then 63, then 127 until we reach a limit of 4095 for a 12 bit counter and 4 bit backoff exponent.

See faster-cpython/ideas#397 for more details