Do note that THROW/CATCH are dynamically established, and each CATCH setup + THROW invocation take a small amount of runtime. THROW usually takes linear time in the number of enclosing CATCH forms. So, despite how it looks, this solution is still linear in both space and time in the number of branches. (This is the same if you were to bind a special variable N times. The setup and tear down aren’t statically or lexically determined.)
