I suspect if you started using SIMD instructions, the analytical case would get better again (since it's branchless).
I would like to think the rejection algorithm after -O3 is benefiting from branch prediction and all sorts of modern speculation optimizations. But I imagine the real test of that would be running these benchmarks would be running these benchmarks on a 5-10ish year old uarch.
The rejector is going to be faster because more iterations can be kept in the reorder buffer at once. The CPU is going to have to keep all the instructions post-branch in the reorder buffer until the branch is retired. If it's waiting on an instruction with an especially long latency like a square root it's probably speculatively already finished the work anyway, rejected or not.
If the branch rejects after the work is done the reorder buffer can retire each instruction of the random generation algorithm as it comes and then wait on however many branches at the end which can also be run in parallel because those branches aren't dependent on each other. All those branches which are doing a square root will also be pipelined properly instead of putting bubbles everywhere.
If you talked about running on a 30-year-old architecture, then sure, that would tell you something about the effect of modern speculation on the code.