I have tested the patch and it does not seem to solve the stability
problem.

With patch:
python performance/bm_json_v2.py -n 10 --timer perf_counter
0.02829067991115153
0.027778947027400136
0.027756798081099987
0.027362094027921557
0.027256828034296632
0.02766443998552859
0.027390124974772334
0.027398303849622607
0.02731629996560514
0.02743363007903099

Without patch:
python performance/bm_json_v2.py -n 10 --timer perf_counter
2.732215315802023
2.7394272631499916
2.731212269049138
2.7511520159896463
2.739834441104904
2.754247901029885
2.734024364966899
2.7447318979538977
2.744731454877183
2.7513630259782076

Instead, I notice that, especially for the first runs, the measured
values tend to be higher. This is expected, since the cache has not
been populated yet, but this can also happen after a context switch.
Therefore, we could eliminate these "odd" values by calculating the
median value of all the runs and only keeping measurements within 1%
of that median value.

What do you think?