julia> @btime ρ($d, Intersection($X, $H))
  27.810 μs (463 allocations: 41.88 KiB)
2.0000000000000004

julia> @btime ρ($d, Intersection($X, Intersection($X, $H)))
  28.197 μs (468 allocations: 42.13 KiB)
2.0

julia> @btime ρ($d, $X∩$H, upper_bound=true)
  31.114 μs (570 allocations: 50.28 KiB)
2.0000000000000004

julia> @btime ρ($d, $X∩($X∩$H), upper_bound=true)
  10.865 ms (182473 allocations: 14.96 MiB)
2.0000000000000004

julia> set = load("set.jld"); # contains A⌜R⋂G⌟⋂I
julia> d = [0.0, 1.0];
julia> S = set["set"];
julia> @time ρ(d, S)
4.173353 seconds (57.84 M allocations: 1.386 GiB, 16.97% gc time)