In indexing data, RTtree search may be far inferior to AVLTree

I had done some tests to find out the performance of indexing data using RBTree or AVLTree,
the results is following:

rbtree = RBTree{Int}()
avltree = AVLTree{Int}()
sets = rand(collect(1:10^6), 10000)

for k in sets
   insert!(rbtree, k)
end


for k in sets
   insert!(avltree, k)
end

testset = collect(1:10^6)
ind = collect(1:9000)

@benchmark rbtree[rand(ind)]

BenchmarkTools.Trial: 
  memory estimate:  2.44 MiB
  allocs estimate:  27788
  --------------
  minimum time:     3.007 ms (0.00% GC)
  median time:      3.379 ms (0.00% GC)
  mean time:        3.816 ms (7.58% GC)
  maximum time:     18.757 ms (61.41% GC)
  --------------
  samples:          1306
  evals/sample:     1



@benchmark avltree[rand(ind)]
BenchmarkTools.Trial: 
  memory estimate:  86 bytes
  allocs estimate:  5
  --------------
  minimum time:     924.000 ns (0.00% GC)
  median time:      1.114 μs (0.00% GC)
  mean time:        1.191 μs (0.00% GC)
  maximum time:     4.403 μs (0.00% GC)
  --------------
  samples:          10000
  evals/sample:     14

I want to know why RBTree is so ineffecient, that is so weird!

Start by reproducing the RBTree and AVLTree lookup benchmarks from the issue with the provided Julia snippets. Then inspect the RBTree and AVLTree implementations and compare their lookup paths and allocations. Done means identifying the cause of the performance gap and documenting or correcting it with a confirming benchmark.