Slowdown of Distributions.jl on 0.7?

I think you are running into a silent deprecation warning. Use --depwarn=yes to get

ERROR: broadcast will default to iterating over its arguments in the future. Wrap arguments of
type `x::Exponential{Float64}` with `Ref(x)` to ensure they broadcast as "scalar" elements.

and then fixing as

        a[i] = mean(logpdf.(Ref(d), y))

yields

julia> @benchmark main()
BenchmarkTools.Trial: 
  memory estimate:  34.02 KiB
  allocs estimate:  102
  --------------
  minimum time:     33.536 μs (0.00% GC)
  median time:      34.602 μs (0.00% GC)
  mean time:        43.728 μs (13.85% GC)
  maximum time:     42.665 ms (99.88% GC)
  --------------
  samples:          10000
  evals/sample:     1

julia> VERSION
v"0.7.0-beta.204"

vs

julia> @benchmark main()
BenchmarkTools.Trial: 
  memory estimate:  34.02 KiB
  allocs estimate:  102
  --------------
  minimum time:     52.695 μs (0.00% GC)
  median time:      53.716 μs (0.00% GC)
  mean time:        60.395 μs (1.65% GC)
  maximum time:     837.051 μs (87.87% GC)
  --------------
  samples:          10000
  evals/sample:     1

julia> VERSION
v"0.6.3"

which is a reasonable improvement, demoing v0.7 awesomeness.