Hi, I’m new here. I’m finally trying out Elixir after hearing and reading about it for quite some time.

I’m implementing simple algorithms first, and already at factorial I found something perplexing. I’ve implemented it in several versions, one of them being tail recursive. I expected that one to be the fastest, but to my surprise it wasn’t - body recursion was.

I’ve read Erlang's Tail Recursion is Not a Silver Bullet and Erlang -- The Seven Myths of Erlang Performance but these only talk about lists; when calculating simple value, like factorial does, tail recursion should be faster, as far as I understand.

I’m doing the benchmark using Benchee, in a script run with mix run benchmark.exs. Project is clean project created using mix new. Below is the code for the benchmark and the functions themselves.

Am I missing something? Are my implementations wrong? Is the benchmark wrong? Am I running it wrong? Is this “idiomatic code being optimized”?

# benchmark.exs
n = 10000
Benchee.run(%{
  "body" => fn -> Factorial.body(n) end,
  "tail" => fn -> Factorial.tail(n) end
})

# factorial.ex
defmodule Factorial do
  def body(n) do
    case n do
      0 -> 1
      1 -> 1
      n -> n * body(n - 1)
    end
  end

  def tail(n) do
    tail_internal(1, n)
  end
  defp tail_internal(acc, 0), do: acc
  defp tail_internal(acc, n) do
    tail_internal(acc * n, n - 1)
  end
end

One output is below, but the situation with tail recursion being 5 - 15% slower repeats consistently and goes down as the input goes up, presumably because there is less and less calls to the function (only 1 when n is 1 000 000).

Operating System: Linux
CPU Information: AMD Ryzen 5 3600 6-Core Processor
Number of Available Cores: 12
Available memory: 12.44 GB
Elixir 1.12.2
Erlang 24.0.5

Benchmark suite executing with the following configuration:
warmup: 2 s
time: 5 s
memory time: 0 ns
parallel: 1
inputs: none specified
Estimated total run time: 14 s

Benchmarking body...
Benchmarking tail...

Name           ips        average  deviation         median         99th %
body        3.20 K      312.96 μs     ±7.01%      309.20 μs      383.20 μs
tail        2.79 K      359.05 μs     ±6.48%         355 μs      441.43 μs

Comparison: 
body        3.20 K
tail        2.79 K - 1.15x slower +46.09 μs