foo.rb

require 'benchmark'

module Foo
  def foo;end
end

times = 1_000_000

Benchmark.bm 30 do |r|
  r.report 'none' do
    times.times do
      o = Object.new
    end
  end
  GC.start
  r.report 'touch singleton_class' do
    times.times do
      o = Object.new
      o.singleton_class
    end
  end
  GC.start
  r.report 'lookup' do
    times.times do
      o = Object.new
      if o.singleton_class.ancestors.include? :hi
      end
    end
  end
  GC.start
  r.report 'extend' do
    times.times do
      o = Object.new
      o.extend Foo
    end
  end
  GC.start
  r.report 'singleton_class include' do
    times.times do
      o = Object.new
      o.singleton_class.include Foo
    end
  end
  GC.start
  r.report 'singleton_class prepend' do
    times.times do
      o = Object.new
      o.singleton_class.include Foo
    end
  end
end

result

                                     user     system      total        real
none                             0.140000   0.000000   0.140000 (  0.139669)
touch singleton_class            1.180000   0.040000   1.220000 (  1.228629)
lookup                           1.700000   0.060000   1.760000 (  1.788575)
extend                           2.090000   0.050000   2.140000 (  2.155467)
singleton_class include          2.090000   0.050000   2.140000 (  2.142550)
singleton_class prepend          1.960000   0.020000   1.980000 (  1.990201)