comparing frequency built using different enumerable methods

frequency_benchmarks.rb

require 'benchmark'

Enumerable.class_eval do

  def frequency_group_by
    group_by{|x| x}.map { |x, xs| [x, xs.length] }
  end

  def frequency_each
    h = Hash.new(0)
    each { |x| h[x] += 1 }
    h.to_a
  end

  def frequency_reduce
    reduce(Hash.new(0)) { |h, x| h[x] += 1; h }.to_a
  end
end

def run_benchmark(arr_size)
  arr = Array.new(arr_size) { rand(1000) }
  n = 1000

  unless arr.frequency_each == arr.frequency_reduce && arr.frequency_reduce == arr.frequency_group_by
    puts "sanity check... failed."
    exit
  end

  Benchmark.bm do |x|
    x.report("freq w/ group_by: ") { n.times { arr.frequency_group_by }}
    x.report("freq w/ each:     ") { n.times { arr.frequency_each }}
    x.report("freq w/ reduce:   ") { n.times { arr.frequency_reduce }}
  end
end

run_benchmark(10000)

# Output
#                         user     system      total        real 
# freq w/ group_by:   5.060000   0.140000   5.200000 (  5.210313)
# freq w/ each:       5.170000   0.040000   5.210000 (  5.218802)
# freq w/ reduce:    10.190000   0.090000  10.280000 ( 10.287221)

I'm very surprised by the difference in performance between each and reduce (the code is nearly identical... even using the same Hash structure). Any ideas why the order of magnitude difference?