Even Fibonacci Numbers

benchmark.rb

require 'benchmark'
require_relative 'fibonacci_operations'

# Determining which formula has better preformance when calculating the answer 1 million times
Benchmark.bm(20) do |bm|
  [4000000, 40000000, 400000000, 4000000000, 40000000000].each {|x|
    puts "For #{x}"
    bm.report("Formula:") {
      1000000.times do
        FibonacciOperations.sum_even(x)
      end
    }

    bm.report("Quotient:") {
      #    puts sum_even_quotient(x)
      10000000.times do
        FibonacciOperations.sum_even_quotient(x)
      end
    }
  }
end

fibonacci_operations.rb

class FibonacciOperations
  # let x represent the previous even fibonacci value
  # let y represent the current even fibonacci value
  # this method utilizes a formula to calculate the next even value
  def self.sum_even(limit)
    sum, x, y = 0, 0, 2 # initialize the variables
    while y <= limit
      sum += y
      y, x = (4 * y) + x, y
    end
    sum
  end

  # let x represent the previous even fibonacci value
  # let y represent the current even fibonacci value
  # this method calculates the next fibonacci value and then determines if it is even
  def self.sum_even_quotient(limit)
    sum, x, y = 0, 0, 1 #initialize the variables
    while y <= limit
      if y % 2 == 0
        sum += y
      end
      y, x = x + y, y
    end
    sum
  end
end

tc_fibonacci_operations.rb

require_relative "fibonacci_operations"
require "test/unit"

class TestFibonacciOperations < Test::Unit::TestCase
  def test_sum_even
    assert_equal(10, FibonacciOperations.sum_even(8))
    assert_equal(44, FibonacciOperations.sum_even(34))
    assert_equal(188, FibonacciOperations.sum_even(144))
    assert_equal(798, FibonacciOperations.sum_even(610))
    assert_equal(257114, FibonacciOperations.sum_even(196418))
    assert_equal(4613732, FibonacciOperations.sum_even(4000000))
  end
end

Sample output from benchmark:

                           user     system      total        real
For 4000000
Formula:               0.420000   0.000000   0.420000 (  0.417578)
Quotient:             14.790000   0.000000  14.790000 ( 14.804420)
For 40000000
Formula:               0.420000   0.000000   0.420000 (  0.428176)
Quotient:             16.780000   0.010000  16.790000 ( 16.795530)
For 400000000
Formula:               0.490000   0.000000   0.490000 (  0.494462)
Quotient:             20.710000   0.130000  20.840000 ( 21.155406)
For 4000000000
Formula:               0.540000   0.000000   0.540000 (  0.548307)
Quotient:             21.130000   0.030000  21.160000 ( 21.175395)
For 40000000000
Formula:               0.610000   0.000000   0.610000 (  0.609224)
Quotient:             22.590000   0.010000  22.600000 ( 22.614486)

The formula to calculate the next even fibonacci value is clearly the more performant option.