benchmark1.rb

require 'active_support'
require 'active_record'
require 'benchmark/ips'

ActiveRecord::Base.establish_connection(
  adapter: 'mysql2',
  encoding: 'utf8',
  reconnect: true,
  pool: 25,
  host: 'localhost',
  database: 'test_database',
  username: 'root',
  password: ''
)

class Customer < ActiveRecord::Base; end

name = 'Luciano Sousa'

Benchmark.ips do |x|
  x.report('where_first')  { Customer.where(name: name).first }
  x.report('find_by_name') { Customer.find_by_name(name)      }
  x.report('find_by')      { Customer.find_by(name: name)     }
  x.compare!
end

$ ruby benchmark1.rb
Calculating -------------------------------------
         where_first   130.000  i/100ms
        find_by_name   223.000  i/100ms
             find_by   224.000  i/100ms
-------------------------------------------------
         where_first      1.400k (± 6.5%) i/s -      7.020k
        find_by_name      2.304k (± 6.9%) i/s -     11.596k
             find_by      2.330k (± 7.3%) i/s -     11.648k

Comparison:
             find_by:     2330.4 i/s
        find_by_name:     2303.5 i/s - 1.01x slower
         where_first:     1399.6 i/s - 1.67x slower