first twelve reallocations:
  at push #   old capacity   new capacity   growth ratio
          1              0              1          0.000
          2              1              2          2.000
          3              2              4          2.000
          5              4              8          2.000
          9              8             16          2.000
         17             16             32          2.000
         33             32             64          2.000
         65             64            128          2.000
        129            128            256          2.000
        257            256            512          2.000
        513            512           1024          2.000
       1025           1024           2048          2.000

over 1000000 push_back calls:
  reallocations              = 21
  elements copied in total   = 1048575
  total element writes       = 2048575  (copies plus the pushes themselves)
  writes per push_back       = 2.048575
  the 3n bound of Section 14.7 = 3000000
  final size = 1000000, final capacity = 1048576
