EDIT: this formula doesn't make any sense I know, just playing around 
Just for fun the average of this:
Code:
1.00000000
1.50000000
1.75000000
1.00000000
1.31250000
1.53125000
1.18750000
1.75000000
1.82421875
1.00390625
1.12792969
1.31005859
1.27343750
1.28710938
1.63983154
1.57196045
1.46214294
1.51572418
1.36388779
1.64664650
1.72783279
1.43408918
1.33485842
1.72003222
1.97801048
1.62538475
1.66818412
1.69600850
1.49275696
1.92441434
1.95800192
1.44051053
1.66181426
1.64530614
1.17072322
1.23364647
1.45885221
1.06935867
1.17770458
1.82563129
1.50000000
1.75000000
1.00000000
1.31250000
1.53125000
1.18750000
1.75000000
1.82421875
1.00390625
1.12792969
1.31005859
1.27343750
1.28710938
1.63983154
1.57196045
1.46214294
1.51572418
1.36388779
1.64664650
1.72783279
1.43408918
1.33485842
1.72003222
1.97801048
1.62538475
1.66818412
1.69600850
1.49275696
1.92441434
1.95800192
1.44051053
1.66181426
1.64530614
1.17072322
1.23364647
1.45885221
1.06935867
1.17770458
1.82563129
Is 1.482530615
So starting at 1.482530615 into the next range and doing a butterfly search might be a tiny bit faster.