I just read Can this algorithm still be considered a Binary Search algorithm? and recalled that a few years back I wrote an indexer/search for log files to find log entries in large plain text files by date/time window.
Whilst doing this, I decided to try interpolation search (I didn't know that was what it was called, I kind of stumbled across the idea by myself). Then for some reason I continued to the idea of alternating interpolation steps with binary split steps: On step 0 I would interpolate to decide test point, then step 1 I would take the exact midpoint etc.
I then benchmarked the system using pure interpolation search, pure binary search and my combination attempt. The alternating approach was a clear winner, both in time and number of tests required before finding a set of randomly chosen times.
Inspired by the linked question, I just made a quick search for "alternating interpolation search and binary search" and found nothing. I also tried "hedged interpolation search" as suggested on my comment on one of the answers.
Have I stumbled across a known thing? Is there any theoretical justification for it being faster for certain types of data? The log files were typically large for the time (e.g. 1-2 GB of text with maybe 10 million rows to search), and the spread of dates/times in them was complex with heavy bursts of activity, general peak times and quiet times. My benchmark tests sampled from an even distribution of target times to find.