Re #7656. Remove test that's been replaced by a system test.

Note that this test wasn't testing what it purported to because lines
235 & 280 were identical! When this error was fixed the test failed
(the reason for which has been addressed in the new system test).
Re #7656. Consolidate some of the test methods.

This means that the algorithm is run fewer times, but the same things
are still tested.
Also don't load the logs where possible.