Generally speaking, I do the dive/deco planning with DPlan, GAP or more recently iDeco on my iPhone, and use the custom table on a slate or wet note page along with lost gas contingency plans. I have at times also used the plan feature on my Shearwater.
Regardless of how it gets developed, once developed I basically dive the plan, but also monitor the computer. The computer makes nice back up and also potentially provides a much quicker exit in the event you curtail the dive prior to reaching your planned run time.
In the real world, which is primary and which is back up becomes a little blurred once the dive starts, but the important point is to ensure you do sufficient gas planning and contingency planning rather than just diving to thirds for gas planning and riding the computer and assuming it will all work out.
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Something I have noted when using different softwars applications is that even if they use the same algorythm and conservatism facotrs or bradient factors, two applications can create what appear to be different profiles, but the differences are often related to some underlying assumptions about gas switch times, etc with the result some will show a stop another will not - but accounts for in the schedule. In the water, the difference is one will result in a profile where the deeper stops clear before I get to them and where the other has sahllower stops - but they are real stops I actually reach before the computer clears or the run time is reached. In short, people get too concerned with differences of a minute or two here and there and forget it is all theory, not a dyed in the wool fact.