Algorithm accuracy vs calculator precision

[Johnh]

One perspective on algo accuracy is, is it better to have a more sophisticated routine that achieves adequate accuracy in fewer cycles? Or a simpler one that needs more cycles? Which is actually faster in terms of run time on a given machine? and which is likely to be more reliable if you just let it run without worrying about the details?

On my old TI58, it came with integration built in (to a module that came with the machine), using Simpson's rule. This is a step or two more accurate than a basic trapezium method, but by no means the most sophisticated method. But I took great confidence in it from having studied it in detail at high-school, so I knew about what it was doing. On contempory hp calcs such as the 15c, it's much cleverer and adapts to the accuracy of the display. The results are better but its more of a black-box. I'm less confident about how it is working.