Euler Identity in Home

[HP67]

I don't pick up from Colin's post that there is any confusion, just a general sense that accuracy and to a lesser extent precision haven't kept paces with advances in hardware. And that is certainly true. Gains in accuracy after you get the basic stuff right come at very high incremental cost and they don't come at the same rate as more powerful hardware. It could be argued cheap hardware is causally-related to the decreasing rate of progress in algorithms But that is another discussion.

A middle ground might be some kind of heuristic that deals with defined values of common functions so that sin(pi) is always returned as zero, etc. Then again, the addition of CAS and the options of various settings (exact vs. approx mode) often complicate getting the intended results unless documented clearly, etc. We are now past the point where anything is simple.

Tim's answer was very helpful giving food for thought about some of the issues and engineering tradeoffs involved in implementing math in hardware.