Summation based benchmark for calculators

[DavidM]

(11-17-2018 11:37 PM)pier4r Wrote:  (I wonder if the savage test can be optimized as well as it trivially use a function and its inverse)

The formula for the Savage test can definitely be simplified by the 50g CAS:

Code:

'TAN(ATAN(EXP(LN(√SQ(X)))))+1'
SIMPLIFY

...yields:

Code:

'|X|+1'

You could probably come up with an implementation that starts with the long version of the above, then SIMPLIFY it and loop the modified algebraic to come up with a total. It would be fast, and of course accurate as well. But it wouldn't be running the actual Savage test, would it? I see this as the same issue, and the result would be similarly meaningless in the context of that benchmark.

After a bit of playing around with this, it appears that the UserRPL SIMPLIFY command will skip this particular optimization if you set system flag -111. However, the Σ command's simplification doesn't use the same code as SIMPLIFY. It appears to be hard-wired to simplify regardless of that flag's setting (it uses an internal SysRPL routine called SimplifyExpression instead).

Just to be clear, I actually think it's a Good Thing that Σ performs this simplification, in that the typical use case for that command will normally only benefit or remain neutral from that step. Benchmarking and performance comparisons are the only situations I can think of where this feature may actually be problematic, since you can end up running entirely different code than you originally intended.