[VA] SRC#004- Fun with Sexagesimal Trigs

[J-F Garnier]

(02-11-2019 09:26 PM)J-F Garnier Wrote:  Programming (especially on the 71) is immediate - no need to post it -

Well, straightforward programming is indeed immediate and enough to get an idea of the results, but it is possible to do slightly better "in accurately evaluating them"

Let's see on value A.
Straightforward programming:
>A=1 @ FOR I=1 TO 29 @ A=A*(SQR(3)+TAN(I)) @ NEXT I @ DISP A
536870912.011

The rounding error on SQR(3), accumulated on 29 successive iterations introduces a systematic bias.
We can reduce this effect by factoring SQR(3) and evaluating SQR(3)^29 directly:
>A=1 @ FOR I=1 TO 29 @ A=A*(1+TAN(I)/SQR(3)) @ NEXT I @ A=A*3^14*SQR(3) @ DISP A
536870912.002

This gives us more confidence in identifying it to a certain simple integer expression.

J-F