(41/42) AGM - Arithmetic-Geometric Mean

[Werner]

If I can do AM=(a+b)/2 instead of a+(b-a)/2, and I test for GM convergence, then:

Code:

00 { 22-Byte Prgm }
01▸LBL 02
02 R↑
03▸LBL "AGM" @    a       b
04 ENTER
05 RCL+ ST Z
06 2
07 ÷ @            AM      a       b       b
08 R↓
09 ×
10 SQRT
11 X≠Y? @         GM      b       AM      AM
12 GTO 02
13 END

to make it 41-compatible, replace lines 4 and 5 with
RCL ST Y
RCL ST Y
+
at the expense of 1 byte.

If you don't like that the global label gets excuted in the loop, put it before LBL 02 and place a Rv in between, again at the expense of 1 byte

Cheers, Werner