HP49-50G: help for recursive

[Gil]

I have, from Albert Chan, the following recursive program:

200 DEF FNL(X) ! = ln(1+X) - X, but more accurate
210 IF ABS(X)>=.4 THEN X=X/(SQRT(1+X)+1) @ FNL=FNL(X)*2-X*X @ GOTO 250
220 X2=X/(X+2) @ X4=X2*X2
230 X4=X4*(5005-X4*(5082-X4*969))/(15015-X4*(24255-X4*(11025-X4*1225)))
240 FNL=X2*(X4+X4-X)
250 END DEF

I transformed the FNL function for the HP50G, but without the recursion formulae:

« 0 0 0 { } -> x X2 X4 fnl l
«
WHILE x .4 >=
REPEAT x l + 'l' STO 'x/(sqrt(1+x)+1)' ->NUM 'x' STO
END 'x/(x+2)' ->NUM 'X2' STO X2 DUP * 'X4' STO 'X4*(5005-X4*(5082-X4*969))/(15015-X4*(24255-X4*(11025-X4*1225)))' ->NUM 'X4' STO 'X2*(X4+X4-x)' ->NUM 'fnl' STO x l + 'l' STO l SIZE 1 >
IF
THEN 1 l SIZE 1 -
FOR i fnl 2 * l i GET SQ - 'fnl' STO
NEXT
END fnl »
»
'FNL' STO


Or, with INOUT transcription:

Code:

\<< 0 0 0 { } \-> x X2 X4 fnl l
  \<<
    WHILE x ABS .4 \>=
    REPEAT x l + 'l' STO 'x/(\v/(1+x)+1)' \->NUM 'x' STO
    END 'x/(x+2)' \->NUM 'X2' STO X2 DUP * 'X4' STO 'X4*(5005-X4*(5082-X4*969))/(15015-X4*(24255-X4*(11025-X4*1225)))' \->NUM 'X4' STO 'X2*(X4+X4-x)' \->NUM 'fnl' STO x l + 'l' STO l SIZE 1 >
    IF
    THEN 1  l SIZE 1 -
      FOR i fnl 2 * l i GET SQ - 'fnl' STO
      NEXT
    END fnl
  \>>

\>>

I try now to have a HP50G recursive version FNL2:
« 0 0 0 -> x X2 X4 fnl
«
IF x .4 >≠
THEN 'x/(sqrt(1+x)+1
)' ->NUM FNL2 2 * x SQ
-
ELSE 'x/(x+2)'
->NUM 'X2' STO X2 DUP
* 'X4' STO 'X4*(5005-
X4*(5082-X4*969))/(
15015-X4*(24255-X4*(
11025-X4*1225)))'
->NUM 'X4' STO 'X2*(X4
+X4-x)' ->NUM
END
»
»

Suppose I have an initial value of 2 for x.
Then its successive values will be, as expected:
.732050807569 and .316074012953.
Then, as .316074012953 <0.4, we jump to the ELSE branch to get a value of -4.14209407856E-2 before the END instruction.
Now the program carries on just after the FNL2.
Unfortunately, before multiplying the last result -4.14209407856E-2 by 2, it closes one of the ».
Consequence: the last value of x, 316074012953, disappears, and we get instead the previous value of x, 732050807569.

Question:
How could we change the program into a correct recursive version?

Thanks for your help.

Regards,
Gil