[VA] SRC#002- Almost integers and other beasties

[Gerson W. Barbosa]

(02-09-2019 10:56 PM)Valentin Albillo Wrote:  .
Hi, Gerson:

(02-09-2019 09:53 PM)Gerson W. Barbosa Wrote:  Beautiful one! Hope you don’t mind if I uglify it a bit:

Sin(9*(Sin 1 + Cos 40) + 5/(e*10^8))

I don't understand ...

Hi, Valentin,

The factor of e doesn´t appear to fit nicely in the trigonometric expression, but it makes the result get a bit closer to 1:

Sin(9*(Sin 1 + Cos 40) + 5/(e*10^8)) = 0.99999999999999999999999997740056822767

(02-09-2019 10:56 PM)Valentin Albillo Wrote:  Also, could you accurately evaluate the expression I gave in my post #21 in this thread (the previous one to yours) and if so, what accurate result did you get ? The proximity to the exact integer 1 is not a coincidence, there are deep mathematical reasons for it.

Best regards and have a nice weekend.
V.
.

%%HP: T(3)A(R)F(.);
\<< 126 40 'DIGITS' STO 0 1 ROT
  FOR k 1 FNEG k FY\|^X k FDIV 2 k FY\|^X 1 FSUB FDIV FADD
  NEXT DUP FADD 2 FLN FDIV 1 12 FDIV FADD FPI FSQ 6 FDIV 2 FLN FSQ FDIV FADD ZZ\<-\->F DROP \->STR DUP HEAD "." + SWAP TAIL +
\>>

EVAL ->

"1.000000000001237412575736110228719610648"

The RPL program above requires the LongFloat library.

Number of iterations = Ceil(W(10^n*ln(2))/ln(2)), where n = number of digits and W(x) is the Lambert W function.

Best regards,

Gerson.