wp34s mini-challenge
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09-23-2020, 12:59 AM
Post: #1
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wp34s mini-challenge
√(5 + (ϕ^2 + 1) - (5×10^5)/((ϕ^2 + 1) + 10^5))
Evaluate the above expression on the wp34s striving to use the least number of steps. You might need to rewrite it in order to do it in less than 12 steps. Notice ϕ is a built-in constant. Have fun! |
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09-23-2020, 09:14 PM
(This post was last modified: 09-23-2020 09:26 PM by Namir.)
Post: #2
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RE: wp34s mini-challenge
My 11 step solution is 41ish.
Let a = phi^2 + 1 let b = 10^5 The expression is sqrt(5 + a - 5b/(a + b)) ... upon simplification we get: sqrt(5a/(a+b) + a) The pseudo-code is based on the last equation. Code: Phi |
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09-23-2020, 11:41 PM
(This post was last modified: 09-23-2020 11:51 PM by Gerson W. Barbosa.)
Post: #3
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RE: wp34s mini-challenge
(09-23-2020 09:14 PM)Namir Wrote: My 11 step solution is 41ish. Namir, thank you very much for your interest! Unfortunately, however, EEX 5 requires two steps on the wp34s. Also, your solution doesn’t return the expected result unless I’m mistaken. Tip: ϕ^2 + 1 = ϕ + 2 |
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09-24-2020, 03:05 AM
Post: #4
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RE: wp34s mini-challenge
(09-23-2020 11:41 PM)Gerson W. Barbosa Wrote:(09-23-2020 09:14 PM)Namir Wrote: My 11 step solution is 41ish. :-( |
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09-24-2020, 10:31 AM
Post: #5
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RE: wp34s mini-challenge
Here is a 12-step solution using your simplification:
001:# Φ 002:x² 003:INC X 004:RCL X 005:# 005 006:× 007:RCL L 008:10ᵡ 009:RCL+ Z 010:/ 011:+ 012:√ |
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09-24-2020, 07:49 PM
Post: #6
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RE: wp34s mini-challenge
Here is the corrected version based on your comments and hint:
Code: Phi |
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09-24-2020, 08:00 PM
Post: #7
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RE: wp34s mini-challenge | |||
09-24-2020, 08:18 PM
Post: #8
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RE: wp34s mini-challenge
Here is the corrected version based on your comments and hint:
Code: Phi |
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09-24-2020, 09:17 PM
(This post was last modified: 09-24-2020 09:18 PM by Gerson W. Barbosa.)
Post: #9
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RE: wp34s mini-challenge
(09-24-2020 08:00 PM)Didier Lachieze Wrote:(09-24-2020 10:31 AM)Gerson W. Barbosa Wrote: Here is a 12-step solution using your simplification: And using ordinary wp34s instructions only. Formidable ! I had to rewrite the original expression and to resort to a somewhat obscure instruction: √(7 + ϕ - 5/(1 + (ϕ + 2)/10^5)) 001:# 007 002:# ϕ 003:+ 004:# 005 005:# 002 006:RCL+ L 007:Pa→bar 008:INC X 009:/ 010:- 011:√ → 1.9021605831 That’s an approximation to a mathematical constant which is know to only nine significant digits, according to OEIS. Anyway, it agrees to Pascal Sebah’s result to 12 significant digits. |
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09-24-2020, 09:29 PM
Post: #10
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RE: wp34s mini-challenge
(09-24-2020 08:18 PM)Namir Wrote: Here is the corrected version based on your comments and hint: It looks like my hint was somewhat misleading, as your simplification does allow for an 11-step solution (see Didier’s solution above). Sorry! Your fourth step should be replaced with FILL (fill up the stack with a constant) as you need an extra copy of Phi on the stack. |
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09-27-2020, 07:07 PM
Post: #11
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RE: wp34s mini-challenge
It can be done in 10 steps. Any takers?
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10-02-2020, 02:47 PM
Post: #12
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RE: wp34s mini-challenge
(09-27-2020 07:07 PM)Gerson W. Barbosa Wrote: It can be done in 10 steps. Any takers? Ok, then I'll take it! (See solution #2, solution #1 and some variations thereof is what I already had). 1) √{5||[5(ϕ + 2)/10^5] + ϕ + 2} [ a||b = ab/(a + b) ] 001:# ϕ 002:# 002 003:+ 004:# 005 005:SDR 005 006:RCL× Y 007:# 005 008:|| 009:+ 010:√ → 1.902160583101354 2) √{ϕ + 2 + [0.2 + 20000/(ϕ + 2)]⁻¹} 001:# 002 002:SDR 001 003:# ϕ 004:RCL+ L 005:# 200 006:%T 007:RCL+ Z 008:1/x 009:+ 010:√ |
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