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12:15 < jeremyrubin> Policy question:
12:16 < jeremyrubin> suppose I want to output a tree of Or's where each leaf has the same chance of satisfaction, is there a convenient way of doing this if the size of the tree is not known in advance?
12:17 < sanket1729> Do you know the structure of the tree?
12:17 < jeremyrubin> I don't care about the structure of the tree
12:17 < jeremyrubin> so I could do e.g. CONS style or tree style
12:18 < jeremyrubin> OR(OR(A, B, OR(C, D)) OR(A, OR(B, OR(C, D))
12:18 < jeremyrubin> if I were to naively set each to relative odds 1
12:18 < jeremyrubin> then solution A would be 'fair' and solution B would make D much less likely 
12:18 < jeremyrubin> if I understand correctly
12:19 < sanket1729> I think you would have to calculate the odds leaf to root.
12:19 < jeremyrubin> Yeah, which is sort of odd
12:20 < jeremyrubin> because that implies no online algorithm
12:20 < jeremyrubin> of course could always do Thresh(1, ....) but then that would have O(N) dissats 
12:21 < jeremyrubin> Thresh could be tweaked to check the cost of an OR tree if k=1 is set 
12:22 < sanket1729> One of the problems with converting thresh() to or() is that the compiler complexity is exponential in ORs
12:24 < jeremyrubin> ah right
12:25 < jeremyrubin> I guess the key observation is this:
12:26 < jeremyrubin> Thresh(1, ....) always outperforms OR(OR(...),...) because the IF ELSE wrappers are at least 2 bytes *N
12:26 < jeremyrubin> even if you have only log N dissats to select a branch
12:26 < jeremyrubin> you lose because the script, which goes in the witness, is O(N) bigger
12:26 < jeremyrubin> so thresh should always be better
12:27 < sanket1729> I don't think it's that simple
12:27 < sanket1729> thresh can perform better, because ORs have lot of freedom in terms of wrappers they accept
12:27 < jeremyrubin> If you need wrappers around the types I guess
12:27 < jeremyrubin> hmm     
12:27 < jeremyrubin> which for CTV I would need 
12:28 < sanket1729> thresh requires things to expressions that output unit type on the stack. 
12:29 < jeremyrubin> Well I guess at least it's never *asymptotically* worse
12:29 < jeremyrubin> which is what I care about
12:29 < sanket1729> yeah
12:30 < jeremyrubin> Wasn't there something funky where we banned thresh with k = 1?
12:30 < jeremyrubin> or K=n?
12:30 < sanket1729> I have to fix the c++ version to support that.
12:30 < sanket1729> It's not banned in rust-miniscript. 
12:32 < sanket1729> What is your `n` that online algorithm is a concern?
12:33 < sanket1729> nevermind, you cannot use the compiler for very large `n` anyways. 
12:33 < jeremyrubin> it's not about N being large
12:34 < jeremyrubin> it's just about compilation being able to run as a 'forward pass'
12:34 < jeremyrubin> e.g., if I'm accumulating some tokens or something, can I directly convert to ORs
12:34 < jeremyrubin> or do I need to accumulate a vector of sub clauses
12:35 < jeremyrubin> I think Threshold is better anyways
12:35 < jeremyrubin> because it makes it more clear when eventually taproot
12:35 < sanket1729> yeah
12:36 < jeremyrubin> but perhaps threshold should take probs
12:36 < jeremyrubin> so that you can use it to structure taproot tree
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12:37 < sanket1729> yeah, we havn't much thought about policy compiler for taproot. But clearly, thresh(k=1) is exactly what taproot is for. 
12:40 < jeremyrubin> interestingly for AND clauses the tree structure doesn't matter at all because they just get concat'd
12:42 < sipa> the C++ compiler will try compiling thresh(1,...) to a cascade of ORs (with uniform probability for every leaf)
12:42 < sipa> and thresh(N,...) to a cascade of ANDs
12:42 < sipa> s/to/as/
12:49 < sipa> (but it only tries one configuration, to avoid exponential blowup)
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13:01 < jeremyrubin> Interesting!
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