20191206, 12:44  #12  
Oct 2017
89 Posts 
Quote:
y=x*x, f(x)=(a*y+b)*y+..., because we have to find „ an expression with no more than 15 operations ...“. In my understanding it has to be one expression (ein geschlossener Ausdruck). 

20191206, 16:43  #13 
Feb 2017
Nowhere
6647_{8} Posts 
I have submitted a solution to the December 2019 "Ponder This."

20191206, 20:03  #14 
Dec 2019
Kansas
2^{4} Posts 
So brackets are not allowed, ex. x*(5*x+2) would have to be written as 5*x*x+2*x?
Last fiddled with by what on 20191206 at 20:14 
20191206, 20:46  #15 
"Ed Hall"
Dec 2009
Adirondack Mtns
2·3·13·43 Posts 

20191206, 23:47  #16 
Dec 2019
Kansas
2^{4} Posts 
so far I got 0.0005108359660008244 with 11 operations using fourier approximation with some tweaking. I think i need a different approach
Last fiddled with by what on 20191206 at 23:55 
20191207, 02:35  #17 
Romulan Interpreter
Jun 2011
Thailand
19×461 Posts 
Nobody said anything about separate expressions.
Of course, you have to write everything in one expression, y=f(x), where you expand f. Parenthesis are allowed, see their example. 
20191207, 02:45  #18  
Dec 2019
Kansas
10000_{2} Posts 
Quote:
how do you do so? Last fiddled with by what on 20191207 at 02:46 

20191207, 04:59  #19 
Dec 2019
Kansas
2^{4} Posts 

20191208, 01:05  #20 
Feb 2019
73 Posts 
I chose a nonpolynomial approach and got a MSE of 1.4107e05 with 11 operations by optimizing coefficients of the ansatz function.

20191211, 04:54  #21 
Romulan Interpreter
Jun 2011
Thailand
19·461 Posts 
I may be able to prove that the best you can do in such a way that all constants that you use are integers that fit in 16bit word (two's complement. i.e. from 32768 to +32767), is about 2.3e5 (which is a viable solution) regardless of arrangement of operations.
Last fiddled with by LaurV on 20191211 at 04:55 
20191213, 22:41  #22 
"Max"
Jun 2016
Toronto
701 Posts 
Nine operations did it for me (plot 1). I sent the solution yesterday. The coefficients were decimal though. The plot goes off beyond [1, 1] of course (plot 2).
The fifteen operations produce the MSE ten times better than expected (plot 3). Last fiddled with by Max0526 on 20191213 at 22:52 Reason: added two more plots 
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