20191218, 21:59  #23 
Dec 2019
Kansas
2^{4} Posts 
I got mse of 8.27604×10^6 (12 times better)
Last fiddled with by what on 20191218 at 22:52 
20191224, 09:02  #24 
Jun 2016
8_{10} Posts 
Brackets
I think there was some discussion earlier about whether expressions would be allowed which used brackets in such a way that they have subexpressions that can't be evaluated in a single pass without storing intermediate results.
Could one of the people who has had a solution accepted please confirm whether an expression like (x  1) * (x + 2) would be allowed for example? 
20191225, 00:23  #25  
Sep 2017
1100010_{2} Posts 
Quote:
x*x*x*x*x*x*x*x requires 7 operations, but you can do it using only 3 operations if you were allowed to save and substitute the results: y = x*x z = y*y z*z so z would be x*x*x*x and z*z would give the x*x*x*x*x*x*x*x In your case you can do it in 3 operations in any case, by finding the subexpressions and mutliply them or x*x+x2 or (1+x)*x  2 In computer language: keeping the intermediate results in registers is allowed, but you can't assign them to variables and reuse them later. 

20191225, 01:10  #26 
Dec 2019
Kansas
2^{4} Posts 
I wonder how someone got an error of only 1.803E7. The best I have managed is 2.9E6, and I can't think of anything to decrease it.
Last fiddled with by what on 20191225 at 02:04 
20191225, 03:26  #27  
Oct 2017
1100111_{2} Posts 
Quote:
„Is it allowed to write for example y=x*x (one operation) and f =(a*y+b)*y+... (the other operations), or have all 15 operations to be in the same expression?“ The answer was: You can not define new variables. 

20191225, 03:57  #28  
Oct 2017
103 Posts 
Quote:
You will say: in ONE Register. Otherwise I could write: movsd xmm1,x mulsd xmm1,x (x*x in xmm1) movsd xmm0,a mulsd xmm0,xmm1 addsd xmm0,b (a*x*x+b in xmm0) mulsd xmm0,xmm1 addsd xmm0,c ((a*x*x+b)*x*x+c in xmm0) and so on. I think that this is not allowed. 

20191225, 10:25  #29  
Sep 2017
1100010_{2} Posts 
Quote:


20191226, 05:21  #30 
Sep 2017
2·7^{2} Posts 

20191226, 14:36  #31 
Feb 2017
Nowhere
2·17·127 Posts 
I note that they corrected the MSE for their example from .125 to 1/6.
I fault the statement of the problem, in that it did not specify the type(s) of constants that were acceptable. I guessed that decimal fractions were OK since the MSE bound and the original, incorrect MSE value for the example were stated as such. I note that they also changed the criteria for "bonus" asterisk(s). In the original statement of the problem, they referred to "elegant" solutions. In the current incarnation, they refer to smallest MSE to date. 
20191226, 21:24  #32 
Dec 2019
Kansas
2^{4} Posts 

20191227, 20:51  #33 
Dec 2019
Kansas
2^{4} Posts 
I only managed to get the 1.803E7 MSE after using 21 operations. I wonder what I'm missing

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