Sorting an Association by FindMaximum

Question

Prompted by my wrestling with this earlier question:

Changing the opacity of lines on a plot based on their value

I want to sort an association by the maximum value for each of the 3 members of the association over a specific range {x, 2/26, 1}.

assoc = <|"a:b" -> (2.888888888888889` x + 158.5679012345679` x^2 + 
       972.4261545496113` x^3 + 2782.574803223688` x^4 + 
       4689.153835062141` x^5 + 6158.852000788219` x^6 + 
       6193.345446598874` x^7 + 4759.487380195244` x^8 + 
       2828.1047688854555` x^9 + 1262.2623444432436` x^10 + 
       396.8075199523231` x^11 + 87.10349331793769` x^12 + 
       15.918345899682585` x^13 + 2.358273466619642` x^14)/(2 x + 
       142 x^2 + 994 x^3 + 3068 x^4 + 5440 x^5 + 7516 x^6 + 
       8061 x^7 + 6591 x^8 + 4215 x^9 + 2029 x^10 + 694 x^11 + 
       181 x^12 + 33 x^13 + 4 x^14), 
   "a:c" -> (1.9259259259259258` x + 154.85871056241427` x^2 + 
       1000.1077071584616` x^3 + 2910.6970670309593` x^4 + 
       4824.123299147454` x^5 + 6433.145771926378` x^6 + 
       6287.788973741406` x^7 + 4729.911569226189` x^8 + 
       2616.6377204567093` x^9 + 1072.3401991902406` x^10 + 
       300.41168315858073` x^11 + 66.12235989098919` x^12 + 
       9.795905169035438` x^13 + 1.179136733309821` x^14)/(2 x + 
       142 x^2 + 994 x^3 + 3068 x^4 + 5440 x^5 + 7516 x^6 + 
       8061 x^7 + 6591 x^8 + 4215 x^9 + 2029 x^10 + 694 x^11 + 
       181 x^12 + 33 x^13 + 4 x^14), 
   "a:e" -> (1.9259259259259258` x + 154.85871056241427` x^2 + 
       1177.8054158410812` x^3 + 3305.3824300345664` x^4 + 
       5174.381478951672` x^5 + 6568.697926267911` x^6 + 
       6234.040624961103` x^7 + 4385.353371436694` x^8 + 
       2365.2980972400514` x^9 + 900.9303208030539` x^10 + 
       255.51499204916647` x^11 + 41.96226685389699` x^12 + 
       6.122440730647148` x^13 + 1.179136733309821` x^14)/(2 x + 
       142 x^2 + 994 x^3 + 3068 x^4 + 5440 x^5 + 7516 x^6 + 
       8061 x^7 + 6591 x^8 + 4215 x^9 + 2029 x^10 + 694 x^11 + 
       181 x^12 + 33 x^13 + 4 x^14)|>; 

FindMaximum[#, {x, 2/26, 1}] & /@ assoc
Keys[Sort[%]]
assoc[#] & /@ %

This seems to work, but have I missed something?

Answer 1

You could use SortBy instead:

SortBy[assoc, FindMaxValue[#, {x, 2/26,1}]&]

FindMaxValue::fmmp: Machine precision is insufficient to achieve the requested accuracy or precision.

<|"a:c" -> (1.92593 x + 154.859 x^2 + 1000.11 x^3 + 2910.7 x^4 + 4824.12 x^5 + 6433.15 x^6 + 6287.79 x^7 + 4729.91 x^8 + 2616.64 x^9 + 1072.34 x^10 + 300.412 x^11 + 66.1224 x^12 + 9.79591 x^13 + 1.17914 x^14)/(2 x + 142 x^2 + 994 x^3 + 3068 x^4 + 5440 x^5 + 7516 x^6 + 8061 x^7 + 6591 x^8 + 4215 x^9 + 2029 x^10 + 694 x^11 + 181 x^12 + 33 x^13 + 4 x^14), "a:e" -> (1.92593 x + 154.859 x^2 + 1177.81 x^3 + 3305.38 x^4 + 5174.38 x^5 + 6568.7 x^6 + 6234.04 x^7 + 4385.35 x^8 + 2365.3 x^9 + 900.93 x^10 + 255.515 x^11 + 41.9623 x^12 + 6.12244 x^13 + 1.17914 x^14)/(2 x + 142 x^2 + 994 x^3 + 3068 x^4 + 5440 x^5 + 7516 x^6 + 8061 x^7 + 6591 x^8 + 4215 x^9 + 2029 x^10 + 694 x^11 + 181 x^12 + 33 x^13 + 4 x^14), "a:b" -> (2.88889 x + 158.568 x^2 + 972.426 x^3 + 2782.57 x^4 + 4689.15 x^5 + 6158.85 x^6 + 6193.35 x^7 + 4759.49 x^8 + 2828.1 x^9 + 1262.26 x^10 + 396.808 x^11 + 87.1035 x^12 + 15.9183 x^13 + 2.35827 x^14)/(2 x + 142 x^2 + 994 x^3 + 3068 x^4 + 5440 x^5 + 7516 x^6 + 8061 x^7 + 6591 x^8 + 4215 x^9 + 2029 x^10 + 694 x^11 + 181 x^12 + 33 x^13 + 4 x^14)|>