Most efficiently insert a number in a maintained large sorted variable - performance

Question

I need to most efficiently insert a number in a maintained large sorted variable. Is there a better method than test1?
test1 is quite a bit faster vs test2 which is just to append a variable then resort.
q←1000000⍴0 ⋄ q←10 9 8 7 6 5 4 3 2,q ⍝q is kept sorted
test1←{
y←⍺(⍳∘1≤)⍵ ⍝ very fast
(y↑⍺),⍵,(y↓⍺) ⍝ is there a tacit version here and without copying?
}
10↑q test1 6
10 9 8 7 6 6 5 4 3 2
cmpx 'q test1 6'
3.2E¯4
test2←{y←⍵,⍺ ⋄ y[⍒y]}
10↑q test2 6
10 9 8 7 6 6 5 4 3 2
cmpx 'q test2 6'
1.5E¯3
I tried presorted variable. With test1 is quicker than appending then sorting. Perhaps test1 refactored with better tacit?

Answer 1

Possibly not the answer you are looking for, but in a production application, if access to these sorted keys with frequent appends was an important performance consideration in a Dyalog APL application, you might resort to something like the following class. The strategy is to have an unsorted variable data which can be appended to efficiently using a method called Append. Sorting is done on demand, if needed (there is room for further optimisation by checking whether the appended value is greater than the last element in the list, which would be worthwhile if that was a common case).
:Class Sorted
:Property Values
:Access Public
∇Set value
data←value
sorted←0
∇
∇r←Get value
:If ~sorted
sorteddata←data[⍒data]
sorted←1
:EndIf
r←sorteddata
∇
:EndProperty
∇ Make initial
:Implements Constructor
:Access Public
data←initial
sorted←0
∇
∇ r←Append values
:Access Public
data,←values
r←sorted←0
∇
:EndClass
Usage would be along the lines of:
s←⎕NEW Sorted (10 9 8 7 6 5 4 3 2,1E6⍴0)
s.Append 6
s.Append 7
≢s.Values
100011