I started using Symbolics.jl build_function() to accelerate various calculations and it works beautifully in many situations. I currently use it mostly to accelerate loss function calculation for curve fitting but I suspect I’ll use whenever I need extra speed.

I ran into the following problem that I was hoping someone could help me with.

Summary: I cannot figure out how to use build_function() on any function that uses sorting like median(), mad() etc that are often useful for loss functions like bisquare or huber.

Here’s MWE without build_function():

```
using Symbolics, Statistics, StatsBase, IfElse
@variables α, β
sym_array = [rand()*α + rand()*β for i in 1:10]
median(sym_array)
ERROR: LoadError: TypeError: non-boolean (Num) used in boolean context
Stacktrace:
[1] sort!(v::Vector{Num}, lo::Int64, hi::Int64, #unused#::Base.Sort.InsertionSortAlg, o::Base.Order.ForwardOrdering)
@ Base.Sort ./sort.jl:502
[2] sort!(v::Vector{Num}, lo::Int64, hi::Int64, a::PartialQuickSort{UnitRange{Int64}}, o::Base.Order.ForwardOrdering)
@ Base.Sort ./sort.jl:626
[3] partialsort!
@ ./sort.jl:97 [inlined]
[4] #partialsort!#2
@ ./sort.jl:156 [inlined]
[5] partialsort!
@ ./sort.jl:156 [inlined]
[6] median!(v::Vector{Num})
@ Statistics /Users/julia/buildbot/worker/package_macos64/build/usr/share/julia/stdlib/v1.6/Statistics/src/Statistics.jl:800
```

I believe the above error is due to known issue where Core.ifelse() cannot be overloaded to use Num as discussed here: The alternative to `ifelse` · Issue #16 · JuliaSymbolics/Symbolics.jl · GitHub.

This issue is being worked on (make `ifelse` generic · Issue #32844 · JuliaLang/julia · GitHub) and it can be bypassed using IfElse.jl.

To see if I can get around above I wrote a quicksort function using IfElse.ifelse().

Here’s a MWE:

```
using Symbolics, Statistics, StatsBase, IfElse
@variables α, β
sym_array = [rand()*α + rand()*β for i in 1:10]
function hacky_partition!(array, lo, hi)
pivot = array[hi]
i = lo
for j in lo:hi
temp_i = deepcopy(array[i])
temp_j = deepcopy(array[j])
i_counter = IfElse.ifelse(array[j] < pivot, 1, 0)
array[i] = IfElse.ifelse(array[j] < pivot,temp_j,temp_i)
array[j] = IfElse.ifelse(array[j] < pivot,temp_i,temp_j)
i += i_counter
end
array[hi], array[i] = array[i], array[hi]
return i
end
function hacky_quicksort!(array, lo, hi)
if lo < hi
p = hacky_partition!(array, lo, hi)
hacky_quicksort!(array, lo, p - 1)
hacky_quicksort!(array, p + 1, hi)
end
end
hacky_quicksort!(array) = hacky_quicksort!(array, 1, length(array))
#Check to make sure my hacky_quicksort!(array) works
sorted_array = rand(50)
hacky_quicksort!(sorted_array)
issorted(sorted_array) #true
hacky_quicksort!(sym_array)
ERROR: LoadError: ArgumentError: invalid index: 1 + IfElse.ifelse(IfElse.ifelse(IfElse.ifelse((0.6824293224486493α + 0.9942479004750877β) < (0.1508782122896153α + 0.1253984208459693β), 0.6824293224486493α + 0.9942479004750877β, 0.6824293224486493α + 0.9942479004750877β) < (0.1508782122896153α + 0.1253984208459693β), 0.6824293224486493α + 0.9942479004750877β, 0.6824293224486493α + 0.9942479004750877β) < (0.1508782122896153α + 0.1253984208459693β), 1, 0) of type Num
Stacktrace:
[1] to_index(i::Num)
@ Base ./indices.jl:300
[2] to_index(A::Vector{Num}, i::Num)
@ Base ./indices.jl:277
[3] to_indices
@ ./indices.jl:333 [inlined]
[4] to_indices
@ ./indices.jl:325 [inlined]
[5] getindex
@ ./abstractarray.jl:1170 [inlined]
[6] hacky_partition!(array::Vector{Num}, lo::Int64, hi::Int64)
@ Main ~/.../symbolics_test.jl:15
[7] hacky_quicksort!(array::Vector{Num}, lo::Int64, hi::Int64)
@ Main ~/.../symbolics_test.jl:28
[8] hacky_quicksort!(array::Vector{Num})
@ Main ~/.../symbolics_test.jl:33
[9] top-level scope
@ ~/.../symbolics_test.jl:37
in expression starting at /.../symbolics_test.jl:37
```

So it looks like the error is due to the fact that in my hacky_quicksort!() there’s a step where Num is used to switch index of an array as part of sorting algorithm and that’s not allowed.

Is there some workaround to allow calculation of median() on Num arrays or is this currently not supported?