Differential & expand_derivatives missing derivatives of linear terms

[michakraus]

I came across a strange issue when computing derivatives of linear terms. Consider the following MWE:

@variables x
@derivatives Dx'~x
@parameters a, b
a₀ = 1; b₀ = -2;

If I define an expression with unspecified parameters (a,b), everything works as expected:

julia> H = a * x + b * log(x)
(a * x) + (b * log(x))

julia> expand_derivatives(Dx(H))
a + (b * inv(x))

But when I define the same expression with fixed parameters (a₀,b₀), the derivatives are missing some terms:

julia> H₀ = a₀ * x + b₀ * log(x)
(1 * x) + (-2 * log(x))

julia> expand_derivatives(Dx(H₀))
-2 * inv(x)

Funnily, if I have an expression with only the linear terms, everything is fine as well:

julia> K₀ = a₀ * x
1 * x

julia> expand_derivatives(Dx(K₀))
1

I am on the latest #master as of this morning.

Edit: Simplified MWE.

[ChrisRackauckas]

Yeah, that's strange. @shashi let's discuss this one in 15.

[shashi]

This is fixed by #627

[michakraus]

It seems a variant of this error has resurfaced in MTK v5.0 (the following still worked in v4.5):

@variables X[1:4]
@variables V[1:4]
DX = Differential.(X)

H(x) = sum(x)
K(x,v) = sum(log.(x) .* v)

let K = K(X, V), H = H(X)
    f = [expand_derivatives(DX[i](K-H)) for i in eachindex(DX)]
    f̄ = [expand_derivatives(DX[i](K+H)) for i in eachindex(DX)]
    println("f-f̄ = ", f.-f̄)

    g = [expand_derivatives(DX[i](-H)) for i in eachindex(DX)]
    ḡ = [expand_derivatives(DX[i](+H)) for i in eachindex(DX)]
    println("g+ḡ = ", g.+ḡ)
end

yields

f-f̄ = Num[0, 0, 0, 0]
g+ḡ = Num[0, 0, 0, 0]

where the latter is correct, but the former is nonsense. Specifically, the derivative of K-H is identical to the derivative of K+H, while the derivative of -H is indeed the negation of the derivative of +H.

[shashi]

@michakraus thanks for the report, the problem turned out to be that K-H itself is wrong! fixed here JuliaSymbolics/SymbolicUtils.jl#176

[michakraus]

Thanks for the quick fix!

[shashi]

This scared me so we wrote a fuzzer for the construction JuliaSymbolics/SymbolicUtils.jl#177 -- this would have caught this bug emphatically.