Bug in structural_simplify: equations unbalanced with negative RHS term

[jwharington]

When RHS equations of ODE include negative term, structural_simplify causes the system to become unbalanced.
Example below (note leading sign on y in dx/dt term in failing case).

function ex_bug()
    @variables t
    @variables x(t)=1
    @variables y(t)=1
    @parameters pp= -1
    der = Differential(t)

    sys1 = ODESystem([der(x)~ y; der(y)~ 1-y+x], t, name=:ex)
    sys2 = ODESystem([der(x)~ pp*y; der(y)~ 1-y+x], t, name=:ex)
    sys3 = ODESystem([der(x)~ -x; der(y)~ 1-y+x], t, name=:ex)
    sys4 = ODESystem([der(x)~ -y; der(y)~ 1-y+x], t, name=:ex)

    sys1s = structural_simplify(sys1)    # works
    sys2s = structural_simplify(sys2)    # works
    sys3s = structural_simplify(sys3)    # works
    sys4s = structural_simplify(sys4)    # fails
end

Tested on

julia 1.7.3
ModelingToolkit v8.18.3
Symbolics v4.10.3

Error is

ERROR: ExtraVariablesSystemException: The system is unbalanced. There are 2 highest order derivative variables and 1 equations.
More variables than equations, here are the potential extra variable(s):
 Differential(t)(x(t))
 -Differential(t)(x(t))
 x(t)

Summarising:

• dx/dt = -x works
• dx/dt = y works
• dx/dt = pp*y with pp negative works
• dx/dt = -y fails

[YingboMa]

Ah, the bug is caused by substituting y = -D(x) back to D(y). We should get -D(D(x)) but got D(-D(x)) instead.