BoundsError when using expand_derivatives on a particular expression in y, but not the same expression in x

[krsteffen]

MWE (Julia Version 1.10.2, Symbolics v5.28.0, SymbolicUtils v1.5.1):

using Symbolics

expr_gen = (var, fun) -> Differential(var)(Differential(var)(((-Differential(var)(Differential(var)(fun))) / g(var))))

@syms y f(y) g(y) h(y)

expr = expr_gen(y, f(y))
expand_derivatives(expr)
expr = expr_gen(y, g(y))
expand_derivatives(expr) # Error
expr = expr_gen(y, h(y))
expand_derivatives(expr) # Error

The error message:

> show(err)
1-element ExceptionStack:
BoundsError: attempt to access 1-element Vector{Any} at index [2]
Stacktrace:
 [1] getindex(A::Vector{Any}, i1::Int64)
   @ Base ./essentials.jl:13
 [2] expand_derivatives(O::SymbolicUtils.BasicSymbolic{Number}, simplify::Bool; occurrences::SymbolicUtils.BasicSymbolic{Real}) (repeats 2 times)
   @ Symbolics ~/.julia/packages/Symbolics/Eas9m/src/diff.jl:245
 [3] expand_derivatives(O::SymbolicUtils.BasicSymbolic{Number}, simplify::Bool; occurrences::Nothing)
   @ Symbolics ~/.julia/packages/Symbolics/Eas9m/src/diff.jl:245
 [4] expand_derivatives
   @ ~/.julia/packages/Symbolics/Eas9m/src/diff.jl:171 [inlined]
 [5] expand_derivatives(O::SymbolicUtils.BasicSymbolic{Number})
   @ Symbolics ~/.julia/packages/Symbolics/Eas9m/src/diff.jl:171
 [6] top-level scope
   @ REPL[9]:1

For some reason all of the following run successfully. The only difference is replacing y with x.

using Symbolics

expr_gen = (var, fun) -> Differential(var)(Differential(var)(((-Differential(var)(Differential(var)(fun))) / g(var))))

@syms x f(x) g(x) h(x)

expr = expr_gen(x, f(x))
expand_derivatives(expr)
expr = expr_gen(x, g(x))
expand_derivatives(expr)
expr = expr_gen(x, h(x))
expand_derivatives(expr)

[bowenszhu]

This is still a problem of ordering.

• <ₑ not fully reliable SymbolicUtils.jl#483
• better ordering of terms SymbolicUtils.jl#549

As a result, inner_args[i] and arguments(occurrences)[i] sometimes does not actually match inside expand_derivatives.

Symbolics.jl/src/diff.jl

Lines 239 to 245 in 45de9b8

	inner_args = arguments(arg)
	l = length(inner_args)
	exprs = []
	c = 0
	for i in 1:l
	t2 = expand_derivatives(D(inner_args[i]),false, occurrences=arguments(occurrences)[i])