Patch to correct bug introduced when added conditionals in PR https://github.com/brianguenter/FastDifferentiation.jl/pull/90#issue-2487795686

[brianguenter]

This corrects a bug introduced in #90 (comment) when conditionals were added.

Bug manifested when computing derivative of x^y which has this definition in DiffRules.jl:

@define_diffrule Base.:^(x, y) = :( $y * ($x^($y - 1)) ), :( ($x isa Real && $x<=0) ? Base.oftype(float($x), NaN) : ($x^$y)*log($x) )

FastDifferentiation.jl does not support the ? : operator so this caused an exception.

This rule has been update to use the new if_else operator which has the semantics of if ... else ..., i.e., only the true or false branch is executed.

DiffRules.@define_diffrule Base.:^(x, y) = :($y * ($x^($y - 1))), :(if_else($x isa Real && $x <= 0, Base.oftype(float($x), NaN), ($x^$y) * log($x)))

The builtin ifelse is also supported.

Many functions need the new if_else because exceptions may be thrown in one of the branches, for example:

julia> f = ifelse(x<0,NaN,sqrt(x))
(ifelse  (x < 0) NaN sqrt(x))

julia> g = make_function([f],[x])
...
julia> g([-1])
ERROR: DomainError with -1.0:
sqrt was called with a negative real argument but will only return a complex result if called with a complex argument. Try sqrt(Complex(x)).

For these cases the new if_else operator is appropriate:

julia> f = if_else(x<0,NaN,sqrt(x))
(if_else  (x < 0) NaN sqrt(x))

julia> g = make_function([f],[x])
...
julia> g([-1])
1-element Vector{Float64}:
 NaN

julia> g([2])