Add symbolics_to_float converter

[ChrisRackauckas]

No description provided.

[fgerick]

I think comparing to Float64 is not the best/for some cases the substitution gives a BigFloat instead. E.g here from the discourse discussion example:

julia> using Symbolics, Nemo

julia> @variables x
1-element Vector{Num}:
 x

julia> eq =-279//16 + x^2 ~ 0
-(279//16) + x^2 ~ 0

julia> sol = symbolic_solve(s,x)[1]
(1//2)*√(279//4)

julia> typeof(sol)
SymbolicUtils.BasicSymbolic{Real}

julia> typeof(substitute(sol,Dict()))
BigFloat

julia> y = (1//2*x)/x
1//2

julia> typeof(y)
Num

julia> typeof(substitute(y,Dict()))
Num

julia> typeof(substitute(Symbolics.unwrap(sol),Dict()))
BigFloat

julia> typeof(substitute(Symbolics.unwrap(y),Dict()))
Rational{Int64}

[ChrisRackauckas]

That depends on the types inside of the symbolic expression. Symbolic solving uses bigints which is the cause for the bigfloats. It's just the same behavior as float. Float64 is the right answer for those tests.

[fgerick]

Is there a reason why we cannot use Base.float instead of symbolic_to_float ? I guess there is a reason this is defined like this:

Symbolics.jl/src/num.jl

Line 34 in f4d53fe

Base.float(x::Num) = x

[ChrisRackauckas]

It would effect tracing as it would make the tracers become non-lazy in numerical contexts that use float, like linear algebra.