fix: define derivatives of ssqrt, scbrt, slog

[AayushSabharwal]

Expressions returned from symbolic_solve would not work with expand_derivatives prior to this change.

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All modified and coverable lines are covered by tests ✅

Project coverage is 80.45%. Comparing base (47cfd60) to head (6aa6759).
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@@             Coverage Diff             @@
##           master    #1273       +/-   ##
===========================================
+ Coverage    8.30%   80.45%   +72.14%     
===========================================
  Files          46       47        +1     
  Lines        4549     4641       +92     
===========================================
+ Hits          378     3734     +3356     
+ Misses       4171      907     -3264     

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[ChrisRackauckas]

Expressions returned from symbolic_solve

Why not fix that?

[AayushSabharwal]

This does fix the derivatives. The intention with ssqrt etc being used in symbolic_solve (as per the comment) is to represent the sqrt of negative/complex numbers covariantly. For example, the roots of a quadratic could by complex depending on the coefficients, and if sqrt is used it would just error if evaluated with coefficients that result in complex roots.

[ChrisRackauckas]

The problem isn't the derivatives, so why does this fix the derivatives?

[AayushSabharwal]

The implicit constraints are a different issue. This fixes taking the derivative of expressions returned from symbolic_solve.

Before:

julia> Symbolics.derivative_idx((Symbolics.ssqrt(64+ 64z^2)), 1)
Symbolics.NoDeriv()

After:

julia> Symbolics.derivative_idx((Symbolics.ssqrt(64+ 64z^2)), 1)
1 / (2√(64 + 64(z^2))

[ChrisRackauckas]

Why just the derivative expressions instead of the expressions?

[AayushSabharwal]

I'm not sure I follow 😅 the expressions themselves are fine, ssqrt is necessary to handle complex roots.