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Validate accuracy of standard rules in various domains #34

@HarrisonGrodin

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@HarrisonGrodin

We should test our standard rules to confirm accuracy when working in various domains. This was started in #30, but there are still many improvements which should be made, both to the test suite and to the rules themselves.

  • The variable substitutions provided by the test suite are very naive, substituting the same test value for all variables. We should test combinations of different variable types.
  • We currently only test on integers, which should be changed. We should be testing using various common types (Complex, Matrix, etc.) and updating rule variable images accordingly.
  • We currently don't test differentiation, since this is not a functionality that exists in Base, but we should probably test for various values using numerical approximations to validate the rules in DiffRules.jl.

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