using FiniteDifferences v0.11 required relaxing a bunch of tests

[oxinabox]

This is the commit
9fc8c57#diff-18f60c608d1cadf3013a4e16d696c43ea9f488fa49caa48cb6b582481025bc0fR57

It might be that FiniteDifferences v0.11 need ssome changes to improve accuracy,
or it might be that we should be using a different set of settings in ChainRulesTestUtils.jl by default for fdm

[wesselb]

A quick check suggests that real-valued imputs compute well, at least for Base.FastMath.atan_fast.

julia> central_fdm(5, 1)(Base.FastMath.atan_fast, -4.1) - df(-4.1)
-4.273664755416462e-14
julia> central_fdm(5, 1)(Base.FastMath.atan_fast, -6.1) - df(-6.1)
-1.5747819714917455e-14
julia> central_fdm(5, 1)(Base.FastMath.atan_fast, 0.0) - df(0.0)
2.220446049250313e-16

Could the issue be for complex-valued inputs?

[oxinabox]

yes, I am pretty sure it is for Complex valued inputs

[oxinabox]

@wesselb and I had a meeting on this. here are our notes:

Observations i.e. what we are seeing

• Tests that passed with FiniteDifferences v0.10 don’t with v0.11
• Mostly Complex ones
• Mostly FastMath
• Float32 behaves badly, but that might not have changed
• Fails for x=2.6, but passes for x=2.5 and x=2.3

Diagnosis _ i.e. the challenge_

• Step size change means we are crossing over discontinoualities
• Could be similar but for ill-conditioned.

Actions _ i.e. what we are going to do_

• Check for crossing Discontinuality
  • Would be explained as we changed the step-size. Possibly old size just happened to work for size we were looking at
  • Move away from them. regardless of the change we don't really want to be clsoe to them in the first place
  • Use forward_fdm where necessary
• Produce small test cases that fail
  • Make those unit test for FiniteDifferences
• Double check 1e-40