Modifies implementation of expected_loglik and add tests for it

[theogf]

This addresses the discussions in #82 by implementing @devmotion and adding tests for Zygote compatibility.
It adds a dependency on IrrationalConstants which was already there implicitly anyway.

[codecov]

Codecov Report

Merging #93 (2b102de) into master (094bb40) will increase coverage by 0.09%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master      #93      +/-   ##
==========================================
+ Coverage   95.69%   95.78%   +0.09%     
==========================================
  Files           4        4              
  Lines         279      285       +6     
==========================================
+ Hits          267      273       +6     
  Misses         12       12              

Impacted Files	Coverage Δ
src/expected_loglik.jl	95.34% <100.00%> (+0.75%)	⬆️

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[theogf]

I am not sure why, but the examples are unable to compile ApproximateGPs....

[theogf]

@st-- I addressed your comments and made one more change. Now there is also a "unit" expected_loglik for one observation and one q_f. This allows splitting the code more easily and allows to compute things for one observation as well.

[st--]

According to your benchmarks in #82, not quite as fast as the old code, but I like how clean it is:)

[theogf]

According to your benchmarks in #82, not quite as fast as the old code, but I like how clean it is:)

The speed is more or less the same but the allocations are massively different.

It would be good to compare gradients as well though. Although we could have a frule and rrule with the reparametrization trick :D

[st--]

It would be good to compare gradients as well though. Although we could have a frule and rrule with the reparametrization trick :D

Do you want to do that within this PR?

[theogf]

It would be good to compare gradients as well though. Although we could have a frule and rrule with the reparametrization trick :D

Do you want to do that within this PR?

No, I think it deserves a PR of its own

[st--]

Can you please remove the atol 1e-6 -> 1e-5 change before merging it? Otherwise looks good to me.