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The latest version of Mooncake supports differentiating through the matrix exponential, so the hacky rule in this package is not needed. As such, this PR removes all of this functionality.
Locally I was seeing a known Mooncake-related problem, so it might be that this PR cannot be resolved until compintell/Mooncake.jl#319 is resolved. See upstream Julialang issue for more info: JuliaLang/julia#56193