Not at present.
I can think of some things that it would be good to test. For example, user-entered data producing the appropriate results.
But when I think of bugs we fixed so far (Elm app), writing tests would not have caught most of them up front. They were fundamentally because two pages or controls inappropriately shared state -- either squashing the other's changes or leaving a mess the other wasn't expecting. But initial tests would have been for each thing in isolation and so would not have caught it. Testing all permutations is not really feasible due to finite resources such as money and human lifespans.
Our general policy when these bugs crop up is to separate concerns and, where possible, make the illegal state unrepresentable. This can entail some restructuring of the UI model. It takes perhaps longer than writing a test for the failure and patching in defensive code. But it prevents regressions as well as improving the flow and organization of the code. It is not too terrible to do in Elm as the compiler is great at telling you when you structurally break things.
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