_DistributedLazilyCompilingFunctionCaller._dag_to_compiled_func loses metadata.
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Description
We preprocess each partitioned DAG and doing so loses some information on the way.
Consider this DAG:

Notice how the knowledge of "x1" being a DOFArray is unavailable during the preprocessing of "Partition 2" and this leads to some inference failures.
/cc @matthiasdiener @inducer
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