{"action":"created","issue":{"url":"https://api.github.com/repos/ekmett/ad/issues/40","labels_url":"https://api.github.com/repos/ekmett/ad/issues/40/labels{/name}","comments_url":"https://api.github.com/repos/ekmett/ad/issues/40/comments","events_url":"https://api.github.com/repos/ekmett/ad/issues/40/events","html_url":"https://github.com/ekmett/ad/issues/40","id":61730974,"number":40,"title":"Determining when Jacobians are sparse","user":{"login":"dmcclean","id":603347,"avatar_url":"https://avatars.githubusercontent.com/u/603347?v=3","gravatar_id":"","url":"https://api.github.com/users/dmcclean","html_url":"https://github.com/dmcclean","followers_url":"https://api.github.com/users/dmcclean/followers","following_url":"https://api.github.com/users/dmcclean/following{/other_user}","gists_url":"https://api.github.com/users/dmcclean/gists{/gist_id}","starred_url":"https://api.github.com/users/dmcclean/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/dmcclean/subscriptions","organizations_url":"https://api.github.com/users/dmcclean/orgs","repos_url":"https://api.github.com/users/dmcclean/repos","events_url":"https://api.github.com/users/dmcclean/events{/privacy}","received_events_url":"https://api.github.com/users/dmcclean/received_events","type":"User","site_admin":false},"labels":[{"url":"https://api.github.com/repos/ekmett/ad/labels/limitation","name":"limitation","color":"d7e102"},{"url":"https://api.github.com/repos/ekmett/ad/labels/question","name":"question","color":"0b02e1"}],"state":"closed","locked":false,"assignee":null,"milestone":null,"comments":19,"created_at":"2015-03-15T02:22:40Z","updated_at":"2015-03-16T02:17:00Z","closed_at":"2015-03-16T00:45:36Z","body":"To what extent is it possible for automatic differentiation to tell us when the partial derivative of a function with respect to one of its inputs is everywhere zero?\r\n\r\nThe general approach works by evaluating derivatives only at finitely many explicitly specified points.\r\n\r\nBut it seems that this analysis, or at least a very good conservative approximation of it, is syntax-directed on the grammar of math expressions that `Num` and `Floating` and friends let us construct, so maybe there is hope?"},"comment":{"url":"https://api.github.com/repos/ekmett/ad/issues/comments/81351855","html_url":"https://github.com/ekmett/ad/issues/40#issuecomment-81351855","issue_url":"https://api.github.com/repos/ekmett/ad/issues/40","id":81351855,"user":{"login":"dmcclean","id":603347,"avatar_url":"https://avatars.githubusercontent.com/u/603347?v=3","gravatar_id":"","url":"https://api.github.com/users/dmcclean","html_url":"https://github.com/dmcclean","followers_url":"https://api.github.com/users/dmcclean/followers","following_url":"https://api.github.com/users/dmcclean/following{/other_user}","gists_url":"https://api.github.com/users/dmcclean/gists{/gist_id}","starred_url":"https://api.github.com/users/dmcclean/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/dmcclean/subscriptions","organizations_url":"https://api.github.com/users/dmcclean/orgs","repos_url":"https://api.github.com/users/dmcclean/repos","events_url":"https://api.github.com/users/dmcclean/events{/privacy}","received_events_url":"https://api.github.com/users/dmcclean/received_events","type":"User","site_admin":false},"created_at":"2015-03-16T02:17:00Z","updated_at":"2015-03-16T02:17:00Z","body":"Oh, now I get it. (Sorry, this takes me a while sometimes.) The problem is that there is no way to write a useful `Ord` instance or to otherwise teach it that the abstract interpretation for branching constructs is the conservative combination of what each of the branches would do."}}