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Feb 1, 2018 at 0:59 comment added Max Fair point about my lazy handling of y[x]. If there's a way you think I can clarify that in the question I could edit it. You could also keep your answer and add a note to help others avoid the confusion in the future.
Jan 31, 2018 at 11:31 comment added Michael E2 @Max Ah, I think I didn't realize it was the same y[x] throughout the post. I never do things like y[x_] = Evaluate[y[x] /. sol[[1]]] because it destroys y (you can't use y[x] or the original ODE as symbolic expressions). I overlooked its importance to your question. -- Yes InterpolatingFunction seems to be mishandled. Will delete.
Jan 31, 2018 at 5:53 comment added Max But FindRoot doesn't issue a warning when the function y[x] is insufficient precision. If I understand your answer, you're saying "that's just how FindRoot works", which doesn't seem to answer my problem. My problem is that FindRoot deceives me where it should warn me. I accidentally feed it a function y[x] of insufficient precision, and it glazes over that issue and tells me it found me a very precise answer. That's just mathematically incorrect. Is there a reason I'm not seeing for why the precision of a function y[x] shouldn't be inherited by its argument x during FindRoot?
Jan 27, 2018 at 15:24 history edited Michael E2 CC BY-SA 3.0
Added explanation
Jan 27, 2018 at 3:56 history answered Michael E2 CC BY-SA 3.0