Why when dividing histograms with reasonable error bars sometimes I get massive error bars in the resulting histogram?

Well, I assume your errors scale as sqrt(entries) so, if you want to reduce errors by a factor 3 (4, 5, …), you would need 9 (16, 25, …) times more events.

Note that there exists another method which optionally computes binomial errors: TH1::Divide (const TH1 *h1, const TH1 *h2, Double_t c1=1, Double_t c2=1, Option_t *option=“”)

And maybe you should try (it allows several different errors’ treatment methods): TRatioPlot

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