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  • $\begingroup$ Thank you for the trick of defining at $sp$ with the Limit. However, the workaround with the workingprecision and recursion is for the Plot. However, I would like to smooth out the function for the purposes of applying RandomVariate on it efficiently. I should have probably been more precise in the question, I will try to amend it if possible. ( I will try just defining well on sp, wether that improves the randomVariate) $\endgroup$ Commented Oct 17, 2022 at 15:43
  • $\begingroup$ You can also specify a WorkingPrecision with RandomVariate and RandomReal $\endgroup$ Commented Oct 17, 2022 at 15:45
  • $\begingroup$ Will try that ! Edit : Adding explicitely the WorkingPrecision in RandomVariate (although I though that 15 was the default) indeed solves also the problem and evaluates fast. I will mark this question as accepted as it applies more broadly to the problem, unlike the other valid answer which is specific to my function. $\endgroup$ Commented Oct 17, 2022 at 15:58