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In Mathematica 11.3:

InverseBetaRegularized[0.001, 4501, 500]

Never finishes calculating.

InverseBetaRegularized[0.001`50, 4501, 500]

Gives "Indeterminate" (which is a wrong result), also it gives warnings:

"Power::infy: Infinite expression 1/0^500 encountered."

"Infinity::indet: Indeterminate expression 0 ComplexInfinity encountered."

Trying to make the calculation exact and then rounding doesn't work either:

Floor[10^16*InverseBetaRegularized[1/1000, 4501, 500]]/10^16

Returns the input as is, and gives the warning

Floor::meprec: Internal precision limit $MaxExtraPrecision = 50.` reached while evaluating Floor[10000000000000000 InverseBetaRegularized[1/1000,4501,500]].

The same error happens even if I raise $MaxExtraPrecision to 1000., if I keep increasing it, it just takes more time calculating and then fails with the same error message.

There are several other instances where InverseBetaRegularized gives errors, or never finishes calculating. In Mathematica 11.2, the function behaved much more nicely:

InverseBetaRegularized[0.001, 4501, 500]

Gives 0.88646

InverseBetaRegularized[0.001`50, 4501, 500]

Gives 0.886460350710515650598296037307790832086968197199659

Floor[10^16*InverseBetaRegularized[1/1000, 4501, 500]]/10^16

Gives 4432301753552759/5000000000000000

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This is fixed in version M12:

InverseBetaRegularized[0.001, 4501, 500]

0.886471

InverseBetaRegularized[0.001`50,4501,500]

0.886460350710515650598296037307790832086968197199659

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  • 1
    $\begingroup$ Yes, today I installed M12. Though, I have noticed that results are slightly different in M12 compared to M11.2. Which version gives more accurate results? $\endgroup$ – Dropped Bass Apr 28 '19 at 9:05

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