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BUILT-IN MATHEMATICA SYMBOL

$MaxExtraPrecision

$MaxExtraPrecision
gives the maximum number of extra digits of precision to be used in functions such as N.

You can use Block to reset the value of $MaxExtraPrecision temporarily during the evaluation of expr.

$MaxExtraPrecision is used implicitly in various exact numerical computations, including equality tests, comparisons, and functions such as Round and Sign.

Allow up to 1000 digits of extra precision to complete a numerical approximation:

Out[1]=

Allow as much extra precision as possible:

The default of 50 is not sufficient for some calculations:

The result does not have the requested precision:

Often raising $MaxExtraPrecision by just over the precision deficit will be sufficient:

For hidden zeros, rasing $MaxExtraPrecision will not help:

Allowing unlimited extra precision can lead to running out of memory:

Relative error measured by Precision is not defined at zero, so use Accuracy as a goal:

Symbolic simplification may resolve the dilemma conclusively: