Quiz: which is better 1 div $x or pow($x,-1)?

Hi Folks,

I am writing a Machine Learning (ML) program using XML and XSLT. Part of the program involves evaluating something called a Sigmoid function:

The right-hand side of that expression can be expressed in XPath this way:

1 div (1 + math.exp(-$x))

An equivalent expression is this:

math:pow(1 + math:exp(-$x), -1)

Which expression is better? By "better" I mean any one of these:

produces more accurate results
is faster
is easier to understand, more intuitive

Or, are the two expressions equally good?

Scroll down for the answer …

The first one is better. Here’s why.

They are not equivalent! 1 div 0.0 and math:pow(0.0,-1) produce different results. The first throws an error with the message, “Decimal divide by zero.” The second silently (without error) returns INF; it might not be till some remote downstream process that the INF finally manifests an error. I want to be informed immediately of an error, so the first is definitely better for me.

Thank you David Carlisle for pointing out this difference to me.

/Roger