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Re: [xml-dev] Quiz: which is better 1 div \$x or pow(\$x,-1)?
• From: David Carlisle <d.p.carlisle@gmail.com>
• To: Roger L Costello <costello@mitre.org>
• Date: Sat, 27 Jun 2020 20:38:28 +0100

that wasn't the conclusion that I expected you to draw from my reply:-)

I was just pointing out the functions were different, not saying one was better than the other,
The division by zero can't happen for 1/(1+e^-x)  anyway but even for your original question
just asking about 1/x, returning inf may be preferable to returning an error, depending on what you want to do,

you didn't highlight it but -1 is a double so math:pow(\$x,-1) is quite a tricky function, math:pow(\$x(xs:int(-1)) with an integer power is much simpler to define.

https://www.w3.org/TR/xpath-functions/#func-math-pow  references the integer and double case separately.

David

On Sat, 27 Jun 2020 at 20:13, Roger L Costello <costello@mitre.org> wrote:

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

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