Which version of Modified Dietz is better?

This week I'm reviewing a software vendor client's system and saw that they used a version of Modified Dietz which we typically don't see. Here's the normal form:

and here's what they use:

In reality they will provide the same result so it really shouldn't matter which we use, right? In fact, I was first introduced to the second formula way back in the 1980s. I prefer the first version because I think it's more intuitive. What are we doing in the second? Does it make sense? Can you explain it?

I have reflected on the first form quite a bit and think its meaning is clear:

To me you can rationalize what is being done; not so easy with the first version. I think the first is a bit more challenging to implement, too, so I vote for #1! How about you?