Mostly thinking out loud and this probably doesn't make much sense, but:

subtract "derivative of all tasks" "derivative of closed tasks" is meaningless

This isn't exactly meaningless, I think, it's just a weird operation.

That is, we currently store this data:

All Tasks
10:00 AM  +1
10:03 AM  +1
10:32 AM  +1
...

...that is, a single "+1" every time the value increased. This is basically the derivative of the actual "all tasks" line users would expect.

Right now, we apply a function like accumulate(that-data) to draw the line, which approximately takes the integral of the dataset (by adding all the numbers up) and turns that into a new dataset.

Then we connect the dots in a vaguely misleading way: if there were 5 tasks at 10AM and 6 tasks at 11AM, we draw a graph which shows there were 5.5 tasks at 10:30 AM. There weren't -- the number of tasks was 5 until 10:59:59.9999, then it jumped to 6, and there's a discontinuity there. But this is a convenient fiction which makes the data easier to read visually.

To subtract two derivative sets, we just invert all the values in the second one, then combine the points, summing the values where both are defined. We can then accumulate that set to get the line we want -- that is, these operations are equivalent:

add(accumulate(all-tasks), accumulate(closed-tasks))
accumulate(add(all-tasks, closed-tasks))

...assuming add() knows that it needs different behavior when the functions are derivative functions vs integrated functions.

So -- what if one function has been accumulated and the other one has not?

I think we can mostly use the same logic, we just need to know if the function is defined everywhere or not. If it's defined everywhere, we treat its value everywhere as the value of the last discrete point. If it's defined almost nowhere, we only process distinct values. Then an accumluate anywhere works like we expect it to?

So we're still left with the three classes of functions: continuous and defined everywhere ("constant(3)"), discontinuous and defined everywhere (on some domain) ("accumulate(open tasks)"), and discontinuous and defined almost nowhere / discrete points (raw "open tasks").

The first class is now "canEvaluateFunction()". The second class is like "isDefinedEverywhereInDomain()"? That's pretty wordy and unclear so I'm inclined to label the third class as "isRawFunction()" or "isDatapointFunction()" or "isImpulseFunction()" or something, instead, I guess? "Impulse" sounds super cool.

That screenshot produces quite the intense optical effect. I thought I was looking at moiré effect from a cellphone camera.

I'm sure you mean an intense productivity effect, optimizing your leverage to achieve key performance results.