Somebody did this back in the DOS era. The program was sometimes called "the crooked accountant's spreadsheet", because you could start with the outputs you wanted and get the input numbers adjusted to fit.

Anyone remember?

I think the concept is solid. I’ve only had a few minutes of playing with it, but I have the opinion is that from a UX perspective constants are more common than variables. So perhaps a cell containing a constant should not have a #, but a variable should.

Ah, two way data binding. If you've used any frameworks before React (and a couple earlier ones with the same philosophy) you'll understand how it becomes a spaghetti mess over time.

A bidirectional formula is also known as an integrity constraint in databases (plus some triggers for restoring the constraint upon updates)!

This is great.

Since you've asked about bugs, I tried pushing the limits and found the following:

    A1: 100          B1: =100-A1
    A2: =A1*(100-A1)
    A3: =A1*B1

A2 can be successfully set to anything reasonable (up to 2500)

However, setting A3 to exactly 100 doesn't work, even though setting it to 101 or 99 (or even 100.000001) does work.

Another limit:

    A1: 100          B1: 100
    A2: =A1+B1
    A3: =A1*B1
    A4: =abs(A2-100) + abs(A3-100)

Setting A4 to zero (or anything below 80) doesn't work. This doesn't improve if the constants in the A4 formula are moved a short distance away from 100.

In case you can't tell from that last example, I think being able to fix the intended values of multiple outputs simultaneously would be interesting. If you were to give more details about the solver's internals, I'd be keen to hear them.

The idea is very interesting. As a default strategy you could preserve the ratio of inputs by scaling them to match the scaling of the output, instead of making them equal (for addition). Similarly, for multiplication, you could preserve the ratio of inputs as well, by scaling them by nth root of the scaling factor of the output.

The examples are great and these bidirectional calculators are something that people would love to have in traditional spreadsheets.

So much so that Credit Suisse, which basically was running everything on heavily modded Excel, created a full language whose outputs were Excel spreadsheets capable of doing that. That thing called “paradise” was a total monstrosity but showed how much people wanted this.

That said, you really need a way to set which cells are fixed and which cells are allowed to move if you want to move past basic examples.

Most times you know what you want to do. like => if the user modifies that cell, find a solution for those specific ones.

If you can enter that info, then you have a lot more constrains for your solver and will avoid a lot of edge cases where everything goes to 0, and you can check that the calculation entered is indeed reversible or not, or if it could have multiple solutions, and so on.

Could you build an inverse kinematics solver with this? (I recently watched a youtube video of someone iteratively working out the solutions for a robotic arm, by alternating modifying the inputs and the results)

Spredsheet but no VLOOKUP?

you might like https://omrelli.ug/g9/ which is a similar concept but for graphics