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As a professional software engineer with decades of experience, I can assure you that this mod now works as well as possible given the intrinsic limitations of JavaScript floating point and the algorithm that Orteil uses to calculate new prestige. The perfect match of this mod's output with that of Cookie Monster, which was derived independently, is strong evidence of this. Do you want to update your mod with my revised version, which I've linked to in the post below? Otherwise, I'd like to simply publish a fork of your mod containing my changes. Please let me know what you'd like to do.
If you haven't read the following three posts of mine, you can skip them, as they are included in the new Discussions thread.
It turns out that this was not a precision problem after all. In fact, the zero result for chips per second is completely correct! The fact that the mod would flash out of existence whenever the CPS was zero through me off a bit, but it was easy to see why it was doing that, and I fixed it.
The reason that zero is the proper result in many cases has to do with the ubiquitous presence of exponential growth throughout Cookie Clicker, combined with the fact that the rate of exponential growth varies greatly depending on what quantities are being examined.
if you look at the Wiki section Calculating Heavenly Chips, [cookieclicker.fandom.com] you see at the line that starts "Heavenly Chips = " that to find out how many heavenly chips you get from a certain number of cookies, you divide the number of cookies by a trillion and then take the cube root of that result. (This is explained slightly differently earlier on the Wiki page.) The cube root function is the killer here, especially as the number of cookies always includes all the cookies you have ever baked, even across ascensions.
What is happening here is that as the total number of heavenly chips rises, a given amount of cookies will produce fewer heavenly chips. This is easily noticeable. At some point, the number of CPS falls below one, and so it is reported as zero. If you have Cookie Monster installed, you can verify this by looking at the bottom of the tooltip that appears when you hover the cursor over the Legacy info.
The mod was also calculating the number of cookies somewhat incorrectly, and I have fixed this.
Once my work on the mod is finished and ready for release, I'll post a brief notice here and point to a thread in the Discussions area, where I will explain the details.
JavaScript numbers start to break when their absolute value exceeds about 9 quadrillion. Not only are numbers of this size not uncommon in Cookie Clicker, but this seems to roughly correspond to the range where this mod stops working. Further research is necessary, and I will see what I can find. If this is indeed the problem, there are workarounds.
Edit: Sure enough, that's the problem. One number adds a number that is 15 orders of magnitude smaller than it, and then subtracts the first number from the second. The result is (incorrectly) computed to be zero, and so nothing is displayed.
I've taken a brief look at the code, and I found that when the box does not appear, the crucial routine chipsPerSec() always returns zero. This is clearly incorrect. I've recently learned a bit about how prestige works, so I'll take a look soon and see if I can find a quick fix. (From a quick look, the current code for chipsPerSec() does not look correct.) I'll try to get back with a fix soon.