This is... complicated.
How would I calculate the growth stages for Qi's Crop WITHOUT Agriculturalist? I.e. is there any point in investing in Hyper SG while still staying with Artisan?
Incidentally, the wiki shows how long each crop takes to grow with each combination of fertilizer and farming perk. It's on the page for the crop, not the seed - e.g. check the Qi Fruit page, not the Qi Bean page. I think the pumpkin one was wrong a while back (before the bug fix Blade mentioned), but hopefully they're all correct now.
For Qi fruit, it says that with DSG + Artisan you get a harvest every 3 days, while with HSG + Artisan you get a harvest every other day. I know that one's definitely correct, because I just used hyper speed-gro to finish that quest.
But anyways, here's the math, for fun.
With no fertilizer or perks, Qi fruit takes 4 days to grow. With DSG, you lose 0.25*4 = 1 day from that, so it takes three days.
With HSG, you lose 0.33 * 4 = 1.33 days, which rounds up to 2 days taken off, so it takes two days.
So HSG does improve it.
You don't really need to know the exact length of each grown cycle for any reason (since that bug was fixed), but here's the math on that.
Qi fruit has 4 growth cycles, each of which takes 1 day, or in other words the lengths are 1 1 1 1.
With DSG, the one day taken off can't be taken from the first stage, since the seed stage must have length at least 1. So the second stage is decreased by 1 and the lengths of the stages become 1 0 1 1 (i.e. the second stage is removed).
With HSG, the second stage is decreased by 1, and then the third stage is decreased by 1, for a total of two days removed as above. So the lengths become 1 0 0 1 (i.e the second and third stages are skipped).
You can see this matches what's shown on the wiki page for Qi fruit.
Also, if I recall correctly, hyper speed-grow is rarely if ever worth it on the main farm since even when it does decrease the length of growing time compared to DSG, it doesn't decrease it enough to get in an extra harvest. (I think I checked those numbers assuming the player has Artisan, they might be different with Agriculturalist.) But it does have value in the greenhouse or on Ginger Island, since you can grow stuff year-round. You can get in a couple extra harvests of starfruit each year.
(Plus the fertilizer never goes away in the greenhouse or Ginger Island, if you have stuff planted on top of it. So you only have to collect the radioactive ore once.)
This was incorrect. What I was thinking of was that it doesn't improve the number of harvests for the high-value, long growth time crops like starfruit, melons, and pumpkins. It does increase the number of harvests you can get of crops that take either 4, 7, 8, or 10 days (without any fertilizer), if my math is right.