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I also confirmed the rest of the data following your methodology on the derivative calculations; the only errors I found are carryovers from the differences in our observed Rice and Orange times.
In-game testing. While I haven't gone to the trouble of ensuring the listed percentages are correct, I can confirm that the beans 'double harvest' only gives 1 extra produce and the tomatoes only give 2. The orange double harvest does work as advertised.
How are you calculating the harvest size? Those numbers don't line up with the in-game tooltips for the crops that have chances for double yields assuming a perfect average: Beans(30%)= 2.6, Tomato(35%)= 4.05, Orange(40%)= 5.6
I can't corroborate your derivative calculations yet because when I did mine I didn't time the scientists planting, so my data is even more idealized than yours and it'll take a while to redo my spreadsheet.