Pythagorean Potato Hoe

The Pythagorean Potato Hoe is a to  rarity Hoe. It can be crafted from the Mathematical Hoe Blueprint. This hoe can be upgraded, increasing its Potato harvest yield, and XP rate. The hoe's bonus XP rate is directly proportional to its rarity. It's rarity is increased by 1 level each time the item is upgraded - twice through materials and by 1 level at 100k and 10 million potatos collected, using the hoe; it can be also be recombobulated to reach rarity. When upgraded through materials or collection, the hoe will keep its reforge, enchantments, and potato count.

Upgradeable
Harvest +10% Potato Gain +1% Farming Exp
 * -|Common Stats=

Harvest +25% Potato Gain +2% Farming Exp Logarithmic Counter = Harvest +16% Potato per digits on the Counter, minus 4! Bonus Potato percent increases your Farmhand perk's chances
 * -|Uncommon Stats=

Harvest +50% Potato Gain +3% Farming Exp Logarithmic Counter = Harvest +16% Potato per digits on the Counter, minus 4! Collection Analysis = Harvest +8% Potato per digits of your collection, minus 4! Bonus Potato percent increases your Farmhand perk's chances
 * -|Rare Stats=

Tiers
Harvest +10% Potato Gain +1% Farming Exp
 * -|Common Stats=

Harvest +25% Potato Gain +2% Farming Exp
 * -|Uncommon Stats=

Harvest +50% Potato Gain +3% Farming Exp Reach 1M Counter for +1 Rarity!
 * -|Rare Stats=

Harvest +50% Potato Gain +5% Farming Exp Reach 10M Counter for +1 Rarity!
 * -|Epic Stats=

Harvest +50% Potato Gain +8% Farming Exp
 * -|Legendary Stats=

Harvest +50% Potato Gain +12% Farming Exp
 * -|Mythic Stats=

Formulas
The number of digits on the counter may be calculated using:
 * $$n = \left\lfloor\log_{10} counter\right\rfloor + 1$$

In order to mathematically represent the and  ability scaling, the following formula has to be used:
 * $$\text{Logarithmic Counter Bonus} =

\begin{cases} 0 & n \leq 4 \\ (n - 4) \times 16% & otherwise \end{cases}$$
 * $$\text{Collection Analysis Bonus} =

\begin{cases} 0 & n \leq 4 \\ (n - 4) \times 8% & otherwise \end{cases}$$

Trivia

 * Since the introduction of Farming Fortune, all bonuses are applied as Farming Fortune as well, converting its previously multiplicative bonuses into additive bonuses.
 * The Rarity will increase by 1, whether you are upgrading it through crafting, or by counter(collecting potatoes). All 3 upgrades, and all 3 counter tiers are obtainable for the hoe, no matter the order you do them in. For example, if you have a Pythagorean Potato Hoe with 100k counter, it will increase to, and then you can increase it to by using the crafting recipe for , listed above, under "Upgradeable." The order you do them in does not matter, the Rarity will always increase by 1.