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 Exp rate. The hoe's bonus Exp rate is directly proportional to its rarity. It's rarity is increased 1 level each time the item is upgraded twice through materials and 1 level at 100k, 1mil, and 10mil potatoes collected by the hoe and can be recombobulated to Mythic. When upgraded through materials; 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
 * -|Rare Stats=

Harvest +50% Potato Gain +5% Farming Exp
 * -|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}$$