Infinity Upgrades

Infinity Upgrades are early-game upgrades that help in Big Crunching in a faster time. Upon performing a Big Crunch, you will unlock some upgrades.
==Pre-Broken Infinity==
ID 	Prerequisite 	Description 	Details 	Cost
timeMult 	 	 	 	
Initial
Antimatter dimensions gain a multiplier based on time played.
Charged
Antimatter dimensions gain a power effect based on time played and Teresa Level.	Initial
\begin{matrix}\left(\frac{m}{2}\right)^{0.15} \\ \text{where } m = \begin{matrix}\text{minutes played} \\ \text{(game time)}\end{matrix}\end{matrix}
Charged
\begin{matrix} \left(1 + \frac{\log_{10}(\log_{10}(t))*\sqrt{L}}{150}\right) \\ \text{ where }\begin{matrix} t = & \begin{matrix}\text{milliseconds played} \\ \text{(game time)}\end{matrix} \\ L = & \text{Teresa level} \end{matrix} \end{matrix}	1 	 	
18Mult 	timeMult 	Initial
1st and 8th Antimatter Dimensions gain a multiplier based on Infinities.
Charged
1st and 8th Antimatter Dimensions gain a power effect based on Infinities and Teresa Level.	Initial
1+\frac{I}{5} \text{ where }I =\text{infinities}
Charged
\begin{matrix} \left(1 + \frac{\log_{10}(\max(1,\log_{10}(I)))*\sqrt{L}}{150}\right) \\ \text{ where }\begin{matrix} I = & \text{Infinities} \\ L = & \text{Teresa level} \end{matrix} \end{matrix}	1
36Mult 	18Mult 	Initial
3rd and 6th Antimatter Dimensions gain a multiplier based on Infinities.
Charged
3rd and 6th Antimatter Dimensions gain a power effect based on Infinities and Teresa Level.	Initial
1+\frac{I}{5} \text{ where }I =\text{infinities}
Charged
\begin{matrix} \left(1 + \frac{\log_{10}(\max(1,\log_{10}(I)))*\sqrt{L}}{150}\right) \\ \text{ where }\begin{matrix} I = & \text{Infinities} \\ L = & \text{Teresa level} \end{matrix} \end{matrix}	1
resetBoost 	36Mult 	Initial
Decrease the number of Dimensions needed for Dimensional Boosts and galaxies by 9.
Charged
Decrease Dimension Boost requirement based on Teresa Level.	Charged
\frac{1}{1+\frac{\sqrt{L}}{10}} \text{ where } L = \text{Teresa level}	1
dimMult 	 	 	 	
Initial
Increase the multiplier for buying 10 Dimensions (2x -> 2.2x)
Charged
The multiplier of buying 10 Antimatter Dimensions gains a power effect based on Teresa Level.	Charged
1+\frac{L}{200} \text{ where } L = \text{Teresa level}	1 	 	
27Mult 	dimMult 	Initial
2nd and 7th Antimatter Dimensions gain a multiplier based on Infinities.
Charged
2nd and 7th Antimatter Dimensions gain a power effect based on Infinities and Teresa Level.	Initial
1+\frac{I}{5} \text{ where }I =\text{infinities}
Charged
\begin{matrix} \left(1 + \frac{\log_{10}(\max(1,\log_{10}(I)))*\sqrt{L}}{150}\right) \\ \text{ where }\begin{matrix} I = & \text{Infinities} \\ L = & \text{Teresa level} \end{matrix} \end{matrix}	1
45Mult 	27Mult 	Initial
4th and 5th Antimatter Dimensions gain a multiplier based on Infinities.
Charged
4th and 5th Antimatter Dimensions gain a power effect based on Infinities and Teresa Level.	Initial
1+\frac{I}{5} \text{ where }I =\text{infinities}
Charged
\begin{matrix} \left(1 + \frac{\log_{10}(\max(1,\log_{10}(I)))*\sqrt{L}}{150}\right) \\ \text{ where }\begin{matrix} I = & \text{Infinities} \\ L = & \text{Teresa level} \end{matrix} \end{matrix}	1
galaxyBoost 	45Mult 	Initial
All Galaxies are twice as strong.
Charged
All Galaxies are stronger based on Teresa Level.	See Ticks
Charged
+(100 + \sqrt{L})% \text{ where }L =\text{ Teresa level}	2
timeMult2 	 	 	 	
Initial
Antimatter Dimensions gain a multiplier based on time spent in current infinity.
Charged
Antimatter Dimensions gain a power effect based on time spent in current Infinity and Teresa Level.	Initial
\left(\frac{m}{4}\right)^{0.25} \text{where } m = \begin{matrix}\text{minutes in Infinity} \\ \text{(game time)}\end{matrix}
Charged
\begin{matrix} \left(1 + \frac{\log_{10}(\log_{10}(t))*\sqrt{L}}{150}\right) \\ \text{ where }\begin{matrix} t = & \begin{matrix}\text{milliseconds in Infinity} \\ \text{(game time)}\end{matrix} \\ L = & \text{Teresa level} \end{matrix} \end{matrix}	3 	 	
unspentBonus 	timeMult2 	Initial
Multiplier to 1st Antimatter Dimension based on unspent Infinity Points.
Charged
Multiplier to 1st Antimatter Dimension based on unspent Infinity Points, powered by Teresa Level.	Initial
\begin{matrix}1+\left(\frac{IP}{2}\right)^{1.5}\\\text{where }IP =\text{Infinity Points}\end{matrix}
Charged
\begin{matrix}1+\left(\frac{IP}{2}\right)^{1.5\sqrt{L}} \\ \text{where }\begin{matrix}IP =& \text{Infinity Points}\\L =& \text{Teresa level}\end{matrix}\end{matrix}	5
resetMult 	unspentBonus 	Initial
Increase Dimension Boost multiplier (2x -> 2.5x)
Charged
Dimension Boost multiplier gains a power effect based on Teresa Level.	Charged
1+\frac{L}{200} \text{ where } L = \text{Teresa level}	7
passiveGen 	resetMult 	Initial
Infinity Point generation (based on fastest infinity) (Currently (a) every (b))
Charged
Gain Reality Machines each real-time second proportional to amount gained on Reality, increasing with Teresa level.	a = amount gained per crunch (no break)
b = fastest inf*10
Charged: level^2%, multiplied by V Level 10 effect	10
skipReset1 	 	 	 	
You start with the 5th dimension unlocked	1 Dimension Boost on Galaxy/InfinityWhen not in challenge	20 	 	
skipReset2 	skipReset1 	You start with the 6th dimension unlocked 	2 Dimension Boosts on Galaxy/Infinity 	40
skipReset3 	skipReset2 	You start with the 7th dimension unlocked 	3 Dimension Boosts on Galaxy/Infinity 	80
skipResetGalaxy 	skipReset3 	You start with the 8th dimension unlocked, and a Galaxy 	4 Dimension Boost on Galaxy/Infinity; 1 Galaxy on Infinity	300
ipOffline 	"No DLC Required" Achievement 	Only while offline, gain 50% of your best IP/min without using Max All	 	1000
These upgrades reset on eternity, until you reach 4 eternities.
=== x2 IP Multiplier ===
Referred to as the Infinity Point multiplier, it unlocks once you have "No DLC Required". It is a special rebuyable upgrade that has a base cost of 10 IP, multiplying by 10 with every upgrade.
You unlock its Autobuyer at 1 Eternity.
If the Autobuyer bulk buys this upgrade, you will only be deducted IP for the most expensive one, cutting actual IP costs by up to 11% at once.
After the cost reaches 1e3,000,000 IP (3 million purchases, 9.70e903,089x IP gain), the cost scaling will be increased to x1e10 per upgrade. The upgrade is capped and can no longer be bought after the cost reaches 1e6,000,000 IP (3.3 million total purchases, 9.6e993,398x IP gain), at which point the multiplier will automatically increase to 1e1,000,000x.
== Post-Broken Infinity ==
You unlock more upgrades once you Break Infinity. These have no prerequisites.
=== Non-Repeatable ===
ID 	Description 	Details 	Cost
totalMult 	Power up all dimensions based on total antimatter produced
Currently: ()x	\sqrt{\lfloor \log_{10}(AM)+1\rfloor} 	1e4
currentMult 	Power up all dimensions based on current antimatter
Currently: ()x	\sqrt{\lfloor \log_{10}(AM)+1\rfloor} 	5e4
infinitiedMult 	Power up all dimensions based on amount infinitied
Currently: ()x	1+10*\log_{10}(\max(I,1))This is affected by study 31.	1e5
achievementMult 	Power up all dimensions based on achievements completed
Currently: ()x	\max\left(1,\frac{(A-30)^{3}}{40}\right) 	1e6
challengeMult 	Increase the production of all dimensions based on slowest challenge run
Currently: ()x	\max\left(1,\frac{3000}{\max(t,0.1)}\right)
t = seconds	1e7
infinitiedGeneration	You passively generate Infinitied stat based on your fastest infinity.
1 Infinity every ()	fastest inf * 5 	2e7
bulkBoost 	You can buy max Dimension Boosts	See Autobuyers#Dimension_Boost 	5e9
postGalaxy 	Makes galaxies 50% stronger 	See Ticks 	5e11
autoBuyerUpgrade 	Autobuyers work twice as fast 	See Autobuyers 	1e15
=== Repeatable ===
DescriptionUpon reaching the max amount, it will simply display the max amount instead of both the current and the next amounts.	Base Amount	Effect 	Max Amount	Base Price	Price increase
Tickspeed cost multiplier increase
(now)x -> (after)x 	10 	 	 	 	
2 (8 level) 	1e6 	5 	 	 	
Generates (now)% > (after)% of your best IP/min from last 10 infinities, works offline 	0 	50 (10 level)	1e7 	10 	
Dimension cost multiplier increase
(now)x -> (after)x 	10 	 	 	 	
3 (7 level) 	1e7 	5000