we will make 10 page of a AI paper, we began with the first and name of the paper

the name of paper is ( improve it pls)''A Millions of env''

you need to make 4 long text of like 12 line
you need to write like a expert of AI, giving hard term, like a real study paper

this is 8 thing to know about :
1. the project is Rocketsim
A C++ library for simulating Rocket League games at maximum efficiency

RocketSim is a complete simulation of Rocket League's gameplay logic and physics that is completely standalone. RocketSim supports the game modes: Soccar, Hoops, Heatseeker, and Snowday.

Speed
RocketSim is designed to run extremely fast, even when complex collisions and suspension calculations are happening every tick. On an average PC running a single thread of RocketSim with two cars, RocketSim can simulate around 20 minutes of game time every second. This means that with 12 threads running RocketSim, you can simulate around 10 days of game time every minute!

Accuracy
RocketSim is not a perfectly accurate replication of Rocket League, but is close enough for most applications (such as training ML bots). Perceivable differences between the simulation and the real game usually take at least a second to accumulate from an initial state. This means RocketSim is accurate enough to:

Train machine learning bots
Simulate different shots on the ball at different angles to find the best input combination
Simulate air control to find the optimal orientation input
Simulate ground and floor pinches
However, RocketSim is NOT accurate enough to:

Accurately re-create entire games from inputs alone
Perfectly simulate long sequences of jumps and landings
Installation
Clone this repo and build it
Use https://github.com/ZealanL/RLArenaCollisionDumper to dump all of Rocket League's arena collision meshes
Move those assets into RocketSim's executing directory
Documentation
Documentation is available at: https://zealanl.github.io/RocketSimDocs/

Bindings
If you don't want to work in C++, here are some (unofficial) bindings written in other languages:

Python: https://github.com/mtheall/RocketSim by mtheall
Python: https://github.com/uservar/pyrocketsim by uservar
Rust: https://github.com/VirxEC/rocketsim-rs by VirxEC
Official Python bindings are currently in the works.

Performance Details
RocketSim already heavily outperforms the speed of Rocket League's physics tick step without optimization.

Version performance comparison:

OS: Windows 10 (Process Priority = Normal)
CPU: Intel i5-11400 @ 2.60GHz
Ram Speed: 3200MZ
Compiler: MSVC 14.16
=================================
Arena: Default (Soccar)
Cars: 2 on each team (2v2)
Inputs: Randomly pre-generated, changed every 2-60 ticks for each car
=================================
Single-thread performance (calculated using average CPU cycles per tick on the RocketSim thread) (1M ticks simulated):
v1.0.0 = 30,334tps
v1.1.0 = 48,191tps
v1.2.0 = 50,763tps
v2.0.0 = ~50,000tps
v2.1.0 = 114,481tps
Issues & PRs
Feel free to make issues and pull requests if you encounter any issues!

You can also contact me on Discord if you have questions: Zealan#5987

Legal Notice
RocketSim was written to replicate Rocket League's game logic, but does not actually contain any code from the game. To Epic Games/Psyonix: If any of you guys have an issue with this, let me know on Discord and we can resolve it.
2. in the study we talk that we made Rocketsim in gpu instead of cpu
3. giving an substencial improvement
4. we can in theory enter it in one millions of env with low vram usage like 8gb of vram


page one was already made :

for the page two :
you need to talk about improvement more precisly. by giving some goofy math and formula and scientific math thing and say that he have some help of Evil Aech that discovers a new method of learning, that can improve by 100x the speed of each env, and that formula can being using in Alphazero env, be smart and not make it dumb math, try to be the more obvious and the most correct.