I did some looking around and I found a log from when I made a brand new world to see if my game would close during a brand new save (I had a BUNCH of stuff in my main worlds). The game closed after six minutes. I have no clue how pastebin works, so I'll put it here.
[19:06:37] [main/INFO]: Setting user: EHAshe
[19:06:38] [Client thread/INFO]: LWJGL Version: 2.9.1
[19:06:46] [Client thread/INFO]: Reloading ResourceManager: Default, FMLFileResourcePack:Forge Mod Loader, FMLFileResourcePack:Minecraft Forge, FMLFileResourcePack:Not Enough Items, FMLFileResourcePack:DivineRPG, FMLFileResourcePack:Better Furnaces, FMLFileResourcePack:Backpack, FMLFileResourcePack:ChickenChunks, FMLFileResourcePack:Damage Indicators, FMLFileResourcePack:Inventory Tweaks, FMLFileResourcePack:Iron Chest, FMLFileResourcePack:Rei's Minimap, FMLFileResourcePack:Thaumcraft, FMLFileResourcePack:The Twilight Forest, FMLFileResourcePack:Baubles
[19:06:50] [Sound Library Loader/INFO]: Sound engine started
[19:06:53] [Client thread/INFO]: Created: 16x16 textures/blocks-atlas
[19:06:53] [Client thread/INFO]: Created: 16x16 textures/items-atlas
[19:06:54] [Client thread/INFO]: Reloading ResourceManager: Default, FMLFileResourcePack:Forge Mod Loader, FMLFileResourcePack:Minecraft Forge, FMLFileResourcePack:Not Enough Items, FMLFileResourcePack:DivineRPG, FMLFileResourcePack:Better Furnaces, FMLFileResourcePack:Backpack, FMLFileResourcePack:ChickenChunks, FMLFileResourcePack:Damage Indicators, FMLFileResourcePack:Inventory Tweaks, FMLFileResourcePack:Iron Chest, FMLFileResourcePack:Rei's Minimap, FMLFileResourcePack:Thaumcraft, FMLFileResourcePack:The Twilight Forest, FMLFileResourcePack:Baubles
[19:06:55] [Client thread/ERROR]: Using missing texture, unable to load divinerpg:textures/blocks/ayeracoSpawn.png, java.io.FileNotFoundException
[19:06:55] [Client thread/ERROR]: Using missing texture, unable to load divinerpg:textures/blocks/apalachiaRails_powered.png, java.io.FileNotFoundException
[19:06:55] [Client thread/ERROR]: Using missing texture, unable to load divinerpg:textures/blocks/arcaniteRails_powered.png, java.io.FileNotFoundException
[19:06:56] [Client thread/ERROR]: Using missing texture, unable to load divinerpg:textures/blocks/firewoodLeaves_fast.png, java.io.FileNotFoundException
[19:06:56] [Client thread/ERROR]: Using missing texture, unable to load divinerpg:textures/blocks/hyrewoodLeaves_fast.png, java.io.FileNotFoundException
[19:06:56] [Client thread/ERROR]: Using missing texture, unable to load divinerpg:textures/blocks/dreamwoodLeaves_fast.png, java.io.FileNotFoundException
[19:06:56] [Client thread/ERROR]: Using missing texture, unable to load divinerpg:textures/blocks/mintwoodLeaves_fast.png, java.io.FileNotFoundException
[19:06:56] [Client thread/INFO]: textures/blocks: dropping miplevel from 4 to 3, because of minTexel: 14
[19:06:56] [Client thread/INFO]: Created: 1024x1024 textures/blocks-atlas
[19:06:57] [Client thread/INFO]: Created: 1024x1024 textures/items-atlas
[19:06:58] [Sound Library Loader/INFO]: Sound engine started
[19:07:07] [Server thread/INFO]: Starting integrated minecraft server version 1.7.10
[19:07:07] [Server thread/INFO]: Generating keypair
[19:07:07] [Server thread/INFO]: Converting map!
[19:07:07] [Server thread/INFO]: Scanning folders...
[19:07:07] [Server thread/INFO]: Total conversion count is 0
[19:07:09] [Server thread/WARN]: Unable to find spawn biome
[19:07:09] [Server thread/INFO]: Preparing start region for level 0
[19:07:10] [Server thread/INFO]: Preparing spawn area: 18%
[19:07:11] [Server thread/INFO]: Preparing spawn area: 33%
[19:07:12] [Server thread/INFO]: Preparing spawn area: 43%
[19:07:13] [Server thread/INFO]: Preparing spawn area: 54%
[19:07:14] [Server thread/INFO]: Preparing spawn area: 66%
[19:07:15] [Server thread/INFO]: Preparing spawn area: 76%
[19:07:16] [Server thread/INFO]: Preparing spawn area: 88%
[19:07:18] [Server thread/INFO]: EHAshe[local:E:a0dcd3a3] logged in with entity id 265 at (241.5, 68.0, 263.5)
[19:07:18] [Server thread/INFO]: EHAshe joined the game
[19:07:18] [Client thread/INFO]: [CHAT] A new §eOptiFine§f version is available: §eHD Ultra E7§f
[19:07:18] [Client thread/INFO]: [CHAT] You can install §e64-bit Java§f to increase performance.
[19:07:19] [Client thread/INFO]: [CHAT] Damage Indicators was unable to check for updates!
[19:07:19] [Client thread/INFO]: [CHAT] InvTweaks: Configuration loaded.
[19:07:19] [Client thread/INFO]: [CHAT] §bThank you EHAshe for downloading and playing §aDivineRPG!
[19:07:31] [Client thread/INFO]: Warning: Clientside chunk ticking took 237 ms
[19:07:38] [Client thread/INFO]: Warning: Clientside chunk ticking took 114 ms
[19:07:38] [Client thread/INFO]: Warning: Clientside chunk ticking took 105 ms
[19:07:39] [Client thread/INFO]: Warning: Clientside chunk ticking took 105 ms
[19:07:39] [Client thread/INFO]: Warning: Clientside chunk ticking took 106 ms
[19:07:39] [Client thread/INFO]: Warning: Clientside chunk ticking took 106 ms
[19:07:45] [Server thread/INFO]: EHAshe has just earned the achievement [Taking Inventory]
[19:07:45] [Client thread/INFO]: [CHAT] EHAshe has just earned the achievement [Taking Inventory]
[19:07:45] [Client thread/INFO]: Warning: Clientside chunk ticking took 571 ms
[19:07:50] [Client thread/INFO]: Warning: Clientside chunk ticking took 236 ms
[19:07:50] [Server thread/INFO]: EHAshe has just earned the achievement [Getting Wood]
[19:07:50] [Server thread/INFO]: Saving and pausing game...
[19:07:50] [Server thread/INFO]: Saving chunks for level 'Test World'/Overworld
[19:07:50] [Server thread/INFO]: Saving chunks for level 'Test World'/Nether
[19:07:51] [Client thread/INFO]: [CHAT] EHAshe has just earned the achievement [Getting Wood]
[19:07:52] [Client thread/INFO]: Warning: Clientside chunk ticking took 243 ms
[19:07:55] [Client thread/INFO]: Warning: Clientside chunk ticking took 281 ms
[19:07:58] [Client thread/INFO]: Warning: Clientside chunk ticking took 126 ms
[19:07:59] [Client thread/INFO]: Warning: Clientside chunk ticking took 223 ms
[19:08:03] [Client thread/INFO]: Warning: Clientside chunk ticking took 107 ms
[19:08:04] [Client thread/INFO]: Warning: Clientside chunk ticking took 165 ms
[19:08:04] [Client thread/INFO]: Warning: Clientside chunk ticking took 118 ms
[19:08:05] [Client thread/INFO]: Warning: Clientside chunk ticking took 171 ms
[19:08:06] [Client thread/INFO]: Warning: Clientside chunk ticking took 242 ms
[19:08:12] [Client thread/INFO]: Warning: Clientside chunk ticking took 251 ms
[19:08:13] [Client thread/INFO]: Warning: Clientside chunk ticking took 266 ms
[19:08:15] [Client thread/INFO]: Warning: Clientside chunk ticking took 261 ms
[19:08:15] [Client thread/INFO]: Warning: Clientside chunk ticking took 247 ms
[19:08:19] [Client thread/INFO]: Warning: Clientside chunk ticking took 123 ms
[19:08:23] [Client thread/INFO]: Warning: Clientside chunk ticking took 273 ms
[19:08:31] [Client thread/INFO]: Warning: Clientside chunk ticking took 278 ms
[19:08:31] [Server thread/INFO]: EHAshe has just earned the achievement [Benchmarking]
[19:08:31] [Client thread/INFO]: [CHAT] EHAshe has just earned the achievement [Benchmarking]
[19:08:31] [Client thread/INFO]: Warning: Clientside chunk ticking took 213 ms
[19:08:34] [Client thread/INFO]: Warning: Clientside chunk ticking took 275 ms
[19:08:43] [Server thread/INFO]: EHAshe has just earned the achievement [Time to Mine!]
[19:08:43] [Client thread/INFO]: [CHAT] EHAshe has just earned the achievement [Time to Mine!]
[19:08:44] [Client thread/INFO]: Warning: Clientside chunk ticking took 291 ms
[19:08:53] [Client thread/INFO]: Warning: Clientside chunk ticking took 310 ms
[19:09:41] [Client thread/INFO]: Warning: Clientside chunk ticking took 265 ms
[19:09:52] [Server thread/INFO]: EHAshe has just earned the achievement [Getting an Upgrade]
[19:09:52] [Client thread/INFO]: [CHAT] EHAshe has just earned the achievement [Getting an Upgrade]
[19:10:12] [Client thread/INFO]: Warning: Clientside chunk ticking took 225 ms
[19:10:13] [Server thread/INFO]: EHAshe has just earned the achievement [Hot Topic]
[19:10:13] [Client thread/INFO]: [CHAT] EHAshe has just earned the achievement [Hot Topic]
[19:10:15] [Client thread/INFO]: Warning: Clientside chunk ticking took 216 ms
[19:10:21] [Client thread/INFO]: Warning: Clientside chunk ticking took 228 ms
[19:10:38] [Server thread/INFO]: EHAshe has just earned the achievement [Acquire Hardware]
[19:10:38] [Client thread/INFO]: [CHAT] EHAshe has just earned the achievement [Acquire Hardware]
[19:10:53] [Server thread/INFO]: Saving and pausing game...
[19:10:53] [Server thread/INFO]: Saving chunks for level 'Test World'/Overworld
[19:10:53] [Server thread/INFO]: Saving chunks for level 'Test World'/Nether
[19:11:53] [Server thread/INFO]: EHAshe has just earned the achievement [Time to Strike!]
[19:11:53] [Client thread/INFO]: [CHAT] EHAshe has just earned the achievement [Time to Strike!]
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory
[19:12:31] [Client thread/ERROR]: ########## GL ERROR ##########
[19:12:31] [Client thread/ERROR]: @ Post render
[19:12:31] [Client thread/ERROR]: 1285: Out of memory