Put the summary of the bug you're having here
What I expected to happen was...:
Minecraft should have launched
What actually happened was...:
It crashed
Steps to Reproduce:
1. Try to launch minecraft, attached crash log...
2. ...
3. ...
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I have a crash log for the same problem for 1.8.7, it is word for word the same, I simply submitted the log from when we tried 1.8.6 to see if it worked.

This is a technical support issue; this site is for bug reports only. For technical support please use the Mojang Support Center.

You're running out of memory:
Memory: 3945024 bytes (3 MB) / 1060372480 bytes (1011 MB) up to 1060372480 bytes (1011 MB)
Assign more heap to Minecraft, see MC-12949

Thanks for taking another look at my post and linking to some solutions. I'll take a look at the other threads and use the advice there.
Cheers!