Simplify hanging.

[thunderkid]

KAS hangs when I run the following:

const kasHang = 'x - ( ( - 2 ^ ( - 1 ) * y + z - 2 ^ ( - 1 ) * x * y + 2 * x * z + x ^ 2 * z ) * ( 1 + x ) ^ ( - 2 ) + 2 ^ ( - 1 ) * y - z ) / ( - ( - 2 ^ ( - 1 ) * y + z - 2 ^ ( - 1 ) * x * y + 2 * x * z + x ^ 2 * z ) * ( 1 + x ) ^ ( - 2 ) + z )';
const dd = KAS.parse(kasHang).expr;
const hung = dd.simplify().print(); 

It gets stuck in some infinite loop with stack traces like simplify -> factor -> simplify -> expand.

I haven't tried to hunt down the simplest case in which it hangs.

[zkorz]

I have also experienced this bug in production. I just managed to track it down. There are probably many cases where the simplify function results in an infinite loop of sorts. In my case, it happened with a fraction inside a fraction, but interestingly, it worked fine in very similar cases.

For example, this case hangs:
KAS.parse('\\frac{2}{1+\\frac{2}{-x+1}}').expr.isSimplified()

But all of these work just fine:
KAS.parse('\\frac{2}{1+\\frac{2}{x+1}}').expr.isSimplified()
KAS.parse('\\frac{2}{1+\\frac{1}{-x+1}}').expr.isSimplified()
KAS.parse('\\frac{2}{\\frac{2}{-x+1}}').expr.isSimplified()
KAS.parse('\\frac{1}{1+\\frac{2}{-x+1}}').expr.isSimplified()

I noticed the one that hangs iterates simplify a few times, and ends up producing a very odd intermediate result, and ultimately it fails on the .expand() step, which can be reproduced with this one statement:
KAS.parse("\displaystyle 2\left(1+-15x+105x^{2}+-455x^{3}+1365x^{4}+-3003x^{5}+5005x^{6}+-6435x^{7}+6435x^{8}+-5005x^{9}+3003x^{10}+-1365x^{11}+455x^{12}+-105x^{13}+15x^{14}+-1x^{15}+2\left(1+-1x\right)^{-1}+-30\left(1+-1x\right)^{-1}x+210\left(1+-1x\right)^{-1}x^{2}+-910\left(1+-1x\right)^{-1}x^{3}+2730\left(1+-1x\right)^{-1}x^{4}+-6006\left(1+-1x\right)^{-1}x^{5}+10010\left(1+-1x\right)^{-1}x^{6}+-12870\left(1+-1x\right)^{-1}x^{7}+12870\left(1+-1x\right)^{-1}x^{8}+-10010x^{9}\left(1+-1x\right)^{-1}+6006x^{10}\left(1+-1x\right)^{-1}+-2730x^{11}\left(1+-1x\right)^{-1}+910x^{12}\left(1+-1x\right)^{-1}+-210x^{13}\left(1+-1x\right)^{-1}+30x^{14}\left(1+-1x\right)^{-1}+-2x^{15}\left(1+-1x\right)^{-1}\right)^{-1}").expr.expand()

I see there is a lot of recursion happening. If the root cause cannot be found, I wonder if a simpler way of fixing the issue is setting some max iteration constraint. Perhaps that is more useful for my use case of isSimplified() and just return false.