Tangling and Untangling

Twisting has the effect of adding 1: $$x\rightarrow x + 1$$ Turning transforms any number into the negative of its reciprocal: $$x\rightarrow -\frac{1}{x}$$ Starting at zero, the first five moves: Twist, twist, twist, turn, twist

Can you continue from there and then return to zero? You can use the reciprocal button on a calculator ($\frac{1}{x}$ ) to help with the calculations.