How deterministic is arcade physics?

Hello,

I am working on a platformer in Phaser and have experienced a very strange behaviour with the physics engine. Namely, my character ends up in different places to the very same input. Is there any way to make the engine deterministic? What could cause this problem? I have set up a small example that can be accessed here. In the example the character will automatically jump to the right and his current position is printed on the screen. If the window is refreshed the character will (probably) end up in a different position, although the input has been the same. Thank you!