I had looked at append's behavior when I wrote that post, and for large slices it was increasing the size by 25% each time. That (or any proportion) gives you O(1) amortized time.
cap: 1
cap: 2
cap: 4
...
cap: 512
cap: 1024
cap: 1312
cap: 1696
cap: 2208
cap: 3072
cap: 4096
cap: 5120
cap: 7168
...
cap: 192797696
cap: 240997376
So it looks like it starts by doubling, then it gets weird between 1024 and 4096, and then it multiplies by 1.25.