First of all, you should absolutely put money into savings until you have at least a 6 month cushion, and preferably longer. It doesn't matter if you get 0% interest in your savings and have a high interest rate mortgage, the cushion is still more important.
Once you have a nice emergency fund, you can then consider the question of whether to pay more towards the mortgage if the numbers make sense. However, in my opinion, it's not just a straight comparison of interest rates. In other words, if your savings account gives you 1% and your mortgage is 5%, that's still not an automatic win for the mortgage.
The reason is that by putting the money into your mortgage, you're locking it up and can't access it. To me, money in the hand is worth a lot more than money that's yours on paper but not easily accessible.
I don't know the math well enough, but you don't really need the math. Just keep in mind that you have to weight the present value of putting that money into savings vs the future value of putting it into your mortgage and paying less interest at some point in the future. Do the math and see how much you will save by paying the mortgage down faster, but also keep in mind that future money is worth less than present money. A LOT less if you suddenly have an emergency or decide on a major purchase and need the money, but then have to jump through hoops to get to it.
To me, you need to save a considerable amount by paying down the mortgage, and also understand that your money is getting locked away, for it to make sense.