Is it possible to rewrite path to make shorter url with VirtualService in Istio?

Question

This is my VirtualService in Istio:

apiVersion: networking.istio.io/v1alpha3
kind: VirtualService
metadata:
  name: api-vs
spec:
  gateways:
    - istio-system/gateway
    - mesh
  hosts:
    - api.xyz.com
  http:
    - match:
        - uri:
            prefix: /public/api/booking/
      rewrite:
        uri: /
      route:
        - destination:
            host: public-api
            port:
              number: 80
            subset: v1
          weight: 100

Currently I am able to access my status page using this URL:

https://api.xyz.com/public/api/booking/health 

but I want to make the link shorter.

https://api.xyz.com/public/api/booking/health

should be accessible under

https://api.xyz.com/v3/health

So, in theory, /public/api/booking will become just /v3. I am not sure how to do this in Istio, I don't want to break the page, I should still be able to see the same page.

I tried to use rewrite function but doesn't work.

Is this possible?

Thanks for your suggestions.