Fitness Tracker with always on Heart Rate display

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Any suggestions for a fitness tracker (or watch) that has the following features:

- Good Heart Rate Monitor
- I should be able to have the display always on, and the HR should always show on the display
- It should fit on a very small wrist
- Battery life at least 8 hours (with HR and display always on)

The following are not requirements but would be nice:
- Relatively small and thin
- Alert when Heart Rate goes above certain level
- Splash proof
- Not very expensive (under $150 preferably)

Thanks!