The generic algorithm for determining maximum HR should not be relied upon.
In lieu of having a properly supervised exercise stress test, try the following. Just be careful and aware of the inherent risks of stressing your heart et al.
Find online a RPE (rate of perceive exertion) scale of 10 - see below, and use that in conjunction with your HRM. If you don't trust your HRM then first manually take your own pulse to verify.
After a suitable warm up find a longish hill, gear up and go at it. The goal is reach the point where where you cannot continue any further without dumping a lot of gears or stopping altogether. You don't want to push yourself to the level of collapse so don't over do it.
At that point you will have a heart rate that is close enough to use as your maximum. Consider that most of effective exercising takes place between RPE 4-7.
1-2 Extremely easy. You can easily carry on a conversation.
3 Very easy. You can converse with almost no effort.
4 Moderately easy. You can converse with a little bit of effort.
5 Starting to get challenging. Conversation requires more effort.
6-7 Difficult. Conversation requires a lot of effort.
8 Very difficult. Conversation requires maximum effort.
9-10 Full-out effort. No conversation is possible.
Keep in mind the risk associated with stressing your heart like this, so if anything your RPE should override any readout on your HRM.