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Angular performance with function expression

What are the performance implications of running a function within an Angular expression? For example:
<button ng-if="isValid()">Valid</button>
I'm assuming the function isValid() is being run for each digest loop, which occur many times per second. What options are available within Angular for improving the performance here?
One idea would be to run isValid() within a timeout function a few times a second, then setting a scope variable, so I can control the speed of the "digest". Are there other options people use?

I think if function body is just a simple logic comparison, won't affect performance, but if it gets complex, you can try profiling your code via chrome tools to see how much is performing,
Another alternative is also you can try binding the ng-if to a controller scope property instead and modify the value from other part of your controller's code, so maybe you can apply kind of debounce (https://github.com/shahata/angular-debounce) technique to avoid set the scope variable tons of times

It looks like you're checking if a form is valid before submitting. First of all, your ng-if on the button defeats the purpose of using the same function to conditionally apply a class, since it won't even be in the DOM if isValid() returns false.
You should be able to use ng-pattern, ng-change hooks on your inputs to determine validity as the user is entering form values. Then on your button you can apply the class based on the form's validity:
<button ng-class="{
'btn-success': myFormName.$valid,
'btn-danger': !myFormName.$valid
}" ng-bind="(myFormName.$valid) ? 'Valid' : 'Invalid'"></button>
If you want to suppress form submission, you can check validity of the form inside a function with ng-submit on the <form> tag:
<form name="myFormName" ng-submit="myFormName.$valid && mySubmitFunction()">

One way is to run the isValid function within an interval function, setting a simple scope variable within. For example:
$interval(function() {
scope.isvalid = scope.isValid();
}, 100);
This will run every 100ms, but is probably preferable to the number of calls the digest makes. You can also use $watch or $observe to reduce the number of calls.

When exactly is ng-checked called

While using AngularMaterial, I have ng-checked like this:
<md-list>
<md-list-item ng-repeat="option in options">
<p> {{ option }} </p>
<md-checkbox class="md-secondary" aria-label="{{$index}}" ng-checked="exists($index)" ng-click="toggle($index)"></md-checkbox>
</md-list-item>
</md-list>
And my exists function:
$scope.exists = function (optionNum) {
console.log('Inside $scope.exists. option: '+optionNum);
};
My timer:
function updateTimer() {
var onTimeout = function(){
mytimeout = $timeout(onTimeout,1000);
}
var mytimeout = $timeout(onTimeout,1000);
}
With this, the $scope.exists function is getting called every second. Can someone please explain how ng-checked and $timeout related ? and how to avoid this ?

Reason in one word is: digest cycle. Since your function is bound to the view, every time digest cycle happens those expressions gets evaluated as a part of dirty check to make sure if respective DOM needs to be updated or not. This is nothing to do with angular material alone, it is the core angular implementation. Now in your case you are calling $timeout infinitely which means after each timeout execution digest cycle happens to perform dirty check.
Now what you have is fine, but whenever you bind a function to DOM (as a part of view binding, interpolation or property state attributes or even DOM filters - of course events are fine) you should be aware of the fact that you do not perform extensive operation in that function accidentally or intentionally as the app grows, it will slow down the entire app, and will be hard to refactor and diagnose when the app grows larger and problems starts happening. As much as possible bind to a property instead of a function. Note that even if you bind a property still angular $parse creates a getter on it and adds it to the $$watchers queue to be dirty checked every digest cycle, but difference is that it is a simple getter function.
So basically for instance in your case you could bind ng-checked to property
..ng-checked="doesExist"
and set the property doesExist whenever it needs to be updated. So with this instead of checking for the existence every time, you explicitly set the respective property when a respective event happens. That makes the logic explicit as well.

ng-checked, like many of angular's directives are based on watches. Anytime a digest cycle is called, it evaluates all of the watchers (which the function you are using is one of). So every time $timeout evaluates it is starting a new $digest cycle and evaluating all of the watchers. This is part of the "magic" that keeps the view updated with all of the data in your controllers and directives.
Watchers can become a performance issue if you make your functions complex, or make TONS of watchers. It is generally best to have simple logic that returns true or false very quickly and to avoid setting watches on everything.

$watch vs. ngChange

Say that you want to do something when a property of $scope changes. And say that this property is bound to an input field. What are the advantages/disadvantages of using $watch vs. using ngChange?
html
<input ng-model="foo" ng-change="increment()">
<p>foo: {{foo}}</p>
<!-- I want to do something when foo changes.
In this case keep track of the number of changes. -->
<p>fooChangeCount: {{fooChangeCount}}</p>
js
// Option 1: $watch
$scope.$watch('foo', function() {
$scope.fooChangeCount++;
});
// Option 2: ngChange
$scope.fooChangeCount = 0;
$scope.increment = function() {
$scope.fooChangeCount++;
};
http://plnkr.co/edit/4xJWpU6AN9HIp0OSZjgm?p=preview
I understand that there are times when you need to use $watch (if the value you're looking to watch isn't bound to an input field). And I understand that there are times when you need to use ngChange (when you want to do something in response to a change in an input, but not necessarily in response to a scope property change).
However, in this case both accomplish the same thing.
My thoughts:
ngChange seems cleaner, and easier to understand what's happening.
$watch seems like it might be slightly faster, but probably negligible. With ngChange, I think Angular would have to do some extra work in the compile phase to set up the event listeners, and perhaps extra event listeners decrease speed a bit. Regardless of whether or not you use ngChange, the digest cycle runs on changes, so you have an opportunity to listen for something and call a function in response to changes.

Bottom line - You can achieve with $watch every thing you can achieve with ng-change but not vice-versa.
Purposes:
ngChange - binded to a HTML element
$watch - observing scope's model objects (HTML object models included)
My rule of thumb - if you can use ng-change use it to match your scenario, otherwise use $watch
Why you shouldnt use $watch?
It’s inefficient - Adding complexity to your $digest
It’s hard to test effectively
It's not clean

You have it mostly right. ng-change is very DOM specific and for evaluating an expression when the change event fires on a DOM element.
$watch however, is a lower-level (and more general purpose) utility that watches your view model or $scope. So your watch function will fire every time the user types a key (in the example of an input).
So to contrast, one listens to DOM events, the other watches your data.

$watch adds more complexity do the $digest, making it less efficient. In your case ngChange it's a cleaner and easier solution...
Font: http://www.benlesh.com/2013/10/title.html

When digest loop is called, how to $watch know value change at back - end?

I want to know about how the digest cycle works at back end of angularjs with respect to $watch
How does $watch handle a new value in comparison with the old value?
When the digest loop is called, how does $watch know the value change in angular's back-end?
Thank you!

$watch registers a listener function that is called whenever the given expression changes by comparing the old and new expressions with === in the digest loop.
This is pretty well explained in the docs
https://docs.angularjs.org/api/ng/type/$rootScope.Scope#$watch

I am not sure what you mean by back-end. I am assuming that you are asking how do you know if some other action has changes your model object, value etc.
Here is some pseudo example..
scope.$watch('lastLatency', function (val) {... you got your new value here ....}
In this example "lastLatency" value is being watched to take action.

What $watch method in angularjs really returns and how it works?

I have difficulty understanding the following codes even with the comments
// Store the initial cell value so we can reset to it if need be
var oldCellValue;
var dereg = scope.$watch('ngModel', function() {
oldCellValue = ngModel.$modelValue;
dereg(); // only run this watch once, we don't want to overwrite our stored value when the input changes
});
How many time does function dereg got called in this case? Is this a recursion?

The code you've shown is in a nutshell
storing reference to (just added) $watch() returned value (see below $rootScope.$watch returned value)
once first time is that $watch() called, it calls that referenced function - which leads to ubinding of that $watch()
Read this nice article
Unbinding $watch() Listeners In AngularJS
a small extract from a summary:
As you can see, we're storing the function reference returned by the $watch() statement; then, once the $watch() fires a few times, we invoke that stored method, unbinding the $watch() listener.
In that example, there is an if statement, which could help us to decide, when is the best time to remove that $watch() (e.g. after the first evaluation) ...
The more detailed defintion of the scope.$watch() could be found here:
$rootScope.Scope
And as we can see from this extract:
$watch(watchExpression, [listener], [objectEquality]);
...
Returns a deregistration function for this listener.