remember {} with key is same as derivedStateOf

remember {}

@Composable
fun ATest() {
    val frequentlyChangedState = remember { mutableStateOf(0) }
    LaunchedEffect(Unit) {
        launch {
            delay(5000) // delay so you can attach with Layout Inspector if you don't trust logs enough.
            while (frequentlyChangedState.value < 10) {
                delay(200)
                frequentlyChangedState.value++
            }
        }
    }

    val valueToDisplay = remember(frequentlyChangedState.value) {
        frequentlyChangedState.value / 2
    }
    Timber.i("test_ ATest outer") // 1 initial composition + 10 recompositions

    ATestInner(valueToDisplay)
}

@Composable
fun ATestInner(value: Int) {
    Timber.i("test_ ATestInner")  // 1 initial composition + 5 recompositions
    Text(text = "value: $value")
}

Well, looks like crucial distinction is that remember {} is Composable whereas derivedStateOf {} not and therefore a new State stream can be created even outside Composable.