Difference between 'turn up' and 'turn out'
This occurred to me when I was drafting an email. I wanted to mention in the email that something that I had estimated earlier to take 5 days was not as complex, and I could finish it in 1 day.
Which of the following is correct?
It turned out (to be?) much simpler that I had thought.
It turned up (to be?) much simpler than I had thought.
The correct choice in your case is "It turned out to be much simpler than I had thought". (Notice, not "that", but "than"). This means you discovered that the thing was simple.
"It turned up" means that something appeared physically. For example, "My sister didn't turn up for my birthday party" means that she did not come to the party. Or "The sweater I thought lost turned up in laundry". This means that I had thought that I had lost it, but I found it in the laundry.
Both of those verbs have other meanings too, but the ones I give here are very common in everyday speach.