(I'm assuming that you mean that the other person is another subordinate to the same manager, rather than being someone subordinate to you)
It's a bit of a delicate balance. The golden rule is that Snitches get Stitches, but if someone is being unproductive with their time and your manager isn't aware of that fact then letting them know isn't a terrible idea. But it isn't your place to measure how your co-workers are accomplishing their tasks - assuming management isn't out to lunch then performance reviews should fall on their shoulders. Maybe your coworker cleared a rewrite with your manager and your manager was satisfied with the justification and decided that explaining the full reasoning would be a waste of time until the experimental phase was completed.
In theory good management should prevent you from feeling like you need to look over other people's shoulders, because that is their job. So if you are feeling that way you might want to talk to your manager about it, maybe they are bad at managing and are letting things slip through the cracks, maybe they find that allowing someone to experiment with a rewrite is worth the training time - it may be possible that you just need to talk it through with them and find more confidence in their management ability.
It's a bit of a delicate balance. The golden rule is that Snitches get Stitches, but if someone is being unproductive with their time and your manager isn't aware of that fact then letting them know isn't a terrible idea. But it isn't your place to measure how your co-workers are accomplishing their tasks - assuming management isn't out to lunch then performance reviews should fall on their shoulders. Maybe your coworker cleared a rewrite with your manager and your manager was satisfied with the justification and decided that explaining the full reasoning would be a waste of time until the experimental phase was completed.
In theory good management should prevent you from feeling like you need to look over other people's shoulders, because that is their job. So if you are feeling that way you might want to talk to your manager about it, maybe they are bad at managing and are letting things slip through the cracks, maybe they find that allowing someone to experiment with a rewrite is worth the training time - it may be possible that you just need to talk it through with them and find more confidence in their management ability.