Infrahuman, par-human, superhuman, efficient, optimal

Some thresholds in 'sufficiently advanced' machine intelligence are not absolute ability levels within a domain, but abilities relative to the human programmers or operators of the AI. When this is true, it's useful to think about relative ability levels within a domain; and one generic set of distinguished thresholds in relative ability is:

• Strictly infrahuman: The AI cannot do anything its human operators / programmers cannot do. Computer chess in 1966 relative to a human master.
• Infrahuman: The AI is definitely weaker than its operators but can deploy some surprising moves. Computer chess in 1986 relative to a human master.
• (Roughly) human-level: If competing in that domain, the AI would sometimes win, sometimes lose; it's better than human at some things and worse in others; it just barely wins or loses. Computer chess in 1996 relative to Garry Kasparov.
• Superhuman: The AI almost always wins. Computer chess in 2006.
• Efficient: Human advice contributes no marginal improvement to the AI's competence. Computer chess was somewhere around this level in 2016, with "advanced" / "freestyle" / "hybrid" / "centaur" chess starting to lose out against purely machine players.
• Strongly superhuman: The ceiling of possible performance in the domain is far above the human level; the AI can perform orders of magnitudes better. The domain is rich enough that humans don't understand the key generalizations, leaving them shocked at the AI's surprising tactics. Computer Go relative to human masters in 2017 may be starting to approach this level ("We thought we were one or two stones below God, but after playing AlphaGo, we think it is more like three or four"). Or consider a human grandmaster playing Go against a human novice; even after being defeated the novice may not know what happened. (Or consider a human and computer competing at how fast they can do arithmetic. In principle the domain is simple, but competing with respect to speed leaves room overhead for the computer to do literally billions of times better.)
• Optimal: The AI's performance is perfect for the domain; God could do no better. Computer play in checkers (English draughts) as of 2007.

The above ordering isn't correct for every domain. For example, in the extremely simple domain of logical Tic-Tac-Toe, humans can play optimally after a small amount of training. Optimal play in Tic-Tac-Toe is therefore not superhuman. Similarly, if an AI is playing in a rich domain but still has strange weak spots, the AI might be strongly superhuman (its play is much better and shocks human masters) but not efficient (the AI still sometimes plays wrong moves that human masters can see are wrong).