Non-deterministic CPU's.

The first rule of digital electronics is they should be predictable -
ie. when the same data is fed into a circuit twice, the output should
be the same every time.

I'm trying to do a thought experiment to see what could happen if this
restriction was to be relaxed for CPU's.

Current CPU's should process every instruction with 100% accuracy.
What if I remove that restriction and say an error may be made in one
in every 1000 instructions. The error could effect anything, from
simple incorrect results of an arithmetic operation to incorrect
branching in the flow of control. After an "incorrect" instruction, I
understand that any further instructions executed could depend on the
"faulty" one, and therefore also produce unexpected results.

My question is what optimizations and speedups could be applied to CPU
design if they were allowed to occasionally produce "wrong" results?

For example I suspect a higher clock speed would be ok, higher
operating temperature range would be possible, on-die defects would be
ok (provided they only affect a few operations), due to more defects
being allowed, feature size could be reduced with the same
manufacturing process, and therefore clock speeds increased further,
and finally I'm guessing operating voltage could be reduced, reducing
power consumption.

My main question is could a CPU design expert take an "out of the air"
estimate how much faster a CPU could be made if it only had to produce
mainly-correct results, and not perfect results?


Before anyone asks why I want such a CPU, it's just a thought
experiment to see how an algorithm that can't be multi-threaded could
be run fastest. By having multiple CPU's running on the same code and
data data and being "synched" every 100 instructions or so, the
current state of each processor could be compared, and a majority
decision taken. Any CPU which isn't in the correct state would be
reset by copying the state of another CPU, and execution would
continue.