However Some functions have a power level of infinity.

And this makes it nontrivial to even decide if this strategy is helpful.

More investigation is neccessary.

Unfortunately i lack time.

For example exp(x) has a power level of infinity.

Exp(x)^a = exp(a x).

The analogue idea of using semi-logarithms instead of sqrt comes to mind.

Another idea is to write

F(x) = exp(a(x)) b(x)

With b(x) growing slower than exp.

Then repeat if necc with a(x) until we get functions a*(x),b(x) that grow slower then exp , and then use the power level tricks on them.

[ this assumes F(x) grows slower then some power tower exp^[k](x). ]

Regards

Tommy1729

And this makes it nontrivial to even decide if this strategy is helpful.

More investigation is neccessary.

Unfortunately i lack time.

For example exp(x) has a power level of infinity.

Exp(x)^a = exp(a x).

The analogue idea of using semi-logarithms instead of sqrt comes to mind.

Another idea is to write

F(x) = exp(a(x)) b(x)

With b(x) growing slower than exp.

Then repeat if necc with a(x) until we get functions a*(x),b(x) that grow slower then exp , and then use the power level tricks on them.

[ this assumes F(x) grows slower then some power tower exp^[k](x). ]

Regards

Tommy1729