regular vs intuitive (formerly: natural)

[bo198214]

I computed \( \delta:=\text{rsexp}_{\sqrt{2}}(\text{nslog}_{\sqrt{2}}(0.3))-0.3 \) with a precision of rsexp of 20 digits and varying matrix sizes for nslog from 10 to 100. The following graphs show \( \delta \) in dependence on the matrix size (x-Axis).
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This looks quite as if regular and natural method are equal. Yippee!

And here we see again how numerics can be misleading.
Actually I increased the matrix size to 300.
And plotted the difference \( \text{rslog}-\text{islog} \), the result is the expected dilated oscillation for two different Abel functions:
   

In other words we can be quite sure that regular and intuitive tetration is different.