> Show me a way to physically compute exp or ln that is less gates than add.

IIRC a resistor in series to a capacitor does the trick, for exp.

No, it approximates exp poorly over an infinitesimally small interval compared to exp. Resistors and capacitors are no where ideal components, which is why they have spec sheets to show how quickly they diverge.

If we’re making sloppy approximations to a tiny range of exp, then I too can do it with a few terms.