I couldn't find any information on this, but is it possible that given how nicely exponentiation and logarithms differentiate and integrate, is it possible that this operator may be useful to simplify the process of finding symbolic solutions to integrals and derivatives?
It transform a simple expression like x+y into a long chain of "eml" applications, so:
Derivatives: No. Exercise: Write the derivative of f(x)=eml(x,x)
Integrals: No. No. No. Integrals of composition are a nightmare, and here they use long composition chain like g(x)=eml(1,eml(eml(1,x),1)).