It transform a simple expression like x+y into a long chain of "eml" applications, so:
replyDerivatives: 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)).
Agreed on integrals, but the derivative is relatively simple?
replyIf f(x) = exp(x) - ln(x) then f’(x) = exp(x) - 1/x, which is representable in eml form as well.
To the overall point though, I don’t think it helps make derivatives easier though. To refactor a function to eml’s is far more work than refactoring into something that’s trivially differentiable with the product rule and chain rule.
You mean
reply f'(x) = eml(x,x) + eml(1,eml(eml(1,x)),1) + eml(eml(1, exp(eml(1, 1))),-eml(1, eml(eml(1, x))),1)
x-y = eml(eml(1, exp(eml(1, x))), eml(y,1))