add primitives with better numerical properties

[ghorn]

sqrt(x*x+y*y) = hypot(x,y)
log(1+x) = log1p(x)
expm1(x) = exp x - 1

[jaeandersson]

I didn't know about "hypot". Looks like a useful function and the derivative rule is trivial: If f = hypot(x,y), then, df/dx = x/f.

[jaeandersson]

If you want to avoid a not-a-number, you could define the derivative rule as x/(f + std::numeric_limits<double>::min())...

[ghorn]

That derivative is undefined, what is casadi's policy on such things?

Either way, I would try to keep the properties of hypot(x,y) the same as sqrt(x*x+y*y)

[jaeandersson]

Policy is that 0/0 will give you a not a number. But you're never guaranteed to get not-a-number. x/x will simplify to 1, for example. Derivative of sqrt(x*x+y*y) will follow the chain rule, of course.For f=sqrt(x), derivative is 0.5/f, so and multiplied with 2*x, the expression may or may not simplify to x/f. So there might not be any gain.