simplifying expressions - Mathematica performs insufficient or too slow or too memory consuming simplification

Using Mathematica 10,

Simplify[Sqrt[Sin[x]^6 ((a^2 + r[]^2)^2 - 

  a^2 (q^2 + a^2 - 2 m r[] + r[]^2) Sin[x]^2)^2]/((a^2 + 
  a^2 Cos[2 x] + 2 r[]^2)^2 (-a^2 q^2 + a^4 + 
  2 m a^2 r[] + 3 a^2 r[]^2 + 2 r[]^4 + a^2 Cos[2 x] (q^2 + a^2 - 2 m r[] + r[]^2))),
 Assumptions -> {(a^2 + r[]^2)^2 - a^2 (q^2 + a^2 - 2 m r[] + 
    r[]^2) Sin[x]^2 > 0}]

yields the weird expression: $$\begin{cases} \frac{\sin ^3(x)}{2 \left(a^2 \cos (2 x)+a^2+2r()^2\right)^2} & \sin (x)\geq 0 \\ -\frac{\sin ^3(x)}{2 \left(a^2 \cos (2 x)+a^2+2r()^2\right)^2} & \text{True} \\ \end{cases}.$$ If I add the assumption $0 \leq x \leq \pi$, then the result becomes: $$\begin{cases} \frac{\sin ^3(x)}{2 \left(a^2 \cos (2 x)+a^2+2r()^2\right)^2} & a^2 (a^2+q^2 -2 m r() +r^2) \sin^2(x)\leq (a^2 + r()^2)^2\\ -\frac{\sin ^3(x)}{2 \left(a^2 \cos (2 x)+a^2+2r()^2\right)^2} & \text{True} \\ \end{cases},$$ in which the first conditional is actually the first assumption! The correct result is of course the first without the extra conditional.

What does the "True" conditional mean? Why is the second result still not sufficiently simplified?

Another example (2):

Simplify[Conjugate[a + I Cos[θ] r], Assumptions -> {a > 0, θ > 0, r > 0}]

yields Conjugate[a + I r Cos[θ]]. If I attempt simplification of each part in the sum, the result is the expected one!

Simplify seems to be a extremely sensitive to input. Is there any advice to work around these issues?

Another example (3):

Is it possible to make FullSimplify apply only to expressions that include Conjugate, so that the expression can be simplified quickly? I have a long expression and only simplification of the Conjugate is necessary; FullSimplify on the full expression takes more than an hour. Any ideas?

Solution The fastest way (mere seconds) I could find to simplify an expression enclosed in Conjugate is to define the expression as Map[Simplify[Conjugate[#]]&, expr,{-1}]. This has the drawback that the simplified Conjugate is mapped only on "objects that have no subparts", according to the documentation, which suits my purpose fine at the moment.

Another example (4):

When trying to simplify a very long expression, Simplify and FullSimplify cache intermediate results of the simplification in order to speed up the process, but this has certain disadvantages:

1. Long expressions tend to create extremely big caches, which is apparent as the memory size of the kernel reaches many GB and is never released after the simplification is aborted.



2. The result changes depending on the cache created earlier, which reduces the determinism of the process.


3. The cache created earlier may cause next simplifications to last too long for various reasons.

Is there a way to disable or control the cache created by Simplify and FullSimplify?