Thanks everyone for all the Mma help. What I just don't get is how this product can be so mature (ca. 20 years old) and so expensive, yet need so much manual help before it can get anywhere close to solving a relatively simple problem (which in fact is an applied problem translated into equations). THE ORIGINAL PROBLEM, in case anyone is interested, probably has an elegant solution with minimal computation:

From a recent NY Times article in the science section:

PUZZLE: --------------------------------------------------------------- Let there be a lake on the plane filling up the unit circle centered at the origin. The rest of the plane is level ground. Find the quickest path from (-2,0) to (3,1), possibly passing through the lake, for an amphibious vehicle whose land speed is 1 unit/hour, and whose water speed is 1.25 units/hour. --------------------------------------------------------------- --Dan Rich writes: << You can usually lose all the trig functions with cos u -> (1 - u^2)/(1 + u^2), sin u -> 2 u / (1 + u^2), and similar for v. The new u has range [-1,1], assuming the original u was real. This is the ancient tan(u/2) -> u substitution. In your case, you also want sin((u-v)/2) to be a rational function, so u & v should be halved: cos(u/2) -> (1-u^2)/(1+u^2) etc. cos(u) -> (1 - 6 u^2 + u^4)/(1+u^2)^2 sin(u) -> (4 u - 4 u^3)/(1+u^2)^2 sin((u-v)/2) = sin(u/2 - v/2) = sin(u/2) cos(v/2) - sin(v/2) cos(u/2) -> [ 2u(1-v^2) - 2v(1-u^2) ] / [(1+u^2)(1+v^2)] The sqrts will still mess up the derivatives. If you are looking for critical points, you can multiply through by (1+u^2)(1+v^2) before differentiating to simplify things a little.

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Sometimes the brain has a mind of its own.