A very simple maths query displays the result 0.166667 when the exact result is 1/6 .Wolfram alpha should at least indicate that 0.166667 is rounded.Why is wolfram alpha imprecise in this instance?
Input was: 1/3 * p^2 − 0.5(1/3 *p)^2 − (1/3 *p)^2
1/3 * p^2 − 0.5(1/3 *p)^2 − (1/3 *p)^2
Try your example with 1/2 replacing 0.5