Kata

Your task is to parse and Calculate Mathematical Expressions.
 
Don't use any 'parse', 'compile' or 'eval' function of the Compiler (by the way C# has no 'eval' function like Java/Javascript/..., but surely there are ways to use similar methods, or parts of it) - write your own parser/evaluation function.

I don't want to write down each syntactical fineness of the mathematical expressions you have to evaluate, but here are some infos or rules and later on some examples:

Generally "normal programming code syntax and operator priority" for the expression/input string

Operators: *, /, +, -, & (last one instead of Math.Pow, i.e. 2&3= 8)

Operator- priority: "&" > "* /" > "+ -"; [hint: -2+2=0, but -2&2=-4 i.e. -2&2=-(2&2) and not (-2)&2]

-- => + is ok; ++ is not allowed (---5 [=-5] or (-5+1) [=-4] is allowed, but not ++5 or (+5+1))

Numbers: integers, doubles, scientific notation too (0.01= 1e-2 and 100= 1e2 or 1e+2, -0.1= -1e-1 for example)

List of allowed mathematical functions: "log", "ln", "exp", "sqrt", "abs", "atan", "acos", "asin", "sinh", "cosh", "tanh", "tan", "sin", "cos" (all exist in "C#/Math" and can be used for concrete calculation)

Simple error- handling is required (minimal output on errors is string "ERROR", details aren't necessary, for example (5+2)) or 5/0 are errors)

Now some easy examples:
 

--- 5* 2 = -10

2 * 3 + 2 & 2 * 4 = 22

5 -- 6 = 11

((2 + 3) * (1 + 2)) * 4 & 2 = 240 or ((2 + 3) * (1 + 2)) * 4 & -2 = 0.9375

sqrt (sin(2 + 3)*cos (1+2)) * 4 & 2 = 15.5893529757165

sqrt (-2) = ERROR and 1 / 0 = ERROR (not 'NaN')

abs(-2 * 1e-3) = 0.002

4 & 3 & 2 = 262144

I think it's clear and enough;-)

Some generall infos for coding and testcases:

You have to implement a function "public string eval (string expression)" which returns the result of the calculated expression as a string. If the result is valid, you have to convert the double to a string (the expression value is a double, the eval output a string) and if an error occurs, you have to return "ERROR" (with optional message like "ERROR: Stack overflow"). The expression can contain [Spaces], so "sin  ( 2) ist ok, 5  + 6  -2 too, but not "si   n (2)" (function names not splitted). The included mathematical functions can use a mix of upper and lower letters, so Sin(2), SIN(2) and sin(2) are allowed.
 
The test cases contain some "constant/static expressions", but the later and more difficult tests for your code- submission include random tests too. Here your results are accepted, if there's not more than 1e-8 difference to the calculated test- results.
 

Hope you have fun;-)!