Is BIMDAS busted?

[PhilOfPerth]

The BIMDAS rules (universal priority rules for math) sets priority for math operations as
Brackets, Indices, Multiplication, Division, Addition, Subtraction.
Within the BIMDAS rules, the expression 5+4*3^2-1/2 becomes (3^2)*4/2+5-1
                                                                                               B   I   M  D   A  S
and the result is 22.

With the re-arrangement, Phoenix returns 22, as expected.
but when entered as 5 + 4 * 3 ^ 2 - 1 / 2, it returns 40.5

Does this mean we must apply the BIMDAS rules manually, or am I missing something? 
Print "Am I missing something here?"

[SMcNeill]

You're doing it all wrong, even by BIMDAS standards:
5+4*3^2-1/2 --- original
5 + 4 * (3^2) -1/2 --- first step with Indices (the parenthesis was just my way to highlight this step.)
5 + 4 * 9 - 1/2 -- what we get after we solve that step.
5 + (4 * 9) - 1/2 -- the next step, where we do multiplication.
5 + 36 - 1/2 --- the result from that step
5 + 36 - (1/2) -- the next step, where we do Division
5 + 36 - 0.5 --- the result from that step
(5 + 36) - 0.5 --- Now we do the addition.
41 - 0.5 ---- which gives us this result
(41 - 0.5) --- Finally do your subtraction
40.5

Looks like the answer is correct!!

---

And, if you want to know the extended ruleset that we use for order of operations, then look below.




QB64's order of operations (as ripped from my math evaluator): 
'Exponents with PL 20
i = i + 1: OName(i) = "^": PL(i) = 20
i = i + 1: OName(i) = "SQR": PL(i) = 20
i = i + 1: OName(i) = "ROOT": PL(i) = 20
'Multiplication and Division PL 30
i = i + 1: OName(i) = "*": PL(i) = 30
i = i + 1: OName(i) = "/": PL(i) = 30
'Integer Division PL 40
i = i + 1: OName(i) = "\": PL(i) = 40
'MOD PL 50
i = i + 1: OName(i) = "MOD": PL(i) = 50
'Addition and Subtraction PL 60
i = i + 1: OName(i) = "+": PL(i) = 60
i = i + 1: OName(i) = "-": PL(i) = 60

'Relational Operators =, >, <, <>, <=, >= PL 70
i = i + 1: OName(i) = "<>": PL(i) = 70 'These next three are just reversed symbols as an attempt to help process a common typo
i = i + 1: OName(i) = "><": PL(i) = 70
i = i + 1: OName(i) = "<=": PL(i) = 70
i = i + 1: OName(i) = ">=": PL(i) = 70
i = i + 1: OName(i) = "=<": PL(i) = 70 'I personally can never keep these things straight. Is it < = or = <...
i = i + 1: OName(i) = "=>": PL(i) = 70 'Who knows, check both!
i = i + 1: OName(i) = ">": PL(i) = 70
i = i + 1: OName(i) = "<": PL(i) = 70
i = i + 1: OName(i) = "=": PL(i) = 70
'Logical Operations PL 80+
i = i + 1: OName(i) = "NOT": PL(i) = 80
i = i + 1: OName(i) = "AND": PL(i) = 90
i = i + 1: OName(i) = "OR": PL(i) = 100
i = i + 1: OName(i) = "XOR": PL(i) = 110
i = i + 1: OName(i) = "EQV": PL(i) = 120
i = i + 1: OName(i) = "IMP": PL(i) = 130
i = i + 1: OName(i) = ",": PL(i) = 1000

[PhilOfPerth]

Thanks Steve.
You're right, I had it all wrong!
Not sure why, but it seems we can't just re-phrase the whole expression, but just complete each operation step-by-step.
Sorry for the trivia, it just didn't "add up" for me!
I'll go away and play some more.