Determine the type of an input
JavaScript (ES6), 99
x=>(z=x.match(/^([+-])?\d+(\.\d+)?$/))?'SU'[+!z[1]]+'DI'[+!z[2]]:x[1]?'ST':parseInt(x,36)?'LE':'SY'
Test
f=x=>(z=x.match(/^([+-])?\d+(\.\d+)?$/))?'SU'[+!z[1]]+'DI'[+!z[2]]:x[1]?'ST':parseInt(x,36)?'LE':'SY'
console.log=x=>O.textContent+=x+'\n'
;console.log(['0','01','34','12938219383278319086135768712319838871631827319218923'].map(x=>f(x)+' '+x).join`\n`)
;console.log(['-0','+01','+1','-123','+123'].map(x=>f(x)+' '+x).join`\n`)
;console.log(['0.0','3.1415','2.718281828459045235360287471352662497757'].map(x=>f(x)+' '+x).join`\n`)
;console.log(['+0.0','-3.1415','+2.718281828459045235360287471352662497757'].map(x=>f(x)+' '+x).join`\n`)
;console.log([...'akLZ'].map(x=>f(x)+' '+x).join`\n`)
;console.log([...'@"+-'].map(x=>f(x)+' '+x).join`\n`)
;console.log(['Hello, World!','f2!"','+23df','1234A',`'"!`,'.012','1.','UI','+-1','5+3'].map(x=>f(x)+' '+x).join`\n`)<pre id=O></pre>Turing Machine Code, 1544 bytes
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0 + _ r s
0 - _ r s
0 0 _ r u
0 1 _ r u
0 2 _ r u
0 3 _ r u
0 4 _ r u
0 5 _ r u
0 6 _ r u
0 7 _ r u
0 8 _ r u
0 9 _ r u
0 a _ r l
0 b _ r l
0 c _ r l
0 d _ r l
0 e _ r l
0 f _ r l
0 g _ r l
0 h _ r l
0 i _ r l
0 j _ r l
0 k _ r l
0 l _ r l
0 m _ r l
0 n _ r l
0 o _ r l
0 p _ r l
0 q _ r l
0 r _ r l
0 s _ r l
0 t _ r l
0 u _ r l
0 v _ r l
0 w _ r l
0 x _ r l
0 y _ r l
0 z _ r l
0 A _ r l
0 B _ r l
0 C _ r l
0 D _ r l
0 E _ r l
0 F _ r l
0 G _ r l
0 H _ r l
0 I _ r l
0 J _ r l
0 K _ r l
0 L _ r l
0 M _ r l
0 N _ r l
0 O _ r l
0 P _ r l
0 Q _ r l
0 R _ r l
0 S _ r l
0 T _ r l
0 U _ r l
0 V _ r l
0 W _ r l
0 X _ r l
0 Y _ r l
0 Z _ r l
0 * _ r y
s 0 _ r s
s 1 _ r s
s 2 _ r s
s 3 _ r s
s 4 _ r s
s 5 _ r s
s 6 _ r s
s 7 _ r s
s 8 _ r s
s 9 _ r s
s . _ r d
s _ _ r i
s * _ r T
u 0 _ r u
u 1 _ r u
u 2 _ r u
u 3 _ r u
u 4 _ r u
u 5 _ r u
u 6 _ r u
u 7 _ r u
u 8 _ r u
u 9 _ r u
u . _ r D
u _ _ r I
u * _ r T
l _ _ r L
l * _ r T
y _ _ r S
y * _ r T
d 0 _ r d
d 1 _ r d
d 2 _ r d
d 3 _ r d
d 4 _ r d
d 5 _ r d
d 6 _ r d
d 7 _ r d
d 8 _ r d
d 9 _ r d
d _ _ r e
d * _ r T
i 0 _ r i
i 1 _ r i
i 2 _ r i
i 3 _ r i
i 4 _ r i
i 5 _ r i
i 6 _ r i
i 7 _ r i
i 8 _ r i
i 9 _ r i
i _ _ r j
i * _ r T
D 0 _ r D
D 1 _ r D
D 2 _ r D
D 3 _ r D
D 4 _ r D
D 5 _ r D
D 6 _ r D
D 7 _ r D
D 8 _ r D
D 9 _ r D
D _ _ r E
D * _ r T
I 0 _ r I
I 1 _ r I
I 2 _ r I
I 3 _ r I
I 4 _ r I
I 5 _ r I
I 6 _ r I
I 7 _ r I
I 8 _ r I
I 9 _ r I
I _ _ r J
I * _ r T
L * L r M
M * E r halt
S * S r Y
Y * Y r halt
e * S r f
f * D r halt
j * S r k
k * I r halt
E * U r f
J * U r k
T _ S r U
T * _ r T
U * T r halt
Retina, 98 97 bytes
A nice way to practise my regex skills indeed.
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^(?![+-]?\d+(\.\d+)?$)..+
ST
^([+-]?)\d+$
$1UI
^([+-]?)\d+\.\d+$
$1UD
i`^[a-z]$
LE
^.$
SY
[+-]U
S