[RobMurray]

Wow what a lot of parentheses! To me the first example is perfectly clear because it follows the same precedence rules I learned for arithmetic at school, along with most programming languages. There's nothing special about Haskell here, in Python I would write:

    >>> math.sqrt(2) + 1 * 3 + 3 * 2 + 1 / 7  
    10.557070705230238

The only difference I see is the parentheses used for function application in python.

[indigosun]

You should see when negative numbers are involved.

Due to Haskell's rigor in regard negative numbers:

    ghci> -1 + 2
    1
    ghci> 2 + -1
    <interactive>:12:1: error:
    Precedence parsing error
        cannot mix ‘+’ [infixl 6] and prefix `-' [infixl 6] in the same infix expression
    ghci> 2 + (-1)
    1
    ghci> -1 * 3
    -3
    ghci> 3^-1
    <interactive>:3:2: error:
    • Variable not in scope: (^-) :: t0 -> t1 -> t
    • Perhaps you meant one of these:
        ‘^’ (imported from Prelude), ‘-’ (imported from Prelude),
        ‘^^’ (imported from Prelude)
    ghci> 3^^-1
    <interactive>:4:2: error:
    • Variable not in scope: (^^-) :: t0 -> t1 -> t
    • Perhaps you meant ‘^^’ (imported from Prelude)
    ghci> 3**-1
    <interactive>:5:2: error:
    • Variable not in scope: (**-) :: t0 -> t1 -> t
    • Perhaps you meant ‘**’ (imported from Prelude)
    ghci> 3**(-1)
    0.3333333333333333
    
    ghci> sqrt 2 + 1 * 3 + 3 * 2 + 1 / 7
    10.557070705230238
    ghci> sqrt $ 2  + 1 * 3 + 3 * 2 + 1 / 7
    3.3380918415851206
    ghci> -sqrt 2  + 1 * 3 + 3 * 2 + 1 / 7
    7.728643580484048
    ghci> -sqrt $ 2  + 1 * 3 + 3 * 2 + 1 / 7
    <interactive>:25:1: error:
    • Non type-variable argument in the constraint: Num (a -> a)
      (Use FlexibleContexts to permit this)
    • When checking the inferred type
        it :: forall {a}. (Floating a, Num (a -> a)) => a

    ghci> sin -1
    <interactive>:7:1: error:
    • Non type-variable argument in the constraint: Num (a -> a)
      (Use FlexibleContexts to permit this)
    • When checking the inferred type
        it :: forall {a}. (Floating a, Num (a -> a)) => a -> a
    ghci> (sin -1)
    <interactive>:10:1: error:
    • Non type-variable argument in the constraint: Num (a -> a)
      (Use FlexibleContexts to permit this)
    • When checking the inferred type
        it :: forall {a}. (Floating a, Num (a -> a)) => a -> a
    ghci> sin (-1)  -- -0.8414709848078965

Let's see,

    ghci> (sin (-1))  -- -0.8414709848078965

Ahh, now that's better.