Expression too complex for compiler - How to break up this expression into distinct sub-expressions?

Question

Error is with the multiplier variable. Why is it too complex for the compiler? How would I rewrite it? Should I post the entire drawRect func?

Expression was too complex to be solved in reasonable time; consider breaking up the expression into distinct sub-expressions

// Progress is a value between 1.0 and -0.5, determined by the current wave idx, which is used to alter the wave's amplitude.
        var progress = CGFloat(1.0 - Float(i) / Float(numberOfWaves))
        var normedAmplitude = (1.5 * progress - 0.5) * amplitude

        var multiplier = CGFloat(min(1.0, (progress / 3.0 * 2.0) + (1.0 / 3.0))) // error point
        waveColor.colorWithAlphaComponent(multiplier * CGColorGetAlpha(waveColor.CGColor)).set()

Answer 1

Just make the calculation of progress / 3.0 * 2.0 separately.

let calc = progress / 3.0 * 2.0
var multiplier = CGFloat(min(1.0, (calc) + (1.0 / 3.0)))

This error can occur when it´s too much calculations in a single row.

Answer 2

Answer to the question

One way to rewrite your code and break it into smaller pieces:

let firstValue = CGFloat(1.0)
let secondValue = ((progress * 2.0) + 1.0) / 3
var multiplier = min(firstValue, secondValue)
waveColor.colorWithAlphaComponent(multiplier * CGColorGetAlpha(waveColor.CGColor)).set()

The compiler won't complain anymore.

In general, it's a good idea to write shorter lines of code because it's not only helping the compiler to resolve your expressions, it's also making it a lot easier for you or other programmers to understand what the code is doing. Would you know at the first glance, what CGFloat(min(1.0, (progress / 3.0 * 2.0) + (1.0 / 3.0))) means and why you're adding, multiplying and dividing by all those numbers if you look at the code in a month or two?

Here's a good explanation why this error occurs in the first place.

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Algebraic excursion ;)

How to mathematically transform the algebraic expression for secondValue

You'll need these mathematical properties of algebraic operations:

1. Commutative property: You're allowed to swap the operands.

   Applies to addition and multiplication:

   • a + b = b + a
   • a * b = b * a

2. Associative property: The order in which you evaluate the expressions doesn't matter. You can add or remove parenthesis as you like.

   Applies to addition and multiplication:

   • (a + b) + c = a + (b + c)
   • (a * b) * c = a * (b * c)

3. Distributive property: You're allowed to pull common factors out of parentheses.

   Applies to addition of two products with a common factor:

   • (a * c) + (b * c) = (a + b) * c

Furthermore you'll need the rules of operator precedence:

4. In mathematics and common programming languages operators are evaluated in this order:

   1. Paranthesis ()
   2. Exponents x²
   3. Multiplication * and Division /
   4. Addition + and Subtraction -

And then there is one other trick to it:

5. Express division in terms of multiplication:

   • a / b = a * (1 / b)

Now let's use these properties to transform your algebraic expression:

     (progress / 3 * 2)         +  (1 / 3)         
  =   progress / 3 * 2          +   1 / 3          | removed parentheses (4)
  =   progress * (1 / 3) * 2    +   1 / 3          | (5)
  =   progress * 2  * (1 / 3)   +   1 / 3          | swapped factors (1)
  =   progress * 2  * (1 / 3)   +   1 * (1 / 3)    | 1 * x = x
  =  (progress * 2) * (1 / 3)   +   1 * (1 / 3)    | added parenthesis (2)
  = ((progress * 2) + 1) * (1 / 3)                 | pulled common factor out (3)
  = ( progress * 2  + 1) * (1 / 3)                 | removed parenthesis (4)
  = ( progress * 2  + 1) / 3                       | (5)

And thus,

 (progress / 3.0 * 2.0) + (1.0 / 3.0) = ((progress * 2.0) + 1.0) / 3