Solving Fizz Buzz with Cosines

EDIT: the llm gods do recreational mathematics as well. claude actually thinks it was able to come up with and verify a solution...

https://claude.ai/share/5664fb69-78cf-4723-94c9-7a381f947633

Anyway an interesting read.

(The divisions will get optimized away.)

arr = [];

y = 0;

setInterval(()=>{arr[y]=x},10)

setInterval(()=>{x=y++},1000)

setInterval(()=>{x="fizz"},3000)

setInterval(()=>{x="buzz"},5000)

setInterval(()=>{x="fizzbuzz"},15000)

* Generate a tuple from 1 to 1000 and name it 'Sequence'

tuple_gen_sequence (1, 1000, 1, Sequence)

* Replace elements in 'Sequence' divisible by 3 with 'Fizz', storing the result in 'SequenceModThree'

tuple_mod (Sequence, 3, Mod)

tuple_find (Mod, 0, Indices)

tuple_replace (Sequence, Indices, 'Fizz', SequenceModThree)

* Replace elements in 'Sequence' divisible by 5 with 'Buzz', storing the result in 'SequenceModFive'

tuple_mod (Sequence, 5, Mod)

tuple_find (Mod, 0, Indices)

tuple_replace (SequenceModThree, Indices, 'Buzz', SequenceModFive)

* Replace elements in 'Sequence' divisible by 15 with 'FizzBuzz', storing the final result in 'SequenceFinal'

tuple_mod (Sequence, 15, Mod)

tuple_find (Mod, 0, Indices)

tuple_replace (SequenceModFive, Indices, 'FizzBuzz', SequenceFinal)

Alternatively, this process can be written more compactly using inline operators:

tuple_gen_sequence (1, 1000, 1, Sequence)

tempThree:= replace(Sequence, find(Sequence % 3, 0), Fizz')

tempFive:= replace(tempThree, find(Sequence % 5, 0), 'Buzz')

FinalSequence := replace(tempFive, find(Sequence % 15, 0), 'FizzBuzz')

In this program, I applied a vectorization approach, which is an efficient technique for processing large datasets. Instead of iterating through each element individually in a loop (a comparatively slower process), I applied operations directly to the entire data sequence in one step. This method takes advantage of Halcon's optimized, low-level implementations to significantly improve performance and streamline computations.

  fizzbuzz n = case (n^4 `mod` 15) of
    1  -> show n
    6  -> "fizz"
    10 -> "buzz"
    0  -> "fizzbuzz"

  fb :: IO ()
  fb = print $ map fizzbuzz [1..30]

TFA implies that branches (if statements and piecewise statements) are not allowed, but I don't see why not. Seems like a basic operation to me.

Nevermind that `s[i]` is essentially a piecewise statement.

  from pysr import PySRRegressor

  def f(n):
      if n % 15 == 0:
          return 3
      elif n%5 == 0:
          return 2
      elif n%3 == 0:
          return 1
      return 0

  n = 500
  X = np.array(range(1,n)).reshape(-1,1)
  Y = np.array([f(n) for n in range(1,n)]).reshape(-1,1)
  model = PySRRegressor(
          maxsize=25,
          niterations=200,  # < Increase me for better results
          binary_operators=["+", "*"],
          unary_operators=["cos", "sin", "exp"],
          elementwise_loss="loss(prediction, target) = (prediction - target)^2",

  model.fit(X,Y)

((cos((x0 + x0) * 1.0471969) * 0.66784626) + ((cos(sin(x0 * 0.628323) * -4.0887628) + 0.06374673) * 1.1508249)) + 1.1086457

with compleixty 22 loss: 0.000015800686 The first term is close to 2/3 * cos(2pi*n/3) which is featured in the actual formula in the article. the constant doesn't compare to 11/15 though

[0] https://github.com/MilesCranmer/PySR

I see a case for 3 * 5 in here:

  for n in range(1, 101):
      if n % 15 == 0:
          print('FizzBuzz')
      elif n % 3 == 0:
          print('Fizz')
      elif n % 5 == 0:
          print('Buzz')
      else:
          print(n)

If we add 'Bazz' for mod 7, are we going to hardcode:

  for n in range(1, 105):
      if n % 105 == 0:          # 3 * 5 * 7
          print('FizzBuzzBazz')
      elif n % 15 == 0:         # 3 * 5
          print('FizzBuzz')
      elif n % 21 == 0:         # 3 * 7
          print('FizzBazz')
      elif n % 35 == 0:         # 5 * 7
          print('BuzzBazz')
      elif n % 3 == 0:
          print('Fizz')
      elif n % 5 == 0:
          print('Buzz')
      elif n % 7 == 0:
          print('Bazz')
      else:
          print(n)

  for n in range(1, 105):
      out = ''
  
      if n % 3 == 0:
          out += 'Fizz'
      if n % 5 == 0:
          out += 'Buzz'
      if n % 7 == 0:
          out += 'Bazz'
  
      print(out or n)

Sort of fun to muse whether almost all FizzBuzz implementations are a bit wrong.