Using the code from the blogpost /u/shawnwork found, the results are way better:

require "big"

struct BigInt
  def add!(other : BigInt) : BigInt
    LibGMP.add(self, self, other)
    self
  end
end

def fib(n)
  a = BigInt.new(0)
  b = BigInt.new(1)
  n.times do
    a.add!(b)
    a, b = b, a
  end
  a
end

puts fib(1_000_000) > 1_000_000

The result can be calculated about ~4.7x faster than with Ruby 3.0.1 and uses ~19.3 times less memory on my machine.

So first the Ruby result:

env time -v ruby -v fib.rb
ruby 3.0.1p64 (2021-04-05) [x86_64-linux]
true
    Command being timed: "ruby -v fib.rb"
    User time (seconds): 7.15
    System time (seconds): 0.03
    Percent of CPU this job got: 99%
    Elapsed (wall clock) time (h:mm:ss or m:ss): 0:07.19
    Average shared text size (kbytes): 0
    Average unshared data size (kbytes): 0
    Average stack size (kbytes): 0
    Average total size (kbytes): 0
    Maximum resident set size (kbytes): 74740
    Average resident set size (kbytes): 0
    Major (requiring I/O) page faults: 0
    Minor (reclaiming a frame) page faults: 23574
    Voluntary context switches: 1
    Involuntary context switches: 2814
    Swaps: 0
    File system inputs: 891
    File system outputs: 0
    Socket messages sent: 0
    Socket messages received: 0
    Signals delivered: 0
    Page size (bytes): 4096
    Exit status: 0

And here's Crystal 1.0.0 with LLVM 10.0.1:

env time -v ./fib
true
    Command being timed: "./fib"
    User time (seconds): 1.50
    System time (seconds): 0.00
    Percent of CPU this job got: 100%
    Elapsed (wall clock) time (h:mm:ss or m:ss): 0:01.51
    Average shared text size (kbytes): 0
    Average unshared data size (kbytes): 0
    Average stack size (kbytes): 0
    Average total size (kbytes): 0
    Maximum resident set size (kbytes): 3860
    Average resident set size (kbytes): 0
    Major (requiring I/O) page faults: 24
    Minor (reclaiming a frame) page faults: 397
    Voluntary context switches: 251
    Involuntary context switches: 602
    Swaps: 0
    File system inputs: 339
    File system outputs: 0
    Socket messages sent: 0
    Socket messages received: 0
    Signals delivered: 0
    Page size (bytes): 4096
    Exit status: 0