http://qs321.pair.com?node_id=1009126

I've managed to reduce the Hospelian Arabic to Roman Transform by one byte.

As a lead-in, I've read most of your nodes at some point (always good reading, btw), and when I first saw Ton's amazing formula, I spent a few moments dissecting it to figure out how it did what it did. Recently, while working on a similar problem, I decided to see if I could reproduce his formula, armed with the knowledge of how it worked.

A few hours of brute forcing later, and I had a result. Naturally, I wanted to check back here to see how I had done. I was pleasantly surprised to find that I had stumbled upon a formula that was one byte shorter!

Ton's original formula:
y/CLXVI6240-9/MDCLXXVI/dfor\$\$_.=5x\$&*8%29628

The one byte improvement:
y/CLXVI60-9/MDCLXVIX/dfor\$\$_.="32e\$&"%72726

Alternative:
y/CLXVI0-9/MDCLXIXV/dfor\$\$_.="57e\$&"%474976

Even though "32e\$&"%72726 is one byte longer than Ton's 5x\$&*8%29628, it saves 2 bytes in the transliteration, because 01 is transliterated with IX. The alternative transliterates 012 with IXV, saving yet another byte, but it uses a modulus that's one digit longer.

Update:
Since originally posting, I've found several more alternatives of the same length, using multiple substitutions for I and/or V:

```y/CLXVI0-9/MDCLXIVXI/dfor\$\$_.="49e\$&"%87971

y/CLXVI0-9/MDCLXIIXIV/dfor\$\$_.="7e\$&"%10606  #
y/CLXVI0-9/MDCLXIIXIV/dfor\$\$_.="7e\$&"%15909  #
y/CLXVI0-9/MDCLXIIXIV/dfor\$\$_.="7e\$&"%31818  # These are all essential
+ly the same

y/CLXVI0-9/MDCLXIIX V/dfor\$\$_.="8e\$&"%61535  # Doesn't contain 3 anywh
+ere

# although this is one byte longer, it saved a byte in the challenge I
+ was working on
y/CLXVI60-9/MDCLXXI V/dfor\$\$_.="37e\$&"%97366 # Doesn't contain 1 anywh
+ere