[xdenser]

my 2 cents to defend NodeJs

   329 837799
   naive 3.06 sec
   329 837799
   decompozed 3.03 sec
   329 837799
   memoized decompozed 0.52 sec

The program https://gist.github.com/xdenser/7722083

[dbaupp]

Presumably the Lua, c and Haskell programs would also be 6× faster if you use the memoised algorithm, so that's a pretty meaningless comparison.

[xdenser]

Ok this intArithm variant (w/o memoization) for NodeJS is 6 times faster (0.54 sec) comparing to naive

        function intArithm(){
        var
            max_a0 = +process.argv[2],
            longest = 0,
            max_len = 0, a0,len, a,z;

        for(a0=1;a0<=max_a0;++a0){
            a = a0;
            len = 0;
            while( a != 1){
                len++;
                z = a >>> 1;
                a = (!(a&1))?z:(a+z+1);
            }
            if(len>max_len){
                max_len = len;
                longest = a0;
            }
        }
        console.log(max_len,longest);
        }

the problem was with division by 2 operation which is not integer in js. So replacing it with shift >>> makes the trick. Formula optimization gives additional 200 ms.

And I doubt memoized c or lua variant will be 6 times faster than non-memoized. As it is not that linear.