Problem 42937. Project Euler: Problem 14, Longest Collatz sequence

Probably internal input/output argument checks. Multiply it via millions of iterations and you get significant difference. Your algorithm saves tons of time (in comparison) because you didn't bother to store all the steps, therefore you didn't fell into "dynamic indexing" trap which saves some steps, but drastically slows down the process during saving values to the main array.

I guess this is one of those times where saving the intermediate steps doesn't help your computation time. Nicely done. As a comparison, using mod(b,2) takes about two-thirds longer than 2*floor(b/2) on my machine; 18.8 sec vs 11.3 sec for n=1e8, and 38 sec vs 23 sec for 2e8. That's good to know for speeding things up in other codes I need to run millions of times!

mod(b,k) takes about 10x longer than b-k*floor(b/k) on my machine (2016b win64):
a = randi(1e7,1e8,1); m = 37;
tic, b = mod(a,m); toc;
tic, c = a - floor(a/m)*m; toc;
norm(b - c)
Elapsed time is 3.131306 seconds.
Elapsed time is 0.253768 seconds.
ans =
0