I haven't minified it so it doesn't fit on a business card, I have however made some improvements
The original wrote directly to stdout and redirected stdout to a file in order to reduce code and rather put that work on the shell. This version does all of that for you and uses stdout as an information stream to track progress.
I've converted it to rather use a global random, to use a local random variable. I've also made it write to a buffer of chars which are then all written to a file only at the end.
These 2 changes allow for the algorithm to be broken up so that each pixel or group of pixels can be calculated completely independantly. This means it can easily be parallelelized which has been done on a line basis.
Also I use a 2D array for the data and it now writes "NIM"
I'm working on getting refraction working, it's currently very broken.
I've tested this on a Ryzen R7 2700X (8 core 16 thread) with 1024 samples per pixel at 1080p resolution perf stat shows
47,259,627.96 msec task-clock # 15.790 CPUs utilized
6,674,340 context-switches # 0.141 K/sec
7,245 cpu-migrations # 0.000 K/sec
2,131 page-faults # 0.000 K/sec
183,021,382,277,936 cycles # 3.873 GHz (83.33%)
1,987,619,295,630 stalled-cycles-frontend # 1.09% frontend cycles idle (83.33%)
26,923,029,033,766 stalled-cycles-backend # 14.71% backend cycles idle (83.33%)
252,678,712,192,192 instructions # 1.38 insn per cycle
# 0.11 stalled cycles per insn (83.33%)
32,757,139,314,024 branches # 693.132 M/sec (83.33%)
167,256,353,422 branch-misses # 0.51% of all branches (83.33%)
2992.948517901 seconds time elapsed
47233.038144000 seconds user
20.222541000 seconds sys
I'm not very familar with perf stat, the most significant performance issue I think is the
back end idles which I suspect are mostly the result of using sqrt when normalizing vectors.