Performance & SIMD

V3 replaces V2's Eigen with my own spatial algebra on xsimd, and stores every field as a structure of arrays: each component of each field, say the x angular velocity of every joint, is its own contiguous, aligned array. Joints are sorted by their depth in the tree, and each group of SIMD lanes holds joints at the same depth. With many copies of one robot, that puts the same joint of different robots side by side, so one instruction can load, update or store a quantity for eight robots at once (eight lanes with AVX2, four in the default SSE2 build). A Valgrind trace of the compiled binary confirms it: 88.9% of all accesses to simulation data are whole, aligned 8-lane vector loads or stores. The payoff is that filling the lanes is nearly free. On a seven-link arm, one robot takes 3.1 µs per step, while eight robots in the 8-lane build take 4.3 µs, 5.7× the robot-steps per second.

To see where V3 stood, I benchmarked it against MuJoCo 3.15 on the same arm scenes, converted from the same .arow files, at the same 2 ms step, single-threaded on my laptop (Intel Core Ultra 9 285H). Batched across SIMD lanes, Achilles steps a seven-link arm 3.3× faster than MuJoCo's best single-threaded mode, reaching 5.45 million robot-steps per second at 64 robots. In double precision, MuJoCo's own, Achilles is still 1.5–1.6× faster at most batch sizes, and its results match MuJoCo's to about one part in 10¹¹. The one loss is a single seven-link arm, where most SIMD lanes sit empty (0.97×).

For V3, I wrote a full design document before writing any code. The target was concrete: simulate my club's six-robot arena of holonomic turret robots fast enough to train RL policies on a laptop CPU, since we don't have much GPU compute. Training takes millions of steps, so throughput was the goal, and V3 doubled as a performance learning exercise. One rule drove most decisions: only costs paid every frame matter. Only joint state, plus the contact solver's last solution, persists between frames. Everything else is either static data built at load time or scratch memory rebuilt each step and reused between passes. That rule became three pieces: fields; small operations that declare exactly which fields they read and write; and traversals that apply those operations across the joint tree, all checked at compile time. What the compiler can't check, the engine checks as it starts, and CI runs death tests confirming that a bad setup, like a model that doesn't fit its layout or an overflowing arena, stops it with a clear message instead of quietly corrupting a run. I kept V2's physically meaningful types but moved them into the math rather than the structure, so adding collisions or rendering meant adding passes instead of rewiring classes.