WebAssembly MVP SIMD (128-bit Fixed SIMD) mandated strict determinism across all CPU architectures. While determinism is ideal for reproducibility, it severely penalized performance on operations where x86-64 (Intel/AMD) and ARM64 (Apple Silicon) implement slightly different hardware semantics — particularly Fused Multiply-Add (FMA), dot products, and vector swizzles. To guarantee identical results, Wasm engines previously had to emit extra software masking and rounding instructions. Relaxed SIMD relaxes deterministic constraints for a specific set of vector instructions, allowing browser JIT compilers to emit 100% native CPU instructions (e.g. vfmadd213ps on x86, fmla on ARM) with zero emulation overhead.

Fused Multiply-Add computes (a * b) + c in a single hardware cycle with a single rounding step, doubling floating-point throughput compared to separate multiply and add instructions. For large language model (LLM) inference, matrix multiplications (GEMM) are composed almost entirely of dot products. Using f32x4.relaxed_fma in WebAssembly allows browser runtimes like WebLLM, ONNX Runtime Web, and Transformers.js to achieve native C++ GFLOPS execution speeds directly on client hardware.

Quantized neural networks (INT8/INT4 weights) represent the state of the art for mobile edge inference. The instruction i8x16.relaxed_dot_i8x16_i7x16 multiplies 16 pairs of 8-bit signed integers and accumulates them into 8 pairs of 16-bit integers in parallel. On x86 CPUs with VNNI (Vector Neural Network Instructions), this compiles to a single vpdpbusd instruction, and on ARM CPUs with NEON Dot Product extensions, it compiles to sdot/udot, delivering massive 3x to 5x speedups for quantized tensor processing.

Under standard IEEE 754, different CPU architectures handle NaN sign bits and quiet/signaling NaN propagation differently when calculating min, max, or FMA. Relaxed SIMD defines an allowed output set (for example, allowing either +0.0 or -0.0, or any quiet NaN representation). For machine learning, audio DSP, and computer graphics, these microscopic bit-level differences are completely harmless, while the performance gains of running native machine instructions are immense.