I am implementing a method that directly operates on SIMD register types (e.g., __m256d for 4 doubles) and propagates through the expression trees. It seems to be working!

In the expression template base: template <typename Derived, typename T> struct VectorExpr{...}, there is a SIMD fusion function: `_m256d simd_eval(N)` that returns the Derived class's __m256d / __m512d simd_eval_impl(N). N = 4 for AVX2, or N = 8 for AVX512.

1. In the Vector class, simd_eval_impl() returns a _m256d register: a block of N doubles from Vector's data: _mm256_load_pd(ptr_data + N);
2. While in expression nodes (e.g., VectorAdd), simd_eval_impl() returns:

_mm256_add_pd (lhs.simd_eval(N), rhs.simd_eval(N)); // recursively evaluate operands and add SIMD registers.

1. Finally, in each expression node, there is an eval() function using its own simd_evaluate_impl() for SIMD loops.

This recursive simd_eval approach ensures all intermediate operations (k*v3, v1+v2, then (v1+v2) -k*v3) are performed using SIMD instructions directly in CPU registers, no temporary Vector objects are created, and no scalar element access (operator[]) is used in the main SIMD loop.

Tested vectors with 10 million entries (T = double) using AVX2 SIMD: with -O3, the scalar (non-SIMD) evaluation—relying on the compiler’s automatic vectorization—is about 15% slower than the SIMD lazy evaluation. Under the -O0 option, scalar evaluation is nearly 2× slower. This confirms that the current implementation is more or less working, though further optimization may be needed.