Performance Audit

RMath benchmarks are executed head-to-head against industry standards. Below are verified results from our v0.1.5+ performance suite, including micro-benchmarks per module and a real-world 5M-row data pipeline comparison.

Detailed Vector Speedups (N=100,000)

Across descriptive statistics and linear algebra, RMath provides significant latency reduction on CPU.

Operation	Baseline	Speedup	Description
sum_range	Python sum(range)	4,568.30x	O(1) Rust math vs O(n) loop.
diff	Python List Comp	261.32x	Parallel difference kernel.
sqrt	Python List Comp	222.26x	SIMD-accelerated square root.
variance	statistics.variance	98.60x	Single-pass Welford algorithm.
vector add	Python List Comp	86.68x	Parallel element-wise ops.
randn	random.gauss	84.00x	Parallel PRNG filling.

Array Operations (500x200)

RMath excels at memory layout transformations and specialized neural network kernels.

Operation	Baseline	Speedup	Description
from_numpy	NumPy Array	113.35x	Zero-copy buffer handoff.
transpose	NumPy .T	108.88x	Lazy dimension remapping.
inverse	NumPy inv	12.55x	Parallel LU decomposition.
gelu	NumPy Logic	11.55x	SIMD-accelerated activation.
randn	NumPy randn	7.44x	Parallel Gaussian filling.

Statistical Inference (N=100,000)

RMath implements distribution kernels in native Rust, significantly reducing function call overhead and improving numerical stability.

Operation	Baseline	Speedup	Description
cdf/pdf	SciPy norm	500x+	Bypassing Python wrapper overhead.
median	statistics	50.96x	Optimized introselect algorithm.
describe()	SciPy describe	13.35x	One-pass summary statistics.
correlation	SciPy pearsonr	7.61x	Parallel Pearson correlation.
t-test	SciPy ttest	1.99x	High-precision Welch kernel.

Calculus & Integration

RMath provides high-precision numerical integration and exact Automatic Differentiation (AD) using Dual Numbers.

Operation	Baseline	Speedup	Description
trapezoidal	NumPy trapz	7.79x	Parallel integration kernel.
Exact Grad	Analytic	Native	Zero-error Dual Number AD.

Spatial Geometry & Signal

Native Rust kernels for spatial analysis and spectral transformations.

Operation	Baseline	Speedup	Description
3D Cross	NumPy cross	49.99x	SIMD-accelerated cross product.
Convex Hull	Python Algo	6.11x	Monotone Chain algorithm in Rust.
Minkowski	NumPy norm	4.78x	Parallel spatial distance metric.
FFT (4096)	NumPy fft	3.62x	High-performance spectral transform.

Scalar Pipelines (N=100,000)

RMath uses a LazyPipeline architecture for scalar operations. While individual scalar arithmetic pays an FFI tax, bulk pipeline processing bypasses the Python interpreter entirely.

Operation	Baseline	Speedup	Description
var of range	Python _py_var	75.35x	Fused Welford variance pipeline.
filter + sum	Python GenExp	72.38x	SIMD-accelerated branchless filtering.
sum of range	Python sum()	54.06x	Parallel reduction across CPU cores.
sin+sqrt+sum	Python Loop	44.72x	Operation fusion (zero allocation).

Tensor Training Steps (200x200)

RMath Autograd is optimized for smaller to medium-sized tensors where framework overhead in PyTorch/TensorFlow usually dominates.

Operation	Baseline	Speedup	Description
reshape	PyTorch .view	7.04x	O(1) layout transformation.
add (grad)	PyTorch +	7.00x	Fused addition with gradient tape.
backward	PyTorch .backward	5.99x	Lean tape traversal in native Rust.
sigmoid	PyTorch sigmoid	5.53x	Vectorized activation with Autograd.
transpose	PyTorch .T	1.90x	Lazy dimension remapping.

Real-World Data Pipeline — rmath vs NumPy

End-to-end benchmark on a 5 million row financial dataset. Measured on Windows (CPython 3.13, AMD64). Both libraries perform identical pipeline stages: generation, cleaning, feature engineering, statistics, correlation, segmentation, and linear signal extraction.

Pipeline Step	rmath Time	rmath Mem	NumPy Time	NumPy Mem	Speedup
Data Generation	0.30s	153 MB	1.31s	137 MB	4.3× faster
Data Cleaning	0.15s	0.5 MB	0.17s	4.8 MB	1.1× faster
Feature Engineering	0.07s	76 MB	0.12s	76 MB	1.8× faster
Descriptive Stats	0.26s	0.07 MB	0.25s	0.03 MB	Comparable
Correlation Analysis	0.038s	0.04 MB	0.43s	0.13 MB	11.2× faster
Segmentation	0.47s	120 MB	0.93s	38 MB	2.0× faster
Linear Signal	0.16s	0.03 MB	0.13s	0.00 MB	NumPy slight edge