Update README.md [ci skip]

README.md

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 # math_approx
 
-A C++ library for math approximations.
+`math_approx` is a C++ library for math approximations.
 
 Currently supported:
 
 - sin/cos/tan
 - exp/exp2/exp10
 - log/log2/log10
 - sinh/cosh/tanh
+- arcsinh
 - sigmoid
 - Wright-Omega function
 - Dilogarithm function
+
+Showing my work:
+TODO
+
+At the moment, most of these implementations have been "good enough"
+for my own use cases (both in terms of performance and accuracy). That
+said, I definitely believe that it's possible to achieve better results
+for many of these functions. If you have ideas for improving these
+approximations, either by:
+- Modifying an approximation to achieve better accuracy with the same (or similar) performance
+- Modifying an approximation to achieve better performance with the same (or similar) accuracy
+
+then please get in touch with a GitHub issue or pull request!
+
+## A few other thoughts
+
+### Accuracy vs. Performance
+
+Most of the methods in this library are provided with template
+arguments which control the "order" of the approximation. The
+"order" typically refers to the order of a polynomial used in
+the approximation. In general, higher-order approximations will
+achieve greater accuracy, while taking longer to compute.
+
+### Measuring Accuracy
+
+This library uses three approaches for measuring accuracy:
+- Absolute error (`Error = |actual - approx|`)
+- Relative error (`Error = |(actual - approx) / actual|`)
+- [ULP Distance](https://en.wikipedia.org/wiki/Unit_in_the_last_place#:~:text=In%20computer%20science%20and%20numerical,of%20accuracy%20in%20numeric%20calculations.)
+
+### SIMD
+
+These approximations are intended to work for both scalar floating-point
+data types, as well as SIMD floating-point data types. At the moment,
+the library is set up to be compatible with the [XSIMD library](https://github.com/xtensor-stack/xsimd).
+That said, I would like to make it as easy as possible to use this
+library with other SIMD libraries (or matrix math libraries), so if
+anyone has some suggestions, please let me know!