Most impressive/complex/amazing C-series program?

[Albert Chan]

(08-10-2018 06:03 PM)Thomas Klemm Wrote:  The HP-11C can solve a linear, symmetric 2×2 system using the built-in linear regression with a single operation ...

This is used in Bairstow's Method.

Just a comment of using linear regression to solve linear problems.
Linear regression routine involves subtraction, that may lose significant digits.

Example, this is from the post that led me to signup for this forum: Five Minutes Challenge

Solve sin(x)/x = 5280/5281, correct value for x ~ 0.03370775881 radians

x value y = sin(x)/x
0.0337 0.9998107291
0.0338 0.9998096042

2-points fitted linear regression, we get 0.03370764002, error ~ -1.19e-7
Interpolated for y = 5280/5281, we get 0.03370774834, error ~ -1.05e-8, 11X better

We can reduce linear regression errors, by making y values different.

x value y = sin(x)/x - 5280/5281
0.0337 +8.7159e-8
0.0338 -1.037714e-6

With these values, solve for y = 0, both methods get the same 0.03370774834