As my first prompt I asked OpenAI o1 to write different approaches for an accurate inverse approximation of sin(x)+x and it took me 2 hours for me to cut out and cram all screenshots manually by hand into a
single JPG, it suggested the Newton-Raphson method, fixed-point iteration, Taylor series expansion, the secant method, analytical approximation, Lagrange inversion theorem, Brent's method (numerical root-finding), lookup tables with interpolation (then I ran out of credits immediately), definitely already better than whatever ChatGPT responded me with when it first came out…
