Fast Polynomial Evaluation

Horner's method evaluates a degree-n polynomial with n multiplications. Thomas Ahle's page compiles the other route: preprocess the coefficients once, and ⌊n/2⌋+1 multiplications are enough for any monic polynomial, with one extra for a general one. You type the polynomial, choose the field (rationals, reals, complex numbers, a Mersenne prime or a binary field) and get the resulting chain as math, C code or a circuit, all computed in the browser. Suggested uses include approximating exp, sin and cos and evaluating polynomials in cryptography, hashing and coding theory. The method is written up in the 2026 arXiv paper Fast Evaluation of Polynomials with Rational Preprocessing (arXiv:2609.06022).