// polynomial for approximating erfc(x)*exp(x*x)
//
// Copyright (c) 2022-2023, Arm Limited.
// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception

deg = 15; // poly degree

// interval bounds
a = 0x1.0p-26;
b = 2;

f = proc(y) {
  return erfc(y) * exp(y*y);
};

approx = proc(poly, d) {
  return remez(1 - poly(x)/f(x), deg-d, [a;b], x^d/f(x), 1e-10);
};

poly = 0;
for i from 0 to deg do {
  p = roundcoefficients(approx(poly,i), [|D ...|]);
  poly = poly + x^i*coeff(p,0);
  print(i);
};

display = hexadecimal;
print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30));
print("in [",a,b,"]");
print("coeffs:");
for i from 0 to deg do coeff(poly,i);