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+// polynomial for approximating e^x
+//
+// Copyright (c) 2019, Arm Limited.
+// SPDX-License-Identifier: MIT
+
+deg = 4; // poly degree
+N = 128; // table entries
+b = log(2)/(2*N); // interval
+a = -b;
+
+// find polynomial with minimal abs error
+
+// return p that minimizes |exp(x) - poly(x) - x^d*p(x)|
+approx = proc(poly,d) {
+ return remez(exp(x)-poly(x), deg-d, [a;b], x^d, 1e-10);
+};
+
+// first 2 coeffs are fixed, iteratively find optimal double prec coeffs
+poly = 1 + x;
+for i from 2 to deg do {
+ p = roundcoefficients(approx(poly,i), [|D ...|]);
+ poly = poly + x^i*coeff(p,0);
+};
+
+display = hexadecimal;
+print("rel error:", accurateinfnorm(1-poly(x)/exp(x), [a;b], 30));
+print("abs error:", accurateinfnorm(exp(x)-poly(x), [a;b], 30));
+print("in [",a,b,"]");
+print("coeffs:");
+for i from 0 to deg do coeff(poly,i);