;; <= 2|d0| + 2|d1| + 4|d0 (1 + d1)|
;; = 2|d0| + 2|d1| + 4|d0 + d0 d1)|
;; <= 2|d0| + 2|d1| + 4|d0| + 4|d0 d1|
- ;; <= 6 eps + 4 eps^2.
+ ;; <= 8 eps + 4 eps^2.
;;
;; By Lemma 4, the relative error of using log1p is compounded
;; by no more than 8|d'|, so the relative error of the result
;; is bounded by
;;
;; |d2| + |d'| + |d2 d'|
- ;; <= eps + 6 eps + 4 eps^2 + eps*(6 eps + 4 eps^2)
- ;; = 7 eps + 10 eps^2 + 4 eps^3.
+ ;; <= eps + 8 eps + 4 eps^2 + eps*(6 eps + 4 eps^2)
+ ;; = 9 eps + 10 eps^2 + 4 eps^3.
;;
(let ((e^t (exp t)))
(- (log1p (/ (- 1 (* 2 e^t)) e^t)))))