* [misc]progress: [Phase 1 of 3] Setting up. * * * [misc]progress: [1/2] Preparing points * * * [misc]progress: [2/2] Setting up program. * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (42 enodes) * [exit]simplify: Simplified to (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)) * [misc]progress: [Phase 2 of 3] Improving. * * [misc]progress: iteration 1 / 4 * * * [misc]progress: picking best candidate * * * * [misc]pick: Picked # * * * [misc]progress: localizing error * * * [misc]progress: generating rewritten candidates * * * * [misc]progress: [ 1 / 3 ] rewriting at (2 1 1) * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1) * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 3 ] generating series at (2 1 1) * [misc]approximate: Taking taylor expansion of (* (+ n n) PI) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (+ n n) PI) in n * [misc]taylor: Taking taylor expansion of (+ n n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (+ n n) PI) in n * [misc]taylor: Taking taylor expansion of (+ n n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 2 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (+ (/ 1 n) (/ 1 n)) PI) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 n) (/ 1 n)) PI) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 n) (/ 1 n)) PI) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ -1 -1) into -2 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) * * * * [misc]progress: [ 2 / 3 ] generating series at (2 1) * [misc]approximate: Taking taylor expansion of (pow (* (+ n n) PI) (/ (- 1 k) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (+ n n) PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (+ n n) PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (+ n n) PI))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (+ n n) PI)) in k * [misc]taylor: Taking taylor expansion of (* (+ n n) PI) in k * [misc]taylor: Taking taylor expansion of (+ n n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ n n) into (* 2 n) * [misc]backup-simplify: Simplify (* (* 2 n) PI) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* (+ n n) PI) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (+ n n) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (+ n n) PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* (+ n n) PI)) in n * [misc]taylor: Taking taylor expansion of (* (+ n n) PI) in n * [misc]taylor: Taking taylor expansion of (+ n n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (+ n n) PI) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (+ n n) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (+ n n) PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* (+ n n) PI)) in n * [misc]taylor: Taking taylor expansion of (* (+ n n) PI) in n * [misc]taylor: Taking taylor expansion of (+ n n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (+ (log (* 2 PI)) (log n))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 2 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log (* 2 PI)) (log n)))) into (- (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))))) * [misc]approximate: Taking taylor expansion of (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ (- 1 (/ 1 k)) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (+ (/ 1 n) (/ 1 n)) PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (+ (/ 1 n) (/ 1 n)) PI))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (+ (/ 1 n) (/ 1 n)) PI)) in k * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 n) (/ 1 n)) PI) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ (/ 1 n) (/ 1 n)) into (* 2 (/ 1 n)) * [misc]backup-simplify: Simplify (* (* 2 (/ 1 n)) PI) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (+ (/ 1 n) (/ 1 n)) PI)))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (+ (/ 1 n) (/ 1 n)) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (+ (/ 1 n) (/ 1 n)) PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (+ (/ 1 n) (/ 1 n)) PI)) in n * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 n) (/ 1 n)) PI) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (+ (/ 1 n) (/ 1 n)) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (+ (/ 1 n) (/ 1 n)) PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (+ (/ 1 n) (/ 1 n)) PI)) in n * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 n) (/ 1 n)) PI) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]approximate: Taking taylor expansion of (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ (- 1 (/ 1 (- k))) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI)) in k * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ (/ -1 n) (/ -1 n)) into (- (* 2 (/ 1 n))) * [misc]backup-simplify: Simplify (* (- (* 2 (/ 1 n))) PI) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) * [misc]taylor: Taking taylor expansion of (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI)) in n * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ -1 -1) into -2 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI)) in n * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ -1 -1) into -2 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * * * * [misc]progress: [ 3 / 3 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (pow (* (+ n n) PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (+ n n) PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (+ n n) PI))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (+ n n) PI)) in k * [misc]taylor: Taking taylor expansion of (* (+ n n) PI) in k * [misc]taylor: Taking taylor expansion of (+ n n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ n n) into (* 2 n) * [misc]backup-simplify: Simplify (* (* 2 n) PI) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (pow (* 2 (* n PI)) 1/2) +nan.0) into (* +nan.0 (sqrt (* n (* 2 PI)))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (pow (* (+ n n) PI) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (+ n n) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (+ n n) PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* (+ n n) PI)) in n * [misc]taylor: Taking taylor expansion of (* (+ n n) PI) in n * [misc]taylor: Taking taylor expansion of (+ n n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (pow (* (+ n n) PI) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (+ n n) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (+ n n) PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* (+ n n) PI)) in n * [misc]taylor: Taking taylor expansion of (* (+ n n) PI) in n * [misc]taylor: Taking taylor expansion of (+ n n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (+ (log (* 2 PI)) (log n))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (* 0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 2 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (/ 0 (sqrt k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log (* 2 PI)) (log n)))) into (- (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (+ (* 0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))))) (+ (* +nan.0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2)))))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2))))))))) (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))))) (+ (* +nan.0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))))))))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n)))))))))))))))))))))))) * [misc]approximate: Taking taylor expansion of (/ (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (+ (/ 1 n) (/ 1 n)) PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (+ (/ 1 n) (/ 1 n)) PI))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (+ (/ 1 n) (/ 1 n)) PI)) in k * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 n) (/ 1 n)) PI) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ (/ 1 n) (/ 1 n)) into (* 2 (/ 1 n)) * [misc]backup-simplify: Simplify (* (* 2 (/ 1 n)) PI) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (+ (/ 1 n) (/ 1 n)) PI)))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (+ (/ 1 n) (/ 1 n)) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (+ (/ 1 n) (/ 1 n)) PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (+ (/ 1 n) (/ 1 n)) PI)) in n * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 n) (/ 1 n)) PI) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (/ (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (+ (/ 1 n) (/ 1 n)) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (+ (/ 1 n) (/ 1 n)) PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (+ (/ 1 n) (/ 1 n)) PI)) in n * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 n) (/ 1 n)) PI) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) k))))))) * [misc]approximate: Taking taylor expansion of (/ (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI)) in k * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ (/ -1 n) (/ -1 n)) into (- (* 2 (/ 1 n))) * [misc]backup-simplify: Simplify (* (- (* 2 (/ 1 n))) PI) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI)) in n * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ -1 -1) into -2 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI)) in n * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ -1 -1) into -2 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k * [misc]taylor: Taking taylor expansion of (/ -1 k) in k * [misc]taylor: Taking taylor expansion of -1 in k * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ -1 1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))))) into (- (+ (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) k))))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 73 ] simplifiying candidate # * * * * [misc]progress: [ 2 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (+ n n) PI)) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (11 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * * [misc]simplify: iters left: 1 (41 enodes) * [exit]simplify: Simplified to (log (* PI (+ n n))) * [exit]simplify: Simplified to (log (* PI (+ n n))) * * * * [misc]progress: [ 3 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (+ n n) PI)) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (32 enodes) * * [misc]simplify: iters left: 1 (47 enodes) * [exit]simplify: Simplified to (pow (exp n) (+ PI PI)) * [exit]simplify: Simplified to (pow (exp n) (+ PI PI)) * * * * [misc]progress: [ 4 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* (+ n n) PI)) (cbrt (* (+ n n) PI))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * * [misc]simplify: iters left: 2 (23 enodes) * [exit]simplify: Simplified to (* (cbrt (* PI (+ n n))) (cbrt (* PI (+ n n)))) * [exit]simplify: Simplified to (* (cbrt (* PI (+ n n))) (cbrt (* PI (+ n n)))) * [enter]simplify: Simplifying (cbrt (* (+ n n) PI)) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * * [misc]simplify: iters left: 3 (15 enodes) * * [misc]simplify: iters left: 2 (21 enodes) * [exit]simplify: Simplified to (cbrt (* PI (+ n n))) * [exit]simplify: Simplified to (cbrt (* PI (+ n n))) * * * * [misc]progress: [ 5 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (+ n n) PI) (* (+ n n) PI)) (* (+ n n) PI)) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (237 enodes) * * [misc]simplify: iters left: 1 (465 enodes) * [exit]simplify: Simplified to (pow (* PI (+ n n)) 3) * [exit]simplify: Simplified to (pow (* PI (+ n n)) 3) * * * * [misc]progress: [ 6 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (+ n n) PI)) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * * [misc]simplify: iters left: 3 (15 enodes) * * [misc]simplify: iters left: 2 (21 enodes) * [exit]simplify: Simplified to (sqrt (* PI (+ n n))) * [exit]simplify: Simplified to (sqrt (* PI (+ n n))) * [enter]simplify: Simplifying (sqrt (* (+ n n) PI)) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * * [misc]simplify: iters left: 3 (15 enodes) * * [misc]simplify: iters left: 2 (21 enodes) * [exit]simplify: Simplified to (sqrt (* PI (+ n n))) * [exit]simplify: Simplified to (sqrt (* PI (+ n n))) * * * * [misc]progress: [ 7 / 73 ] simplifiying candidate # * * * * [misc]progress: [ 8 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (+ n n)) PI) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * [exit]simplify: Simplified to (* (cbrt (+ n n)) PI) * [exit]simplify: Simplified to (* (cbrt (+ n n)) PI) * * * * [misc]progress: [ 9 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (+ n n)) PI) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * [exit]simplify: Simplified to (* (sqrt (+ n n)) PI) * [exit]simplify: Simplified to (* (sqrt (+ n n)) PI) * * * * [misc]progress: [ 10 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* (+ n n) PI) * * [misc]simplify: iters left: 4 (4 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * * [misc]simplify: iters left: 2 (14 enodes) * * [misc]simplify: iters left: 1 (20 enodes) * [exit]simplify: Simplified to (* PI (+ n n)) * [exit]simplify: Simplified to (* PI (+ n n)) * * * * [misc]progress: [ 11 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* n PI) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* PI n) * [exit]simplify: Simplified to (* PI n) * * * * [misc]progress: [ 12 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* (+ (pow n 3) (pow n 3)) PI) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (38 enodes) * * [misc]simplify: iters left: 1 (58 enodes) * [exit]simplify: Simplified to (* (pow n 3) (+ PI PI)) * [exit]simplify: Simplified to (* (pow n 3) (+ PI PI)) * * * * [misc]progress: [ 13 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (* n n) (* n n)) PI) * * [misc]simplify: iters left: 6 (5 enodes) * * [misc]simplify: iters left: 5 (7 enodes) * [exit]simplify: Simplified to 0 * [exit]simplify: Simplified to 0 * * * * [misc]progress: [ 14 / 73 ] simplifiying candidate # * * * * [misc]progress: [ 15 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* (+ n n) PI)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (106 enodes) * * [misc]simplify: iters left: 1 (154 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (+ PI PI) n))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (+ PI PI) n))) * * * * [misc]progress: [ 16 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* (+ n n) PI)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (106 enodes) * * [misc]simplify: iters left: 1 (154 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (+ PI PI) n))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (+ PI PI) n))) * * * * [misc]progress: [ 17 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (28 enodes) * * [misc]simplify: iters left: 1 (32 enodes) * [exit]simplify: Simplified to (/ (- 1 k) 2) * [exit]simplify: Simplified to (/ (- 1 k) 2) * * * * [misc]progress: [ 18 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (+ n n) PI) (/ 1 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (25 enodes) * [exit]simplify: Simplified to (pow (+ (* n PI) (* n PI)) (/ 1 2)) * [exit]simplify: Simplified to (pow (+ (* n PI) (* n PI)) (/ 1 2)) * [enter]simplify: Simplifying (pow (* (+ n n) PI) (/ k 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (17 enodes) * * [misc]simplify: iters left: 2 (23 enodes) * [exit]simplify: Simplified to (pow (* (+ PI PI) n) (/ k 2)) * [exit]simplify: Simplified to (pow (* (+ PI PI) n) (/ k 2)) * * * * [misc]progress: [ 19 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (+ n n) PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * * * [misc]progress: [ 20 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (+ n n) PI) (sqrt (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (32 enodes) * [exit]simplify: Simplified to (pow (* PI (+ n n)) (sqrt (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow (* PI (+ n n)) (sqrt (/ (- 1 k) 2))) * * * * [misc]progress: [ 21 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (+ n n) PI) 1) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (11 enodes) * * [misc]simplify: iters left: 3 (18 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * * [misc]simplify: iters left: 1 (25 enodes) * [exit]simplify: Simplified to (* PI (+ n n)) * [exit]simplify: Simplified to (* PI (+ n n)) * * * * [misc]progress: [ 22 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (+ n n) PI) (- 1 k)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (26 enodes) * [exit]simplify: Simplified to (pow (+ (* n PI) (* n PI)) (- 1 k)) * [exit]simplify: Simplified to (pow (+ (* n PI) (* n PI)) (- 1 k)) * * * * [misc]progress: [ 23 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (+ n n) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (15 enodes) * [exit]simplify: Simplified to (pow (+ n n) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (+ n n) (/ (- 1 k) 2)) * [enter]simplify: Simplifying (pow PI (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * [exit]simplify: Simplified to (pow PI (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow PI (/ (- 1 k) 2)) * * * * [misc]progress: [ 24 / 73 ] simplifiying candidate # * * * * [misc]progress: [ 25 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (log (pow (* (+ n n) PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (91 enodes) * * [misc]simplify: iters left: 1 (129 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (+ PI PI) n))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (+ PI PI) n))) * * * * [misc]progress: [ 26 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (pow (* (+ n n) PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (32 enodes) * [exit]simplify: Simplified to (exp (pow (* PI (+ n n)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (exp (pow (* PI (+ n n)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 27 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (* (+ n n) PI) (/ (- 1 k) 2))) (cbrt (pow (* (+ n n) PI) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (cbrt (pow (* (+ n n) PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (32 enodes) * [exit]simplify: Simplified to (cbrt (pow (* PI (+ n n)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (cbrt (pow (* PI (+ n n)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 28 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (pow (* (+ n n) PI) (/ (- 1 k) 2))) (pow (* (+ n n) PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (36 enodes) * [exit]simplify: Simplified to (pow (pow (* PI (+ n n)) (/ (- 1 k) 2)) 3) * [exit]simplify: Simplified to (pow (pow (* PI (+ n n)) (/ (- 1 k) 2)) 3) * * * * [misc]progress: [ 29 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (32 enodes) * [exit]simplify: Simplified to (sqrt (pow (* PI (+ n n)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* PI (+ n n)) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (32 enodes) * [exit]simplify: Simplified to (sqrt (pow (* PI (+ n n)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* PI (+ n n)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 30 / 73 ] simplifiying candidate # * * * * [misc]progress: [ 31 / 73 ] simplifiying candidate # * * * * [misc]progress: [ 32 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* (+ n n) PI)) (/ (- 1 k) 2)) (log (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (81 enodes) * * [misc]simplify: iters left: 2 (116 enodes) * * [misc]simplify: iters left: 1 (170 enodes) * [exit]simplify: Simplified to (- (/ (log (* PI (+ n n))) (/ 2 (- 1 k))) (log (sqrt k))) * [exit]simplify: Simplified to (- (/ (log (* PI (+ n n))) (/ 2 (- 1 k))) (log (sqrt k))) * * * * [misc]progress: [ 33 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* (+ n n) PI)) (/ (- 1 k) 2)) (log (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (81 enodes) * * [misc]simplify: iters left: 2 (116 enodes) * * [misc]simplify: iters left: 1 (170 enodes) * [exit]simplify: Simplified to (- (/ (log (* PI (+ n n))) (/ 2 (- 1 k))) (log (sqrt k))) * [exit]simplify: Simplified to (- (/ (log (* PI (+ n n))) (/ 2 (- 1 k))) (log (sqrt k))) * * * * [misc]progress: [ 34 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* (+ n n) PI) (/ (- 1 k) 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (102 enodes) * * [misc]simplify: iters left: 1 (160 enodes) * [exit]simplify: Simplified to (- (/ (log (* PI (+ n n))) (/ 2 (- 1 k))) (log (sqrt k))) * [exit]simplify: Simplified to (- (/ (log (* PI (+ n n))) (/ 2 (- 1 k))) (log (sqrt k))) * * * * [misc]progress: [ 35 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (85 enodes) * * [misc]simplify: iters left: 1 (140 enodes) * [exit]simplify: Simplified to (- (* (log (* PI (+ n n))) (/ (- 1 k) 2)) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (log (* PI (+ n n))) (/ (- 1 k) 2)) (log (sqrt k))) * * * * [misc]progress: [ 36 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * * [misc]simplify: iters left: 2 (34 enodes) * [exit]simplify: Simplified to (exp (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (exp (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 37 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (pow (* (+ n n) PI) (/ (- 1 k) 2))) (pow (* (+ n n) PI) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (85 enodes) * * [misc]simplify: iters left: 2 (112 enodes) * * [misc]simplify: iters left: 1 (134 enodes) * [exit]simplify: Simplified to (/ (* (pow (* PI (+ n n)) (/ (- 1 k) 2)) (pow (* PI (+ n n)) (/ (- 1 k) 2))) (/ (* k (sqrt k)) (pow (* PI (+ n n)) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (* (pow (* PI (+ n n)) (/ (- 1 k) 2)) (pow (* PI (+ n n)) (/ (- 1 k) 2))) (/ (* k (sqrt k)) (pow (* PI (+ n n)) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 38 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) * [enter]simplify: Simplifying (cbrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * * [misc]simplify: iters left: 2 (34 enodes) * [exit]simplify: Simplified to (cbrt (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (cbrt (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 39 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (113 enodes) * [exit]simplify: Simplified to (/ (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 40 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * * [misc]simplify: iters left: 2 (34 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k))) * [enter]simplify: Simplifying (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * * [misc]simplify: iters left: 2 (34 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 41 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (- (pow (* (+ n n) PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (32 enodes) * [exit]simplify: Simplified to (- (pow (* PI (+ n n)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (- (pow (* PI (+ n n)) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (- (sqrt k)) * * [misc]simplify: iters left: 3 (3 enodes) * [exit]simplify: Simplified to (- (sqrt k)) * [exit]simplify: Simplified to (- (sqrt k)) * * * * [misc]progress: [ 42 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (+ n n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k))) * * * * [misc]progress: [ 43 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (+ n n) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) * * * * [misc]progress: [ 44 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (+ n n) (/ (- 1 k) 2)) 1) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ (- 1 k) 2)) 1) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ (- 1 k) 2)) 1) * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 45 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* (+ n n) PI) (/ (- 1 k) 2))) (cbrt (pow (* (+ n n) PI) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* PI (+ n n)) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* PI (+ n n)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* PI (+ n n)) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* PI (+ n n)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (cbrt (pow (* (+ n n) PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * * * [misc]progress: [ 46 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* (+ n n) PI) (/ (- 1 k) 2))) (cbrt (pow (* (+ n n) PI) (/ (- 1 k) 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* (+ PI PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (+ PI PI) n) (/ (- 1 k) 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* (+ PI PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (+ PI PI) n) (/ (- 1 k) 2)))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (cbrt (pow (* (+ n n) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 47 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* (+ n n) PI) (/ (- 1 k) 2))) (cbrt (pow (* (+ n n) PI) (/ (- 1 k) 2)))) 1) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* PI (+ n n)) (/ (- 1 k) 2))) (cbrt (pow (* PI (+ n n)) (/ (- 1 k) 2)))) 1) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* PI (+ n n)) (/ (- 1 k) 2))) (cbrt (pow (* PI (+ n n)) (/ (- 1 k) 2)))) 1) * [enter]simplify: Simplifying (/ (cbrt (pow (* (+ n n) PI) (/ (- 1 k) 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * * [misc]simplify: iters left: 2 (34 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* PI (+ n n)) (/ (- 1 k) 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (cbrt (pow (* PI (+ n n)) (/ (- 1 k) 2))) (sqrt k)) * * * * [misc]progress: [ 48 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (+ PI PI) n) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (+ PI PI) n) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * * * [misc]progress: [ 49 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 50 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2))) 1) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) 1) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) 1) * [enter]simplify: Simplifying (/ (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * * [misc]simplify: iters left: 2 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (+ n n)) (/ (- 1 k) 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (+ n n)) (/ (- 1 k) 2))) (sqrt k)) * * * * [misc]progress: [ 51 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * * [misc]simplify: iters left: 2 (34 enodes) * [exit]simplify: Simplified to (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (cbrt (sqrt k))) * * * * [misc]progress: [ 52 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * * [misc]simplify: iters left: 2 (34 enodes) * [exit]simplify: Simplified to (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * * * [misc]progress: [ 53 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to 1 * [exit]simplify: Simplified to 1 * [enter]simplify: Simplifying (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 54 / 73 ] simplifiying candidate # * * * * [misc]progress: [ 55 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt k)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * * * * [misc]progress: [ 56 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (pow (* (+ n n) PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* (+ PI PI) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* (+ PI PI) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 57 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 58 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * * [misc]simplify: iters left: 2 (34 enodes) * [exit]simplify: Simplified to (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * * * [misc]progress: [ 59 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) 1) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (32 enodes) * [exit]simplify: Simplified to (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) 1) * [exit]simplify: Simplified to (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) 1) * * * * [misc]progress: [ 60 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (pow PI (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (pow PI (/ (- 1 k) 2))) * [exit]simplify: Simplified to (/ (sqrt k) (pow PI (/ (- 1 k) 2))) * * * * [misc]progress: [ 61 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (cbrt (pow (* (+ n n) PI) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (pow (+ (* n PI) (* n PI)) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (pow (+ (* n PI) (* n PI)) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 62 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow (+ (* n PI) (* n PI)) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow (+ (* n PI) (* n PI)) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 63 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (pow (* (+ n n) PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* (+ PI PI) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* (+ PI PI) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 64 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt k) (pow (* (+ n n) PI) (/ k 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * * [misc]simplify: iters left: 2 (27 enodes) * [exit]simplify: Simplified to (* (sqrt k) (pow (+ (* n PI) (* n PI)) (/ k 2))) * [exit]simplify: Simplified to (* (sqrt k) (pow (+ (* n PI) (* n PI)) (/ k 2))) * * * * [misc]progress: [ 65 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (31 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 66 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (31 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 67 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (31 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 68 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))))) (sqrt k)) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (93 enodes) * * [misc]simplify: iters left: 4 (187 enodes) * * [misc]simplify: iters left: 3 (381 enodes) * [exit]simplify: Simplified to (/ (- (+ (+ (* (sqrt (+ PI PI)) (sqrt n)) (* (* (log (+ PI PI)) (* (* k k) (log n))) (* 1/4 (* (sqrt (+ PI PI)) (sqrt n))))) (* 1/8 (* (* (* k k) (* (sqrt (+ PI PI)) (sqrt n))) (+ (* (log n) (log n)) (* (log (+ PI PI)) (log (+ PI PI))))))) (* (* 1/2 k) (* (* (sqrt (+ PI PI)) (sqrt n)) (+ (log (+ PI PI)) (log n))))) (sqrt k)) * * * * [misc]progress: [ 69 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (110 enodes) * [exit]simplify: Simplified to (/ (pow (pow (exp 1/2) (- 1 (/ 1 k))) (- (log (+ PI PI)) (log n))) (sqrt k)) * * * * [misc]progress: [ 70 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt k)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (/ (exp (* (- (log (* PI -2)) (log n)) (+ 1/2 (/ 1/2 k)))) (sqrt k)) * * * * [misc]progress: [ 71 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n)))))))))))))))))))))))) * * * * [misc]progress: [ 72 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) k))))))) * * * * [misc]progress: [ 73 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) k))))))) * * * [misc]progress: adding candidates to table * * [misc]progress: iteration 2 / 4 * * * [misc]progress: picking best candidate * * * * [misc]pick: Picked # * * * [misc]progress: localizing error * * * [misc]progress: generating rewritten candidates * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2 1) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 1 1) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 1) * [misc]approximate: Taking taylor expansion of (pow PI (/ (- 1 k) 2)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log PI)) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log PI)) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [misc]backup-simplify: Simplify (pow PI 1/2) into (pow PI 1/2) * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (/ -1 2) (+ (* 1/2 (/ 0 2)))) into -1/2 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) * [misc]backup-simplify: Simplify (* -1/2 (* (log PI) (sqrt PI))) into (* -1/2 (* (log PI) (sqrt PI))) * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) * [misc]backup-simplify: Simplify (* 1/8 (* (pow (log PI) 2) (sqrt PI))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) * [misc]backup-simplify: Simplify (+ (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (log PI) (sqrt PI))) k) (pow PI 1/2))) into (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) * [misc]approximate: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 k)) 2)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log PI)) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) into (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log PI)) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) into (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) into (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) into (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) * [misc]approximate: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 (- k))) 2)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log PI)) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log PI)) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2) * [misc]approximate: Taking taylor expansion of (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log PI)) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (pow PI 1/2) +nan.0) into (* +nan.0 (sqrt PI)) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log PI)) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (pow PI 1/2) +nan.0) into (* +nan.0 (sqrt PI)) * [misc]backup-simplify: Simplify (* +nan.0 (sqrt PI)) into (* +nan.0 (sqrt PI)) * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (/ -1 2) (+ (* 1/2 (/ 0 2)))) into -1/2 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ (* -1/2 (* (log PI) (sqrt PI))) +nan.0) (+ (* (* +nan.0 (sqrt PI)) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ (* 1/8 (* (pow (log PI) 2) (sqrt PI))) +nan.0) (+ (* (* +nan.0 (sqrt PI)) (/ +nan.0 +nan.0)) (* (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) k) (+ (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) (* (* +nan.0 (sqrt PI)) (/ 1 k)))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (+ (* +nan.0 (* (* (log PI) k) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) k)) (- (+ (* +nan.0 (* (sqrt PI) (/ 1 k))) (- (* +nan.0 (* (* (pow (log PI) 2) k) (sqrt PI)))))))))))))) * [misc]approximate: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log PI)) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) into (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log PI)) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) into (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) into (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) into (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) into (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) (pow (/ 1 k) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) (/ 1 k)) (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) k)) (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))))))) * [misc]approximate: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log PI)) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log PI)) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) (/ 1 (- k))) (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))))) into (- (+ (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) k)) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (pow k 2)))))))) * * * * [misc]progress: [ 3 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (+ n n) (/ (- 1 k) 2)) 1) in k * [misc]taylor: Taking taylor expansion of (pow (+ n n) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (+ n n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (+ n n))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ n n)) in k * [misc]taylor: Taking taylor expansion of (+ n n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (+ n n) into (* 2 n) * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (pow (* 2 n) 1/2) 1) into (sqrt (* n 2)) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log PI)) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (pow PI 1/2) +nan.0) into (* +nan.0 (sqrt PI)) * [misc]taylor: Taking taylor expansion of (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (+ n n) (/ (- 1 k) 2)) 1) in n * [misc]taylor: Taking taylor expansion of (pow (+ n n) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (+ n n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (+ n n))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (+ n n)) in n * [misc]taylor: Taking taylor expansion of (+ n n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log 2))) into (* 1/2 (* (- 1 k) (+ (log n) (log 2)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) 1) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log PI)) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (log PI)) into (* 1/2 (* (- 1 k) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (log PI)))) into (exp (* 1/2 (* (- 1 k) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI))))) * [misc]taylor: Taking taylor expansion of (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (+ n n) (/ (- 1 k) 2)) 1) in n * [misc]taylor: Taking taylor expansion of (pow (+ n n) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (+ n n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (+ n n))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (+ n n)) in n * [misc]taylor: Taking taylor expansion of (+ n n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log 2))) into (* 1/2 (* (- 1 k) (+ (log n) (log 2)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) 1) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log PI)) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (log PI)) into (* 1/2 (* (- 1 k) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (log PI)))) into (exp (* 1/2 (* (- 1 k) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI)))))) into (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2)))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (log PI)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (log PI))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (log PI)) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (* 1 (log PI)) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log 2)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log n) (log 2))) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log n) (log 2)) in k * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (+ (log n) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* 1 (+ (log n) (log 2))) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log 2))) into (* 1/2 (+ (log n) (log 2))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log 2)))) into (exp (* 1/2 (+ (log n) (log 2)))) * [misc]backup-simplify: Simplify (* (pow PI 1/2) (exp (* 1/2 (+ (log n) (log 2))))) into (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))) * [misc]backup-simplify: Simplify (* 0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (log PI))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI))))) (/ 0 (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log 2)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) 0) (* 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log n) (log 2)))) into (- (+ (log n) (log 2))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log n) (log 2)))) (* 0 (+ (log n) (log 2)))) into (- (+ (* 1/2 (log n)) (* 1/2 (log 2)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log 2)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log 2))) (exp (* 1/2 (+ (log n) (log 2)))))) * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (log PI))) into (- (log PI)) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (log PI))) (* 0 (log PI))) into (- (* 1/2 (log PI))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) * [misc]backup-simplify: Simplify (+ (* (pow PI 1/2) (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log 2))) (exp (* 1/2 (+ (log n) (log 2))))))) (* (* -1/2 (* (log PI) (sqrt PI))) (exp (* 1/2 (+ (log n) (log 2)))))) into (- (+ (* 1/2 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/2 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (* 1/2 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))))) * [misc]backup-simplify: Simplify (+ (* 0 (- (+ (* 1/2 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/2 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (* 1/2 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))))))) (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))))) into (- (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))))) into (- (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))))) * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (log PI)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log PI)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI))))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log 2))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) 0) (+ (* 0 0) (* 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI)))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log n) (log 2)))) (* 0 (+ (log n) (log 2))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log 2)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log 2))) (* 1/8 (pow (log 2) 2))))) * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (log PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (log PI))) (* 0 (log PI)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) * [misc]backup-simplify: Simplify (+ (* (pow PI 1/2) (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log 2))) (* 1/8 (pow (log 2) 2)))))) (+ (* (* -1/2 (* (log PI) (sqrt PI))) (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log 2))) (exp (* 1/2 (+ (log n) (log 2))))))) (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (exp (* 1/2 (+ (log n) (log 2))))))) into (+ (* 1/8 (* (sqrt PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/4 (* (* (log PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/4 (* (sqrt PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (* 1/8 (* (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (+ (* 1/4 (* (* (log PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (* 1/8 (* (sqrt PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2)))))))))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 (+ (* 1/8 (* (sqrt PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/4 (* (* (log PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/4 (* (sqrt PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (* 1/8 (* (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (+ (* 1/4 (* (* (log PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (* 1/8 (* (sqrt PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2))))))))))))) (+ (* +nan.0 (- (+ (* 1/2 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/2 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (* 1/2 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))))))) (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))))) into (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))) (- (* +nan.0 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))) (- (* +nan.0 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))))))))) into (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))))))))))) * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log PI)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI))))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log 2)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI))))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log n) (log 2)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (+ (log n) (log 2)))) (* 0 (+ (log n) (log 2)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log 2)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log 2)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/48 (pow (log 2) 3)) (+ (* 1/16 (* (pow (log n) 2) (log 2))) (* 1/16 (* (log n) (pow (log 2) 2)))))) (exp (* 1/2 (+ (log n) (log 2)))))) * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (log PI))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (log PI))) (* 0 (log PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 3) 6)) (* (/ (pow (- (* 1/2 (log PI))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log PI) 3) (sqrt PI))) * [misc]backup-simplify: Simplify (+ (* (pow PI 1/2) (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/48 (pow (log 2) 3)) (+ (* 1/16 (* (pow (log n) 2) (log 2))) (* 1/16 (* (log n) (pow (log 2) 2)))))) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* (* -1/2 (* (log PI) (sqrt PI))) (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log 2))) (* 1/8 (pow (log 2) 2)))))) (+ (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log 2))) (exp (* 1/2 (+ (log n) (log 2))))))) (* (* -1/48 (* (pow (log PI) 3) (sqrt PI))) (exp (* 1/2 (+ (log n) (log 2)))))))) into (- (+ (* 1/16 (* (sqrt PI) (* (pow (log n) 2) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (* 1/16 (* (* (log PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/16 (* (* (pow (log PI) 2) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/48 (* (sqrt PI) (* (pow (log 2) 3) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/16 (* (* (log PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/16 (* (sqrt PI) (* (log n) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (* 1/8 (* (* (log PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (sqrt PI))) (+ (* 1/16 (* (* (pow (log PI) 2) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/48 (* (* (pow (log PI) 3) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (* 1/48 (* (sqrt PI) (* (pow (log n) 3) (exp (* 1/2 (+ (log n) (log 2))))))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 (- (+ (* 1/16 (* (sqrt PI) (* (pow (log n) 2) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (* 1/16 (* (* (log PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/16 (* (* (pow (log PI) 2) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/48 (* (sqrt PI) (* (pow (log 2) 3) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/16 (* (* (log PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/16 (* (sqrt PI) (* (log n) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (* 1/8 (* (* (log PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (sqrt PI))) (+ (* 1/16 (* (* (pow (log PI) 2) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/48 (* (* (pow (log PI) 3) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (* 1/48 (* (sqrt PI) (* (pow (log n) 3) (exp (* 1/2 (+ (log n) (log 2)))))))))))))))))) (+ (* +nan.0 (+ (* 1/8 (* (sqrt PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/4 (* (* (log PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/4 (* (sqrt PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (* 1/8 (* (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (+ (* 1/4 (* (* (log PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (* 1/8 (* (sqrt PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2))))))))))))) (+ (* +nan.0 (- (+ (* 1/2 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/2 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (* 1/2 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))))))) (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))))))) into (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (* +nan.0 (* (* (log PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI)))))))))))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (* +nan.0 (* (* (log PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI)))))))))))))))))))))) into (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (* +nan.0 (* (* (log PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI)))))))))))))))))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (* +nan.0 (* (* (log PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI)))))))))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))))))))))) (* k 1)) (- (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))))))) into (- (+ (* +nan.0 (* (sqrt PI) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* k (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log n) 2) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (log PI) (* (pow k 2) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log PI) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow k 2) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* (log 2) (* (exp (* 1/2 (+ (log n) (log 2)))) (pow k 2)))))) (- (+ (* +nan.0 (* (* (log PI) (* k (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow k 2) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (log PI) (* (log n) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2))))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* k (exp (* 1/2 (+ (log n) (log 2)))))))) (- (* +nan.0 (* (sqrt PI) (* k (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))))))))))))))))))))))))))))))))) * [misc]approximate: Taking taylor expansion of (* (/ (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) 1) (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) 1) (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) 1) in k * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 n) (/ 1 n))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]backup-simplify: Simplify (+ (/ 1 n) (/ 1 n)) into (* 2 (/ 1 n)) * [misc]backup-simplify: Simplify (log (* 2 (/ 1 n))) into (log (/ 2 n)) * [misc]backup-simplify: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ 1 n)))))) * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ 1 n)))))) 1) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 2 n))))) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log PI)) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) into (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) * [misc]taylor: Taking taylor expansion of (* (/ (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) 1) (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) 1) in n * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 n) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log 2) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) 1) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log PI)) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (log PI)) into (* 1/2 (* (log PI) (- 1 (/ 1 k)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) into (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) (sqrt (/ 1 k))) into (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) * [misc]taylor: Taking taylor expansion of (* (/ (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) 1) (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) 1) in n * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 n) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log 2) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) 1) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log PI)) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (log PI)) into (* 1/2 (* (log PI) (- 1 (/ 1 k)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) into (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) (sqrt (/ 1 k))) into (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) into (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log 2) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log 2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* -1 (- (log 2) (log n))) into (* -1 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log 2) (log n)))) into (* -1/2 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log PI) (- 1 (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (log PI) (- 1 (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (* (log PI) -1) into (* -1 (log PI)) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (log PI))) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) into (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) * [misc]backup-simplify: Simplify (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (log PI))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) 0) (* 0 (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) 0) (* 0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (log PI)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) 0) (+ (* 0 0) (* 0 (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (pow k 3))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) k))))))) * [misc]approximate: Taking taylor expansion of (* (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) 1) (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) 1) (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) 1) in k * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 (- n)) (/ 1 (- n)))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]backup-simplify: Simplify (+ (/ -1 n) (/ -1 n)) into (- (* 2 (/ 1 n))) * [misc]backup-simplify: Simplify (log (- (* 2 (/ 1 n)))) into (log (- (* 2 (/ 1 n)))) * [misc]backup-simplify: Simplify (* 1/2 (log (- (* 2 (/ 1 n))))) into (* 1/2 (log (- (* 2 (/ 1 n))))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (- (* 2 (/ 1 n))))))) * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (- (* 2 (/ 1 n))))))) 1) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (- (* 2 (/ 1 n))))))) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log PI)) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) * [misc]taylor: Taking taylor expansion of (* (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) 1) (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) 1) in n * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 (- n)) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (+ -1 -1) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log -2) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) 1) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log PI)) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (log PI)) into (* 1/2 (* (+ 1 (/ 1 k)) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (* (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) 1) (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) 1) in n * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 (- n)) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (+ -1 -1) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log -2) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) 1) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) * [misc]taylor: Taking taylor expansion of (/ (pow PI (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (pow PI (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log PI))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log PI)) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (log PI)) into (* 1/2 (* (+ 1 (/ 1 k)) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k)))) into (/ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (/ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (sqrt (/ -1 k))) in k * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (- (log -2) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log -2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log -2) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* 1 (- (log -2) (log n))) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log PI))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (log PI)) in k * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (* 1 (log PI)) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k * [misc]taylor: Taking taylor expansion of (/ -1 k) in k * [misc]taylor: Taking taylor expansion of -1 in k * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ -1 1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) into (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) * [misc]backup-simplify: Simplify (/ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) +nan.0) into (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) into (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (log PI))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log -2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) 0) (* 0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) 0) (* 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))))) * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (log PI)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) 0) (+ (* 0 0) (* 0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))))) into (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) k)) (- (+ (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (pow k 2)))))))) * * * * [misc]progress: [ 4 / 4 ] generating series at (2 1 1) * [misc]approximate: Taking taylor expansion of (pow (+ n n) (/ (- 1 k) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (+ n n) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (+ n n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (+ n n))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ n n)) in k * [misc]taylor: Taking taylor expansion of (+ n n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (+ n n) into (* 2 n) * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) * [misc]taylor: Taking taylor expansion of (pow (+ n n) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (+ n n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (+ n n))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (+ n n)) in n * [misc]taylor: Taking taylor expansion of (+ n n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log 2))) into (* 1/2 (* (- 1 k) (+ (log n) (log 2)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) * [misc]taylor: Taking taylor expansion of (pow (+ n n) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (+ n n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (+ n n))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (+ n n)) in n * [misc]taylor: Taking taylor expansion of (+ n n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log 2))) into (* 1/2 (* (- 1 k) (+ (log n) (log 2)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log 2)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log n) (log 2))) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log n) (log 2)) in k * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (+ (log n) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* 1 (+ (log n) (log 2))) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log 2))) into (* 1/2 (+ (log n) (log 2))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log 2)))) into (exp (* 1/2 (+ (log n) (log 2)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log 2)))) into (exp (* 1/2 (+ (log n) (log 2)))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log 2)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log n) (log 2)))) into (- (+ (log n) (log 2))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log n) (log 2)))) (* 0 (+ (log n) (log 2)))) into (- (+ (* 1/2 (log n)) (* 1/2 (log 2)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log 2)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log 2))) (exp (* 1/2 (+ (log n) (log 2)))))) * [misc]backup-simplify: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log 2))) (exp (* 1/2 (+ (log n) (log 2)))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log 2))) (exp (* 1/2 (+ (log n) (log 2)))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log 2))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log n) (log 2)))) (* 0 (+ (log n) (log 2))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log 2)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log 2))) (* 1/8 (pow (log 2) 2))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log 2))) (* 1/8 (pow (log 2) 2))))) into (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log 2))) (* 1/8 (pow (log 2) 2))))) * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log 2))) (* 1/8 (pow (log 2) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log 2))) (exp (* 1/2 (+ (log n) (log 2)))))) (* k 1)) (exp (* 1/2 (+ (log n) (log 2)))))) into (- (+ (* 1/8 (* (pow k 2) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/4 (* (log 2) (* (pow k 2) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (exp (* 1/2 (+ (log n) (log 2)))) (* 1/8 (* (pow k 2) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))))))) (+ (* 1/2 (* k (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (* 1/2 (* k (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))))) * [misc]approximate: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 n) (/ 1 n))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]backup-simplify: Simplify (+ (/ 1 n) (/ 1 n)) into (* 2 (/ 1 n)) * [misc]backup-simplify: Simplify (log (* 2 (/ 1 n))) into (log (/ 2 n)) * [misc]backup-simplify: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ 1 n)))))) * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 n) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log 2) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 n) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log 2) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log 2) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log 2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* -1 (- (log 2) (log n))) into (* -1 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log 2) (log n)))) into (* -1/2 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]approximate: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 (- n)) (/ 1 (- n)))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]backup-simplify: Simplify (+ (/ -1 n) (/ -1 n)) into (- (* 2 (/ 1 n))) * [misc]backup-simplify: Simplify (log (- (* 2 (/ 1 n)))) into (log (- (* 2 (/ 1 n)))) * [misc]backup-simplify: Simplify (* 1/2 (log (- (* 2 (/ 1 n))))) into (* 1/2 (log (- (* 2 (/ 1 n))))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (- (* 2 (/ 1 n))))))) * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 (- n)) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (+ -1 -1) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log -2) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 (- n)) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (+ -1 -1) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log -2) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (- (log -2) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log -2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log -2) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* 1 (- (log -2) (log n))) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log -2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log PI) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * * [misc]simplify: iters left: 2 (27 enodes) * * [misc]simplify: iters left: 1 (30 enodes) * [exit]simplify: Simplified to (/ (log PI) (/ 2 (- 1 k))) * [exit]simplify: Simplified to (/ (log PI) (/ 2 (- 1 k))) * * * * [misc]progress: [ 2 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (pow PI (/ 1 2)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * [exit]simplify: Simplified to (pow PI (/ 1 2)) * [exit]simplify: Simplified to (pow PI (/ 1 2)) * [enter]simplify: Simplifying (pow PI (/ k 2)) * * [misc]simplify: iters left: 3 (5 enodes) * [exit]simplify: Simplified to (pow PI (/ k 2)) * [exit]simplify: Simplified to (pow PI (/ k 2)) * * * * [misc]progress: [ 3 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (pow PI (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * [exit]simplify: Simplified to (pow PI (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (pow PI (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * * * [misc]progress: [ 4 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (pow PI (sqrt (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * [exit]simplify: Simplified to (pow PI (sqrt (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow PI (sqrt (/ (- 1 k) 2))) * * * * [misc]progress: [ 5 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (pow PI 1) * * [misc]simplify: iters left: 1 (3 enodes) * [exit]simplify: Simplified to PI * [exit]simplify: Simplified to PI * * * * [misc]progress: [ 6 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (pow PI (- 1 k)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * [exit]simplify: Simplified to (pow PI (- 1 k)) * [exit]simplify: Simplified to (pow PI (- 1 k)) * * * * [misc]progress: [ 7 / 107 ] simplifiying candidate # * * * * [misc]progress: [ 8 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (log (pow PI (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * * [misc]simplify: iters left: 1 (29 enodes) * [exit]simplify: Simplified to (* (log PI) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (* (log PI) (/ (- 1 k) 2)) * * * * [misc]progress: [ 9 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (pow PI (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * [exit]simplify: Simplified to (exp (pow PI (/ (- 1 k) 2))) * [exit]simplify: Simplified to (exp (pow PI (/ (- 1 k) 2))) * * * * [misc]progress: [ 10 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * [exit]simplify: Simplified to (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (cbrt (pow PI (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * [exit]simplify: Simplified to (cbrt (pow PI (/ (- 1 k) 2))) * [exit]simplify: Simplified to (cbrt (pow PI (/ (- 1 k) 2))) * * * * [misc]progress: [ 11 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (pow PI (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (pow (pow PI (/ (- 1 k) 2)) 3) * [exit]simplify: Simplified to (pow (pow PI (/ (- 1 k) 2)) 3) * * * * [misc]progress: [ 12 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow PI (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * [exit]simplify: Simplified to (sqrt (pow PI (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow PI (/ (- 1 k) 2))) * [enter]simplify: Simplifying (sqrt (pow PI (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * [exit]simplify: Simplified to (sqrt (pow PI (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow PI (/ (- 1 k) 2))) * * * * [misc]progress: [ 13 / 107 ] simplifiying candidate # * * * * [misc]progress: [ 14 / 107 ] simplifiying candidate # * * * * [misc]progress: [ 15 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * * [misc]simplify: iters left: 2 (30 enodes) * * [misc]simplify: iters left: 1 (35 enodes) * [exit]simplify: Simplified to (- (* (/ (log PI) 2) (- 1 k)) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (log PI) 2) (- 1 k)) (log (sqrt k))) * * * * [misc]progress: [ 16 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow PI (/ (- 1 k) 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * * [misc]simplify: iters left: 2 (27 enodes) * * [misc]simplify: iters left: 1 (32 enodes) * [exit]simplify: Simplified to (- (/ (log PI) (/ 2 (- 1 k))) (log (sqrt k))) * [exit]simplify: Simplified to (- (/ (log PI) (/ 2 (- 1 k))) (log (sqrt k))) * * * * [misc]progress: [ 17 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * * [misc]simplify: iters left: 2 (25 enodes) * * [misc]simplify: iters left: 1 (29 enodes) * [exit]simplify: Simplified to (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt k))) * * * * [misc]progress: [ 18 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * [exit]simplify: Simplified to (exp (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (exp (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 19 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (pow PI (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (94 enodes) * * [misc]simplify: iters left: 1 (113 enodes) * [exit]simplify: Simplified to (/ (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (/ (* k (sqrt k)) (pow PI (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (/ (* k (sqrt k)) (pow PI (/ (- 1 k) 2)))) * * * * [misc]progress: [ 20 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt k)))) * [enter]simplify: Simplifying (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * [exit]simplify: Simplified to (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 21 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (69 enodes) * * [misc]simplify: iters left: 1 (92 enodes) * [exit]simplify: Simplified to (pow (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) 3) * [exit]simplify: Simplified to (pow (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) 3) * * * * [misc]progress: [ 22 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * [enter]simplify: Simplifying (sqrt (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 23 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (pow PI (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * [exit]simplify: Simplified to (- (pow PI (/ (- 1 k) 2))) * [exit]simplify: Simplified to (- (pow PI (/ (- 1 k) 2))) * [enter]simplify: Simplifying (- (sqrt k)) * * [misc]simplify: iters left: 3 (3 enodes) * [exit]simplify: Simplified to (- (sqrt k)) * [exit]simplify: Simplified to (- (sqrt k)) * * * * [misc]progress: [ 24 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (39 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (* (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt k))) * * * * [misc]progress: [ 25 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (* (cbrt (pow PI (/ (- 1 k) 2))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (pow PI (/ (- 1 k) 2))) (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 26 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) 1) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) 1) * [exit]simplify: Simplified to (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) 1) * [enter]simplify: Simplifying (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (cbrt (pow PI (/ (- 1 k) 2))) (sqrt k)) * * * * [misc]progress: [ 27 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow PI (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow PI (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt k))) * * * * [misc]progress: [ 28 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 29 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) 1) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow PI (/ (- 1 k) 2))) 1) * [exit]simplify: Simplified to (/ (sqrt (pow PI (/ (- 1 k) 2))) 1) * [enter]simplify: Simplifying (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt k)) * * * * [misc]progress: [ 30 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k))) * * * * [misc]progress: [ 31 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) * * * * [misc]progress: [ 32 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to 1 * [exit]simplify: Simplified to 1 * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 33 / 107 ] simplifiying candidate # * * * * [misc]progress: [ 34 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt k)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * * * * [misc]progress: [ 35 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (pow PI (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (pow PI (/ (- 1 k) 2))) * [exit]simplify: Simplified to (/ (sqrt k) (pow PI (/ (- 1 k) 2))) * * * * [misc]progress: [ 36 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 37 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) * * * * [misc]progress: [ 38 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) 1) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) 1) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) 1) * * * * [misc]progress: [ 39 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (cbrt (pow PI (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (pow PI (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (pow PI (/ (- 1 k) 2)))) * * * * [misc]progress: [ 40 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (pow PI (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow PI (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow PI (/ (- 1 k) 2)))) * * * * [misc]progress: [ 41 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (pow PI (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (pow PI (/ (- 1 k) 2))) * [exit]simplify: Simplified to (/ (sqrt k) (pow PI (/ (- 1 k) 2))) * * * * [misc]progress: [ 42 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt k) (pow PI (/ k 2))) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to (* (pow PI (/ k 2)) (sqrt k)) * [exit]simplify: Simplified to (* (pow PI (/ k 2)) (sqrt k)) * * * * [misc]progress: [ 43 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (65 enodes) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (/ (sqrt k) (pow (+ n n) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (/ (sqrt k) (pow (+ n n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 44 / 107 ] simplifiying candidate # * * * * [misc]progress: [ 45 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (98 enodes) * * [misc]simplify: iters left: 1 (174 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (+ n n)) (log PI))) (+ (log 1) (log (sqrt k)))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (+ n n)) (log PI))) (+ (log 1) (log (sqrt k)))) * * * * [misc]progress: [ 46 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) (- (log (pow PI (/ (- 1 k) 2))) (log (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (95 enodes) * * [misc]simplify: iters left: 1 (160 enodes) * [exit]simplify: Simplified to (+ (- (* (/ (- 1 k) 2) (log (+ n n))) (log 1)) (- (* (/ (log PI) 2) (- 1 k)) (log (sqrt k)))) * [exit]simplify: Simplified to (+ (- (* (/ (- 1 k) 2) (log (+ n n))) (log 1)) (- (* (/ (log PI) 2) (- 1 k)) (log (sqrt k)))) * * * * [misc]progress: [ 47 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) (log (/ (pow PI (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (147 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (+ n n)) (log PI))) (+ (log 1) (log (sqrt k)))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (+ n n)) (log PI))) (+ (log 1) (log (sqrt k)))) * * * * [misc]progress: [ 48 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (116 enodes) * * [misc]simplify: iters left: 1 (169 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log PI) (log (+ n n)))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log PI) (log (+ n n)))) (log (sqrt k))) * * * * [misc]progress: [ 49 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (exp (/ (* (pow PI (/ (- 1 k) 2)) (pow (+ n n) (/ (- 1 k) 2))) (sqrt k))) * [exit]simplify: Simplified to (exp (/ (* (pow PI (/ (- 1 k) 2)) (pow (+ n n) (/ (- 1 k) 2))) (sqrt k))) * * * * [misc]progress: [ 50 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) (/ (* (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (pow PI (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (102 enodes) * * [misc]simplify: iters left: 3 (201 enodes) * * [misc]simplify: iters left: 2 (324 enodes) * [exit]simplify: Simplified to (* (/ (pow (pow (+ n n) (/ (- 1 k) 2)) 3) k) (/ (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (/ (sqrt k) (pow PI (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (* (/ (pow (pow (+ n n) (/ (- 1 k) 2)) 3) k) (/ (* (pow PI (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (/ (sqrt k) (pow PI (/ (- 1 k) 2))))) * * * * [misc]progress: [ 51 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) (* (* (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (212 enodes) * * [misc]simplify: iters left: 1 (317 enodes) * [exit]simplify: Simplified to (* (pow (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) 3) (/ (* (pow (+ n n) (/ (- 1 k) 2)) (pow (+ n n) (/ (- 1 k) 2))) (/ 1 (pow (+ n n) (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (* (pow (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) 3) (/ (* (pow (+ n n) (/ (- 1 k) 2)) (pow (+ n n) (/ (- 1 k) 2))) (/ 1 (pow (+ n n) (/ (- 1 k) 2))))) * * * * [misc]progress: [ 52 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt k)))) (cbrt (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (* (cbrt (* (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) (pow (+ n n) (/ (- 1 k) 2)))) (cbrt (* (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) (pow (+ n n) (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (* (cbrt (* (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) (pow (+ n n) (/ (- 1 k) 2)))) (cbrt (* (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) (pow (+ n n) (/ (- 1 k) 2))))) * [enter]simplify: Simplifying (cbrt (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (cbrt (* (/ (pow (+ n n) (/ (- 1 k) 2)) (sqrt k)) (pow PI (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (cbrt (* (/ (pow (+ n n) (/ (- 1 k) 2)) (sqrt k)) (pow PI (/ (- 1 k) 2)))) * * * * [misc]progress: [ 53 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt k)))) (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (84 enodes) * * [misc]simplify: iters left: 2 (177 enodes) * * [misc]simplify: iters left: 1 (290 enodes) * [exit]simplify: Simplified to (pow (/ (pow PI (/ (- 1 k) 2)) (/ (sqrt k) (pow (+ n n) (/ (- 1 k) 2)))) 3) * [exit]simplify: Simplified to (pow (/ (pow PI (/ (- 1 k) 2)) (/ (sqrt k) (pow (+ n n) (/ (- 1 k) 2)))) 3) * * * * [misc]progress: [ 54 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (sqrt (* (/ (pow (+ n n) (/ (- 1 k) 2)) (sqrt k)) (pow PI (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (sqrt (* (/ (pow (+ n n) (/ (- 1 k) 2)) (sqrt k)) (pow PI (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (sqrt (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (sqrt (* (/ (pow (+ n n) (/ (- 1 k) 2)) (sqrt k)) (pow PI (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (sqrt (* (/ (pow (+ n n) (/ (- 1 k) 2)) (sqrt k)) (pow PI (/ (- 1 k) 2)))) * * * * [misc]progress: [ 55 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (+ n n) (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (* (pow PI (/ (- 1 k) 2)) (pow (+ n n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (pow PI (/ (- 1 k) 2)) (pow (+ n n) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (* 1 (sqrt k)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * [exit]simplify: Simplified to (sqrt k) * [exit]simplify: Simplified to (sqrt k) * * * * [misc]progress: [ 56 / 107 ] simplifiying candidate # * * * * [misc]progress: [ 57 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (* (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt k))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * * [misc]simplify: iters left: 1 (47 enodes) * [exit]simplify: Simplified to (* (* (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt k)))) (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) * [exit]simplify: Simplified to (* (* (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow PI (/ (- 1 k) 2)) (sqrt k)))) (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) * * * * [misc]progress: [ 58 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (sqrt (/ (pow PI (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * * [misc]simplify: iters left: 1 (34 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) * [exit]simplify: Simplified to (* (sqrt (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) * * * * [misc]progress: [ 59 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (94 enodes) * * [misc]simplify: iters left: 2 (126 enodes) * * [misc]simplify: iters left: 1 (245 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt k))) (* (/ (pow (+ n n) (/ (- 1 k) 2)) (cbrt (sqrt k))) (cbrt (pow PI (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (* (/ (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (sqrt k))) (* (/ (pow (+ n n) (/ (- 1 k) 2)) (cbrt (sqrt k))) (cbrt (pow PI (/ (- 1 k) 2))))) * * * * [misc]progress: [ 60 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (101 enodes) * [exit]simplify: Simplified to (/ (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (cbrt (pow PI (/ (- 1 k) 2)))) (/ (sqrt (sqrt k)) (cbrt (pow PI (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (/ (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (cbrt (pow PI (/ (- 1 k) 2)))) (/ (sqrt (sqrt k)) (cbrt (pow PI (/ (- 1 k) 2))))) * * * * [misc]progress: [ 61 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (* (cbrt (pow PI (/ (- 1 k) 2))) (cbrt (pow PI (/ (- 1 k) 2)))) 1)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (* (cbrt (pow PI (/ (- 1 k) 2))) (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (cbrt (pow PI (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (* (cbrt (pow PI (/ (- 1 k) 2))) (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (cbrt (pow PI (/ (- 1 k) 2))))) * * * * [misc]progress: [ 62 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (sqrt (pow PI (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (87 enodes) * * [misc]simplify: iters left: 1 (139 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (pow PI (/ (- 1 k) 2))) (/ (pow (+ n n) (/ (- 1 k) 2)) (cbrt (sqrt k)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (* (sqrt (pow PI (/ (- 1 k) 2))) (/ (pow (+ n n) (/ (- 1 k) 2)) (cbrt (sqrt k)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 63 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (sqrt (pow PI (/ (- 1 k) 2))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (* (/ (pow (+ n n) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (pow PI (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (/ (pow (+ n n) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (pow PI (/ (- 1 k) 2)))) * * * * [misc]progress: [ 64 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (sqrt (pow PI (/ (- 1 k) 2))) 1)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * * [misc]simplify: iters left: 1 (54 enodes) * [exit]simplify: Simplified to (* (sqrt (pow PI (/ (- 1 k) 2))) (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) * [exit]simplify: Simplified to (* (sqrt (pow PI (/ (- 1 k) 2))) (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) * * * * [misc]progress: [ 65 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 66 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ 1 (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (42 enodes) * * [misc]simplify: iters left: 1 (51 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * * * [misc]progress: [ 67 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ 1 1)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * * [misc]simplify: iters left: 2 (27 enodes) * * [misc]simplify: iters left: 1 (28 enodes) * [exit]simplify: Simplified to (pow (+ n n) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (+ n n) (/ (- 1 k) 2)) * * * * [misc]progress: [ 68 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) 1) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * * [misc]simplify: iters left: 2 (27 enodes) * * [misc]simplify: iters left: 1 (28 enodes) * [exit]simplify: Simplified to (pow (+ n n) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (+ n n) (/ (- 1 k) 2)) * * * * [misc]progress: [ 69 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (pow PI (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * * [misc]simplify: iters left: 2 (30 enodes) * * [misc]simplify: iters left: 1 (31 enodes) * [exit]simplify: Simplified to (* (pow (+ n n) (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) 1)) * [exit]simplify: Simplified to (* (pow (+ n n) (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) 1)) * * * * [misc]progress: [ 70 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * * [misc]simplify: iters left: 1 (34 enodes) * [exit]simplify: Simplified to (* (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) (cbrt (/ (pow (+ n n) (/ (- 1 k) 2)) 1))) * [exit]simplify: Simplified to (* (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) (cbrt (/ (pow (+ n n) (/ (- 1 k) 2)) 1))) * * * * [misc]progress: [ 71 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * * [misc]simplify: iters left: 1 (34 enodes) * [exit]simplify: Simplified to (* (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) (sqrt (/ (pow (+ n n) (/ (- 1 k) 2)) 1))) * [exit]simplify: Simplified to (* (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) (sqrt (/ (pow (+ n n) (/ (- 1 k) 2)) 1))) * * * * [misc]progress: [ 72 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (65 enodes) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (/ (sqrt k) (pow (+ n n) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (/ (sqrt k) (pow (+ n n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 73 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * * [misc]simplify: iters left: 2 (28 enodes) * * [misc]simplify: iters left: 1 (29 enodes) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 74 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (pow PI (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * * [misc]simplify: iters left: 2 (30 enodes) * * [misc]simplify: iters left: 1 (31 enodes) * [exit]simplify: Simplified to (* (pow (+ n n) (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) 1)) * [exit]simplify: Simplified to (* (pow (+ n n) (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) 1)) * * * * [misc]progress: [ 75 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (+ n n) (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (31 enodes) * * [misc]simplify: iters left: 1 (32 enodes) * [exit]simplify: Simplified to (* (pow (+ n n) (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (* (pow (+ n n) (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 76 / 107 ] simplifiying candidate # * * * * [misc]progress: [ 77 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (+ n n)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * * [misc]simplify: iters left: 1 (62 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (+ n n))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (+ n n))) * * * * [misc]progress: [ 78 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (+ n n)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * * [misc]simplify: iters left: 1 (62 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (+ n n))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (+ n n))) * * * * [misc]progress: [ 79 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (28 enodes) * * [misc]simplify: iters left: 1 (32 enodes) * [exit]simplify: Simplified to (/ (- 1 k) 2) * [exit]simplify: Simplified to (/ (- 1 k) 2) * * * * [misc]progress: [ 80 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (+ n n) (/ 1 2)) * * [misc]simplify: iters left: 3 (6 enodes) * * [misc]simplify: iters left: 2 (9 enodes) * * [misc]simplify: iters left: 1 (10 enodes) * [exit]simplify: Simplified to (pow (+ n n) (/ 1 2)) * [exit]simplify: Simplified to (pow (+ n n) (/ 1 2)) * [enter]simplify: Simplifying (pow (+ n n) (/ k 2)) * * [misc]simplify: iters left: 3 (6 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * * [misc]simplify: iters left: 1 (8 enodes) * [exit]simplify: Simplified to (pow (+ n n) (/ k 2)) * [exit]simplify: Simplified to (pow (+ n n) (/ k 2)) * * * * [misc]progress: [ 81 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (+ n n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (pow (+ n n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (pow (+ n n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * * * [misc]progress: [ 82 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (+ n n) (sqrt (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (pow (+ n n) (sqrt (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow (+ n n) (sqrt (/ (- 1 k) 2))) * * * * [misc]progress: [ 83 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (+ n n) 1) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (8 enodes) * * [misc]simplify: iters left: 1 (9 enodes) * [exit]simplify: Simplified to (+ n n) * [exit]simplify: Simplified to (+ n n) * * * * [misc]progress: [ 84 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (+ n n) (- 1 k)) * * [misc]simplify: iters left: 3 (6 enodes) * * [misc]simplify: iters left: 2 (10 enodes) * * [misc]simplify: iters left: 1 (11 enodes) * [exit]simplify: Simplified to (pow (+ n n) (- 1 k)) * [exit]simplify: Simplified to (pow (+ n n) (- 1 k)) * * * * [misc]progress: [ 85 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ (- 1 k) 2)) * [enter]simplify: Simplifying (pow (cbrt (+ n n)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * [exit]simplify: Simplified to (pow (cbrt (+ n n)) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (cbrt (+ n n)) (/ (- 1 k) 2)) * * * * [misc]progress: [ 86 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (sqrt (+ n n)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * [exit]simplify: Simplified to (pow (sqrt (+ n n)) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (sqrt (+ n n)) (/ (- 1 k) 2)) * [enter]simplify: Simplifying (pow (sqrt (+ n n)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * [exit]simplify: Simplified to (pow (sqrt (+ n n)) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (sqrt (+ n n)) (/ (- 1 k) 2)) * * * * [misc]progress: [ 87 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (pow 1 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (11 enodes) * [exit]simplify: Simplified to 1 * [exit]simplify: Simplified to 1 * [enter]simplify: Simplifying (pow (+ n n) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (15 enodes) * [exit]simplify: Simplified to (pow (+ n n) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (+ n n) (/ (- 1 k) 2)) * * * * [misc]progress: [ 88 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (pow 2 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (11 enodes) * [exit]simplify: Simplified to (pow 2 (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow 2 (/ (- 1 k) 2)) * [enter]simplify: Simplifying (pow n (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * * * * [misc]progress: [ 89 / 107 ] simplifiying candidate # * * * * [misc]progress: [ 90 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (log (pow (+ n n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (51 enodes) * * [misc]simplify: iters left: 1 (56 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (+ n n))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (+ n n))) * * * * [misc]progress: [ 91 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (pow (+ n n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (exp (pow (+ n n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (exp (pow (+ n n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 92 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (+ n n) (/ (- 1 k) 2))) (cbrt (pow (+ n n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (+ n n) (/ (- 1 k) 2))) (cbrt (pow (+ n n) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (+ n n) (/ (- 1 k) 2))) (cbrt (pow (+ n n) (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (cbrt (pow (+ n n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (cbrt (pow (+ n n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (cbrt (pow (+ n n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 93 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (pow (+ n n) (/ (- 1 k) 2)) (pow (+ n n) (/ (- 1 k) 2))) (pow (+ n n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * [exit]simplify: Simplified to (pow (pow (+ n n) (/ (- 1 k) 2)) 3) * [exit]simplify: Simplified to (pow (pow (+ n n) (/ (- 1 k) 2)) 3) * * * * [misc]progress: [ 94 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (+ n n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (sqrt (pow (+ n n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (+ n n) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (sqrt (pow (+ n n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (sqrt (pow (+ n n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (+ n n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 95 / 107 ] simplifiying candidate # * * * * [misc]progress: [ 96 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) (sqrt k))) * * [misc]simplify: iters left: 6 (28 enodes) * * [misc]simplify: iters left: 5 (57 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (174 enodes) * * [misc]simplify: iters left: 2 (311 enodes) * [exit]simplify: Simplified to (/ (- (* (* (sqrt PI) 1/8) (* (* (log PI) k) (* (log PI) k))) (- (* (* (log PI) 1/2) (* k (sqrt PI))) (sqrt PI))) (/ (sqrt k) (pow (+ n n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 97 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) (sqrt k))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (exp (* (- 1 (/ 1 k)) (* (log PI) 1/2))) (/ (sqrt k) (pow (+ n n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 98 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt k))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (109 enodes) * * [misc]simplify: iters left: 1 (160 enodes) * [exit]simplify: Simplified to (/ (* (pow (+ n n) (/ (- 1 k) 2)) (pow PI (+ (/ 1/2 k) 1/2))) (sqrt k)) * * * * [misc]progress: [ 99 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (+ (* +nan.0 (* (* (log PI) k) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) k)) (- (+ (* +nan.0 (* (sqrt PI) (/ 1 k))) (- (* +nan.0 (* (* (pow (log PI) 2) k) (sqrt PI))))))))))))))) * * * * [misc]progress: [ 100 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) k)) (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))))))) * * * * [misc]progress: [ 101 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (- (+ (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) k)) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (pow k 2))))))))) * * * * [misc]progress: [ 102 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (sqrt PI) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* k (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log n) 2) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (log PI) (* (pow k 2) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log PI) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow k 2) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* (log 2) (* (exp (* 1/2 (+ (log n) (log 2)))) (pow k 2)))))) (- (+ (* +nan.0 (* (* (log PI) (* k (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow k 2) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (log PI) (* (log n) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2))))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* k (exp (* 1/2 (+ (log n) (log 2)))))))) (- (* +nan.0 (* (sqrt PI) (* k (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))))))))))))))))))))))))))))))))) * * * * [misc]progress: [ 103 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (pow k 3))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) k))))))) * * * * [misc]progress: [ 104 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) k)) (- (+ (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (pow k 2)))))))) * * * * [misc]progress: [ 105 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (- (+ (* 1/8 (* (pow k 2) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/4 (* (log 2) (* (pow k 2) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (exp (* 1/2 (+ (log n) (log 2)))) (* 1/8 (* (pow k 2) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))))))) (+ (* 1/2 (* k (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (* 1/2 (* k (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))))) 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (103 enodes) * * [misc]simplify: iters left: 4 (170 enodes) * * [misc]simplify: iters left: 3 (283 enodes) * [exit]simplify: Simplified to (/ (- (+ (+ (* (sqrt 2) (sqrt n)) (* (* 1/8 (* (sqrt 2) (sqrt n))) (* (* k (log 2)) (* k (log 2))))) (* (* (sqrt 2) (sqrt n)) (+ (* (* (* k k) 1/8) (* (log n) (log n))) (* (* (log 2) 1/4) (* (* k k) (log n)))))) (* (* 1/2 k) (* (* (sqrt 2) (sqrt n)) (+ (log n) (log 2))))) (/ 1 (/ (pow PI (/ (- 1 k) 2)) (sqrt k)))) * * * * [misc]progress: [ 106 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (104 enodes) * [exit]simplify: Simplified to (/ (pow (exp 1/2) (* (- (log 2) (log n)) (- 1 (/ 1 k)))) (/ (sqrt k) (pow PI (/ (- 1 k) 2)))) * * * * [misc]progress: [ 107 / 107 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (104 enodes) * * [misc]simplify: iters left: 1 (148 enodes) * [exit]simplify: Simplified to (/ (exp (* (- (log -2) (log n)) (+ 1/2 (/ 1/2 k)))) (/ (sqrt k) (pow PI (/ (- 1 k) 2)))) * * * [misc]progress: adding candidates to table * * [misc]progress: iteration 3 / 4 * * * [misc]progress: picking best candidate * * * * [misc]pick: Picked # * * * [misc]progress: localizing error * * * [misc]progress: generating rewritten candidates * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 1 1) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2 1 1) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2) * [misc]approximate: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]backup-simplify: Simplify (* (log PI) 1/2) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (pow PI 1/2) +nan.0) into (* +nan.0 (sqrt PI)) * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]backup-simplify: Simplify (* (log PI) 1/2) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (pow PI 1/2) +nan.0) into (* +nan.0 (sqrt PI)) * [misc]backup-simplify: Simplify (* +nan.0 (sqrt PI)) into (* +nan.0 (sqrt PI)) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (/ -1 2) (+ (* 1/2 (/ 0 2)))) into -1/2 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) -1/2) (* 0 1/2)) into (- (* 1/2 (log PI))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ (* -1/2 (* (log PI) (sqrt PI))) +nan.0) (+ (* (* +nan.0 (sqrt PI)) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 -1/2) (* 0 1/2))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ (* 1/8 (* (pow (log PI) 2) (sqrt PI))) +nan.0) (+ (* (* +nan.0 (sqrt PI)) (/ +nan.0 +nan.0)) (* (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) k) (+ (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) (* (* +nan.0 (sqrt PI)) (/ 1 k)))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (+ (* +nan.0 (* (* (log PI) k) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) k)) (- (+ (* +nan.0 (* (sqrt PI) (/ 1 k))) (- (* +nan.0 (* (* (pow (log PI) 2) k) (sqrt PI)))))))))))))) * [misc]approximate: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) in k * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]backup-simplify: Simplify (* (log PI) -1/2) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) into (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) in k * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]backup-simplify: Simplify (* (log PI) -1/2) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) into (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) into (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) into (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) into (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) (pow (/ 1 k) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) (/ 1 k)) (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) k)) (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))))))) * [misc]approximate: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k)))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) in k * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]backup-simplify: Simplify (* (log PI) 1/2) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) in k * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]backup-simplify: Simplify (* (log PI) 1/2) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) (/ 1 (- k))) (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))))) into (- (+ (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) k)) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (pow k 2)))))))) * * * * [misc]progress: [ 2 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (+ n n) (/ (- 1 k) 2)) 1) in k * [misc]taylor: Taking taylor expansion of (pow (+ n n) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (+ n n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (+ n n))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ n n)) in k * [misc]taylor: Taking taylor expansion of (+ n n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (+ n n) into (* 2 n) * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (pow (* 2 n) 1/2) 1) into (sqrt (* n 2)) * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]backup-simplify: Simplify (* (log PI) 1/2) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (pow PI 1/2) +nan.0) into (* +nan.0 (sqrt PI)) * [misc]taylor: Taking taylor expansion of (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (+ n n) (/ (- 1 k) 2)) 1) in n * [misc]taylor: Taking taylor expansion of (pow (+ n n) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (+ n n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (+ n n))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (+ n n)) in n * [misc]taylor: Taking taylor expansion of (+ n n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log 2))) into (* 1/2 (* (- 1 k) (+ (log n) (log 2)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) 1) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (log PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]backup-simplify: Simplify (* (log PI) (* 1/2 (- 1 k))) into (* 1/2 (* (- 1 k) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (log PI)))) into (exp (* 1/2 (* (- 1 k) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI))))) * [misc]taylor: Taking taylor expansion of (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (+ n n) (/ (- 1 k) 2)) 1) in n * [misc]taylor: Taking taylor expansion of (pow (+ n n) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (+ n n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (+ n n))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (+ n n)) in n * [misc]taylor: Taking taylor expansion of (+ n n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log 2))) into (* 1/2 (* (- 1 k) (+ (log n) (log 2)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) 1) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (log PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]backup-simplify: Simplify (* (log PI) (* 1/2 (- 1 k))) into (* 1/2 (* (- 1 k) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (log PI)))) into (exp (* 1/2 (* (- 1 k) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI)))))) into (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2)))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (log PI)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (log PI))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (log PI)) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (* 1 (log PI)) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log 2)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log n) (log 2))) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log n) (log 2)) in k * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (+ (log n) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* 1 (+ (log n) (log 2))) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log 2))) into (* 1/2 (+ (log n) (log 2))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log 2)))) into (exp (* 1/2 (+ (log n) (log 2)))) * [misc]backup-simplify: Simplify (* (pow PI 1/2) (exp (* 1/2 (+ (log n) (log 2))))) into (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))) * [misc]backup-simplify: Simplify (* 0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (* 0 (* 1/2 (- 1 k)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI))))) (/ 0 (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log 2)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) 0) (* 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log n) (log 2)))) into (- (+ (log n) (log 2))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log n) (log 2)))) (* 0 (+ (log n) (log 2)))) into (- (+ (* 1/2 (log n)) (* 1/2 (log 2)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log 2)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log 2))) (exp (* 1/2 (+ (log n) (log 2)))))) * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (log PI))) into (- (log PI)) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (log PI))) (* 0 (log PI))) into (- (* 1/2 (log PI))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) * [misc]backup-simplify: Simplify (+ (* (pow PI 1/2) (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log 2))) (exp (* 1/2 (+ (log n) (log 2))))))) (* (* -1/2 (* (log PI) (sqrt PI))) (exp (* 1/2 (+ (log n) (log 2)))))) into (- (+ (* 1/2 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/2 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (* 1/2 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))))) * [misc]backup-simplify: Simplify (+ (* 0 (- (+ (* 1/2 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/2 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (* 1/2 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))))))) (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))))) into (- (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))))) into (- (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (* 0 (* 1/2 (- 1 k))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log PI)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI))))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log 2))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) 0) (+ (* 0 0) (* 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI)))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log n) (log 2)))) (* 0 (+ (log n) (log 2))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log 2)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log 2))) (* 1/8 (pow (log 2) 2))))) * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (log PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (log PI))) (* 0 (log PI)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) * [misc]backup-simplify: Simplify (+ (* (pow PI 1/2) (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log 2))) (* 1/8 (pow (log 2) 2)))))) (+ (* (* -1/2 (* (log PI) (sqrt PI))) (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log 2))) (exp (* 1/2 (+ (log n) (log 2))))))) (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (exp (* 1/2 (+ (log n) (log 2))))))) into (+ (* 1/8 (* (sqrt PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/4 (* (* (log PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/4 (* (sqrt PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (* 1/8 (* (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (+ (* 1/4 (* (* (log PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (* 1/8 (* (sqrt PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2)))))))))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 (+ (* 1/8 (* (sqrt PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/4 (* (* (log PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/4 (* (sqrt PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (* 1/8 (* (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (+ (* 1/4 (* (* (log PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (* 1/8 (* (sqrt PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2))))))))))))) (+ (* +nan.0 (- (+ (* 1/2 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/2 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (* 1/2 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))))))) (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))))) into (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))) (- (* +nan.0 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))) (- (* +nan.0 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))))))))) into (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))))))))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 1/2 (- 1 k)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log PI)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI))))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log 2)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI))))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log n) (log 2)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (+ (log n) (log 2)))) (* 0 (+ (log n) (log 2)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log 2)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log 2)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/48 (pow (log 2) 3)) (+ (* 1/16 (* (pow (log n) 2) (log 2))) (* 1/16 (* (log n) (pow (log 2) 2)))))) (exp (* 1/2 (+ (log n) (log 2)))))) * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (log PI))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (log PI))) (* 0 (log PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 3) 6)) (* (/ (pow (- (* 1/2 (log PI))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log PI) 3) (sqrt PI))) * [misc]backup-simplify: Simplify (+ (* (pow PI 1/2) (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/48 (pow (log 2) 3)) (+ (* 1/16 (* (pow (log n) 2) (log 2))) (* 1/16 (* (log n) (pow (log 2) 2)))))) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* (* -1/2 (* (log PI) (sqrt PI))) (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log 2))) (* 1/8 (pow (log 2) 2)))))) (+ (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log 2))) (exp (* 1/2 (+ (log n) (log 2))))))) (* (* -1/48 (* (pow (log PI) 3) (sqrt PI))) (exp (* 1/2 (+ (log n) (log 2)))))))) into (- (+ (* 1/16 (* (sqrt PI) (* (pow (log n) 2) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (* 1/16 (* (* (log PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/16 (* (* (pow (log PI) 2) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/48 (* (sqrt PI) (* (pow (log 2) 3) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/16 (* (* (log PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/16 (* (sqrt PI) (* (log n) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (* 1/8 (* (* (log PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (sqrt PI))) (+ (* 1/16 (* (* (pow (log PI) 2) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/48 (* (* (pow (log PI) 3) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (* 1/48 (* (sqrt PI) (* (pow (log n) 3) (exp (* 1/2 (+ (log n) (log 2))))))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 (- (+ (* 1/16 (* (sqrt PI) (* (pow (log n) 2) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (* 1/16 (* (* (log PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/16 (* (* (pow (log PI) 2) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/48 (* (sqrt PI) (* (pow (log 2) 3) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/16 (* (* (log PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/16 (* (sqrt PI) (* (log n) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (* 1/8 (* (* (log PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (sqrt PI))) (+ (* 1/16 (* (* (pow (log PI) 2) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/48 (* (* (pow (log PI) 3) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (* 1/48 (* (sqrt PI) (* (pow (log n) 3) (exp (* 1/2 (+ (log n) (log 2)))))))))))))))))) (+ (* +nan.0 (+ (* 1/8 (* (sqrt PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/4 (* (* (log PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/4 (* (sqrt PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (* 1/8 (* (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (+ (* 1/4 (* (* (log PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (* 1/8 (* (sqrt PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2))))))))))))) (+ (* +nan.0 (- (+ (* 1/2 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/2 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (* 1/2 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))))))) (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))))))) into (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (* +nan.0 (* (* (log PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI)))))))))))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (* +nan.0 (* (* (log PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI)))))))))))))))))))))) into (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (* +nan.0 (* (* (log PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI)))))))))))))))))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (* +nan.0 (* (* (log PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI)))))))))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))))))))))) (* k 1)) (- (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))))))) into (- (+ (* +nan.0 (* (sqrt PI) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* k (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log n) 2) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (log PI) (* (pow k 2) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log PI) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow k 2) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* (log 2) (* (exp (* 1/2 (+ (log n) (log 2)))) (pow k 2)))))) (- (+ (* +nan.0 (* (* (log PI) (* k (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow k 2) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (log PI) (* (log n) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2))))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* k (exp (* 1/2 (+ (log n) (log 2)))))))) (- (* +nan.0 (* (sqrt PI) (* k (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))))))))))))))))))))))))))))))))) * [misc]approximate: Taking taylor expansion of (* (/ (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) 1) (/ (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) 1) (/ (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) 1) in k * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 n) (/ 1 n))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]backup-simplify: Simplify (+ (/ 1 n) (/ 1 n)) into (* 2 (/ 1 n)) * [misc]backup-simplify: Simplify (log (* 2 (/ 1 n))) into (log (/ 2 n)) * [misc]backup-simplify: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ 1 n)))))) * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ 1 n)))))) 1) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 2 n))))) * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) in k * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]backup-simplify: Simplify (* (log PI) -1/2) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) into (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) * [misc]taylor: Taking taylor expansion of (* (/ (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) 1) (/ (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) 1) in n * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 n) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log 2) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) 1) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) in n * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (log PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]backup-simplify: Simplify (* (log PI) (* 1/2 (- 1 (/ 1 k)))) into (* 1/2 (* (log PI) (- 1 (/ 1 k)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) into (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) (sqrt (/ 1 k))) into (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) * [misc]taylor: Taking taylor expansion of (* (/ (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) 1) (/ (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) 1) in n * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 n) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log 2) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) 1) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) in n * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (log PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]backup-simplify: Simplify (* (log PI) (* 1/2 (- 1 (/ 1 k)))) into (* 1/2 (* (log PI) (- 1 (/ 1 k)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) into (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) (sqrt (/ 1 k))) into (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) into (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log 2) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log 2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* -1 (- (log 2) (log n))) into (* -1 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log 2) (log n)))) into (* -1/2 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log PI) (- 1 (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (log PI) (- 1 (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (* (log PI) -1) into (* -1 (log PI)) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (log PI))) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) into (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) * [misc]backup-simplify: Simplify (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (* 0 (* 1/2 (- 1 (/ 1 k))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) 0) (* 0 (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) 0) (* 0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (* 0 (* 1/2 (- 1 (/ 1 k)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) 0) (+ (* 0 0) (* 0 (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 1/2 (- 1 (/ 1 k))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (pow k 3))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) k))))))) * [misc]approximate: Taking taylor expansion of (* (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) 1) (/ (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k))))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) 1) (/ (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k))))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) 1) in k * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 (- n)) (/ 1 (- n)))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]backup-simplify: Simplify (+ (/ -1 n) (/ -1 n)) into (- (* 2 (/ 1 n))) * [misc]backup-simplify: Simplify (log (- (* 2 (/ 1 n)))) into (log (- (* 2 (/ 1 n)))) * [misc]backup-simplify: Simplify (* 1/2 (log (- (* 2 (/ 1 n))))) into (* 1/2 (log (- (* 2 (/ 1 n))))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (- (* 2 (/ 1 n))))))) * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (- (* 2 (/ 1 n))))))) 1) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (- (* 2 (/ 1 n))))))) * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) in k * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]backup-simplify: Simplify (* (log PI) 1/2) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) * [misc]taylor: Taking taylor expansion of (* (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) 1) (/ (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k))))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) 1) in n * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 (- n)) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (+ -1 -1) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log -2) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) 1) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) in n * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (log PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]backup-simplify: Simplify (* (log PI) (* 1/2 (+ 1 (/ 1 k)))) into (* 1/2 (* (+ 1 (/ 1 k)) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (* (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) 1) (/ (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k))))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) 1) in n * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 (- n)) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (+ -1 -1) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log -2) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) 1) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) in n * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (log PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]backup-simplify: Simplify (* (log PI) (* 1/2 (+ 1 (/ 1 k)))) into (* 1/2 (* (+ 1 (/ 1 k)) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k)))) into (/ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (/ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (sqrt (/ -1 k))) in k * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (- (log -2) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log -2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log -2) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* 1 (- (log -2) (log n))) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log PI))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (log PI)) in k * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (* 1 (log PI)) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k * [misc]taylor: Taking taylor expansion of (/ -1 k) in k * [misc]taylor: Taking taylor expansion of -1 in k * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ -1 1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) into (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) * [misc]backup-simplify: Simplify (/ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) +nan.0) into (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) into (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (* 0 (* 1/2 (+ 1 (/ 1 k))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log -2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) 0) (* 0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) 0) (* 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (* 0 (* 1/2 (+ 1 (/ 1 k)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) 0) (+ (* 0 0) (* 0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))))) into (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) k)) (- (+ (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (pow k 2)))))))) * * * * [misc]progress: [ 3 / 4 ] generating series at (2 1 1) * [misc]approximate: Taking taylor expansion of (pow (+ n n) (/ (- 1 k) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (+ n n) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (+ n n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (+ n n))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ n n)) in k * [misc]taylor: Taking taylor expansion of (+ n n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (+ n n) into (* 2 n) * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) * [misc]taylor: Taking taylor expansion of (pow (+ n n) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (+ n n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (+ n n))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (+ n n)) in n * [misc]taylor: Taking taylor expansion of (+ n n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log 2))) into (* 1/2 (* (- 1 k) (+ (log n) (log 2)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) * [misc]taylor: Taking taylor expansion of (pow (+ n n) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (+ n n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (+ n n))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (+ n n)) in n * [misc]taylor: Taking taylor expansion of (+ n n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log 2))) into (* 1/2 (* (- 1 k) (+ (log n) (log 2)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log 2)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log n) (log 2))) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log n) (log 2)) in k * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (+ (log n) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* 1 (+ (log n) (log 2))) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log 2))) into (* 1/2 (+ (log n) (log 2))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log 2)))) into (exp (* 1/2 (+ (log n) (log 2)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log 2)))) into (exp (* 1/2 (+ (log n) (log 2)))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log 2)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log n) (log 2)))) into (- (+ (log n) (log 2))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log n) (log 2)))) (* 0 (+ (log n) (log 2)))) into (- (+ (* 1/2 (log n)) (* 1/2 (log 2)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log 2)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log 2))) (exp (* 1/2 (+ (log n) (log 2)))))) * [misc]backup-simplify: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log 2))) (exp (* 1/2 (+ (log n) (log 2)))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log 2))) (exp (* 1/2 (+ (log n) (log 2)))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log 2))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log 2))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log n) (log 2)))) (* 0 (+ (log n) (log 2))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log 2)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log 2))) (* 1/8 (pow (log 2) 2))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log 2))) (* 1/8 (pow (log 2) 2))))) into (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log 2))) (* 1/8 (pow (log 2) 2))))) * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log 2))) (* 1/8 (pow (log 2) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log 2))) (exp (* 1/2 (+ (log n) (log 2)))))) (* k 1)) (exp (* 1/2 (+ (log n) (log 2)))))) into (- (+ (* 1/8 (* (pow k 2) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/4 (* (log 2) (* (pow k 2) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (exp (* 1/2 (+ (log n) (log 2)))) (* 1/8 (* (pow k 2) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))))))) (+ (* 1/2 (* k (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (* 1/2 (* k (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))))) * [misc]approximate: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 n) (/ 1 n))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]backup-simplify: Simplify (+ (/ 1 n) (/ 1 n)) into (* 2 (/ 1 n)) * [misc]backup-simplify: Simplify (log (* 2 (/ 1 n))) into (log (/ 2 n)) * [misc]backup-simplify: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ 1 n)))))) * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 n) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log 2) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (+ (/ 1 n) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 n) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log 2) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log 2) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log 2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* -1 (- (log 2) (log n))) into (* -1 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log 2) (log n)))) into (* -1/2 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) * [misc]approximate: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 (- n)) (/ 1 (- n)))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]backup-simplify: Simplify (+ (/ -1 n) (/ -1 n)) into (- (* 2 (/ 1 n))) * [misc]backup-simplify: Simplify (log (- (* 2 (/ 1 n)))) into (log (- (* 2 (/ 1 n)))) * [misc]backup-simplify: Simplify (* 1/2 (log (- (* 2 (/ 1 n))))) into (* 1/2 (log (- (* 2 (/ 1 n))))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (- (* 2 (/ 1 n))))))) * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 (- n)) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (+ -1 -1) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log -2) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (+ (/ 1 (- n)) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 (- n)) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (+ -1 -1) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log -2) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (- (log -2) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log -2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log -2) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* 1 (- (log -2) (log n))) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log -2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2 1 1) * [misc]approximate: Taking taylor expansion of (* (log PI) (/ (- 1 k) 2)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]backup-simplify: Simplify (* (log PI) 1/2) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (/ -1 2) (+ (* 1/2 (/ 0 2)))) into -1/2 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) -1/2) (* 0 1/2)) into (- (* 1/2 (log PI))) * [misc]backup-simplify: Simplify (- (* 1/2 (log PI))) into (- (* 1/2 (log PI))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 -1/2) (* 0 1/2))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 -1/2) (* 0 1/2)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow PI 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow PI 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow PI 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow PI 1)))) 24) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 -1/2) (* 0 1/2))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow PI 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow PI 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow PI 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow PI 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow PI 1)))) 120) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 -1/2) (* 0 1/2)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow PI 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow PI 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow PI 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow PI 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow PI 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow PI 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow PI 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow PI 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow PI 1)))) 720) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 -1/2) (* 0 1/2))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 720 (/ (* (pow (* 1 0) 7)) (pow PI 7))) (* -2520 (/ (* (pow (* 1 0) 5) (pow (* 2 0) 1)) (pow PI 6))) (* 2520 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 2)) (pow PI 5))) (* 840 (/ (* (pow (* 1 0) 4) 1 (pow (* 6 0) 1)) (pow PI 5))) (* -630 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 3)) (pow PI 4))) (* -1260 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 4))) (* -210 (/ (* (pow (* 1 0) 3) 1 1 (pow (* 24 0) 1)) (pow PI 4))) (* 210 (/ (* 1 (pow (* 2 0) 2) (pow (* 6 0) 1)) (pow PI 3))) (* 140 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 2)) (pow PI 3))) (* 210 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow PI 3))) (* 42 (/ (* (pow (* 1 0) 2) 1 1 1 (pow (* 120 0) 1)) (pow PI 3))) (* -35 (/ (* 1 1 (pow (* 6 0) 1) (pow (* 24 0) 1)) (pow PI 2))) (* -21 (/ (* 1 (pow (* 2 0) 1) 1 1 (pow (* 120 0) 1)) (pow PI 2))) (* -7 (/ (* (pow (* 1 0) 1) 1 1 1 1 (pow (* 720 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 1 1 (pow (* 5040 0) 1)) (pow PI 1)))) 5040) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 -1/2) (* 0 1/2)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (log PI))) k) (* 1/2 (log PI))) into (- (* 1/2 (log PI)) (* 1/2 (* (log PI) k))) * [misc]approximate: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 k)) 2)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]backup-simplify: Simplify (* (log PI) -1/2) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (- (/ 1 2) (+ (* -1/2 (/ 0 2)))) into 1/2 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 1/2) (* 0 -1/2)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* -1/2 (/ 0 2)) (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 1/2) (* 0 -1/2))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* -1/2 (/ 0 2)) (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 1/2) (* 0 -1/2)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* -1/2 (/ 0 2)) (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow PI 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow PI 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow PI 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow PI 1)))) 24) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1/2) (* 0 -1/2))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* -1/2 (/ 0 2)) (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow PI 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow PI 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow PI 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow PI 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow PI 1)))) 120) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1/2) (* 0 -1/2)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* -1/2 (/ 0 2)) (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow PI 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow PI 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow PI 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow PI 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow PI 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow PI 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow PI 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow PI 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow PI 1)))) 720) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1/2) (* 0 -1/2))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* -1/2 (/ 0 2)) (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 720 (/ (* (pow (* 1 0) 7)) (pow PI 7))) (* -2520 (/ (* (pow (* 1 0) 5) (pow (* 2 0) 1)) (pow PI 6))) (* 2520 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 2)) (pow PI 5))) (* 840 (/ (* (pow (* 1 0) 4) 1 (pow (* 6 0) 1)) (pow PI 5))) (* -630 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 3)) (pow PI 4))) (* -1260 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 4))) (* -210 (/ (* (pow (* 1 0) 3) 1 1 (pow (* 24 0) 1)) (pow PI 4))) (* 210 (/ (* 1 (pow (* 2 0) 2) (pow (* 6 0) 1)) (pow PI 3))) (* 140 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 2)) (pow PI 3))) (* 210 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow PI 3))) (* 42 (/ (* (pow (* 1 0) 2) 1 1 1 (pow (* 120 0) 1)) (pow PI 3))) (* -35 (/ (* 1 1 (pow (* 6 0) 1) (pow (* 24 0) 1)) (pow PI 2))) (* -21 (/ (* 1 (pow (* 2 0) 1) 1 1 (pow (* 120 0) 1)) (pow PI 2))) (* -7 (/ (* (pow (* 1 0) 1) 1 1 1 1 (pow (* 720 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 1 1 (pow (* 5040 0) 1)) (pow PI 1)))) 5040) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1/2) (* 0 -1/2)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 (log PI)) (* (* -1/2 (log PI)) (/ 1 (/ 1 k)))) into (- (* 1/2 (log PI)) (* 1/2 (* (log PI) k))) * [misc]approximate: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 (- k))) 2)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]backup-simplify: Simplify (* (log PI) 1/2) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (- (/ 1 2) (+ (* 1/2 (/ 0 2)))) into 1/2 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 1/2) (* 0 1/2)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 1/2) (* 0 1/2))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 1/2) (* 0 1/2)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow PI 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow PI 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow PI 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow PI 1)))) 24) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1/2) (* 0 1/2))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow PI 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow PI 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow PI 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow PI 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow PI 1)))) 120) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1/2) (* 0 1/2)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow PI 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow PI 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow PI 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow PI 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow PI 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow PI 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow PI 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow PI 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow PI 1)))) 720) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1/2) (* 0 1/2))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 720 (/ (* (pow (* 1 0) 7)) (pow PI 7))) (* -2520 (/ (* (pow (* 1 0) 5) (pow (* 2 0) 1)) (pow PI 6))) (* 2520 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 2)) (pow PI 5))) (* 840 (/ (* (pow (* 1 0) 4) 1 (pow (* 6 0) 1)) (pow PI 5))) (* -630 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 3)) (pow PI 4))) (* -1260 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 4))) (* -210 (/ (* (pow (* 1 0) 3) 1 1 (pow (* 24 0) 1)) (pow PI 4))) (* 210 (/ (* 1 (pow (* 2 0) 2) (pow (* 6 0) 1)) (pow PI 3))) (* 140 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 2)) (pow PI 3))) (* 210 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow PI 3))) (* 42 (/ (* (pow (* 1 0) 2) 1 1 1 (pow (* 120 0) 1)) (pow PI 3))) (* -35 (/ (* 1 1 (pow (* 6 0) 1) (pow (* 24 0) 1)) (pow PI 2))) (* -21 (/ (* 1 (pow (* 2 0) 1) 1 1 (pow (* 120 0) 1)) (pow PI 2))) (* -7 (/ (* (pow (* 1 0) 1) 1 1 1 1 (pow (* 720 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 1 1 (pow (* 5040 0) 1)) (pow PI 1)))) 5040) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1/2) (* 0 1/2)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 (log PI)) (* (* 1/2 (log PI)) (/ 1 (/ 1 (- k))))) into (- (* 1/2 (log PI)) (* 1/2 (* (log PI) k))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 111 ] simplifiying candidate # * * * * [misc]progress: [ 2 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * * [misc]simplify: iters left: 2 (30 enodes) * * [misc]simplify: iters left: 1 (35 enodes) * [exit]simplify: Simplified to (- (* (/ (log PI) 2) (- 1 k)) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (log PI) 2) (- 1 k)) (log (sqrt k))) * * * * [misc]progress: [ 3 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * * [misc]simplify: iters left: 1 (74 enodes) * [exit]simplify: Simplified to (- (* (log (sqrt PI)) (- 1 k)) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (log (sqrt PI)) (- 1 k)) (log (sqrt k))) * * * * [misc]progress: [ 4 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (exp (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * [exit]simplify: Simplified to (exp (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * * * * [misc]progress: [ 5 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (exp (* (log PI) (/ (- 1 k) 2))) (exp (* (log PI) (/ (- 1 k) 2)))) (exp (* (log PI) (/ (- 1 k) 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (124 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (291 enodes) * [exit]simplify: Simplified to (/ (pow (pow (sqrt PI) (- 1 k)) 3) (* (sqrt k) k)) * [exit]simplify: Simplified to (/ (pow (pow (sqrt PI) (- 1 k)) 3) (* (sqrt k) k)) * * * * [misc]progress: [ 6 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) (cbrt (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * * [misc]simplify: iters left: 1 (58 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (sqrt (pow PI (- 1 k))) (sqrt k))) (cbrt (/ (sqrt (pow PI (- 1 k))) (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ (sqrt (pow PI (- 1 k))) (sqrt k))) (cbrt (/ (sqrt (pow PI (- 1 k))) (sqrt k)))) * [enter]simplify: Simplifying (cbrt (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (cbrt (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * [exit]simplify: Simplified to (cbrt (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * * * * [misc]progress: [ 7 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (110 enodes) * * [misc]simplify: iters left: 1 (172 enodes) * [exit]simplify: Simplified to (pow (/ (pow (sqrt PI) (- 1 k)) (sqrt k)) 3) * [exit]simplify: Simplified to (pow (/ (pow (sqrt PI) (- 1 k)) (sqrt k)) 3) * * * * [misc]progress: [ 8 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* (log PI) (- 1 k))) k) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * [exit]simplify: Simplified to (/ (pow PI (- 1 k)) k) * [exit]simplify: Simplified to (/ (pow PI (- 1 k)) k) * * * * [misc]progress: [ 9 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (sqrt (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * [enter]simplify: Simplifying (sqrt (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (sqrt (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * * * * [misc]progress: [ 10 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (- (exp (* (log PI) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * * [misc]simplify: iters left: 1 (55 enodes) * [exit]simplify: Simplified to (- (sqrt (pow PI (- 1 k)))) * [exit]simplify: Simplified to (- (sqrt (pow PI (- 1 k)))) * [enter]simplify: Simplifying (- (sqrt k)) * * [misc]simplify: iters left: 3 (3 enodes) * [exit]simplify: Simplified to (- (sqrt k)) * [exit]simplify: Simplified to (- (sqrt k)) * * * * [misc]progress: [ 11 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (exp (* (log PI) (/ (- 1 k) 2)))) (cbrt (exp (* (log PI) (/ (- 1 k) 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow PI (- 1 k)))) (cbrt (sqrt k))) (/ (cbrt (sqrt (pow PI (- 1 k)))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow PI (- 1 k)))) (cbrt (sqrt k))) (/ (cbrt (sqrt (pow PI (- 1 k)))) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (cbrt (exp (* (log PI) (/ (- 1 k) 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * * [misc]simplify: iters left: 1 (58 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow PI (- 1 k)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow PI (- 1 k)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 12 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (exp (* (log PI) (/ (- 1 k) 2)))) (cbrt (exp (* (log PI) (/ (- 1 k) 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow PI (- 1 k)))) (cbrt (sqrt (pow PI (- 1 k))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow PI (- 1 k)))) (cbrt (sqrt (pow PI (- 1 k))))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (cbrt (exp (* (log PI) (/ (- 1 k) 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * * [misc]simplify: iters left: 1 (58 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow PI (- 1 k)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow PI (- 1 k)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 13 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (exp (* (log PI) (/ (- 1 k) 2)))) (cbrt (exp (* (log PI) (/ (- 1 k) 2))))) 1) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * * [misc]simplify: iters left: 1 (62 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow PI (- 1 k)))) (/ (cbrt (sqrt (pow PI (- 1 k)))) 1)) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow PI (- 1 k)))) (/ (cbrt (sqrt (pow PI (- 1 k)))) 1)) * [enter]simplify: Simplifying (/ (cbrt (exp (* (log PI) (/ (- 1 k) 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow PI (- 1 k)))) (sqrt k)) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow PI (- 1 k)))) (sqrt k)) * * * * [misc]progress: [ 14 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (exp (* (log PI) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (52 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (exp (* (log PI) (/ (- 1 k) 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * * [misc]simplify: iters left: 1 (58 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 15 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (exp (* (log PI) (/ (- 1 k) 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * * [misc]simplify: iters left: 1 (58 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (exp (* (log PI) (/ (- 1 k) 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * * [misc]simplify: iters left: 1 (58 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 16 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (exp (* (log PI) (/ (- 1 k) 2)))) 1) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * * [misc]simplify: iters left: 1 (56 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) 1) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) 1) * [enter]simplify: Simplifying (/ (sqrt (exp (* (log PI) (/ (- 1 k) 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) (sqrt k)) * * * * [misc]progress: [ 17 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (exp (* (log PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) (cbrt (sqrt k))) * * * * [misc]progress: [ 18 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) (sqrt (sqrt k))) * * * * [misc]progress: [ 19 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to 1 * [exit]simplify: Simplified to 1 * [enter]simplify: Simplifying (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * * [misc]simplify: iters left: 1 (56 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) (sqrt k)) * * * * [misc]progress: [ 20 / 111 ] simplifiying candidate # * * * * [misc]progress: [ 21 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt k)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * * * * [misc]progress: [ 22 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (exp (* (log PI) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * * [misc]simplify: iters left: 1 (56 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow PI (- 1 k)))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow PI (- 1 k)))) * * * * [misc]progress: [ 23 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* (log PI) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (51 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 24 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) (sqrt (sqrt k))) * * * * [misc]progress: [ 25 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* (log PI) (/ (- 1 k) 2))) 1) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * * [misc]simplify: iters left: 1 (55 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) 1) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) 1) * * * * [misc]progress: [ 26 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (cbrt (exp (* (log PI) (/ (- 1 k) 2))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (sqrt (pow PI (- 1 k))))) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (sqrt (pow PI (- 1 k))))) * * * * [misc]progress: [ 27 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (exp (* (log PI) (/ (- 1 k) 2))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (sqrt (pow PI (- 1 k))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (sqrt (pow PI (- 1 k))))) * * * * [misc]progress: [ 28 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (exp (* (log PI) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * * [misc]simplify: iters left: 1 (56 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow PI (- 1 k)))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow PI (- 1 k)))) * * * * [misc]progress: [ 29 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (89 enodes) * * [misc]simplify: iters left: 1 (109 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (pow PI (- 1 k))) (pow (+ n n) (/ (- 1 k) 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (* (sqrt (pow PI (- 1 k))) (pow (+ n n) (/ (- 1 k) 2))) (sqrt k)) * * * * [misc]progress: [ 30 / 111 ] simplifiying candidate # * * * * [misc]progress: [ 31 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (98 enodes) * * [misc]simplify: iters left: 1 (174 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (+ n n)) (log PI))) (+ (log 1) (log (sqrt k)))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (+ n n)) (log PI))) (+ (log 1) (log (sqrt k)))) * * * * [misc]progress: [ 32 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) (log (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (81 enodes) * * [misc]simplify: iters left: 2 (119 enodes) * * [misc]simplify: iters left: 1 (197 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (+ n n)) (log PI))) (+ (log (sqrt k)) (log 1))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (+ n n)) (log PI))) (+ (log (sqrt k)) (log 1))) * * * * [misc]progress: [ 33 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (149 enodes) * * [misc]simplify: iters left: 1 (228 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (+ n n)) (log PI))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (+ n n)) (log PI))) (log (sqrt k))) * * * * [misc]progress: [ 34 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (92 enodes) * * [misc]simplify: iters left: 1 (112 enodes) * [exit]simplify: Simplified to (exp (/ (pow (+ n n) (/ (- 1 k) 2)) (/ (sqrt k) (sqrt (pow PI (- 1 k)))))) * [exit]simplify: Simplified to (exp (/ (pow (+ n n) (/ (- 1 k) 2)) (/ (sqrt k) (sqrt (pow PI (- 1 k)))))) * * * * [misc]progress: [ 35 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) (/ (* (* (exp (* (log PI) (/ (- 1 k) 2))) (exp (* (log PI) (/ (- 1 k) 2)))) (exp (* (log PI) (/ (- 1 k) 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (124 enodes) * * [misc]simplify: iters left: 3 (258 enodes) * * [misc]simplify: iters left: 2 (443 enodes) * [exit]simplify: Simplified to (* (* (/ (pow (+ n n) (/ (- 1 k) 2)) k) (* (/ (pow PI (- 1 k)) (sqrt k)) (sqrt (pow PI (- 1 k))))) (* (pow (+ n n) (/ (- 1 k) 2)) (/ (pow (+ n n) (/ (- 1 k) 2)) 1))) * [exit]simplify: Simplified to (* (* (/ (pow (+ n n) (/ (- 1 k) 2)) k) (* (/ (pow PI (- 1 k)) (sqrt k)) (sqrt (pow PI (- 1 k))))) (* (pow (+ n n) (/ (- 1 k) 2)) (/ (pow (+ n n) (/ (- 1 k) 2)) 1))) * * * * [misc]progress: [ 36 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) (* (* (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (258 enodes) * * [misc]simplify: iters left: 1 (370 enodes) * [exit]simplify: Simplified to (* (pow (/ (pow (sqrt PI) (- 1 k)) (sqrt k)) 3) (* (* (pow (+ n n) (/ (- 1 k) 2)) (pow (+ n n) (/ (- 1 k) 2))) (/ (pow (+ n n) (/ (- 1 k) 2)) 1))) * [exit]simplify: Simplified to (* (pow (/ (pow (sqrt PI) (- 1 k)) (sqrt k)) 3) (* (* (pow (+ n n) (/ (- 1 k) 2)) (pow (+ n n) (/ (- 1 k) 2))) (/ (pow (+ n n) (/ (- 1 k) 2)) 1))) * * * * [misc]progress: [ 37 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)))) (cbrt (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (91 enodes) * * [misc]simplify: iters left: 1 (111 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (pow (+ n n) (/ (- 1 k) 2)) (/ (sqrt k) (sqrt (pow PI (- 1 k)))))) (cbrt (/ (pow (+ n n) (/ (- 1 k) 2)) (/ (sqrt k) (sqrt (pow PI (- 1 k))))))) * [exit]simplify: Simplified to (* (cbrt (/ (pow (+ n n) (/ (- 1 k) 2)) (/ (sqrt k) (sqrt (pow PI (- 1 k)))))) (cbrt (/ (pow (+ n n) (/ (- 1 k) 2)) (/ (sqrt k) (sqrt (pow PI (- 1 k))))))) * [enter]simplify: Simplifying (cbrt (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (90 enodes) * * [misc]simplify: iters left: 1 (110 enodes) * [exit]simplify: Simplified to (cbrt (/ (* (sqrt (pow PI (- 1 k))) (pow (+ n n) (/ (- 1 k) 2))) (sqrt k))) * [exit]simplify: Simplified to (cbrt (/ (* (sqrt (pow PI (- 1 k))) (pow (+ n n) (/ (- 1 k) 2))) (sqrt k))) * * * * [misc]progress: [ 38 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)))) (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (249 enodes) * * [misc]simplify: iters left: 1 (390 enodes) * [exit]simplify: Simplified to (* (/ (* (pow PI (- 1 k)) (sqrt (pow PI (- 1 k)))) (* k (sqrt k))) (/ (* (pow (+ n n) (/ (- 1 k) 2)) (pow (+ n n) (/ (- 1 k) 2))) (/ 1 (pow (+ n n) (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (* (/ (* (pow PI (- 1 k)) (sqrt (pow PI (- 1 k)))) (* k (sqrt k))) (/ (* (pow (+ n n) (/ (- 1 k) 2)) (pow (+ n n) (/ (- 1 k) 2))) (/ 1 (pow (+ n n) (/ (- 1 k) 2))))) * * * * [misc]progress: [ 39 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (90 enodes) * * [misc]simplify: iters left: 1 (110 enodes) * [exit]simplify: Simplified to (sqrt (/ (* (sqrt (pow PI (- 1 k))) (pow (+ n n) (/ (- 1 k) 2))) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (* (sqrt (pow PI (- 1 k))) (pow (+ n n) (/ (- 1 k) 2))) (sqrt k))) * [enter]simplify: Simplifying (sqrt (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (90 enodes) * * [misc]simplify: iters left: 1 (110 enodes) * [exit]simplify: Simplified to (sqrt (/ (* (sqrt (pow PI (- 1 k))) (pow (+ n n) (/ (- 1 k) 2))) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (* (sqrt (pow PI (- 1 k))) (pow (+ n n) (/ (- 1 k) 2))) (sqrt k))) * * * * [misc]progress: [ 40 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (+ n n) (/ (- 1 k) 2)) (exp (* (log PI) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (52 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (* (pow (+ n n) (/ (- 1 k) 2)) (sqrt (pow PI (- 1 k)))) * [exit]simplify: Simplified to (* (pow (+ n n) (/ (- 1 k) 2)) (sqrt (pow PI (- 1 k)))) * [enter]simplify: Simplifying (* 1 (sqrt k)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * [exit]simplify: Simplified to (sqrt k) * [exit]simplify: Simplified to (sqrt k) * * * * [misc]progress: [ 41 / 111 ] simplifiying candidate # * * * * [misc]progress: [ 42 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (* (cbrt (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) (cbrt (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (pow (+ n n) (/ (- 1 k) 2)) (cbrt (/ (sqrt (pow PI (- 1 k))) (sqrt k)))) (/ 1 (cbrt (/ (sqrt (pow PI (- 1 k))) (sqrt k))))) * [exit]simplify: Simplified to (/ (* (pow (+ n n) (/ (- 1 k) 2)) (cbrt (/ (sqrt (pow PI (- 1 k))) (sqrt k)))) (/ 1 (cbrt (/ (sqrt (pow PI (- 1 k))) (sqrt k))))) * * * * [misc]progress: [ 43 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (sqrt (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (76 enodes) * [exit]simplify: Simplified to (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (sqrt (/ (sqrt (pow PI (- 1 k))) (sqrt k)))) * [exit]simplify: Simplified to (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (sqrt (/ (sqrt (pow PI (- 1 k))) (sqrt k)))) * * * * [misc]progress: [ 44 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (* (cbrt (exp (* (log PI) (/ (- 1 k) 2)))) (cbrt (exp (* (log PI) (/ (- 1 k) 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (158 enodes) * * [misc]simplify: iters left: 1 (254 enodes) * [exit]simplify: Simplified to (/ (* (/ (pow (+ n n) (/ (- 1 k) 2)) (cbrt (sqrt k))) (cbrt (sqrt (pow PI (- 1 k))))) (/ (cbrt (sqrt k)) (cbrt (sqrt (pow PI (- 1 k)))))) * [exit]simplify: Simplified to (/ (* (/ (pow (+ n n) (/ (- 1 k) 2)) (cbrt (sqrt k))) (cbrt (sqrt (pow PI (- 1 k))))) (/ (cbrt (sqrt k)) (cbrt (sqrt (pow PI (- 1 k)))))) * * * * [misc]progress: [ 45 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (* (cbrt (exp (* (log PI) (/ (- 1 k) 2)))) (cbrt (exp (* (log PI) (/ (- 1 k) 2))))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (86 enodes) * * [misc]simplify: iters left: 2 (109 enodes) * * [misc]simplify: iters left: 1 (142 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow PI (- 1 k)))) (/ (sqrt (sqrt k)) (pow (+ n n) (/ (- 1 k) 2)))) (/ 1 (cbrt (sqrt (pow PI (- 1 k)))))) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow PI (- 1 k)))) (/ (sqrt (sqrt k)) (pow (+ n n) (/ (- 1 k) 2)))) (/ 1 (cbrt (sqrt (pow PI (- 1 k)))))) * * * * [misc]progress: [ 46 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (* (cbrt (exp (* (log PI) (/ (- 1 k) 2)))) (cbrt (exp (* (log PI) (/ (- 1 k) 2))))) 1)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (80 enodes) * * [misc]simplify: iters left: 2 (100 enodes) * * [misc]simplify: iters left: 1 (123 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow PI (- 1 k)))) (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) (cbrt (sqrt (pow PI (- 1 k))))) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow PI (- 1 k)))) (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) (cbrt (sqrt (pow PI (- 1 k))))) * * * * [misc]progress: [ 47 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (sqrt (exp (* (log PI) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (121 enodes) * * [misc]simplify: iters left: 1 (181 enodes) * [exit]simplify: Simplified to (* (/ (pow (+ n n) (/ (- 1 k) 2)) (cbrt (sqrt k))) (/ (sqrt (sqrt (pow PI (- 1 k)))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (* (/ (pow (+ n n) (/ (- 1 k) 2)) (cbrt (sqrt k))) (/ (sqrt (sqrt (pow PI (- 1 k)))) (cbrt (sqrt k)))) * * * * [misc]progress: [ 48 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (sqrt (exp (* (log PI) (/ (- 1 k) 2)))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (91 enodes) * * [misc]simplify: iters left: 1 (109 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) (/ (sqrt (sqrt k)) (pow (+ n n) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) (/ (sqrt (sqrt k)) (pow (+ n n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 49 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (sqrt (exp (* (log PI) (/ (- 1 k) 2)))) 1)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (82 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (sqrt (sqrt (pow PI (- 1 k))))) * [exit]simplify: Simplified to (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (sqrt (sqrt (pow PI (- 1 k))))) * * * * [misc]progress: [ 50 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 51 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ 1 (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (42 enodes) * * [misc]simplify: iters left: 1 (51 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * * * [misc]progress: [ 52 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ 1 1)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * * [misc]simplify: iters left: 2 (27 enodes) * * [misc]simplify: iters left: 1 (28 enodes) * [exit]simplify: Simplified to (pow (+ n n) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (+ n n) (/ (- 1 k) 2)) * * * * [misc]progress: [ 53 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) 1) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * * [misc]simplify: iters left: 2 (27 enodes) * * [misc]simplify: iters left: 1 (28 enodes) * [exit]simplify: Simplified to (pow (+ n n) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (+ n n) (/ (- 1 k) 2)) * * * * [misc]progress: [ 54 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (exp (* (log PI) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (65 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ (- 1 k) 2)) (exp (* (/ (log PI) 2) (- (- 1 k))))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ (- 1 k) 2)) (exp (* (/ (log PI) 2) (- (- 1 k))))) * * * * [misc]progress: [ 55 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (76 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) (/ (sqrt k) (sqrt (pow PI (- 1 k))))) * [exit]simplify: Simplified to (/ (cbrt (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) (/ (sqrt k) (sqrt (pow PI (- 1 k))))) * * * * [misc]progress: [ 56 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (76 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) (/ (sqrt k) (sqrt (pow PI (- 1 k))))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) (/ (sqrt k) (sqrt (pow PI (- 1 k))))) * * * * [misc]progress: [ 57 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (89 enodes) * * [misc]simplify: iters left: 1 (109 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (pow PI (- 1 k))) (pow (+ n n) (/ (- 1 k) 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (* (sqrt (pow PI (- 1 k))) (pow (+ n n) (/ (- 1 k) 2))) (sqrt k)) * * * * [misc]progress: [ 58 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) (sqrt k)) * * * * [misc]progress: [ 59 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (exp (* (log PI) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (65 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ (- 1 k) 2)) (exp (* (/ (log PI) 2) (- (- 1 k))))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ (- 1 k) 2)) (exp (* (/ (log PI) 2) (- (- 1 k))))) * * * * [misc]progress: [ 60 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (+ n n) (/ (- 1 k) 2)) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (74 enodes) * [exit]simplify: Simplified to (* (sqrt (pow PI (- 1 k))) (/ (pow (+ n n) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (* (sqrt (pow PI (- 1 k))) (/ (pow (+ n n) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 61 / 111 ] simplifiying candidate # * * * * [misc]progress: [ 62 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (+ n n)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * * [misc]simplify: iters left: 1 (62 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (+ n n))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (+ n n))) * * * * [misc]progress: [ 63 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (+ n n)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * * [misc]simplify: iters left: 1 (62 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (+ n n))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (+ n n))) * * * * [misc]progress: [ 64 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (28 enodes) * * [misc]simplify: iters left: 1 (32 enodes) * [exit]simplify: Simplified to (/ (- 1 k) 2) * [exit]simplify: Simplified to (/ (- 1 k) 2) * * * * [misc]progress: [ 65 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (+ n n) (/ 1 2)) * * [misc]simplify: iters left: 3 (6 enodes) * * [misc]simplify: iters left: 2 (9 enodes) * * [misc]simplify: iters left: 1 (10 enodes) * [exit]simplify: Simplified to (pow (+ n n) (/ 1 2)) * [exit]simplify: Simplified to (pow (+ n n) (/ 1 2)) * [enter]simplify: Simplifying (pow (+ n n) (/ k 2)) * * [misc]simplify: iters left: 3 (6 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * * [misc]simplify: iters left: 1 (8 enodes) * [exit]simplify: Simplified to (pow (+ n n) (/ k 2)) * [exit]simplify: Simplified to (pow (+ n n) (/ k 2)) * * * * [misc]progress: [ 66 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (+ n n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (pow (+ n n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (pow (+ n n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * * * [misc]progress: [ 67 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (+ n n) (sqrt (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (pow (+ n n) (sqrt (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow (+ n n) (sqrt (/ (- 1 k) 2))) * * * * [misc]progress: [ 68 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (+ n n) 1) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (8 enodes) * * [misc]simplify: iters left: 1 (9 enodes) * [exit]simplify: Simplified to (+ n n) * [exit]simplify: Simplified to (+ n n) * * * * [misc]progress: [ 69 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (+ n n) (- 1 k)) * * [misc]simplify: iters left: 3 (6 enodes) * * [misc]simplify: iters left: 2 (10 enodes) * * [misc]simplify: iters left: 1 (11 enodes) * [exit]simplify: Simplified to (pow (+ n n) (- 1 k)) * [exit]simplify: Simplified to (pow (+ n n) (- 1 k)) * * * * [misc]progress: [ 70 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ (- 1 k) 2)) * [enter]simplify: Simplifying (pow (cbrt (+ n n)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * [exit]simplify: Simplified to (pow (cbrt (+ n n)) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (cbrt (+ n n)) (/ (- 1 k) 2)) * * * * [misc]progress: [ 71 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (sqrt (+ n n)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * [exit]simplify: Simplified to (pow (sqrt (+ n n)) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (sqrt (+ n n)) (/ (- 1 k) 2)) * [enter]simplify: Simplifying (pow (sqrt (+ n n)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * [exit]simplify: Simplified to (pow (sqrt (+ n n)) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (sqrt (+ n n)) (/ (- 1 k) 2)) * * * * [misc]progress: [ 72 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (pow 1 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (11 enodes) * [exit]simplify: Simplified to 1 * [exit]simplify: Simplified to 1 * [enter]simplify: Simplifying (pow (+ n n) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (15 enodes) * [exit]simplify: Simplified to (pow (+ n n) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (+ n n) (/ (- 1 k) 2)) * * * * [misc]progress: [ 73 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (pow 2 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (11 enodes) * [exit]simplify: Simplified to (pow 2 (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow 2 (/ (- 1 k) 2)) * [enter]simplify: Simplifying (pow n (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * * * * [misc]progress: [ 74 / 111 ] simplifiying candidate # * * * * [misc]progress: [ 75 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (log (pow (+ n n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (51 enodes) * * [misc]simplify: iters left: 1 (56 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (+ n n))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (+ n n))) * * * * [misc]progress: [ 76 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (pow (+ n n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (exp (pow (+ n n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (exp (pow (+ n n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 77 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (+ n n) (/ (- 1 k) 2))) (cbrt (pow (+ n n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (+ n n) (/ (- 1 k) 2))) (cbrt (pow (+ n n) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (+ n n) (/ (- 1 k) 2))) (cbrt (pow (+ n n) (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (cbrt (pow (+ n n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (cbrt (pow (+ n n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (cbrt (pow (+ n n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 78 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (pow (+ n n) (/ (- 1 k) 2)) (pow (+ n n) (/ (- 1 k) 2))) (pow (+ n n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * [exit]simplify: Simplified to (pow (pow (+ n n) (/ (- 1 k) 2)) 3) * [exit]simplify: Simplified to (pow (pow (+ n n) (/ (- 1 k) 2)) 3) * * * * [misc]progress: [ 79 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (+ n n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (sqrt (pow (+ n n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (+ n n) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (sqrt (pow (+ n n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (sqrt (pow (+ n n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (+ n n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 80 / 111 ] simplifiying candidate # * * * * [misc]progress: [ 81 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log PI) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * * [misc]simplify: iters left: 2 (27 enodes) * * [misc]simplify: iters left: 1 (30 enodes) * [exit]simplify: Simplified to (/ (log PI) (/ 2 (- 1 k))) * [exit]simplify: Simplified to (/ (log PI) (/ 2 (- 1 k))) * * * * [misc]progress: [ 82 / 111 ] simplifiying candidate # * * * * [misc]progress: [ 83 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (log PI)) (log (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (+ (log (/ (- 1 k) 2)) (log (log PI))) * [exit]simplify: Simplified to (+ (log (/ (- 1 k) 2)) (log (log PI))) * * * * [misc]progress: [ 84 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (log PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * * [misc]simplify: iters left: 1 (53 enodes) * [exit]simplify: Simplified to (log (* (- 1 k) (/ (log PI) 2))) * [exit]simplify: Simplified to (log (* (- 1 k) (/ (log PI) 2))) * * * * [misc]progress: [ 85 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (log PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * * [misc]simplify: iters left: 1 (54 enodes) * [exit]simplify: Simplified to (sqrt (pow PI (- 1 k))) * [exit]simplify: Simplified to (sqrt (pow PI (- 1 k))) * * * * [misc]progress: [ 86 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (log PI) (log PI)) (log PI)) (* (* (/ (- 1 k) 2) (/ (- 1 k) 2)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (253 enodes) * [exit]simplify: Simplified to (* (* (/ (- 1 k) 2) (/ (- 1 k) 2)) (* (/ (- 1 k) 2) (pow (log PI) 3))) * [exit]simplify: Simplified to (* (* (/ (- 1 k) 2) (/ (- 1 k) 2)) (* (/ (- 1 k) 2) (pow (log PI) 3))) * * * * [misc]progress: [ 87 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* (log PI) (/ (- 1 k) 2))) (cbrt (* (log PI) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (29 enodes) * * [misc]simplify: iters left: 1 (32 enodes) * [exit]simplify: Simplified to (* (cbrt (* (/ (log PI) 2) (- 1 k))) (cbrt (* (/ (log PI) 2) (- 1 k)))) * [exit]simplify: Simplified to (* (cbrt (* (/ (log PI) 2) (- 1 k))) (cbrt (* (/ (log PI) 2) (- 1 k)))) * [enter]simplify: Simplifying (cbrt (* (log PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * * [misc]simplify: iters left: 2 (28 enodes) * * [misc]simplify: iters left: 1 (31 enodes) * [exit]simplify: Simplified to (cbrt (/ (* (log PI) (- 1 k)) 2)) * [exit]simplify: Simplified to (cbrt (/ (* (log PI) (- 1 k)) 2)) * * * * [misc]progress: [ 88 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (log PI) (/ (- 1 k) 2)) (* (log PI) (/ (- 1 k) 2))) (* (log PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (71 enodes) * * [misc]simplify: iters left: 2 (148 enodes) * * [misc]simplify: iters left: 1 (240 enodes) * [exit]simplify: Simplified to (pow (* (- 1 k) (/ (log PI) 2)) 3) * [exit]simplify: Simplified to (pow (* (- 1 k) (/ (log PI) 2)) 3) * * * * [misc]progress: [ 89 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (log PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * * [misc]simplify: iters left: 2 (28 enodes) * * [misc]simplify: iters left: 1 (31 enodes) * [exit]simplify: Simplified to (sqrt (/ (* (log PI) (- 1 k)) 2)) * [exit]simplify: Simplified to (sqrt (/ (* (log PI) (- 1 k)) 2)) * [enter]simplify: Simplifying (sqrt (* (log PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * * [misc]simplify: iters left: 2 (28 enodes) * * [misc]simplify: iters left: 1 (31 enodes) * [exit]simplify: Simplified to (sqrt (/ (* (log PI) (- 1 k)) 2)) * [exit]simplify: Simplified to (sqrt (/ (* (log PI) (- 1 k)) 2)) * * * * [misc]progress: [ 90 / 111 ] simplifiying candidate # * * * * [misc]progress: [ 91 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (- 1 k) 2)) (* (cbrt (/ (- 1 k) 2)) (log PI))) * [exit]simplify: Simplified to (* (cbrt (/ (- 1 k) 2)) (* (cbrt (/ (- 1 k) 2)) (log PI))) * * * * [misc]progress: [ 92 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log PI) (sqrt (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (- 1 k) 2)) (log PI)) * [exit]simplify: Simplified to (* (sqrt (/ (- 1 k) 2)) (log PI)) * * * * [misc]progress: [ 93 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log PI) 1) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * [exit]simplify: Simplified to (log PI) * [exit]simplify: Simplified to (log PI) * * * * [misc]progress: [ 94 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log PI) (- 1 k)) * * [misc]simplify: iters left: 4 (6 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * [exit]simplify: Simplified to (* (log PI) (- 1 k)) * [exit]simplify: Simplified to (* (log PI) (- 1 k)) * * * * [misc]progress: [ 95 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (log PI)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * * [misc]simplify: iters left: 2 (28 enodes) * * [misc]simplify: iters left: 1 (31 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (cbrt (log PI))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (cbrt (log PI))) * * * * [misc]progress: [ 96 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (log PI)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * * [misc]simplify: iters left: 2 (28 enodes) * * [misc]simplify: iters left: 1 (31 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (sqrt (log PI))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (sqrt (log PI))) * * * * [misc]progress: [ 97 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log PI) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * * [misc]simplify: iters left: 2 (27 enodes) * * [misc]simplify: iters left: 1 (30 enodes) * [exit]simplify: Simplified to (/ (log PI) (/ 2 (- 1 k))) * [exit]simplify: Simplified to (/ (log PI) (/ 2 (- 1 k))) * * * * [misc]progress: [ 98 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log PI) (- 1 k)) * * [misc]simplify: iters left: 4 (6 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * [exit]simplify: Simplified to (* (log PI) (- 1 k)) * [exit]simplify: Simplified to (* (log PI) (- 1 k)) * * * * [misc]progress: [ 99 / 111 ] simplifiying candidate # * * * * [misc]progress: [ 100 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (+ (* +nan.0 (* (* (log PI) k) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) k)) (- (+ (* +nan.0 (* (sqrt PI) (/ 1 k))) (- (* +nan.0 (* (* (pow (log PI) 2) k) (sqrt PI))))))))))))))) * * * * [misc]progress: [ 101 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) k)) (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))))))) * * * * [misc]progress: [ 102 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (- (+ (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) k)) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (pow k 2))))))))) * * * * [misc]progress: [ 103 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (sqrt PI) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* k (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log n) 2) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (log PI) (* (pow k 2) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log PI) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow k 2) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* (log 2) (* (exp (* 1/2 (+ (log n) (log 2)))) (pow k 2)))))) (- (+ (* +nan.0 (* (* (log PI) (* k (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow k 2) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (log PI) (* (log n) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2))))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* k (exp (* 1/2 (+ (log n) (log 2)))))))) (- (* +nan.0 (* (sqrt PI) (* k (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))))))))))))))))))))))))))))))))) * * * * [misc]progress: [ 104 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (pow k 3))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) k))))))) * * * * [misc]progress: [ 105 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) k)) (- (+ (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (pow k 2)))))))) * * * * [misc]progress: [ 106 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (- (+ (* 1/8 (* (pow k 2) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/4 (* (log 2) (* (pow k 2) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (exp (* 1/2 (+ (log n) (log 2)))) (* 1/8 (* (pow k 2) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))))))) (+ (* 1/2 (* k (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (* 1/2 (* k (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))))) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (45 enodes) * * [misc]simplify: iters left: 5 (111 enodes) * * [misc]simplify: iters left: 4 (183 enodes) * * [misc]simplify: iters left: 3 (304 enodes) * [exit]simplify: Simplified to (/ (- (+ (* (* (sqrt n) (sqrt 2)) (+ (* (* (* k k) 1/8) (* (log n) (log n))) (* (* (log 2) 1/4) (* (* k k) (log n))))) (+ (* (sqrt n) (sqrt 2)) (* (* (* (* k k) 1/8) (* (log 2) (log 2))) (* (sqrt n) (sqrt 2))))) (* (* 1/2 k) (* (* (sqrt n) (sqrt 2)) (+ (log n) (log 2))))) (/ 1 (/ (sqrt (pow PI (- 1 k))) (sqrt k)))) * * * * [misc]progress: [ 107 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 2) (log n))))) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (84 enodes) * * [misc]simplify: iters left: 2 (114 enodes) * * [misc]simplify: iters left: 1 (156 enodes) * [exit]simplify: Simplified to (* (pow (exp 1/2) (* (- (log 2) (log n)) (- 1 (/ 1 k)))) (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * * * * [misc]progress: [ 108 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -2) (log n))))) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (113 enodes) * * [misc]simplify: iters left: 2 (141 enodes) * * [misc]simplify: iters left: 1 (202 enodes) * [exit]simplify: Simplified to (* (exp (* (- (log -2) (log n)) (+ (/ 1/2 k) 1/2))) (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * * * * [misc]progress: [ 109 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (exp (- (* 1/2 (log PI)) (* 1/2 (* (log PI) k)))) (sqrt k))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (84 enodes) * * [misc]simplify: iters left: 2 (125 enodes) * * [misc]simplify: iters left: 1 (184 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt PI) (sqrt k)) (pow (sqrt PI) k)) (pow (+ n n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 110 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (exp (- (* 1/2 (log PI)) (* 1/2 (* (log PI) k)))) (sqrt k))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (84 enodes) * * [misc]simplify: iters left: 2 (125 enodes) * * [misc]simplify: iters left: 1 (184 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt PI) (sqrt k)) (pow (sqrt PI) k)) (pow (+ n n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 111 / 111 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ (- 1 k) 2)) 1) (/ (exp (- (* 1/2 (log PI)) (* 1/2 (* (log PI) k)))) (sqrt k))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (84 enodes) * * [misc]simplify: iters left: 2 (125 enodes) * * [misc]simplify: iters left: 1 (184 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt PI) (sqrt k)) (pow (sqrt PI) k)) (pow (+ n n) (/ (- 1 k) 2))) * * * [misc]progress: adding candidates to table * * [misc]progress: iteration 4 / 4 * * * [misc]progress: picking best candidate * * * * [misc]pick: Picked # * * * [misc]progress: localizing error * * * [misc]progress: generating rewritten candidates * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 1 1) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2 1 1) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2) * [misc]approximate: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]backup-simplify: Simplify (* (log PI) 1/2) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (pow PI 1/2) +nan.0) into (* +nan.0 (sqrt PI)) * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]backup-simplify: Simplify (* (log PI) 1/2) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (pow PI 1/2) +nan.0) into (* +nan.0 (sqrt PI)) * [misc]backup-simplify: Simplify (* +nan.0 (sqrt PI)) into (* +nan.0 (sqrt PI)) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (/ -1 2) (+ (* 1/2 (/ 0 2)))) into -1/2 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) -1/2) (* 0 1/2)) into (- (* 1/2 (log PI))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ (* -1/2 (* (log PI) (sqrt PI))) +nan.0) (+ (* (* +nan.0 (sqrt PI)) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 -1/2) (* 0 1/2))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ (* 1/8 (* (pow (log PI) 2) (sqrt PI))) +nan.0) (+ (* (* +nan.0 (sqrt PI)) (/ +nan.0 +nan.0)) (* (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) k) (+ (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) (* (* +nan.0 (sqrt PI)) (/ 1 k)))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (+ (* +nan.0 (* (* (log PI) k) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) k)) (- (+ (* +nan.0 (* (sqrt PI) (/ 1 k))) (- (* +nan.0 (* (* (pow (log PI) 2) k) (sqrt PI)))))))))))))) * [misc]approximate: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) in k * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]backup-simplify: Simplify (* (log PI) -1/2) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) into (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) in k * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]backup-simplify: Simplify (* (log PI) -1/2) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) into (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) into (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) into (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) into (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) (pow (/ 1 k) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) (/ 1 k)) (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) k)) (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))))))) * [misc]approximate: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k)))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) in k * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]backup-simplify: Simplify (* (log PI) 1/2) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) in k * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]backup-simplify: Simplify (* (log PI) 1/2) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) (/ 1 (- k))) (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))))) into (- (+ (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) k)) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (pow k 2)))))))) * * * * [misc]progress: [ 2 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) in k * [misc]taylor: Taking taylor expansion of (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) in k * [misc]taylor: Taking taylor expansion of (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) in k * [misc]taylor: Taking taylor expansion of (pow (+ n n) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (+ n n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (+ n n))) in k * [misc]taylor: Taking taylor expansion of (/ 1 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ n n)) in k * [misc]taylor: Taking taylor expansion of (+ n n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (+ n n) into (* 2 n) * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) * [misc]taylor: Taking taylor expansion of (pow (+ n n) (/ k 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (+ n n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (+ n n))) in k * [misc]taylor: Taking taylor expansion of (/ k 2) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ n n)) in k * [misc]taylor: Taking taylor expansion of (+ n n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (+ n n) into (* 2 n) * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (/ (pow (* 2 n) 1/2) 1) into (sqrt (* n 2)) * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (sqrt (* n 2)) 1) into (* (sqrt n) (sqrt 2)) * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]backup-simplify: Simplify (* (log PI) 1/2) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (pow PI 1/2) +nan.0) into (* +nan.0 (sqrt PI)) * [misc]taylor: Taking taylor expansion of (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) in n * [misc]taylor: Taking taylor expansion of (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) in n * [misc]taylor: Taking taylor expansion of (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (pow (+ n n) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (+ n n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (+ n n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ n n)) in n * [misc]taylor: Taking taylor expansion of (+ n n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log 2))) into (* 1/2 (+ (log n) (log 2))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log 2)))) into (exp (* 1/2 (+ (log n) (log 2)))) * [misc]taylor: Taking taylor expansion of (pow (+ n n) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (+ n n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (+ n n))) in n * [misc]taylor: Taking taylor expansion of (/ k 2) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ k 2) into (* 1/2 k) * [misc]taylor: Taking taylor expansion of (log (+ n n)) in n * [misc]taylor: Taking taylor expansion of (+ n n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log n) (log 2))) into (* 1/2 (* k (+ (log n) (log 2)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* k (+ (log n) (log 2))))) into (exp (* 1/2 (* k (+ (log n) (log 2))))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) into (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) 1) into (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (log PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]backup-simplify: Simplify (* (log PI) (* 1/2 (- 1 k))) into (* 1/2 (* (- 1 k) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (log PI)))) into (exp (* 1/2 (* (- 1 k) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI))))) * [misc]taylor: Taking taylor expansion of (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) in n * [misc]taylor: Taking taylor expansion of (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) in n * [misc]taylor: Taking taylor expansion of (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (pow (+ n n) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (+ n n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (+ n n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ n n)) in n * [misc]taylor: Taking taylor expansion of (+ n n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log 2))) into (* 1/2 (+ (log n) (log 2))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log 2)))) into (exp (* 1/2 (+ (log n) (log 2)))) * [misc]taylor: Taking taylor expansion of (pow (+ n n) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (+ n n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (+ n n))) in n * [misc]taylor: Taking taylor expansion of (/ k 2) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ k 2) into (* 1/2 k) * [misc]taylor: Taking taylor expansion of (log (+ n n)) in n * [misc]taylor: Taking taylor expansion of (+ n n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log n) (log 2))) into (* 1/2 (* k (+ (log n) (log 2)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* k (+ (log n) (log 2))))) into (exp (* 1/2 (* k (+ (log n) (log 2))))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) into (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) 1) into (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (log PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]backup-simplify: Simplify (* (log PI) (* 1/2 (- 1 k))) into (* 1/2 (* (- 1 k) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (log PI)))) into (exp (* 1/2 (* (- 1 k) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (log PI)))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI))))) * [misc]backup-simplify: Simplify (* (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI)))))) into (* (/ (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (+ (log n) (log 2))))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) (sqrt (/ 1 k))) * [misc]taylor: Taking taylor expansion of (* (/ (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (+ (log n) (log 2))))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (/ (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (+ (log n) (log 2))))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) in k * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 k) (log PI)))) (exp (* 1/2 (+ (log n) (log 2))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (log PI)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (log PI))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (log PI)) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (* 1 (log PI)) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (+ (log n) (log 2)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (log n) (log 2))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (+ (log n) (log 2)) in k * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (log n) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log 2))) into (* 1/2 (+ (log n) (log 2))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log 2)))) into (exp (* 1/2 (+ (log n) (log 2)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* k (+ (log n) (log 2))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* k (+ (log n) (log 2)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* k (+ (log n) (log 2))) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log n) (log 2)) in k * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (log n) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* 0 (+ (log n) (log 2))) into 0 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (+ (log n) (log 2)))) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (+ (* 1/2 (+ (log n) (log 2))) (* 0 0)) into (+ (* 1/2 (log n)) (* 1/2 (log 2))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (* (pow PI 1/2) (exp (* 1/2 (+ (log n) (log 2))))) into (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))) * [misc]backup-simplify: Simplify (/ (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))) 1) into (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (* 0 (* 1/2 (- 1 k)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI))))) (/ 0 (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log n) (log 2)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log n) (log 2)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log n) (log 2))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log n) (log 2)))))) (+ (* (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) (/ 0 (exp (* 1/2 (* k (+ (log n) (log 2))))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) 0) (* 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log n) (log 2)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (log PI))) into (- (log PI)) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (log PI))) (* 0 (log PI))) into (- (* 1/2 (log PI))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) * [misc]backup-simplify: Simplify (+ (* (pow PI 1/2) 0) (* (* -1/2 (* (log PI) (sqrt PI))) (exp (* 1/2 (+ (log n) (log 2)))))) into (- (* 1/2 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI)))) * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log 2))) 1) 1)))) into (+ (* 1/2 (log n)) (* 1/2 (log 2))) * [misc]backup-simplify: Simplify (- (/ (- (* 1/2 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI)))) 1) (+ (* (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))) (/ (+ (* 1/2 (log n)) (* 1/2 (log 2))) 1)))) into (- (+ (* 1/2 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/2 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (* 1/2 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))))) * [misc]backup-simplify: Simplify (+ (* (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))) +nan.0) (* (- (+ (* 1/2 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/2 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (* 1/2 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))))) 0)) into (- (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))))) into (- (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (* 0 (* 1/2 (- 1 k))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log PI)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI))))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log 2))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (+ (log n) (log 2))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log n) (log 2))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log n) (log 2)))))) (+ (* (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) (/ 0 (exp (* 1/2 (* k (+ (log n) (log 2))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log n) (log 2))))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) 0) (+ (* 0 0) (* 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI)))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log 2))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (log PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (log PI))) (* 0 (log PI)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) * [misc]backup-simplify: Simplify (+ (* (pow PI 1/2) 0) (+ (* (* -1/2 (* (log PI) (sqrt PI))) 0) (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (exp (* 1/2 (+ (log n) (log 2))))))) into (* 1/8 (* (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (+ (log n) (log 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (+ (log n) (log 2))) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log 2))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log 2))) (* 1/8 (pow (log 2) 2)))) * [misc]backup-simplify: Simplify (- (/ (* 1/8 (* (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) 1) (+ (* (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))) (/ (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log 2))) (* 1/8 (pow (log 2) 2)))) 1)) (* (- (+ (* 1/2 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/2 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (* 1/2 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))))) (/ (+ (* 1/2 (log n)) (* 1/2 (log 2))) 1)))) into (+ (* 1/8 (* (sqrt PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/8 (* (sqrt PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/4 (* (sqrt PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (* 1/8 (* (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (+ (* 1/4 (* (* (log PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (* 1/4 (* (* (log PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI)))))))) * [misc]backup-simplify: Simplify (+ (* (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))) +nan.0) (+ (* (- (+ (* 1/2 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/2 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (* 1/2 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))))) +nan.0) (* (+ (* 1/8 (* (sqrt PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/8 (* (sqrt PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/4 (* (sqrt PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (* 1/8 (* (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (+ (* 1/4 (* (* (log PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (* 1/4 (* (* (log PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI)))))))) 0))) into (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))))))))))) into (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))))))))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 1/2 (- 1 k)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (log PI)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI))))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log 2)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log 2)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log n) (log 2))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log n) (log 2)))))) (+ (* (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) (/ 0 (exp (* 1/2 (* k (+ (log n) (log 2))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log n) (log 2))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log n) (log 2))))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (log PI))))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log 2)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (log PI))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (log PI))) (* 0 (log PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 3) 6)) (* (/ (pow (- (* 1/2 (log PI))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log PI) 3) (sqrt PI))) * [misc]backup-simplify: Simplify (+ (* (pow PI 1/2) 0) (+ (* (* -1/2 (* (log PI) (sqrt PI))) 0) (+ (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 0) (* (* -1/48 (* (pow (log PI) 3) (sqrt PI))) (exp (* 1/2 (+ (log n) (log 2)))))))) into (- (* 1/48 (* (* (pow (log PI) 3) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI)))) * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (+ (log n) (log 2)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (+ (log n) (log 2))) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log 2))) 3) 6)) (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log 2))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (+ (* 1/48 (pow (log n) 3)) (+ (* 1/48 (pow (log 2) 3)) (+ (* 1/16 (* (pow (log n) 2) (log 2))) (* 1/16 (* (log n) (pow (log 2) 2)))))) * [misc]backup-simplify: Simplify (- (/ (- (* 1/48 (* (* (pow (log PI) 3) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI)))) 1) (+ (* (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))) (/ (+ (* 1/48 (pow (log n) 3)) (+ (* 1/48 (pow (log 2) 3)) (+ (* 1/16 (* (pow (log n) 2) (log 2))) (* 1/16 (* (log n) (pow (log 2) 2)))))) 1)) (* (- (+ (* 1/2 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/2 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (* 1/2 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))))) (/ (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log 2))) (* 1/8 (pow (log 2) 2)))) 1)) (* (+ (* 1/8 (* (sqrt PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/8 (* (sqrt PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/4 (* (sqrt PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (* 1/8 (* (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (+ (* 1/4 (* (* (log PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (* 1/4 (* (* (log PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI)))))))) (/ (+ (* 1/2 (log n)) (* 1/2 (log 2))) 1)))) into (- (+ (* 1/16 (* (sqrt PI) (* (pow (log n) 2) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (* 1/16 (* (* (log PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/48 (* (sqrt PI) (* (pow (log 2) 3) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/16 (* (* (pow (log PI) 2) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/16 (* (* (log PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/16 (* (sqrt PI) (* (log n) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (* 1/8 (* (* (log PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (sqrt PI))) (+ (* 1/16 (* (* (pow (log PI) 2) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/48 (* (* (pow (log PI) 3) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (* 1/48 (* (sqrt PI) (* (pow (log n) 3) (exp (* 1/2 (+ (log n) (log 2))))))))))))))))) * [misc]backup-simplify: Simplify (+ (* (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))) +nan.0) (+ (* (- (+ (* 1/2 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/2 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (* 1/2 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))))) +nan.0) (+ (* (+ (* 1/8 (* (sqrt PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/8 (* (sqrt PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/4 (* (sqrt PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (* 1/8 (* (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (+ (* 1/4 (* (* (log PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (* 1/4 (* (* (log PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI)))))))) +nan.0) (* (- (+ (* 1/16 (* (sqrt PI) (* (pow (log n) 2) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (* 1/16 (* (* (log PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/48 (* (sqrt PI) (* (pow (log 2) 3) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (* 1/16 (* (* (pow (log PI) 2) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/16 (* (* (log PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/16 (* (sqrt PI) (* (log n) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (+ (* 1/8 (* (* (log PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (sqrt PI))) (+ (* 1/16 (* (* (pow (log PI) 2) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (+ (* 1/48 (* (* (pow (log PI) 3) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (* 1/48 (* (sqrt PI) (* (pow (log n) 3) (exp (* 1/2 (+ (log n) (log 2))))))))))))))))) 0)))) into (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (* +nan.0 (* (* (log PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI)))))))))))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (* +nan.0 (* (* (log PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI)))))))))))))))))))))) into (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (* +nan.0 (* (* (log PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI)))))))))))))))))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (* +nan.0 (* (* (log PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI)))))))))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (* (log PI) (exp (* 1/2 (+ (log n) (log 2))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))))))))))) (* k 1)) (- (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2))))))))) into (- (+ (* +nan.0 (* (sqrt PI) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* k (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log n) 2) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (log PI) (* (pow k 2) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log PI) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow k 2) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* (log 2) (* (exp (* 1/2 (+ (log n) (log 2)))) (pow k 2)))))) (- (+ (* +nan.0 (* (* (log PI) (* k (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow k 2) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (log PI) (* (log n) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2))))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* k (exp (* 1/2 (+ (log n) (log 2)))))))) (- (* +nan.0 (* (sqrt PI) (* k (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))))))))))))))))))))))))))))))))) * [misc]approximate: Taking taylor expansion of (* (/ (/ (pow (+ (/ 1 n) (/ 1 n)) (/ 1 2)) (pow (+ (/ 1 n) (/ 1 n)) (/ (/ 1 k) 2))) 1) (/ (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (/ (pow (+ (/ 1 n) (/ 1 n)) (/ 1 2)) (pow (+ (/ 1 n) (/ 1 n)) (/ (/ 1 k) 2))) 1) (/ (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of (/ (/ (pow (+ (/ 1 n) (/ 1 n)) (/ 1 2)) (pow (+ (/ 1 n) (/ 1 n)) (/ (/ 1 k) 2))) 1) in k * [misc]taylor: Taking taylor expansion of (/ (pow (+ (/ 1 n) (/ 1 n)) (/ 1 2)) (pow (+ (/ 1 n) (/ 1 n)) (/ (/ 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (+ (/ 1 n) (/ 1 n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (+ (/ 1 n) (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (/ 1 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 n) (/ 1 n))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]backup-simplify: Simplify (+ (/ 1 n) (/ 1 n)) into (* 2 (/ 1 n)) * [misc]backup-simplify: Simplify (log (* 2 (/ 1 n))) into (log (/ 2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ 2 n))) into (* 1/2 (log (/ 2 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (/ 2 n)))) into (pow (/ 2 n) 1/2) * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ (/ 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (+ (/ 1 n) (/ 1 n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (+ (/ 1 n) (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 n) (/ 1 n))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]backup-simplify: Simplify (+ (/ 1 n) (/ 1 n)) into (* 2 (/ 1 n)) * [misc]backup-simplify: Simplify (log (* 2 (/ 1 n))) into (log (/ 2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ 2 n))) into (* 1/2 (log (/ 2 n))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 k) 2) (log (+ (/ 1 n) (/ 1 n))))) into (exp (* 1/2 (/ (log (* 2 (/ 1 n))) k))) * [misc]backup-simplify: Simplify (/ (pow (/ 2 n) 1/2) (exp (* 1/2 (/ (log (* 2 (/ 1 n))) k)))) into (* (sqrt (/ 2 n)) (/ 1 (exp (* 1/2 (/ (log (/ 2 n)) k))))) * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (* (sqrt (/ 2 n)) (/ 1 (exp (* 1/2 (/ (log (/ 2 n)) k))))) 1) into (* (sqrt (/ 1 n)) (/ (sqrt 2) (exp (* 1/2 (/ (log (/ 2 n)) k))))) * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) in k * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]backup-simplify: Simplify (* (log PI) -1/2) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) into (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) * [misc]taylor: Taking taylor expansion of (* (/ (/ (pow (+ (/ 1 n) (/ 1 n)) (/ 1 2)) (pow (+ (/ 1 n) (/ 1 n)) (/ (/ 1 k) 2))) 1) (/ (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ (pow (+ (/ 1 n) (/ 1 n)) (/ 1 2)) (pow (+ (/ 1 n) (/ 1 n)) (/ (/ 1 k) 2))) 1) in n * [misc]taylor: Taking taylor expansion of (/ (pow (+ (/ 1 n) (/ 1 n)) (/ 1 2)) (pow (+ (/ 1 n) (/ 1 n)) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (+ (/ 1 n) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (+ (/ 1 n) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 n) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log 2) (log n))) into (* 1/2 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log 2) (log n)))) into (exp (* 1/2 (- (log 2) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (+ (/ 1 n) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (+ (/ 1 n) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ 1 k) 2) into (/ 1/2 k) * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 n) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log 2) (log n))) into (* 1/2 (/ (- (log 2) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log 2) (log n)) k))) into (exp (* 1/2 (/ (- (log 2) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) into (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) 1) into (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) in n * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (log PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]backup-simplify: Simplify (* (log PI) (* 1/2 (- 1 (/ 1 k)))) into (* 1/2 (* (log PI) (- 1 (/ 1 k)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) into (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) (sqrt (/ 1 k))) into (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) * [misc]taylor: Taking taylor expansion of (* (/ (/ (pow (+ (/ 1 n) (/ 1 n)) (/ 1 2)) (pow (+ (/ 1 n) (/ 1 n)) (/ (/ 1 k) 2))) 1) (/ (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ (pow (+ (/ 1 n) (/ 1 n)) (/ 1 2)) (pow (+ (/ 1 n) (/ 1 n)) (/ (/ 1 k) 2))) 1) in n * [misc]taylor: Taking taylor expansion of (/ (pow (+ (/ 1 n) (/ 1 n)) (/ 1 2)) (pow (+ (/ 1 n) (/ 1 n)) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (+ (/ 1 n) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (+ (/ 1 n) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 n) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log 2) (log n))) into (* 1/2 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log 2) (log n)))) into (exp (* 1/2 (- (log 2) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (+ (/ 1 n) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (+ (/ 1 n) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ 1 k) 2) into (/ 1/2 k) * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 n) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log 2) (log n))) into (* 1/2 (/ (- (log 2) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log 2) (log n)) k))) into (exp (* 1/2 (/ (- (log 2) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) into (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) 1) into (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 (/ 1 k)) 2))) in n * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (log PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]backup-simplify: Simplify (* (log PI) (* 1/2 (- 1 (/ 1 k)))) into (* 1/2 (* (log PI) (- 1 (/ 1 k)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) into (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) (sqrt (/ 1 k))) into (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) * [misc]backup-simplify: Simplify (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) into (* (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (* (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) in k * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (- (log 2) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (- (log 2) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (- (log 2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log 2) (log n))) into (* 1/2 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log 2) (log n)))) into (exp (* 1/2 (- (log 2) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log PI) (- 1 (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (log PI) (- 1 (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (* (log PI) -1) into (* -1 (log PI)) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (log PI))) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) into (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log 2) (log n)) k))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log 2) (log n)) k)) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ (- (log 2) (log n)) k) in k * [misc]taylor: Taking taylor expansion of (- (log 2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (/ (- (log 2) (log n)) 1) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log 2) (log n))) into (* 1/2 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log 2) (log n)) k))) into (exp (* 1/2 (/ (- (log 2) (log n)) k))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) into (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) * [misc]backup-simplify: Simplify (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) into (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (* 0 (* 1/2 (- 1 (/ 1 k))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) 0) (* 0 (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (- (log 2) (log n)))) 0) (* 0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (+ (* (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))))) into (- (* +nan.0 (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (* 0 (* 1/2 (- 1 (/ 1 k)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) 0) (+ (* 0 0) (* 0 (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (- (log 2) (log n)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (+ (* (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))))) into (- (* +nan.0 (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 1/2 (- 1 (/ 1 k))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log 2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt k) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log 2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (- (log 2) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (+ (* (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))))) into (- (* +nan.0 (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow k 2)))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) k))) (- (* +nan.0 (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow k 3))))))))) * [misc]approximate: Taking taylor expansion of (* (/ (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ 1 2)) (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (/ 1 (- k)) 2))) 1) (/ (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k))))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (/ (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ 1 2)) (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (/ 1 (- k)) 2))) 1) (/ (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k))))) in k * [misc]taylor: Taking taylor expansion of (/ (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ 1 2)) (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (/ 1 (- k)) 2))) 1) in k * [misc]taylor: Taking taylor expansion of (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ 1 2)) (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (/ 1 (- k)) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (+ (/ 1 (- n)) (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (/ 1 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 (- n)) (/ 1 (- n)))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]backup-simplify: Simplify (+ (/ -1 n) (/ -1 n)) into (- (* 2 (/ 1 n))) * [misc]backup-simplify: Simplify (log (- (* 2 (/ 1 n)))) into (log (- (* 2 (/ 1 n)))) * [misc]backup-simplify: Simplify (* 1/2 (log (- (* 2 (/ 1 n))))) into (* 1/2 (log (- (* 2 (/ 1 n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (- (* 2 (/ 1 n)))))) into (pow (- (* 2 (/ 1 n))) 1/2) * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (/ 1 (- k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (+ (/ 1 (- n)) (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 (- n)) (/ 1 (- n)))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]backup-simplify: Simplify (+ (/ -1 n) (/ -1 n)) into (- (* 2 (/ 1 n))) * [misc]backup-simplify: Simplify (log (- (* 2 (/ 1 n)))) into (log (- (* 2 (/ 1 n)))) * [misc]backup-simplify: Simplify (* -1/2 (log (- (* 2 (/ 1 n))))) into (* -1/2 (log (- (* 2 (/ 1 n))))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 (- k)) 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) into (exp (* -1/2 (/ (log (- (* 2 (/ 1 n)))) k))) * [misc]backup-simplify: Simplify (/ (pow (- (* 2 (/ 1 n))) 1/2) (exp (* -1/2 (/ (log (- (* 2 (/ 1 n)))) k)))) into (* (sqrt (/ -2 n)) (/ 1 (exp (* -1/2 (/ (log (- (* 2 (/ 1 n)))) k))))) * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (* (sqrt (/ -2 n)) (/ 1 (exp (* -1/2 (/ (log (- (* 2 (/ 1 n)))) k))))) 1) into (/ (sqrt (/ -2 n)) (exp (* -1/2 (/ (log (- (* 2 (/ 1 n)))) k)))) * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) in k * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]backup-simplify: Simplify (* (log PI) 1/2) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) * [misc]taylor: Taking taylor expansion of (* (/ (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ 1 2)) (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (/ 1 (- k)) 2))) 1) (/ (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k))))) in n * [misc]taylor: Taking taylor expansion of (/ (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ 1 2)) (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (/ 1 (- k)) 2))) 1) in n * [misc]taylor: Taking taylor expansion of (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ 1 2)) (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (+ (/ 1 (- n)) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 (- n)) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (+ -1 -1) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log -2) (log n)))) into (exp (* 1/2 (- (log -2) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (+ (/ 1 (- n)) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ -1 k) 2) into (/ -1/2 k) * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 (- n)) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (+ -1 -1) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log -2) (log n))) into (* -1/2 (/ (- (log -2) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log -2) (log n)) k))) into (exp (* -1/2 (/ (- (log -2) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) into (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) 1) into (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) in n * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (log PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]backup-simplify: Simplify (* (log PI) (* 1/2 (+ 1 (/ 1 k)))) into (* 1/2 (* (+ 1 (/ 1 k)) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (* (/ (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ 1 2)) (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (/ 1 (- k)) 2))) 1) (/ (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k))))) in n * [misc]taylor: Taking taylor expansion of (/ (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ 1 2)) (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (/ 1 (- k)) 2))) 1) in n * [misc]taylor: Taking taylor expansion of (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ 1 2)) (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (+ (/ 1 (- n)) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 (- n)) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (+ -1 -1) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log -2) (log n)))) into (exp (* 1/2 (- (log -2) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (+ (/ 1 (- n)) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ -1 k) 2) into (/ -1/2 k) * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 (- n)) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (+ -1 -1) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log -2) (log n))) into (* -1/2 (/ (- (log -2) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log -2) (log n)) k))) into (exp (* -1/2 (/ (- (log -2) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) into (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) 1) into (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (/ (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (exp (* (log PI) (/ (- 1 (/ 1 (- k))) 2))) in n * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (log PI) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]backup-simplify: Simplify (* (log PI) (* 1/2 (+ 1 (/ 1 k)))) into (* 1/2 (* (+ 1 (/ 1 k)) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k))) * [misc]backup-simplify: Simplify (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k)))) into (/ (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt (/ -1 k)))) * [misc]taylor: Taking taylor expansion of (/ (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt (/ -1 k)))) in k * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (- (log -2) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (- (log -2) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (- (log -2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log -2) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log -2) (log n)))) into (exp (* 1/2 (- (log -2) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log PI))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (log PI)) in k * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (* 1 (log PI)) into (log PI) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (sqrt (/ -1 k))) in k * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log -2) (log n)) k))) in k * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log -2) (log n)) k)) in k * [misc]taylor: Taking taylor expansion of -1/2 in k * [misc]backup-simplify: Simplify -1/2 into -1/2 * [misc]taylor: Taking taylor expansion of (/ (- (log -2) (log n)) k) in k * [misc]taylor: Taking taylor expansion of (- (log -2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log -2) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (/ (- (log -2) (log n)) 1) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* -1/2 (- (log -2) (log n))) into (* -1/2 (- (log -2) (log n))) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log -2) (log n)) k))) into (exp (* -1/2 (/ (- (log -2) (log n)) k))) * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k * [misc]taylor: Taking taylor expansion of (/ -1 k) in k * [misc]taylor: Taking taylor expansion of -1 in k * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ -1 1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) into (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) 0) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))) * [misc]backup-simplify: Simplify (/ (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log -2) (log n)) k)))))) into (* +nan.0 (/ (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (exp (* -1/2 (/ (- (log -2) (log n)) k))))) * [misc]backup-simplify: Simplify (* +nan.0 (/ (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (exp (* -1/2 (/ (- (log -2) (log n)) k))))) into (* +nan.0 (/ (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (exp (* -1/2 (/ (- (log -2) (log n)) k))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (* 0 (* 1/2 (+ 1 (/ 1 k))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log -2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log -2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) 0) (* 0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log -2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (- (log -2) (log n)))) 0) (* 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))) * [misc]backup-simplify: Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log -2) (log n)) k)))))) (+ (* (* +nan.0 (/ (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (exp (* -1/2 (/ (- (log -2) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))))))) into (- (* +nan.0 (/ (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))))) into (- (* +nan.0 (/ (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (* 0 (* 1/2 (+ 1 (/ 1 k)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))) (* 0 (/ 0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) 0) (+ (* 0 0) (* 0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (sqrt (/ -1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (- (log -2) (log n)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))) * [misc]backup-simplify: Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log -2) (log n)) k)))))) (+ (* (* +nan.0 (/ (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (exp (* -1/2 (/ (- (log -2) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))))) (* (- (* +nan.0 (/ (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))))))) into (- (* +nan.0 (/ (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))))) into (- (* +nan.0 (/ (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (/ (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))))) (* (/ 1 (- k)) 1)) (* +nan.0 (/ (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (exp (* -1/2 (/ (- (log -2) (log n)) k))))))) into (- (+ (* +nan.0 (/ (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) k))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (pow k 2)))) (- (* +nan.0 (/ (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))))))))) * * * * [misc]progress: [ 3 / 4 ] generating series at (2 1 1) * [misc]approximate: Taking taylor expansion of (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) in k * [misc]taylor: Taking taylor expansion of (pow (+ n n) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (+ n n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (+ n n))) in k * [misc]taylor: Taking taylor expansion of (/ 1 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ n n)) in k * [misc]taylor: Taking taylor expansion of (+ n n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (+ n n) into (* 2 n) * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) * [misc]taylor: Taking taylor expansion of (pow (+ n n) (/ k 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (+ n n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (+ n n))) in k * [misc]taylor: Taking taylor expansion of (/ k 2) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ n n)) in k * [misc]taylor: Taking taylor expansion of (+ n n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (+ n n) into (* 2 n) * [misc]backup-simplify: Simplify (log (* 2 n)) into (log (* 2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (/ (pow (* 2 n) 1/2) 1) into (sqrt (* n 2)) * [misc]taylor: Taking taylor expansion of (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (pow (+ n n) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (+ n n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (+ n n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ n n)) in n * [misc]taylor: Taking taylor expansion of (+ n n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log 2))) into (* 1/2 (+ (log n) (log 2))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log 2)))) into (exp (* 1/2 (+ (log n) (log 2)))) * [misc]taylor: Taking taylor expansion of (pow (+ n n) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (+ n n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (+ n n))) in n * [misc]taylor: Taking taylor expansion of (/ k 2) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ k 2) into (* 1/2 k) * [misc]taylor: Taking taylor expansion of (log (+ n n)) in n * [misc]taylor: Taking taylor expansion of (+ n n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log n) (log 2))) into (* 1/2 (* k (+ (log n) (log 2)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* k (+ (log n) (log 2))))) into (exp (* 1/2 (* k (+ (log n) (log 2))))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) into (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) * [misc]taylor: Taking taylor expansion of (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (pow (+ n n) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (+ n n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (+ n n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ n n)) in n * [misc]taylor: Taking taylor expansion of (+ n n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log 2))) into (* 1/2 (+ (log n) (log 2))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log 2)))) into (exp (* 1/2 (+ (log n) (log 2)))) * [misc]taylor: Taking taylor expansion of (pow (+ n n) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (+ n n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (+ n n))) in n * [misc]taylor: Taking taylor expansion of (/ k 2) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ k 2) into (* 1/2 k) * [misc]taylor: Taking taylor expansion of (log (+ n n)) in n * [misc]taylor: Taking taylor expansion of (+ n n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log n) (log 2))) into (* 1/2 (* k (+ (log n) (log 2)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* k (+ (log n) (log 2))))) into (exp (* 1/2 (* k (+ (log n) (log 2))))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) into (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (+ (log n) (log 2)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (log n) (log 2))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (+ (log n) (log 2)) in k * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (log n) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log 2))) into (* 1/2 (+ (log n) (log 2))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log 2)))) into (exp (* 1/2 (+ (log n) (log 2)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* k (+ (log n) (log 2))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* k (+ (log n) (log 2)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* k (+ (log n) (log 2))) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log n) (log 2)) in k * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (log n) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (* 0 (+ (log n) (log 2))) into 0 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (+ (log n) (log 2)))) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (+ (* 1/2 (+ (log n) (log 2))) (* 0 0)) into (+ (* 1/2 (log n)) (* 1/2 (log 2))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log n) (log 2)))) 1) into (exp (* 1/2 (+ (log n) (log 2)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log 2)))) into (exp (* 1/2 (+ (log n) (log 2)))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log n) (log 2)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log n) (log 2)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log n) (log 2))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log n) (log 2)))))) (+ (* (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) (/ 0 (exp (* 1/2 (* k (+ (log n) (log 2))))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log n) (log 2)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log 2))) 1) 1)))) into (+ (* 1/2 (log n)) (* 1/2 (log 2))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log n) (log 2)))) (/ (+ (* 1/2 (log n)) (* 1/2 (log 2))) 1)))) into (- (+ (* 1/2 (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (* 1/2 (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))))) * [misc]backup-simplify: Simplify (- (+ (* 1/2 (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (* 1/2 (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))))) into (- (+ (* 1/2 (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (* 1/2 (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))))) * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log 2))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log n) (log 2)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (+ (log n) (log 2))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log n) (log 2))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log n) (log 2)))))) (+ (* (/ (exp (* 1/2 (+ (log n) (log 2)))) (exp (* 1/2 (* k (+ (log n) (log 2)))))) (/ 0 (exp (* 1/2 (* k (+ (log n) (log 2))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log n) (log 2))))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log 2))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log 2)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (+ (log n) (log 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (+ (log n) (log 2))) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log 2))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log 2))) (* 1/8 (pow (log 2) 2)))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log n) (log 2)))) (/ (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log 2))) (* 1/8 (pow (log 2) 2)))) 1)) (* (- (+ (* 1/2 (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (* 1/2 (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))))) (/ (+ (* 1/2 (log n)) (* 1/2 (log 2))) 1)))) into (+ (* 1/8 (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))) (+ (* 1/4 (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (* 1/8 (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2)))))))) * [misc]backup-simplify: Simplify (+ (* 1/8 (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))) (+ (* 1/4 (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (* 1/8 (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2)))))))) into (+ (* 1/8 (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))) (+ (* 1/4 (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (* 1/8 (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2)))))))) * [misc]backup-simplify: Simplify (+ (* (+ (* 1/8 (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))) (+ (* 1/4 (* (log n) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (* 1/8 (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (pow (* k 1) 2)) (+ (* (- (+ (* 1/2 (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))) (* 1/2 (* (log n) (exp (* 1/2 (+ (log n) (log 2)))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log 2)))))) into (- (+ (* 1/4 (* (log n) (* (log 2) (* (exp (* 1/2 (+ (log n) (log 2)))) (pow k 2))))) (+ (* 1/8 (* (pow (log n) 2) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (exp (* 1/2 (+ (log n) (log 2)))) (* 1/8 (* (pow k 2) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))))))) (+ (* 1/2 (* (log n) (* k (exp (* 1/2 (+ (log n) (log 2))))))) (* 1/2 (* k (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))))) * [misc]approximate: Taking taylor expansion of (/ (pow (+ (/ 1 n) (/ 1 n)) (/ 1 2)) (pow (+ (/ 1 n) (/ 1 n)) (/ (/ 1 k) 2))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (+ (/ 1 n) (/ 1 n)) (/ 1 2)) (pow (+ (/ 1 n) (/ 1 n)) (/ (/ 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (+ (/ 1 n) (/ 1 n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (+ (/ 1 n) (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (/ 1 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 n) (/ 1 n))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]backup-simplify: Simplify (+ (/ 1 n) (/ 1 n)) into (* 2 (/ 1 n)) * [misc]backup-simplify: Simplify (log (* 2 (/ 1 n))) into (log (/ 2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ 2 n))) into (* 1/2 (log (/ 2 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (/ 2 n)))) into (pow (/ 2 n) 1/2) * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ (/ 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (+ (/ 1 n) (/ 1 n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (+ (/ 1 n) (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 n) (/ 1 n))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]backup-simplify: Simplify (+ (/ 1 n) (/ 1 n)) into (* 2 (/ 1 n)) * [misc]backup-simplify: Simplify (log (* 2 (/ 1 n))) into (log (/ 2 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ 2 n))) into (* 1/2 (log (/ 2 n))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 k) 2) (log (+ (/ 1 n) (/ 1 n))))) into (exp (* 1/2 (/ (log (* 2 (/ 1 n))) k))) * [misc]backup-simplify: Simplify (/ (pow (/ 2 n) 1/2) (exp (* 1/2 (/ (log (* 2 (/ 1 n))) k)))) into (* (sqrt (/ 2 n)) (/ 1 (exp (* 1/2 (/ (log (/ 2 n)) k))))) * [misc]taylor: Taking taylor expansion of (/ (pow (+ (/ 1 n) (/ 1 n)) (/ 1 2)) (pow (+ (/ 1 n) (/ 1 n)) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (+ (/ 1 n) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (+ (/ 1 n) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 n) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log 2) (log n))) into (* 1/2 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log 2) (log n)))) into (exp (* 1/2 (- (log 2) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (+ (/ 1 n) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (+ (/ 1 n) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ 1 k) 2) into (/ 1/2 k) * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 n) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log 2) (log n))) into (* 1/2 (/ (- (log 2) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log 2) (log n)) k))) into (exp (* 1/2 (/ (- (log 2) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) into (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (/ (pow (+ (/ 1 n) (/ 1 n)) (/ 1 2)) (pow (+ (/ 1 n) (/ 1 n)) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (+ (/ 1 n) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (+ (/ 1 n) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 n) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log 2) (log n))) into (* 1/2 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log 2) (log n)))) into (exp (* 1/2 (- (log 2) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 n) (/ 1 n)) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (+ (/ 1 n) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (+ (/ 1 n) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ 1 k) 2) into (/ 1/2 k) * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 n) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 n) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (+ 1 1) into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log 2) (log n))) into (* 1/2 (/ (- (log 2) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log 2) (log n)) k))) into (exp (* 1/2 (/ (- (log 2) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) into (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (- (log 2) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (- (log 2) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (- (log 2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log 2) (log n))) into (* 1/2 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log 2) (log n)))) into (exp (* 1/2 (- (log 2) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log 2) (log n)) k))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log 2) (log n)) k)) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ (- (log 2) (log n)) k) in k * [misc]taylor: Taking taylor expansion of (- (log 2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (/ (- (log 2) (log n)) 1) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log 2) (log n))) into (* 1/2 (- (log 2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log 2) (log n)) k))) into (exp (* 1/2 (/ (- (log 2) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) into (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) into (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log 2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log 2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log 2) (log n)) k))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) into (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) * [misc]approximate: Taking taylor expansion of (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ 1 2)) (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (/ 1 (- k)) 2))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ 1 2)) (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (/ 1 (- k)) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (+ (/ 1 (- n)) (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (/ 1 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 (- n)) (/ 1 (- n)))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]backup-simplify: Simplify (+ (/ -1 n) (/ -1 n)) into (- (* 2 (/ 1 n))) * [misc]backup-simplify: Simplify (log (- (* 2 (/ 1 n)))) into (log (- (* 2 (/ 1 n)))) * [misc]backup-simplify: Simplify (* 1/2 (log (- (* 2 (/ 1 n))))) into (* 1/2 (log (- (* 2 (/ 1 n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (- (* 2 (/ 1 n)))))) into (pow (- (* 2 (/ 1 n))) 1/2) * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (/ 1 (- k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (+ (/ 1 (- n)) (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 2) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 (- n)) (/ 1 (- n)))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]backup-simplify: Simplify (+ (/ -1 n) (/ -1 n)) into (- (* 2 (/ 1 n))) * [misc]backup-simplify: Simplify (log (- (* 2 (/ 1 n)))) into (log (- (* 2 (/ 1 n)))) * [misc]backup-simplify: Simplify (* -1/2 (log (- (* 2 (/ 1 n))))) into (* -1/2 (log (- (* 2 (/ 1 n))))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 (- k)) 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) into (exp (* -1/2 (/ (log (- (* 2 (/ 1 n)))) k))) * [misc]backup-simplify: Simplify (/ (pow (- (* 2 (/ 1 n))) 1/2) (exp (* -1/2 (/ (log (- (* 2 (/ 1 n)))) k)))) into (* (sqrt (/ -2 n)) (/ 1 (exp (* -1/2 (/ (log (- (* 2 (/ 1 n)))) k))))) * [misc]taylor: Taking taylor expansion of (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ 1 2)) (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (+ (/ 1 (- n)) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 (- n)) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (+ -1 -1) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log -2) (log n)))) into (exp (* 1/2 (- (log -2) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (+ (/ 1 (- n)) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ -1 k) 2) into (/ -1/2 k) * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 (- n)) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (+ -1 -1) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log -2) (log n))) into (* -1/2 (/ (- (log -2) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log -2) (log n)) k))) into (exp (* -1/2 (/ (- (log -2) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) into (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (/ (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ 1 2)) (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (+ (/ 1 (- n)) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 (- n)) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (+ -1 -1) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log -2) (log n)))) into (exp (* 1/2 (- (log -2) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (+ (/ 1 (- n)) (/ 1 (- n))) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (+ (/ 1 (- n)) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (+ (/ 1 (- n)) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ -1 k) 2) into (/ -1/2 k) * [misc]taylor: Taking taylor expansion of (log (+ (/ 1 (- n)) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (+ (/ 1 (- n)) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (+ -1 -1) into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log -2) (log n))) into (* -1/2 (/ (- (log -2) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log -2) (log n)) k))) into (exp (* -1/2 (/ (- (log -2) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) into (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (- (log -2) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (- (log -2) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (- (log -2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log -2) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log -2) (log n)))) into (exp (* 1/2 (- (log -2) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log -2) (log n)) k))) in k * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log -2) (log n)) k)) in k * [misc]taylor: Taking taylor expansion of -1/2 in k * [misc]backup-simplify: Simplify -1/2 into -1/2 * [misc]taylor: Taking taylor expansion of (/ (- (log -2) (log n)) k) in k * [misc]taylor: Taking taylor expansion of (- (log -2) (log n)) in k * [misc]taylor: Taking taylor expansion of (log -2) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]backup-simplify: Simplify (log -2) into (log -2) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (/ (- (log -2) (log n)) 1) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (* -1/2 (- (log -2) (log n))) into (* -1/2 (- (log -2) (log n))) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log -2) (log n)) k))) into (exp (* -1/2 (/ (- (log -2) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) into (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) into (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log -2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log -2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log -2) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))) (* 0 (/ 0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))) (* 0 (/ 0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log -2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -2 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -2) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))) (* 0 (/ 0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))) (* 0 (/ 0 (exp (* -1/2 (/ (- (log -2) (log n)) k))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) into (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2 1 1) * [misc]approximate: Taking taylor expansion of (* (log PI) (/ (- 1 k) 2)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]backup-simplify: Simplify (* (log PI) 1/2) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (/ -1 2) (+ (* 1/2 (/ 0 2)))) into -1/2 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) -1/2) (* 0 1/2)) into (- (* 1/2 (log PI))) * [misc]backup-simplify: Simplify (- (* 1/2 (log PI))) into (- (* 1/2 (log PI))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 -1/2) (* 0 1/2))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 -1/2) (* 0 1/2)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow PI 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow PI 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow PI 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow PI 1)))) 24) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 -1/2) (* 0 1/2))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow PI 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow PI 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow PI 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow PI 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow PI 1)))) 120) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 -1/2) (* 0 1/2)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow PI 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow PI 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow PI 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow PI 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow PI 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow PI 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow PI 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow PI 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow PI 1)))) 720) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 -1/2) (* 0 1/2))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 720 (/ (* (pow (* 1 0) 7)) (pow PI 7))) (* -2520 (/ (* (pow (* 1 0) 5) (pow (* 2 0) 1)) (pow PI 6))) (* 2520 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 2)) (pow PI 5))) (* 840 (/ (* (pow (* 1 0) 4) 1 (pow (* 6 0) 1)) (pow PI 5))) (* -630 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 3)) (pow PI 4))) (* -1260 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 4))) (* -210 (/ (* (pow (* 1 0) 3) 1 1 (pow (* 24 0) 1)) (pow PI 4))) (* 210 (/ (* 1 (pow (* 2 0) 2) (pow (* 6 0) 1)) (pow PI 3))) (* 140 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 2)) (pow PI 3))) (* 210 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow PI 3))) (* 42 (/ (* (pow (* 1 0) 2) 1 1 1 (pow (* 120 0) 1)) (pow PI 3))) (* -35 (/ (* 1 1 (pow (* 6 0) 1) (pow (* 24 0) 1)) (pow PI 2))) (* -21 (/ (* 1 (pow (* 2 0) 1) 1 1 (pow (* 120 0) 1)) (pow PI 2))) (* -7 (/ (* (pow (* 1 0) 1) 1 1 1 1 (pow (* 720 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 1 1 (pow (* 5040 0) 1)) (pow PI 1)))) 5040) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 -1/2) (* 0 1/2)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* (- (* 1/2 (log PI))) k) (* 1/2 (log PI))) into (- (* 1/2 (log PI)) (* 1/2 (* (log PI) k))) * [misc]approximate: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 k)) 2)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]backup-simplify: Simplify (* (log PI) -1/2) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (- (/ 1 2) (+ (* -1/2 (/ 0 2)))) into 1/2 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 1/2) (* 0 -1/2)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* -1/2 (/ 0 2)) (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 1/2) (* 0 -1/2))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* -1/2 (/ 0 2)) (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 1/2) (* 0 -1/2)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* -1/2 (/ 0 2)) (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow PI 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow PI 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow PI 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow PI 1)))) 24) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1/2) (* 0 -1/2))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* -1/2 (/ 0 2)) (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow PI 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow PI 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow PI 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow PI 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow PI 1)))) 120) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1/2) (* 0 -1/2)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* -1/2 (/ 0 2)) (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow PI 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow PI 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow PI 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow PI 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow PI 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow PI 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow PI 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow PI 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow PI 1)))) 720) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1/2) (* 0 -1/2))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* -1/2 (/ 0 2)) (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 720 (/ (* (pow (* 1 0) 7)) (pow PI 7))) (* -2520 (/ (* (pow (* 1 0) 5) (pow (* 2 0) 1)) (pow PI 6))) (* 2520 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 2)) (pow PI 5))) (* 840 (/ (* (pow (* 1 0) 4) 1 (pow (* 6 0) 1)) (pow PI 5))) (* -630 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 3)) (pow PI 4))) (* -1260 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 4))) (* -210 (/ (* (pow (* 1 0) 3) 1 1 (pow (* 24 0) 1)) (pow PI 4))) (* 210 (/ (* 1 (pow (* 2 0) 2) (pow (* 6 0) 1)) (pow PI 3))) (* 140 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 2)) (pow PI 3))) (* 210 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow PI 3))) (* 42 (/ (* (pow (* 1 0) 2) 1 1 1 (pow (* 120 0) 1)) (pow PI 3))) (* -35 (/ (* 1 1 (pow (* 6 0) 1) (pow (* 24 0) 1)) (pow PI 2))) (* -21 (/ (* 1 (pow (* 2 0) 1) 1 1 (pow (* 120 0) 1)) (pow PI 2))) (* -7 (/ (* (pow (* 1 0) 1) 1 1 1 1 (pow (* 720 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 1 1 (pow (* 5040 0) 1)) (pow PI 1)))) 5040) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1/2) (* 0 -1/2)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 (log PI)) (* (* -1/2 (log PI)) (/ 1 (/ 1 k)))) into (- (* 1/2 (log PI)) (* 1/2 (* (log PI) k))) * [misc]approximate: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 (- k))) 2)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (* (log PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]backup-simplify: Simplify (* (log PI) 1/2) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (- (/ 1 2) (+ (* 1/2 (/ 0 2)))) into 1/2 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 1/2) (* 0 1/2)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 1/2) (* 0 1/2))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 1/2) (* 0 1/2)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow PI 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow PI 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow PI 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow PI 1)))) 24) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1/2) (* 0 1/2))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow PI 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow PI 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow PI 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow PI 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow PI 1)))) 120) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1/2) (* 0 1/2)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow PI 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow PI 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow PI 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow PI 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow PI 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow PI 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow PI 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow PI 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow PI 1)))) 720) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1/2) (* 0 1/2))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 720 (/ (* (pow (* 1 0) 7)) (pow PI 7))) (* -2520 (/ (* (pow (* 1 0) 5) (pow (* 2 0) 1)) (pow PI 6))) (* 2520 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 2)) (pow PI 5))) (* 840 (/ (* (pow (* 1 0) 4) 1 (pow (* 6 0) 1)) (pow PI 5))) (* -630 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 3)) (pow PI 4))) (* -1260 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow PI 4))) (* -210 (/ (* (pow (* 1 0) 3) 1 1 (pow (* 24 0) 1)) (pow PI 4))) (* 210 (/ (* 1 (pow (* 2 0) 2) (pow (* 6 0) 1)) (pow PI 3))) (* 140 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 2)) (pow PI 3))) (* 210 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow PI 3))) (* 42 (/ (* (pow (* 1 0) 2) 1 1 1 (pow (* 120 0) 1)) (pow PI 3))) (* -35 (/ (* 1 1 (pow (* 6 0) 1) (pow (* 24 0) 1)) (pow PI 2))) (* -21 (/ (* 1 (pow (* 2 0) 1) 1 1 (pow (* 120 0) 1)) (pow PI 2))) (* -7 (/ (* (pow (* 1 0) 1) 1 1 1 1 (pow (* 720 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 1 1 1 1 (pow (* 5040 0) 1)) (pow PI 1)))) 5040) into 0 * [misc]backup-simplify: Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1/2) (* 0 1/2)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 (log PI)) (* (* 1/2 (log PI)) (/ 1 (/ 1 (- k))))) into (- (* 1/2 (log PI)) (* 1/2 (* (log PI) k))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 176 ] simplifiying candidate # * * * * [misc]progress: [ 2 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * * [misc]simplify: iters left: 2 (30 enodes) * * [misc]simplify: iters left: 1 (35 enodes) * [exit]simplify: Simplified to (- (* (/ (log PI) 2) (- 1 k)) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (log PI) 2) (- 1 k)) (log (sqrt k))) * * * * [misc]progress: [ 3 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * * [misc]simplify: iters left: 1 (74 enodes) * [exit]simplify: Simplified to (- (* (log (sqrt PI)) (- 1 k)) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (log (sqrt PI)) (- 1 k)) (log (sqrt k))) * * * * [misc]progress: [ 4 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (exp (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * [exit]simplify: Simplified to (exp (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * * * * [misc]progress: [ 5 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (exp (* (log PI) (/ (- 1 k) 2))) (exp (* (log PI) (/ (- 1 k) 2)))) (exp (* (log PI) (/ (- 1 k) 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (124 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (291 enodes) * [exit]simplify: Simplified to (/ (pow (pow (sqrt PI) (- 1 k)) 3) (* (sqrt k) k)) * [exit]simplify: Simplified to (/ (pow (pow (sqrt PI) (- 1 k)) 3) (* (sqrt k) k)) * * * * [misc]progress: [ 6 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) (cbrt (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * * [misc]simplify: iters left: 1 (58 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (sqrt (pow PI (- 1 k))) (sqrt k))) (cbrt (/ (sqrt (pow PI (- 1 k))) (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ (sqrt (pow PI (- 1 k))) (sqrt k))) (cbrt (/ (sqrt (pow PI (- 1 k))) (sqrt k)))) * [enter]simplify: Simplifying (cbrt (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (cbrt (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * [exit]simplify: Simplified to (cbrt (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * * * * [misc]progress: [ 7 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (110 enodes) * * [misc]simplify: iters left: 1 (172 enodes) * [exit]simplify: Simplified to (pow (/ (pow (sqrt PI) (- 1 k)) (sqrt k)) 3) * [exit]simplify: Simplified to (pow (/ (pow (sqrt PI) (- 1 k)) (sqrt k)) 3) * * * * [misc]progress: [ 8 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* (log PI) (- 1 k))) k) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * [exit]simplify: Simplified to (/ (pow PI (- 1 k)) k) * [exit]simplify: Simplified to (/ (pow PI (- 1 k)) k) * * * * [misc]progress: [ 9 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (sqrt (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * [enter]simplify: Simplifying (sqrt (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (sqrt (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * * * * [misc]progress: [ 10 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (- (exp (* (log PI) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * * [misc]simplify: iters left: 1 (55 enodes) * [exit]simplify: Simplified to (- (sqrt (pow PI (- 1 k)))) * [exit]simplify: Simplified to (- (sqrt (pow PI (- 1 k)))) * [enter]simplify: Simplifying (- (sqrt k)) * * [misc]simplify: iters left: 3 (3 enodes) * [exit]simplify: Simplified to (- (sqrt k)) * [exit]simplify: Simplified to (- (sqrt k)) * * * * [misc]progress: [ 11 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (exp (* (log PI) (/ (- 1 k) 2)))) (cbrt (exp (* (log PI) (/ (- 1 k) 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow PI (- 1 k)))) (cbrt (sqrt k))) (/ (cbrt (sqrt (pow PI (- 1 k)))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow PI (- 1 k)))) (cbrt (sqrt k))) (/ (cbrt (sqrt (pow PI (- 1 k)))) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (cbrt (exp (* (log PI) (/ (- 1 k) 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * * [misc]simplify: iters left: 1 (58 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow PI (- 1 k)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow PI (- 1 k)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 12 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (exp (* (log PI) (/ (- 1 k) 2)))) (cbrt (exp (* (log PI) (/ (- 1 k) 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow PI (- 1 k)))) (cbrt (sqrt (pow PI (- 1 k))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow PI (- 1 k)))) (cbrt (sqrt (pow PI (- 1 k))))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (cbrt (exp (* (log PI) (/ (- 1 k) 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * * [misc]simplify: iters left: 1 (58 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow PI (- 1 k)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow PI (- 1 k)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 13 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (exp (* (log PI) (/ (- 1 k) 2)))) (cbrt (exp (* (log PI) (/ (- 1 k) 2))))) 1) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * * [misc]simplify: iters left: 1 (62 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow PI (- 1 k)))) (/ (cbrt (sqrt (pow PI (- 1 k)))) 1)) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow PI (- 1 k)))) (/ (cbrt (sqrt (pow PI (- 1 k)))) 1)) * [enter]simplify: Simplifying (/ (cbrt (exp (* (log PI) (/ (- 1 k) 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow PI (- 1 k)))) (sqrt k)) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow PI (- 1 k)))) (sqrt k)) * * * * [misc]progress: [ 14 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (exp (* (log PI) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (52 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (exp (* (log PI) (/ (- 1 k) 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * * [misc]simplify: iters left: 1 (58 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 15 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (exp (* (log PI) (/ (- 1 k) 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * * [misc]simplify: iters left: 1 (58 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (exp (* (log PI) (/ (- 1 k) 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * * [misc]simplify: iters left: 1 (58 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 16 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (exp (* (log PI) (/ (- 1 k) 2)))) 1) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * * [misc]simplify: iters left: 1 (56 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) 1) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) 1) * [enter]simplify: Simplifying (/ (sqrt (exp (* (log PI) (/ (- 1 k) 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow PI (- 1 k)))) (sqrt k)) * * * * [misc]progress: [ 17 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (exp (* (log PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) (cbrt (sqrt k))) * * * * [misc]progress: [ 18 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) (sqrt (sqrt k))) * * * * [misc]progress: [ 19 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to 1 * [exit]simplify: Simplified to 1 * [enter]simplify: Simplifying (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * * [misc]simplify: iters left: 1 (56 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) (sqrt k)) * * * * [misc]progress: [ 20 / 176 ] simplifiying candidate # * * * * [misc]progress: [ 21 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt k)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * * * * [misc]progress: [ 22 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (exp (* (log PI) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * * [misc]simplify: iters left: 1 (56 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow PI (- 1 k)))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow PI (- 1 k)))) * * * * [misc]progress: [ 23 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* (log PI) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (51 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 24 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) (sqrt (sqrt k))) * * * * [misc]progress: [ 25 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* (log PI) (/ (- 1 k) 2))) 1) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * * [misc]simplify: iters left: 1 (55 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) 1) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) 1) * * * * [misc]progress: [ 26 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (cbrt (exp (* (log PI) (/ (- 1 k) 2))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (sqrt (pow PI (- 1 k))))) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (sqrt (pow PI (- 1 k))))) * * * * [misc]progress: [ 27 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (exp (* (log PI) (/ (- 1 k) 2))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (sqrt (pow PI (- 1 k))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (sqrt (pow PI (- 1 k))))) * * * * [misc]progress: [ 28 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (exp (* (log PI) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * * [misc]simplify: iters left: 1 (56 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow PI (- 1 k)))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow PI (- 1 k)))) * * * * [misc]progress: [ 29 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (106 enodes) * * [misc]simplify: iters left: 1 (151 enodes) * [exit]simplify: Simplified to (* (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * [exit]simplify: Simplified to (* (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * * * * [misc]progress: [ 30 / 176 ] simplifiying candidate # * * * * [misc]progress: [ 31 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1)) (- (* (log PI) (/ (- 1 k) 2)) (log (sqrt k)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (114 enodes) * * [misc]simplify: iters left: 1 (173 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (+ n n)) (log PI))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (+ n n)) (log PI))) (log (sqrt k))) * * * * [misc]progress: [ 32 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1)) (log (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (134 enodes) * * [misc]simplify: iters left: 1 (203 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (+ n n)) (log PI))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log (+ n n)) (log PI))) (log (sqrt k))) * * * * [misc]progress: [ 33 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (116 enodes) * * [misc]simplify: iters left: 2 (184 enodes) * * [misc]simplify: iters left: 1 (286 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log PI) (log (+ n n)))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (+ (log PI) (log (+ n n)))) (log (sqrt k))) * * * * [misc]progress: [ 34 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (109 enodes) * * [misc]simplify: iters left: 1 (154 enodes) * [exit]simplify: Simplified to (pow (exp (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * [exit]simplify: Simplified to (pow (exp (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * * * * [misc]progress: [ 35 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1)) (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1)) (/ (* (* (exp (* (log PI) (/ (- 1 k) 2))) (exp (* (log PI) (/ (- 1 k) 2)))) (exp (* (log PI) (/ (- 1 k) 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (56 enodes) * * [misc]simplify: iters left: 4 (113 enodes) * * [misc]simplify: iters left: 3 (260 enodes) * * [misc]simplify: iters left: 2 (460 enodes) * [exit]simplify: Simplified to (/ (pow (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 3) (/ (/ (* k (sqrt k)) (pow PI (- 1 k))) (sqrt (pow PI (- 1 k))))) * [exit]simplify: Simplified to (/ (pow (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 3) (/ (/ (* k (sqrt k)) (pow PI (- 1 k))) (sqrt (pow PI (- 1 k))))) * * * * [misc]progress: [ 36 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1)) (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1)) (* (* (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (131 enodes) * * [misc]simplify: iters left: 2 (246 enodes) * * [misc]simplify: iters left: 1 (456 enodes) * [exit]simplify: Simplified to (* (pow (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 3) (pow (/ (pow (sqrt PI) (- 1 k)) (sqrt k)) 3)) * [exit]simplify: Simplified to (* (pow (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 3) (pow (/ (pow (sqrt PI) (- 1 k)) (sqrt k)) 3)) * * * * [misc]progress: [ 37 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)))) (cbrt (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (76 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (153 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (* (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (sqrt (pow PI (- 1 k)))) (sqrt k))) (cbrt (/ (* (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (sqrt (pow PI (- 1 k)))) (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ (* (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (sqrt (pow PI (- 1 k)))) (sqrt k))) (cbrt (/ (* (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (sqrt (pow PI (- 1 k)))) (sqrt k)))) * [enter]simplify: Simplifying (cbrt (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (75 enodes) * * [misc]simplify: iters left: 2 (107 enodes) * * [misc]simplify: iters left: 1 (152 enodes) * [exit]simplify: Simplified to (cbrt (/ (/ (sqrt (pow PI (- 1 k))) (/ (sqrt k) (pow (+ n n) (/ 1 2)))) (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (cbrt (/ (/ (sqrt (pow PI (- 1 k))) (/ (sqrt k) (pow (+ n n) (/ 1 2)))) (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 38 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)))) (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (277 enodes) * * [misc]simplify: iters left: 1 (485 enodes) * [exit]simplify: Simplified to (* (* (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (/ (sqrt (pow PI (- 1 k))) (sqrt k))) (* (* (/ (pow PI (- 1 k)) (sqrt k)) (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (sqrt k)))) * [exit]simplify: Simplified to (* (* (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (/ (sqrt (pow PI (- 1 k))) (sqrt k))) (* (* (/ (pow PI (- 1 k)) (sqrt k)) (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (sqrt k)))) * * * * [misc]progress: [ 39 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (75 enodes) * * [misc]simplify: iters left: 2 (107 enodes) * * [misc]simplify: iters left: 1 (152 enodes) * [exit]simplify: Simplified to (sqrt (/ (/ (sqrt (pow PI (- 1 k))) (/ (sqrt k) (pow (+ n n) (/ 1 2)))) (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (sqrt (/ (/ (sqrt (pow PI (- 1 k))) (/ (sqrt k) (pow (+ n n) (/ 1 2)))) (pow (+ n n) (/ k 2)))) * [enter]simplify: Simplifying (sqrt (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (75 enodes) * * [misc]simplify: iters left: 2 (107 enodes) * * [misc]simplify: iters left: 1 (152 enodes) * [exit]simplify: Simplified to (sqrt (/ (/ (sqrt (pow PI (- 1 k))) (/ (sqrt k) (pow (+ n n) (/ 1 2)))) (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (sqrt (/ (/ (sqrt (pow PI (- 1 k))) (/ (sqrt k) (pow (+ n n) (/ 1 2)))) (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 40 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (exp (* (log PI) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (74 enodes) * [exit]simplify: Simplified to (* (sqrt (pow PI (- 1 k))) (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (* (sqrt (pow PI (- 1 k))) (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * [enter]simplify: Simplifying (* 1 (sqrt k)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * [exit]simplify: Simplified to (sqrt k) * [exit]simplify: Simplified to (sqrt k) * * * * [misc]progress: [ 41 / 176 ] simplifiying candidate # * * * * [misc]progress: [ 42 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (* (cbrt (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) (cbrt (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (75 enodes) * * [misc]simplify: iters left: 2 (106 enodes) * * [misc]simplify: iters left: 1 (142 enodes) * [exit]simplify: Simplified to (* (* (cbrt (/ (sqrt (pow PI (- 1 k))) (sqrt k))) (cbrt (/ (sqrt (pow PI (- 1 k))) (sqrt k)))) (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (* (* (cbrt (/ (sqrt (pow PI (- 1 k))) (sqrt k))) (cbrt (/ (sqrt (pow PI (- 1 k))) (sqrt k)))) (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 43 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (sqrt (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (91 enodes) * * [misc]simplify: iters left: 1 (119 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (sqrt (pow PI (- 1 k))) (sqrt k))) (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (* (sqrt (/ (sqrt (pow PI (- 1 k))) (sqrt k))) (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 44 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (* (cbrt (exp (* (log PI) (/ (- 1 k) 2)))) (cbrt (exp (* (log PI) (/ (- 1 k) 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (117 enodes) * * [misc]simplify: iters left: 2 (178 enodes) * * [misc]simplify: iters left: 1 (321 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow PI (- 1 k)))) (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow PI (- 1 k)))))) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow PI (- 1 k)))) (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow PI (- 1 k)))))) * * * * [misc]progress: [ 45 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (* (cbrt (exp (* (log PI) (/ (- 1 k) 2)))) (cbrt (exp (* (log PI) (/ (- 1 k) 2))))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (81 enodes) * * [misc]simplify: iters left: 2 (113 enodes) * * [misc]simplify: iters left: 1 (153 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow PI (- 1 k)))) (sqrt (sqrt k))) (* (cbrt (sqrt (pow PI (- 1 k)))) (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))))) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow PI (- 1 k)))) (sqrt (sqrt k))) (* (cbrt (sqrt (pow PI (- 1 k)))) (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))))) * * * * [misc]progress: [ 46 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (* (cbrt (exp (* (log PI) (/ (- 1 k) 2)))) (cbrt (exp (* (log PI) (/ (- 1 k) 2))))) 1)) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (125 enodes) * * [misc]simplify: iters left: 1 (172 enodes) * [exit]simplify: Simplified to (* (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (* (cbrt (sqrt (pow PI (- 1 k)))) (cbrt (sqrt (pow PI (- 1 k)))))) * [exit]simplify: Simplified to (* (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (* (cbrt (sqrt (pow PI (- 1 k)))) (cbrt (sqrt (pow PI (- 1 k)))))) * * * * [misc]progress: [ 47 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (sqrt (exp (* (log PI) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (81 enodes) * * [misc]simplify: iters left: 2 (107 enodes) * * [misc]simplify: iters left: 1 (146 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt (pow PI (- 1 k)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt (pow PI (- 1 k)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 48 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (sqrt (exp (* (log PI) (/ (- 1 k) 2)))) (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (76 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (149 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt (pow PI (- 1 k)))) (sqrt (sqrt k))) (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt (pow PI (- 1 k)))) (sqrt (sqrt k))) (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 49 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (sqrt (exp (* (log PI) (/ (- 1 k) 2)))) 1)) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (96 enodes) * * [misc]simplify: iters left: 1 (116 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow PI (- 1 k)))) (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow PI (- 1 k)))) (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 50 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 51 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ 1 (sqrt (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (35 enodes) * * [misc]simplify: iters left: 1 (50 enodes) * [exit]simplify: Simplified to (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 52 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ 1 1)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (39 enodes) * * [misc]simplify: iters left: 1 (43 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) * * * * [misc]progress: [ 53 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) 1) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (40 enodes) * * [misc]simplify: iters left: 1 (42 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) * * * * [misc]progress: [ 54 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (exp (* (log PI) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (88 enodes) * * [misc]simplify: iters left: 1 (120 enodes) * [exit]simplify: Simplified to (* (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (sqrt (pow PI (- 1 k)))) * [exit]simplify: Simplified to (* (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (sqrt (pow PI (- 1 k)))) * * * * [misc]progress: [ 55 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1)) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) (/ (sqrt k) (sqrt (pow PI (- 1 k))))) * [exit]simplify: Simplified to (/ (cbrt (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) (/ (sqrt k) (sqrt (pow PI (- 1 k))))) * * * * [misc]progress: [ 56 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1)) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) (/ (sqrt k) (sqrt (pow PI (- 1 k))))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) (/ (sqrt k) (sqrt (pow PI (- 1 k))))) * * * * [misc]progress: [ 57 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (106 enodes) * * [misc]simplify: iters left: 1 (151 enodes) * [exit]simplify: Simplified to (* (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * [exit]simplify: Simplified to (* (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * * * * [misc]progress: [ 58 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1 k))) (sqrt k)) * * * * [misc]progress: [ 59 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (exp (* (log PI) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (88 enodes) * * [misc]simplify: iters left: 1 (120 enodes) * [exit]simplify: Simplified to (* (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (sqrt (pow PI (- 1 k)))) * [exit]simplify: Simplified to (* (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (sqrt (pow PI (- 1 k)))) * * * * [misc]progress: [ 60 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (90 enodes) * * [misc]simplify: iters left: 1 (113 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (pow PI (- 1 k))) (* (sqrt k) (pow (+ n n) (/ k 2)))) (pow (+ n n) (/ 1 2))) * [exit]simplify: Simplified to (* (/ (sqrt (pow PI (- 1 k))) (* (sqrt k) (pow (+ n n) (/ k 2)))) (pow (+ n n) (/ 1 2))) * * * * [misc]progress: [ 61 / 176 ] simplifiying candidate # * * * * [misc]progress: [ 62 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (- (/ 1 2) (/ k 2)) * * [misc]simplify: iters left: 4 (6 enodes) * * [misc]simplify: iters left: 3 (8 enodes) * [exit]simplify: Simplified to (- (/ 1 2) (/ k 2)) * [exit]simplify: Simplified to (- (/ 1 2) (/ k 2)) * * * * [misc]progress: [ 63 / 176 ] simplifiying candidate # * * * * [misc]progress: [ 64 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (+ n n)) (/ 1 2)) (* (log (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (71 enodes) * * [misc]simplify: iters left: 1 (118 enodes) * [exit]simplify: Simplified to (* (log (+ n n)) (- (/ 1 2) (/ k 2))) * [exit]simplify: Simplified to (* (log (+ n n)) (- (/ 1 2) (/ k 2))) * * * * [misc]progress: [ 65 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (+ n n)) (/ 1 2)) (* (log (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (71 enodes) * * [misc]simplify: iters left: 1 (118 enodes) * [exit]simplify: Simplified to (* (log (+ n n)) (- (/ 1 2) (/ k 2))) * [exit]simplify: Simplified to (* (log (+ n n)) (- (/ 1 2) (/ k 2))) * * * * [misc]progress: [ 66 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (+ n n)) (/ 1 2)) (log (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (119 enodes) * [exit]simplify: Simplified to (* (- (/ 1 2) (/ k 2)) (log (+ n n))) * [exit]simplify: Simplified to (* (- (/ 1 2) (/ k 2)) (log (+ n n))) * * * * [misc]progress: [ 67 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (+ n n)) (/ 1 2)) (* (log (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (71 enodes) * * [misc]simplify: iters left: 1 (118 enodes) * [exit]simplify: Simplified to (* (log (+ n n)) (- (/ 1 2) (/ k 2))) * [exit]simplify: Simplified to (* (log (+ n n)) (- (/ 1 2) (/ k 2))) * * * * [misc]progress: [ 68 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (+ n n)) (/ 1 2)) (* (log (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (71 enodes) * * [misc]simplify: iters left: 1 (118 enodes) * [exit]simplify: Simplified to (* (log (+ n n)) (- (/ 1 2) (/ k 2))) * [exit]simplify: Simplified to (* (log (+ n n)) (- (/ 1 2) (/ k 2))) * * * * [misc]progress: [ 69 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (+ n n)) (/ 1 2)) (log (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (119 enodes) * [exit]simplify: Simplified to (* (- (/ 1 2) (/ k 2)) (log (+ n n))) * [exit]simplify: Simplified to (* (- (/ 1 2) (/ k 2)) (log (+ n n))) * * * * [misc]progress: [ 70 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (+ n n) (/ 1 2))) (* (log (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (88 enodes) * * [misc]simplify: iters left: 1 (133 enodes) * [exit]simplify: Simplified to (* (- (/ 1 2) (/ k 2)) (log (+ n n))) * [exit]simplify: Simplified to (* (- (/ 1 2) (/ k 2)) (log (+ n n))) * * * * [misc]progress: [ 71 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (+ n n) (/ 1 2))) (* (log (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (88 enodes) * * [misc]simplify: iters left: 1 (133 enodes) * [exit]simplify: Simplified to (* (- (/ 1 2) (/ k 2)) (log (+ n n))) * [exit]simplify: Simplified to (* (- (/ 1 2) (/ k 2)) (log (+ n n))) * * * * [misc]progress: [ 72 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (+ n n) (/ 1 2))) (log (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (69 enodes) * * [misc]simplify: iters left: 1 (79 enodes) * [exit]simplify: Simplified to (* (log (+ n n)) (- (/ 1 2) (/ k 2))) * [exit]simplify: Simplified to (* (log (+ n n)) (- (/ 1 2) (/ k 2))) * * * * [misc]progress: [ 73 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * * [misc]simplify: iters left: 2 (42 enodes) * * [misc]simplify: iters left: 1 (52 enodes) * [exit]simplify: Simplified to (* (- (/ 1 2) (/ k 2)) (log (+ n n))) * [exit]simplify: Simplified to (* (- (/ 1 2) (/ k 2)) (log (+ n n))) * * * * [misc]progress: [ 74 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (exp (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (exp (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 75 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ 1 2))) (pow (+ n n) (/ 1 2))) (* (* (pow (+ n n) (/ k 2)) (pow (+ n n) (/ k 2))) (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (pow (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 3) * [exit]simplify: Simplified to (pow (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 3) * * * * [misc]progress: [ 76 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) (cbrt (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) (cbrt (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))))) * [exit]simplify: Simplified to (* (cbrt (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) (cbrt (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))))) * [enter]simplify: Simplifying (cbrt (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (cbrt (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (cbrt (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 77 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (61 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (pow (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 3) * [exit]simplify: Simplified to (pow (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 3) * * * * [misc]progress: [ 78 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (sqrt (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * [enter]simplify: Simplifying (sqrt (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (sqrt (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 79 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (- (pow (+ n n) (/ 1 2))) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (11 enodes) * [exit]simplify: Simplified to (- (pow (+ n n) (/ 1 2))) * [exit]simplify: Simplified to (- (pow (+ n n) (/ 1 2))) * [enter]simplify: Simplifying (- (pow (+ n n) (/ k 2))) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * [exit]simplify: Simplified to (- (pow (+ n n) (/ k 2))) * [exit]simplify: Simplified to (- (pow (+ n n) (/ k 2))) * * * * [misc]progress: [ 80 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ 1 2)) (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ k 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ 1 2)) (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ 1 2)) (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ k 2))) * [enter]simplify: Simplifying (/ (pow (cbrt (+ n n)) (/ 1 2)) (pow (cbrt (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (cbrt (+ n n)) (/ 1 2)) (pow (cbrt (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (cbrt (+ n n)) (/ 1 2)) (pow (cbrt (+ n n)) (/ k 2))) * * * * [misc]progress: [ 81 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (/ (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * [enter]simplify: Simplifying (/ (pow (cbrt (+ n n)) (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (pow (cbrt (+ n n)) (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (cbrt (+ n n)) (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * * * * [misc]progress: [ 82 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ 1 2)) (pow 1 (/ k 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ 1 2)) 1) * [exit]simplify: Simplified to (/ (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ 1 2)) 1) * [enter]simplify: Simplifying (/ (pow (cbrt (+ n n)) (/ 1 2)) (pow (+ n n) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (cbrt (+ n n)) (/ 1 2)) (pow (+ n n) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (cbrt (+ n n)) (/ 1 2)) (pow (+ n n) (/ k 2))) * * * * [misc]progress: [ 83 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ 1 2)) (pow 2 (/ k 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ 1 2)) (pow 2 (/ k 2))) * [exit]simplify: Simplified to (/ (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ 1 2)) (pow 2 (/ k 2))) * [enter]simplify: Simplifying (/ (pow (cbrt (+ n n)) (/ 1 2)) (pow n (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (cbrt (+ n n)) (/ 1 2)) (pow n (/ k 2))) * [exit]simplify: Simplified to (/ (pow (cbrt (+ n n)) (/ 1 2)) (pow n (/ k 2))) * * * * [misc]progress: [ 84 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ 1 2)) (* (cbrt (pow (+ n n) (/ k 2))) (cbrt (pow (+ n n) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * [exit]simplify: Simplified to (/ (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ 1 2)) (* (cbrt (pow (+ n n) (/ k 2))) (cbrt (pow (+ n n) (/ k 2))))) * [exit]simplify: Simplified to (/ (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ 1 2)) (* (cbrt (pow (+ n n) (/ k 2))) (cbrt (pow (+ n n) (/ k 2))))) * [enter]simplify: Simplifying (/ (pow (cbrt (+ n n)) (/ 1 2)) (cbrt (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (pow (cbrt (+ n n)) (/ 1 2)) (cbrt (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow (cbrt (+ n n)) (/ 1 2)) (cbrt (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 85 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (/ (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * [enter]simplify: Simplifying (/ (pow (cbrt (+ n n)) (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (pow (cbrt (+ n n)) (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow (cbrt (+ n n)) (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 86 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ 1 2)) 1) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * [exit]simplify: Simplified to (/ (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ 1 2)) 1) * [exit]simplify: Simplified to (/ (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ 1 2)) 1) * [enter]simplify: Simplifying (/ (pow (cbrt (+ n n)) (/ 1 2)) (pow (+ n n) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (cbrt (+ n n)) (/ 1 2)) (pow (+ n n) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (cbrt (+ n n)) (/ 1 2)) (pow (+ n n) (/ k 2))) * * * * [misc]progress: [ 87 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ k 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ k 2))) * [enter]simplify: Simplifying (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow (cbrt (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow (cbrt (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow (cbrt (+ n n)) (/ k 2))) * * * * [misc]progress: [ 88 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * [enter]simplify: Simplifying (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * * * * [misc]progress: [ 89 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow 1 (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) 1) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) 1) * [enter]simplify: Simplifying (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow (+ n n) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow (+ n n) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow (+ n n) (/ k 2))) * * * * [misc]progress: [ 90 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow 2 (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow 2 (/ k 2))) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow 2 (/ k 2))) * [enter]simplify: Simplifying (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow n (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow n (/ k 2))) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow n (/ k 2))) * * * * [misc]progress: [ 91 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (sqrt (+ n n)) (/ 1 2)) (* (cbrt (pow (+ n n) (/ k 2))) (cbrt (pow (+ n n) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) (* (cbrt (pow (+ n n) (/ k 2))) (cbrt (pow (+ n n) (/ k 2))))) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) (* (cbrt (pow (+ n n) (/ k 2))) (cbrt (pow (+ n n) (/ k 2))))) * [enter]simplify: Simplifying (/ (pow (sqrt (+ n n)) (/ 1 2)) (cbrt (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) (cbrt (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) (cbrt (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 92 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (sqrt (+ n n)) (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * [enter]simplify: Simplifying (/ (pow (sqrt (+ n n)) (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 93 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (sqrt (+ n n)) (/ 1 2)) 1) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) 1) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) 1) * [enter]simplify: Simplifying (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow (+ n n) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow (+ n n) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (sqrt (+ n n)) (/ 1 2)) (pow (+ n n) (/ k 2))) * * * * [misc]progress: [ 94 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow 1 (/ 1 2)) (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ k 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ 1 (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ k 2))) * [exit]simplify: Simplified to (/ 1 (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ k 2))) * [enter]simplify: Simplifying (/ (pow (+ n n) (/ 1 2)) (pow (cbrt (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow (cbrt (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow (cbrt (+ n n)) (/ k 2))) * * * * [misc]progress: [ 95 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow 1 (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ 1 (pow (sqrt (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ 1 (pow (sqrt (+ n n)) (/ k 2))) * [enter]simplify: Simplifying (/ (pow (+ n n) (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * * * * [misc]progress: [ 96 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow 1 (/ 1 2)) (pow 1 (/ k 2))) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * [exit]simplify: Simplified to (/ 1 1) * [exit]simplify: Simplified to (/ 1 1) * [enter]simplify: Simplifying (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (14 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) * * * * [misc]progress: [ 97 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow 1 (/ 1 2)) (pow 2 (/ k 2))) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * [exit]simplify: Simplified to (/ 1 (pow 2 (/ k 2))) * [exit]simplify: Simplified to (/ 1 (pow 2 (/ k 2))) * [enter]simplify: Simplifying (/ (pow (+ n n) (/ 1 2)) (pow n (/ k 2))) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (14 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow n (/ k 2))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow n (/ k 2))) * * * * [misc]progress: [ 98 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow 1 (/ 1 2)) (* (cbrt (pow (+ n n) (/ k 2))) (cbrt (pow (+ n n) (/ k 2))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (pow (+ n n) (/ k 2))) (cbrt (pow (+ n n) (/ k 2))))) * [exit]simplify: Simplified to (/ 1 (* (cbrt (pow (+ n n) (/ k 2))) (cbrt (pow (+ n n) (/ k 2))))) * [enter]simplify: Simplifying (/ (pow (+ n n) (/ 1 2)) (cbrt (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (cbrt (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (cbrt (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 99 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow 1 (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (/ 1 (sqrt (pow (+ n n) (/ k 2)))) * [enter]simplify: Simplifying (/ (pow (+ n n) (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 100 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow 1 (/ 1 2)) 1) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (7 enodes) * [exit]simplify: Simplified to (/ 1 1) * [exit]simplify: Simplified to (/ 1 1) * [enter]simplify: Simplifying (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (14 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) * * * * [misc]progress: [ 101 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow 2 (/ 1 2)) (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ k 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (pow 2 (/ 1 2)) (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ k 2))) * [exit]simplify: Simplified to (/ (pow 2 (/ 1 2)) (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ k 2))) * [enter]simplify: Simplifying (/ (pow n (/ 1 2)) (pow (cbrt (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (pow (cbrt (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (pow (cbrt (+ n n)) (/ k 2))) * * * * [misc]progress: [ 102 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow 2 (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow 2 (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ (pow 2 (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * [enter]simplify: Simplifying (/ (pow n (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * * * * [misc]progress: [ 103 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow 2 (/ 1 2)) (pow 1 (/ k 2))) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * [exit]simplify: Simplified to (/ (pow 2 (/ 1 2)) 1) * [exit]simplify: Simplified to (/ (pow 2 (/ 1 2)) 1) * [enter]simplify: Simplifying (/ (pow n (/ 1 2)) (pow (+ n n) (/ k 2))) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (14 enodes) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (pow (+ n n) (/ k 2))) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (pow (+ n n) (/ k 2))) * * * * [misc]progress: [ 104 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow 2 (/ 1 2)) (pow 2 (/ k 2))) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * [exit]simplify: Simplified to (/ (pow 2 (/ 1 2)) (pow 2 (/ k 2))) * [exit]simplify: Simplified to (/ (pow 2 (/ 1 2)) (pow 2 (/ k 2))) * [enter]simplify: Simplifying (/ (pow n (/ 1 2)) (pow n (/ k 2))) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (11 enodes) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (pow n (/ k 2))) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (pow n (/ k 2))) * * * * [misc]progress: [ 105 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow 2 (/ 1 2)) (* (cbrt (pow (+ n n) (/ k 2))) (cbrt (pow (+ n n) (/ k 2))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ (pow 2 (/ 1 2)) (* (cbrt (pow (+ n n) (/ k 2))) (cbrt (pow (+ n n) (/ k 2))))) * [exit]simplify: Simplified to (/ (pow 2 (/ 1 2)) (* (cbrt (pow (+ n n) (/ k 2))) (cbrt (pow (+ n n) (/ k 2))))) * [enter]simplify: Simplifying (/ (pow n (/ 1 2)) (cbrt (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (cbrt (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (cbrt (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 106 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow 2 (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow 2 (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow 2 (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * [enter]simplify: Simplifying (/ (pow n (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 107 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow 2 (/ 1 2)) 1) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (7 enodes) * [exit]simplify: Simplified to (/ (pow 2 (/ 1 2)) 1) * [exit]simplify: Simplified to (/ (pow 2 (/ 1 2)) 1) * [enter]simplify: Simplifying (/ (pow n (/ 1 2)) (pow (+ n n) (/ k 2))) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (14 enodes) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (pow (+ n n) (/ k 2))) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (pow (+ n n) (/ k 2))) * * * * [misc]progress: [ 108 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (+ n n) (/ 1 2))) (cbrt (pow (+ n n) (/ 1 2)))) (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ k 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (pow (+ n n) (/ 1 2))) (cbrt (pow (+ n n) (/ 1 2)))) (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ k 2))) * [exit]simplify: Simplified to (/ (* (cbrt (pow (+ n n) (/ 1 2))) (cbrt (pow (+ n n) (/ 1 2)))) (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ k 2))) * [enter]simplify: Simplifying (/ (cbrt (pow (+ n n) (/ 1 2))) (pow (cbrt (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (+ n n) (/ 1 2))) (pow (cbrt (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ (cbrt (pow (+ n n) (/ 1 2))) (pow (cbrt (+ n n)) (/ k 2))) * * * * [misc]progress: [ 109 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (+ n n) (/ 1 2))) (cbrt (pow (+ n n) (/ 1 2)))) (pow (sqrt (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (+ n n) (/ 1 2))) (/ (cbrt (pow (+ n n) (/ 1 2))) (pow (sqrt (+ n n)) (/ k 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (+ n n) (/ 1 2))) (/ (cbrt (pow (+ n n) (/ 1 2))) (pow (sqrt (+ n n)) (/ k 2)))) * [enter]simplify: Simplifying (/ (cbrt (pow (+ n n) (/ 1 2))) (pow (sqrt (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (+ n n) (/ 1 2))) (pow (sqrt (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ (cbrt (pow (+ n n) (/ 1 2))) (pow (sqrt (+ n n)) (/ k 2))) * * * * [misc]progress: [ 110 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (+ n n) (/ 1 2))) (cbrt (pow (+ n n) (/ 1 2)))) (pow 1 (/ k 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (+ n n) (/ 1 2))) 1) (cbrt (pow (+ n n) (/ 1 2)))) * [exit]simplify: Simplified to (* (/ (cbrt (pow (+ n n) (/ 1 2))) 1) (cbrt (pow (+ n n) (/ 1 2)))) * [enter]simplify: Simplifying (/ (cbrt (pow (+ n n) (/ 1 2))) (pow (+ n n) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (+ n n) (/ 1 2))) (pow (+ n n) (/ k 2))) * [exit]simplify: Simplified to (/ (cbrt (pow (+ n n) (/ 1 2))) (pow (+ n n) (/ k 2))) * * * * [misc]progress: [ 111 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (+ n n) (/ 1 2))) (cbrt (pow (+ n n) (/ 1 2)))) (pow 2 (/ k 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (+ n n) (/ 1 2))) (pow 2 (/ k 2))) (cbrt (pow (+ n n) (/ 1 2)))) * [exit]simplify: Simplified to (* (/ (cbrt (pow (+ n n) (/ 1 2))) (pow 2 (/ k 2))) (cbrt (pow (+ n n) (/ 1 2)))) * [enter]simplify: Simplifying (/ (cbrt (pow (+ n n) (/ 1 2))) (pow n (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (+ n n) (/ 1 2))) (pow n (/ k 2))) * [exit]simplify: Simplified to (/ (cbrt (pow (+ n n) (/ 1 2))) (pow n (/ k 2))) * * * * [misc]progress: [ 112 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (+ n n) (/ 1 2))) (cbrt (pow (+ n n) (/ 1 2)))) (* (cbrt (pow (+ n n) (/ k 2))) (cbrt (pow (+ n n) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (39 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (+ n n) (/ 1 2))) (cbrt (pow (+ n n) (/ k 2)))) (/ (cbrt (pow (+ n n) (/ 1 2))) (cbrt (pow (+ n n) (/ k 2))))) * [exit]simplify: Simplified to (* (/ (cbrt (pow (+ n n) (/ 1 2))) (cbrt (pow (+ n n) (/ k 2)))) (/ (cbrt (pow (+ n n) (/ 1 2))) (cbrt (pow (+ n n) (/ k 2))))) * [enter]simplify: Simplifying (/ (cbrt (pow (+ n n) (/ 1 2))) (cbrt (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (+ n n) (/ 1 2))) (cbrt (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (/ (cbrt (pow (+ n n) (/ 1 2))) (cbrt (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 113 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (+ n n) (/ 1 2))) (cbrt (pow (+ n n) (/ 1 2)))) (sqrt (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (+ n n) (/ 1 2))) (/ (cbrt (pow (+ n n) (/ 1 2))) (sqrt (pow (+ n n) (/ k 2))))) * [exit]simplify: Simplified to (* (cbrt (pow (+ n n) (/ 1 2))) (/ (cbrt (pow (+ n n) (/ 1 2))) (sqrt (pow (+ n n) (/ k 2))))) * [enter]simplify: Simplifying (/ (cbrt (pow (+ n n) (/ 1 2))) (sqrt (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (+ n n) (/ 1 2))) (sqrt (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (/ (cbrt (pow (+ n n) (/ 1 2))) (sqrt (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 114 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (+ n n) (/ 1 2))) (cbrt (pow (+ n n) (/ 1 2)))) 1) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (18 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (+ n n) (/ 1 2))) 1) (cbrt (pow (+ n n) (/ 1 2)))) * [exit]simplify: Simplified to (* (/ (cbrt (pow (+ n n) (/ 1 2))) 1) (cbrt (pow (+ n n) (/ 1 2)))) * [enter]simplify: Simplifying (/ (cbrt (pow (+ n n) (/ 1 2))) (pow (+ n n) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (+ n n) (/ 1 2))) (pow (+ n n) (/ k 2))) * [exit]simplify: Simplified to (/ (cbrt (pow (+ n n) (/ 1 2))) (pow (+ n n) (/ k 2))) * * * * [misc]progress: [ 115 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (+ n n) (/ 1 2))) (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ k 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ k 2))) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ k 2))) * [enter]simplify: Simplifying (/ (sqrt (pow (+ n n) (/ 1 2))) (pow (cbrt (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) (pow (cbrt (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) (pow (cbrt (+ n n)) (/ k 2))) * * * * [misc]progress: [ 116 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (+ n n) (/ 1 2))) (pow (sqrt (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) (pow (sqrt (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) (pow (sqrt (+ n n)) (/ k 2))) * [enter]simplify: Simplifying (/ (sqrt (pow (+ n n) (/ 1 2))) (pow (sqrt (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) (pow (sqrt (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) (pow (sqrt (+ n n)) (/ k 2))) * * * * [misc]progress: [ 117 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (+ n n) (/ 1 2))) (pow 1 (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) 1) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) 1) * [enter]simplify: Simplifying (/ (sqrt (pow (+ n n) (/ 1 2))) (pow (+ n n) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) (pow (+ n n) (/ k 2))) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) (pow (+ n n) (/ k 2))) * * * * [misc]progress: [ 118 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (+ n n) (/ 1 2))) (pow 2 (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) (pow 2 (/ k 2))) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) (pow 2 (/ k 2))) * [enter]simplify: Simplifying (/ (sqrt (pow (+ n n) (/ 1 2))) (pow n (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) (pow n (/ k 2))) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) (pow n (/ k 2))) * * * * [misc]progress: [ 119 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (+ n n) (/ 1 2))) (* (cbrt (pow (+ n n) (/ k 2))) (cbrt (pow (+ n n) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) (* (cbrt (pow (+ n n) (/ k 2))) (cbrt (pow (+ n n) (/ k 2))))) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) (* (cbrt (pow (+ n n) (/ k 2))) (cbrt (pow (+ n n) (/ k 2))))) * [enter]simplify: Simplifying (/ (sqrt (pow (+ n n) (/ 1 2))) (cbrt (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) (cbrt (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) (cbrt (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 120 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (+ n n) (/ 1 2))) (sqrt (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) (sqrt (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) (sqrt (pow (+ n n) (/ k 2)))) * [enter]simplify: Simplifying (/ (sqrt (pow (+ n n) (/ 1 2))) (sqrt (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) (sqrt (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) (sqrt (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 121 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (+ n n) (/ 1 2))) 1) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) 1) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) 1) * [enter]simplify: Simplifying (/ (sqrt (pow (+ n n) (/ 1 2))) (pow (+ n n) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) (pow (+ n n) (/ k 2))) * [exit]simplify: Simplified to (/ (sqrt (pow (+ n n) (/ 1 2))) (pow (+ n n) (/ k 2))) * * * * [misc]progress: [ 122 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ k 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (/ 1 (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ k 2))) * [exit]simplify: Simplified to (/ 1 (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ k 2))) * [enter]simplify: Simplifying (/ (pow (+ n n) (/ 1 2)) (pow (cbrt (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow (cbrt (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow (cbrt (+ n n)) (/ k 2))) * * * * [misc]progress: [ 123 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (pow (sqrt (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * [exit]simplify: Simplified to (/ 1 (pow (sqrt (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ 1 (pow (sqrt (+ n n)) (/ k 2))) * [enter]simplify: Simplifying (/ (pow (+ n n) (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * * * * [misc]progress: [ 124 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (pow 1 (/ k 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to (/ 1 1) * [exit]simplify: Simplified to (/ 1 1) * [enter]simplify: Simplifying (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (14 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) * * * * [misc]progress: [ 125 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (pow 2 (/ k 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to (/ 1 (pow 2 (/ k 2))) * [exit]simplify: Simplified to (/ 1 (pow 2 (/ k 2))) * [enter]simplify: Simplifying (/ (pow (+ n n) (/ 1 2)) (pow n (/ k 2))) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (14 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow n (/ k 2))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow n (/ k 2))) * * * * [misc]progress: [ 126 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (pow (+ n n) (/ k 2))) (cbrt (pow (+ n n) (/ k 2))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (pow (+ n n) (/ k 2))) (cbrt (pow (+ n n) (/ k 2))))) * [exit]simplify: Simplified to (/ 1 (* (cbrt (pow (+ n n) (/ k 2))) (cbrt (pow (+ n n) (/ k 2))))) * [enter]simplify: Simplifying (/ (pow (+ n n) (/ 1 2)) (cbrt (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (cbrt (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (cbrt (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 127 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (/ 1 (sqrt (pow (+ n n) (/ k 2)))) * [enter]simplify: Simplifying (/ (pow (+ n n) (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 128 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to 1 * [exit]simplify: Simplified to 1 * [enter]simplify: Simplifying (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (14 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) * * * * [misc]progress: [ 129 / 176 ] simplifiying candidate # * * * * [misc]progress: [ 130 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (pow (+ n n) (/ k 2))) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (11 enodes) * * [misc]simplify: iters left: 3 (12 enodes) * [exit]simplify: Simplified to (/ 1 (pow (+ n n) (/ k 2))) * [exit]simplify: Simplified to (/ 1 (pow (+ n n) (/ k 2))) * * * * [misc]progress: [ 131 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (+ n n) (/ k 2)) (pow (+ n n) (/ 1 2))) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (14 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ k 2)) (pow (+ n n) (/ 1 2))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ k 2)) (pow (+ n n) (/ 1 2))) * * * * [misc]progress: [ 132 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (+ n n) (/ 1 2)) (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ k 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow (* (cbrt (+ n n)) (cbrt (+ n n))) (/ k 2))) * * * * [misc]progress: [ 133 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (+ n n) (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow (sqrt (+ n n)) (/ k 2))) * * * * [misc]progress: [ 134 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (+ n n) (/ 1 2)) (pow 1 (/ k 2))) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (14 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) 1) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) 1) * * * * [misc]progress: [ 135 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (+ n n) (/ 1 2)) (pow 2 (/ k 2))) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (14 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow 2 (/ k 2))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (pow 2 (/ k 2))) * * * * [misc]progress: [ 136 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (+ n n) (/ 1 2)) (* (cbrt (pow (+ n n) (/ k 2))) (cbrt (pow (+ n n) (/ k 2))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ (/ (pow (+ n n) (/ 1 2)) (cbrt (pow (+ n n) (/ k 2)))) (cbrt (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (+ n n) (/ 1 2)) (cbrt (pow (+ n n) (/ k 2)))) (cbrt (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 137 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (+ n n) (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (sqrt (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 138 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (+ n n) (/ 1 2)) 1) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (11 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) 1) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) 1) * * * * [misc]progress: [ 139 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (+ n n) (/ k 2)) (pow (cbrt (+ n n)) (/ 1 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ k 2)) (pow (cbrt (+ n n)) (/ 1 2))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ k 2)) (pow (cbrt (+ n n)) (/ 1 2))) * * * * [misc]progress: [ 140 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (+ n n) (/ k 2)) (pow (sqrt (+ n n)) (/ 1 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ k 2)) (pow (sqrt (+ n n)) (/ 1 2))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ k 2)) (pow (sqrt (+ n n)) (/ 1 2))) * * * * [misc]progress: [ 141 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (+ n n) (/ k 2)) (pow (+ n n) (/ 1 2))) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (14 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ k 2)) (pow (+ n n) (/ 1 2))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ k 2)) (pow (+ n n) (/ 1 2))) * * * * [misc]progress: [ 142 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (+ n n) (/ k 2)) (pow n (/ 1 2))) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (14 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ k 2)) (pow n (/ 1 2))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ k 2)) (pow n (/ 1 2))) * * * * [misc]progress: [ 143 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (+ n n) (/ k 2)) (cbrt (pow (+ n n) (/ 1 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ k 2)) (cbrt (pow (+ n n) (/ 1 2)))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ k 2)) (cbrt (pow (+ n n) (/ 1 2)))) * * * * [misc]progress: [ 144 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (+ n n) (/ k 2)) (sqrt (pow (+ n n) (/ 1 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ k 2)) (sqrt (pow (+ n n) (/ 1 2)))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ k 2)) (sqrt (pow (+ n n) (/ 1 2)))) * * * * [misc]progress: [ 145 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (+ n n) (/ k 2)) (pow (+ n n) (/ 1 2))) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (14 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ k 2)) (pow (+ n n) (/ 1 2))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ k 2)) (pow (+ n n) (/ 1 2))) * * * * [misc]progress: [ 146 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log PI) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * * [misc]simplify: iters left: 2 (27 enodes) * * [misc]simplify: iters left: 1 (30 enodes) * [exit]simplify: Simplified to (/ (log PI) (/ 2 (- 1 k))) * [exit]simplify: Simplified to (/ (log PI) (/ 2 (- 1 k))) * * * * [misc]progress: [ 147 / 176 ] simplifiying candidate # * * * * [misc]progress: [ 148 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (log PI)) (log (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (+ (log (/ (- 1 k) 2)) (log (log PI))) * [exit]simplify: Simplified to (+ (log (/ (- 1 k) 2)) (log (log PI))) * * * * [misc]progress: [ 149 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (log PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * * [misc]simplify: iters left: 1 (53 enodes) * [exit]simplify: Simplified to (log (* (- 1 k) (/ (log PI) 2))) * [exit]simplify: Simplified to (log (* (- 1 k) (/ (log PI) 2))) * * * * [misc]progress: [ 150 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (log PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * * [misc]simplify: iters left: 1 (54 enodes) * [exit]simplify: Simplified to (sqrt (pow PI (- 1 k))) * [exit]simplify: Simplified to (sqrt (pow PI (- 1 k))) * * * * [misc]progress: [ 151 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (log PI) (log PI)) (log PI)) (* (* (/ (- 1 k) 2) (/ (- 1 k) 2)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (253 enodes) * [exit]simplify: Simplified to (* (* (/ (- 1 k) 2) (/ (- 1 k) 2)) (* (/ (- 1 k) 2) (pow (log PI) 3))) * [exit]simplify: Simplified to (* (* (/ (- 1 k) 2) (/ (- 1 k) 2)) (* (/ (- 1 k) 2) (pow (log PI) 3))) * * * * [misc]progress: [ 152 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* (log PI) (/ (- 1 k) 2))) (cbrt (* (log PI) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (29 enodes) * * [misc]simplify: iters left: 1 (32 enodes) * [exit]simplify: Simplified to (* (cbrt (* (/ (log PI) 2) (- 1 k))) (cbrt (* (/ (log PI) 2) (- 1 k)))) * [exit]simplify: Simplified to (* (cbrt (* (/ (log PI) 2) (- 1 k))) (cbrt (* (/ (log PI) 2) (- 1 k)))) * [enter]simplify: Simplifying (cbrt (* (log PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * * [misc]simplify: iters left: 2 (28 enodes) * * [misc]simplify: iters left: 1 (31 enodes) * [exit]simplify: Simplified to (cbrt (/ (* (log PI) (- 1 k)) 2)) * [exit]simplify: Simplified to (cbrt (/ (* (log PI) (- 1 k)) 2)) * * * * [misc]progress: [ 153 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (log PI) (/ (- 1 k) 2)) (* (log PI) (/ (- 1 k) 2))) (* (log PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (71 enodes) * * [misc]simplify: iters left: 2 (148 enodes) * * [misc]simplify: iters left: 1 (240 enodes) * [exit]simplify: Simplified to (pow (* (- 1 k) (/ (log PI) 2)) 3) * [exit]simplify: Simplified to (pow (* (- 1 k) (/ (log PI) 2)) 3) * * * * [misc]progress: [ 154 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (log PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * * [misc]simplify: iters left: 2 (28 enodes) * * [misc]simplify: iters left: 1 (31 enodes) * [exit]simplify: Simplified to (sqrt (/ (* (log PI) (- 1 k)) 2)) * [exit]simplify: Simplified to (sqrt (/ (* (log PI) (- 1 k)) 2)) * [enter]simplify: Simplifying (sqrt (* (log PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * * [misc]simplify: iters left: 2 (28 enodes) * * [misc]simplify: iters left: 1 (31 enodes) * [exit]simplify: Simplified to (sqrt (/ (* (log PI) (- 1 k)) 2)) * [exit]simplify: Simplified to (sqrt (/ (* (log PI) (- 1 k)) 2)) * * * * [misc]progress: [ 155 / 176 ] simplifiying candidate # * * * * [misc]progress: [ 156 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (- 1 k) 2)) (* (cbrt (/ (- 1 k) 2)) (log PI))) * [exit]simplify: Simplified to (* (cbrt (/ (- 1 k) 2)) (* (cbrt (/ (- 1 k) 2)) (log PI))) * * * * [misc]progress: [ 157 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log PI) (sqrt (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (- 1 k) 2)) (log PI)) * [exit]simplify: Simplified to (* (sqrt (/ (- 1 k) 2)) (log PI)) * * * * [misc]progress: [ 158 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log PI) 1) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * [exit]simplify: Simplified to (log PI) * [exit]simplify: Simplified to (log PI) * * * * [misc]progress: [ 159 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log PI) (- 1 k)) * * [misc]simplify: iters left: 4 (6 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * [exit]simplify: Simplified to (* (log PI) (- 1 k)) * [exit]simplify: Simplified to (* (log PI) (- 1 k)) * * * * [misc]progress: [ 160 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (log PI)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * * [misc]simplify: iters left: 2 (28 enodes) * * [misc]simplify: iters left: 1 (31 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (cbrt (log PI))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (cbrt (log PI))) * * * * [misc]progress: [ 161 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (log PI)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * * [misc]simplify: iters left: 2 (28 enodes) * * [misc]simplify: iters left: 1 (31 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (sqrt (log PI))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (sqrt (log PI))) * * * * [misc]progress: [ 162 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log PI) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * * [misc]simplify: iters left: 2 (27 enodes) * * [misc]simplify: iters left: 1 (30 enodes) * [exit]simplify: Simplified to (/ (log PI) (/ 2 (- 1 k))) * [exit]simplify: Simplified to (/ (log PI) (/ 2 (- 1 k))) * * * * [misc]progress: [ 163 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log PI) (- 1 k)) * * [misc]simplify: iters left: 4 (6 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * [exit]simplify: Simplified to (* (log PI) (- 1 k)) * [exit]simplify: Simplified to (* (log PI) (- 1 k)) * * * * [misc]progress: [ 164 / 176 ] simplifiying candidate # * * * * [misc]progress: [ 165 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (+ (* +nan.0 (* (* (log PI) k) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) k)) (- (+ (* +nan.0 (* (sqrt PI) (/ 1 k))) (- (* +nan.0 (* (* (pow (log PI) 2) k) (sqrt PI))))))))))))))) * * * * [misc]progress: [ 166 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (log PI) (- 1 (/ 1 k))))) k)) (- (* +nan.0 (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))))))))) * * * * [misc]progress: [ 167 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (- (+ (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) k)) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI)))) (pow k 2))))))))) * * * * [misc]progress: [ 168 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (sqrt PI) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* k (exp (* 1/2 (+ (log n) (log 2))))))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log n) 2) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (log PI) (* (pow k 2) (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))) (sqrt PI))) (- (+ (* +nan.0 (* (* (log PI) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow k 2) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (sqrt PI) (exp (* 1/2 (+ (log n) (log 2)))))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* (log 2) (* (exp (* 1/2 (+ (log n) (log 2)))) (pow k 2)))))) (- (+ (* +nan.0 (* (* (log PI) (* k (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow k 2) (* (log 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2)))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2)))))))) (- (+ (* +nan.0 (* (* (log PI) (* (log n) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2))))))) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) (* (log n) (* k (exp (* 1/2 (+ (log n) (log 2)))))))) (- (* +nan.0 (* (sqrt PI) (* k (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))))))))))))))))))))))))))))))))) * * * * [misc]progress: [ 169 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow k 2)))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) k))) (- (* +nan.0 (/ (* (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (* (log PI) (- 1 (/ 1 k)))))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (pow k 3))))))))) * * * * [misc]progress: [ 170 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) k))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (pow k 2)))) (- (* +nan.0 (/ (* (exp (* 1/2 (- (log -2) (log n)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log PI))))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))))))))) * * * * [misc]progress: [ 171 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (- (+ (* 1/4 (* (log n) (* (log 2) (* (exp (* 1/2 (+ (log n) (log 2)))) (pow k 2))))) (+ (* 1/8 (* (pow (log n) 2) (* (pow k 2) (exp (* 1/2 (+ (log n) (log 2))))))) (+ (exp (* 1/2 (+ (log n) (log 2)))) (* 1/8 (* (pow k 2) (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log 2)))))))))) (+ (* 1/2 (* (log n) (* k (exp (* 1/2 (+ (log n) (log 2))))))) (* 1/2 (* k (* (log 2) (exp (* 1/2 (+ (log n) (log 2))))))))) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (46 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (182 enodes) * * [misc]simplify: iters left: 3 (278 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (pow PI (- 1 k))) (sqrt k)) 1) (- (+ (* (* (sqrt 2) (* (* k k) (sqrt n))) (+ (* (* 1/4 (log 2)) (log n)) (* (* (log n) (log n)) 1/8))) (+ (- (* (sqrt 2) (sqrt n)) (* (* (log n) (* k 1/2)) (* (sqrt 2) (sqrt n)))) (* (* k (* 1/8 k)) (* (* (sqrt 2) (sqrt n)) (* (log 2) (log 2)))))) (* (* (* k 1/2) (log 2)) (* (sqrt 2) (sqrt n))))) * * * * [misc]progress: [ 172 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ (exp (* 1/2 (- (log 2) (log n)))) (exp (* 1/2 (/ (- (log 2) (log n)) k)))) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (53 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (165 enodes) * * [misc]simplify: iters left: 1 (260 enodes) * [exit]simplify: Simplified to (/ (exp (* (- (log 2) (log n)) (- 1/2 (/ 1/2 k)))) (/ (sqrt k) (sqrt (pow PI (- 1 k))))) * * * * [misc]progress: [ 173 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ (exp (* 1/2 (- (log -2) (log n)))) (exp (* -1/2 (/ (- (log -2) (log n)) k)))) 1) (/ (exp (* (log PI) (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (57 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (144 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (exp (* (- (log -2) (log n)) (- 1/2 (/ -1/2 k)))) (/ (sqrt (pow PI (- 1 k))) (sqrt k))) * * * * [misc]progress: [ 174 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (exp (- (* 1/2 (log PI)) (* 1/2 (* (log PI) k)))) (sqrt k))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (149 enodes) * * [misc]simplify: iters left: 1 (236 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt PI) (sqrt k)) (pow (sqrt PI) k)) (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 175 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (exp (- (* 1/2 (log PI)) (* 1/2 (* (log PI) k)))) (sqrt k))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (149 enodes) * * [misc]simplify: iters left: 1 (236 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt PI) (sqrt k)) (pow (sqrt PI) k)) (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * * * * [misc]progress: [ 176 / 176 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2))) 1) (/ (exp (- (* 1/2 (log PI)) (* 1/2 (* (log PI) k)))) (sqrt k))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (149 enodes) * * [misc]simplify: iters left: 1 (236 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt PI) (sqrt k)) (pow (sqrt PI) k)) (/ (pow (+ n n) (/ 1 2)) (pow (+ n n) (/ k 2)))) * * * [misc]progress: adding candidates to table * [misc]progress: [Phase 3 of 3] Extracting. * * [misc]regime-changes: Finding splitpoints for: (# # # # # # # #) * [misc]regimes: Found splitpoints: (#s(sp 0 k +inf.0)) , with alts (#) * [enter]simplify: Simplifying (* (cbrt (+ n n)) PI) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * [exit]simplify: Simplified to (* (cbrt (+ n n)) PI) * [exit]simplify: Simplified to (* (cbrt (+ n n)) PI) * [enter]simplify: Simplifying (/ (pow (+ n n) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (- (+ (+ (* (sqrt (+ PI PI)) (sqrt n)) (* (* (log (+ PI PI)) (* (* k k) (log n))) (* 1/4 (* (sqrt (+ PI PI)) (sqrt n))))) (* 1/8 (* (* (* k k) (* (sqrt (+ PI PI)) (sqrt n))) (+ (* (log n) (log n)) (* (log (+ PI PI)) (log (+ PI PI))))))) (* (* 1/2 k) (* (* (sqrt (+ PI PI)) (sqrt n)) (+ (log (+ PI PI)) (log n))))) * * [misc]simplify: iters left: 6 (30 enodes) * * [misc]simplify: iters left: 5 (67 enodes) * * [misc]simplify: iters left: 4 (154 enodes) * * [misc]simplify: iters left: 3 (327 enodes) * [exit]simplify: Simplified to (+ (* (+ (* (log n) (log n)) (* (log (+ PI PI)) (log (+ PI PI)))) (* (* k (* k 1/8)) (* (sqrt (+ PI PI)) (sqrt n)))) (- (+ (* (sqrt (+ PI PI)) (sqrt n)) (* (* (* (* k k) (log n)) (log (+ PI PI))) (* (sqrt (+ PI PI)) (* (sqrt n) 1/4)))) (* (+ (log n) (log (+ PI PI))) (* (* (* 1/2 k) (sqrt n)) (sqrt (+ PI PI)))))) * [exit]simplify: Simplified to (+ (* (+ (* (log n) (log n)) (* (log (+ PI PI)) (log (+ PI PI)))) (* (* k (* k 1/8)) (* (sqrt (+ PI PI)) (sqrt n)))) (- (+ (* (sqrt (+ PI PI)) (sqrt n)) (* (* (* (* k k) (log n)) (log (+ PI PI))) (* (sqrt (+ PI PI)) (* (sqrt n) 1/4)))) (* (+ (log n) (log (+ PI PI))) (* (* (* 1/2 k) (sqrt n)) (sqrt (+ PI PI)))))) * [enter]simplify: Simplifying (sqrt k) * * [misc]simplify: iters left: 1 (2 enodes) * [exit]simplify: Simplified to (sqrt k) * [exit]simplify: Simplified to (sqrt k) * [enter]simplify: Simplifying (* (sqrt (/ (pow (+ n n) (/ (- 1 k) 2)) 1)) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * * [misc]simplify: iters left: 1 (34 enodes) * [exit]simplify: Simplified to (* (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) (sqrt (/ (pow (+ n n) (/ (- 1 k) 2)) 1))) * [exit]simplify: Simplified to (* (/ (pow PI (/ (- 1 k) 2)) (sqrt k)) (sqrt (/ (pow (+ n n) (/ (- 1 k) 2)) 1))) * [enter]simplify: Simplifying (* (sqrt k) (pow (* (+ n n) PI) (/ k 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * * [misc]simplify: iters left: 2 (27 enodes) * [exit]simplify: Simplified to (* (sqrt k) (pow (+ (* n PI) (* n PI)) (/ k 2))) * [exit]simplify: Simplified to (* (sqrt k) (pow (+ (* n PI) (* n PI)) (/ k 2))) * [enter]simplify: Simplifying (pow (+ n n) (/ 1 2)) * * [misc]simplify: iters left: 3 (6 enodes) * * [misc]simplify: iters left: 2 (9 enodes) * * [misc]simplify: iters left: 1 (10 enodes) * [exit]simplify: Simplified to (pow (+ n n) (/ 1 2)) * [exit]simplify: Simplified to (pow (+ n n) (/ 1 2)) * [enter]simplify: Simplifying (pow (+ n n) (/ k 2)) * * [misc]simplify: iters left: 3 (6 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * * [misc]simplify: iters left: 1 (8 enodes) * [exit]simplify: Simplified to (pow (+ n n) (/ k 2)) * [exit]simplify: Simplified to (pow (+ n n) (/ k 2)) * [enter]simplify: Simplifying (pow (+ n n) (/ 1 2)) * * [misc]simplify: iters left: 3 (6 enodes) * * [misc]simplify: iters left: 2 (9 enodes) * * [misc]simplify: iters left: 1 (10 enodes) * [exit]simplify: Simplified to (pow (+ n n) (/ 1 2)) * [exit]simplify: Simplified to (pow (+ n n) (/ 1 2)) * [enter]simplify: Simplifying (pow (+ n n) (/ k 2)) * * [misc]simplify: iters left: 3 (6 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * * [misc]simplify: iters left: 1 (8 enodes) * [exit]simplify: Simplified to (pow (+ n n) (/ k 2)) * [exit]simplify: Simplified to (pow (+ n n) (/ k 2))