* [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 / 3 * * * [misc]progress: picking best candidate * * * * [misc]pick: Picked # * * * [misc]progress: localizing error * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 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: [ 2 / 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: [ 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: generating rewritten candidates * * * * [misc]progress: [ 1 / 3 ] rewriting at (2 1) * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1 1) * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 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: [ 2 / 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: [ 3 / 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: [ 4 / 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: [ 5 / 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: [ 6 / 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: [ 7 / 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: [ 8 / 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: [ 9 / 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: [ 10 / 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: [ 11 / 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: [ 12 / 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: [ 13 / 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: [ 14 / 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: [ 15 / 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: [ 16 / 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: [ 17 / 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: [ 18 / 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: [ 19 / 73 ] simplifiying candidate # * * * * [misc]progress: [ 20 / 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: [ 21 / 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: [ 22 / 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: [ 23 / 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: [ 24 / 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: [ 25 / 73 ] simplifiying candidate # * * * * [misc]progress: [ 26 / 73 ] simplifiying candidate # * * * * [misc]progress: [ 27 / 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: [ 28 / 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: [ 29 / 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: [ 30 / 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: [ 31 / 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: [ 32 / 73 ] simplifiying candidate # * * * * [misc]progress: [ 33 / 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: [ 34 / 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: [ 35 / 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: [ 36 / 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: [ 37 / 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: [ 38 / 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: [ 39 / 73 ] simplifiying candidate # * * * * [misc]progress: [ 40 / 73 ] simplifiying candidate # * * * * [misc]progress: [ 41 / 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: [ 42 / 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: [ 43 / 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: [ 44 / 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: [ 45 / 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: [ 46 / 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: [ 47 / 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: [ 48 / 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: [ 49 / 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: [ 50 / 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: [ 51 / 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: [ 52 / 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: [ 53 / 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: [ 54 / 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: [ 55 / 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: [ 56 / 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: [ 57 / 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: [ 58 / 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: [ 59 / 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: [ 60 / 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: [ 61 / 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: [ 62 / 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: [ 63 / 73 ] simplifiying candidate # * * * * [misc]progress: [ 64 / 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: [ 65 / 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: [ 66 / 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: [ 67 / 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: [ 68 / 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: [ 69 / 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: [ 70 / 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: [ 71 / 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: [ 72 / 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: [ 73 / 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: adding candidates to table * * [misc]progress: iteration 2 / 3 * * * [misc]progress: picking best candidate * * * * [misc]pick: Picked # * * * [misc]progress: localizing error * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] 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: [ 2 / 4 ] generating series at (2 2) * [misc]approximate: Taking taylor expansion of (/ 1 (sqrt k)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt k)) in 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 (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt k)) in 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 (/ 1 +nan.0) into +nan.0 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* (- +nan.0) k) (+ (- +nan.0) (* +nan.0 (/ 1 k)))) into (- (+ +nan.0 (- (+ (* +nan.0 k) (- (* +nan.0 (/ 1 k))))))) * [misc]approximate: Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) 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]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) 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]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]backup-simplify: Simplify +nan.0 into +nan.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 (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.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 (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 2)) (+ (* (- +nan.0) (/ 1 k)) +nan.0)) into (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2)))))))) * [misc]approximate: Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) 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]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 (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) 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]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 (/ 1 +nan.0) into +nan.0 * [misc]backup-simplify: Simplify +nan.0 into +nan.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 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.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 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2)))))))) * * * * [misc]progress: [ 3 / 4 ] 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: [ 4 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (/ 1 (sqrt k))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (/ 1 (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 (/ 1 (sqrt k)) in 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 (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (/ 1 (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 (/ 1 (sqrt k)) in 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 (/ 1 (sqrt k)) into (sqrt (/ 1 k)) * [misc]taylor: Taking taylor expansion of (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (/ 1 (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 (/ 1 (sqrt k)) in 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 (/ 1 (sqrt k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (sqrt (/ 1 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 (- (+ (* (sqrt (/ 1 k)) (/ 0 (sqrt k))))) 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 (+ (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) 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 (+ (* 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 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (sqrt (/ 1 k)) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) 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 (/ (+ (* -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 (+ (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) 0) (+ (* 0 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 (+ (* 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 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (sqrt (/ 1 k)) (/ 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 (+ (* 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 (+ (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 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 (+ (* 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)) (/ 1 (sqrt (/ 1 k)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ (- 1 (/ 1 k)) 2)) (/ 1 (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 (/ 1 (sqrt (/ 1 k))) 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]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (* (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ (- 1 (/ 1 k)) 2)) (/ 1 (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 (/ 1 (sqrt (/ 1 k))) in 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 (/ 1 (sqrt (/ 1 k))) into (sqrt k) * [misc]taylor: Taking taylor expansion of (* (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ (- 1 (/ 1 k)) 2)) (/ 1 (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 (/ 1 (sqrt (/ 1 k))) in 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 (/ 1 (sqrt (/ 1 k))) into (sqrt k) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt 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 (- (+ (* (sqrt 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 (+ (* 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 (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 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 (+ (* (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 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 (- (+ (* (sqrt 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 (+ (* 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 (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 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 (/ (- 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 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 (- (+ (* (sqrt 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 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 (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 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 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)) (/ 1 (sqrt (/ 1 (- k))))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ (- 1 (/ 1 (- k))) 2)) (/ 1 (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 (/ 1 (sqrt (/ 1 (- k)))) 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]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 (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (* (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ (- 1 (/ 1 (- k))) 2)) (/ 1 (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 (/ 1 (sqrt (/ 1 (- k)))) in 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 (/ 1 (sqrt (/ -1 k))) into (/ 1 (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (* (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ (- 1 (/ 1 (- k))) 2)) (/ 1 (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 (/ 1 (sqrt (/ 1 (- k)))) in 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 (/ 1 (sqrt (/ -1 k))) into (/ 1 (sqrt (/ -1 k))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (/ 1 (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 (- (+ (* (/ 1 (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 (+ (* -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 (+ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) 0) (* 0 (/ 1 (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 (- 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 (- (+ (* (/ 1 (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 (+ (* -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 (+ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (/ 1 (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: generating rewritten candidates * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 1) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 1 1) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 86 ] 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))))) (/ 1 (sqrt k))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (97 enodes) * * [misc]simplify: iters left: 4 (193 enodes) * * [misc]simplify: iters left: 3 (380 enodes) * [exit]simplify: Simplified to (/ (- (+ (+ (* (sqrt (+ PI PI)) (sqrt n)) (* (* (* (log (+ PI PI)) (* (* k k) (log n))) (* (sqrt (+ PI PI)) (sqrt n))) 1/4)) (* 1/8 (* (* (* (sqrt (+ PI PI)) (sqrt n)) (* k k)) (+ (* (log (+ PI PI)) (log (+ PI PI))) (* (log n) (log n)))))) (* (* 1/2 k) (* (* (sqrt (+ PI PI)) (sqrt n)) (+ (log (+ PI PI)) (log n))))) (sqrt k)) * * * * [misc]progress: [ 2 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (/ 1 (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (109 enodes) * * [misc]simplify: iters left: 1 (153 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (+ (/ PI n) (/ PI n)) (- 1 (/ 1 k)))) (sqrt k)) * * * * [misc]progress: [ 3 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (/ 1 (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (115 enodes) * * [misc]simplify: iters left: 1 (190 enodes) * [exit]simplify: Simplified to (/ (pow (/ (* PI -2) n) (+ 1/2 (/ 1/2 k))) (sqrt k)) * * * * [misc]progress: [ 4 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (- (+ +nan.0 (- (+ (* +nan.0 k) (- (* +nan.0 (/ 1 k)))))))) * * * * [misc]progress: [ 5 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2))))))))) * * * * [misc]progress: [ 6 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2))))))))) * * * * [misc]progress: [ 7 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (42 enodes) * [exit]simplify: Simplified to (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 8 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (42 enodes) * [exit]simplify: Simplified to (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 9 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (42 enodes) * [exit]simplify: Simplified to (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 10 / 86 ] 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: [ 11 / 86 ] 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: [ 12 / 86 ] 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: [ 13 / 86 ] 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: [ 14 / 86 ] 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: [ 15 / 86 ] 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: [ 16 / 86 ] 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: [ 17 / 86 ] 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: [ 18 / 86 ] 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: [ 19 / 86 ] 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: [ 20 / 86 ] 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: [ 21 / 86 ] 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: [ 22 / 86 ] simplifiying candidate # * * * * [misc]progress: [ 23 / 86 ] 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: [ 24 / 86 ] 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: [ 25 / 86 ] 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: [ 26 / 86 ] 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: [ 27 / 86 ] 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: [ 28 / 86 ] simplifiying candidate # * * * * [misc]progress: [ 29 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (- 1/2) * * [misc]simplify: iters left: 2 (2 enodes) * [exit]simplify: Simplified to (- 1/2) * [exit]simplify: Simplified to (- 1/2) * * * * [misc]progress: [ 30 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (- 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) * * * * [misc]progress: [ 31 / 86 ] simplifiying candidate # * * * * [misc]progress: [ 32 / 86 ] simplifiying candidate # * * * * [misc]progress: [ 33 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (sqrt k))) * * [misc]simplify: iters left: 4 (4 enodes) * [exit]simplify: Simplified to (- (log (sqrt k))) * [exit]simplify: Simplified to (- (log (sqrt k))) * * * * [misc]progress: [ 34 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (11 enodes) * [exit]simplify: Simplified to (- (log (sqrt k))) * [exit]simplify: Simplified to (- (log (sqrt k))) * * * * [misc]progress: [ 35 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (exp (/ 1 (sqrt k))) * [exit]simplify: Simplified to (exp (/ 1 (sqrt k))) * * * * [misc]progress: [ 36 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (8 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) * [enter]simplify: Simplifying (cbrt (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (cbrt (/ 1 (sqrt k))) * [exit]simplify: Simplified to (cbrt (/ 1 (sqrt k))) * * * * [misc]progress: [ 37 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (39 enodes) * * [misc]simplify: iters left: 1 (45 enodes) * [exit]simplify: Simplified to (/ 1 (* (sqrt k) k)) * [exit]simplify: Simplified to (/ 1 (* (sqrt k) k)) * * * * [misc]progress: [ 38 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) * [enter]simplify: Simplifying (sqrt (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) * * * * [misc]progress: [ 39 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (- 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 (- (sqrt k)) * * [misc]simplify: iters left: 3 (3 enodes) * [exit]simplify: Simplified to (- (sqrt k)) * [exit]simplify: Simplified to (- (sqrt k)) * * * * [misc]progress: [ 40 / 86 ] simplifiying candidate # * * * * [misc]progress: [ 41 / 86 ] 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: [ 42 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) 1) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to (/ (sqrt k) 1) * [exit]simplify: Simplified to (/ (sqrt k) 1) * * * * [misc]progress: [ 43 / 86 ] 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)))) * * * * [misc]progress: [ 44 / 86 ] 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))) * * * * [misc]progress: [ 45 / 86 ] 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 * * * * [misc]progress: [ 46 / 86 ] simplifiying candidate # * * * * [misc]progress: [ 47 / 86 ] 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: [ 48 / 86 ] 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: [ 49 / 86 ] 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: [ 50 / 86 ] 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: [ 51 / 86 ] 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: [ 52 / 86 ] simplifiying candidate # * * * * [misc]progress: [ 53 / 86 ] 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: [ 54 / 86 ] 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: [ 55 / 86 ] 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: [ 56 / 86 ] 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: [ 57 / 86 ] 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: [ 58 / 86 ] 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: [ 59 / 86 ] simplifiying candidate # * * * * [misc]progress: [ 60 / 86 ] simplifiying candidate # * * * * [misc]progress: [ 61 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (log (* (+ n n) PI)) (/ (- 1 k) 2)) (- (log (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 (83 enodes) * * [misc]simplify: iters left: 2 (123 enodes) * * [misc]simplify: iters left: 1 (179 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: [ 62 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (log (* (+ n n) PI)) (/ (- 1 k) 2)) (log (/ 1 (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (148 enodes) * * [misc]simplify: iters left: 1 (205 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: [ 63 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (log (* (+ n n) PI)) (/ (- 1 k) 2)) (- (log (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 (83 enodes) * * [misc]simplify: iters left: 2 (123 enodes) * * [misc]simplify: iters left: 1 (179 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: [ 64 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (log (* (+ n n) PI)) (/ (- 1 k) 2)) (log (/ 1 (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (148 enodes) * * [misc]simplify: iters left: 1 (205 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: [ 65 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (pow (* (+ n n) PI) (/ (- 1 k) 2))) (- (log (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (104 enodes) * * [misc]simplify: iters left: 1 (154 enodes) * [exit]simplify: Simplified to (+ (* (/ (- 1 k) 2) (log (* PI (+ n n)))) (- (log (sqrt k)))) * [exit]simplify: Simplified to (+ (* (/ (- 1 k) 2) (log (* PI (+ n n)))) (- (log (sqrt k)))) * * * * [misc]progress: [ 66 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (pow (* (+ n n) PI) (/ (- 1 k) 2))) (log (/ 1 (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (76 enodes) * * [misc]simplify: iters left: 2 (128 enodes) * * [misc]simplify: iters left: 1 (208 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: [ 67 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (/ 1 (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (126 enodes) * * [misc]simplify: iters left: 1 (199 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* PI (+ n n)))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* PI (+ n n)))) (log (sqrt k))) * * * * [misc]progress: [ 68 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (/ 1 (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (51 enodes) * * [misc]simplify: iters left: 1 (54 enodes) * [exit]simplify: Simplified to (exp (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (exp (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 69 / 86 ] 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))) (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (124 enodes) * * [misc]simplify: iters left: 1 (144 enodes) * [exit]simplify: Simplified to (* (pow (pow (* PI (+ n n)) (/ (- 1 k) 2)) 3) (/ (/ 1 k) (sqrt k))) * [exit]simplify: Simplified to (* (pow (pow (* PI (+ n n)) (/ (- 1 k) 2)) 3) (/ (/ 1 k) (sqrt k))) * * * * [misc]progress: [ 70 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (/ 1 (sqrt k)))) (cbrt (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (/ 1 (sqrt k))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * * [misc]simplify: iters left: 1 (46 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k)))) * [enter]simplify: Simplifying (cbrt (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (/ 1 (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * [exit]simplify: Simplified to (cbrt (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (cbrt (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 71 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (/ 1 (sqrt k))) (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (/ 1 (sqrt k)))) (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (/ 1 (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (71 enodes) * * [misc]simplify: iters left: 2 (92 enodes) * * [misc]simplify: iters left: 1 (111 enodes) * [exit]simplify: Simplified to (pow (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k)) 3) * [exit]simplify: Simplified to (pow (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k)) 3) * * * * [misc]progress: [ 72 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (/ 1 (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (sqrt k))) * [enter]simplify: Simplifying (sqrt (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (/ 1 (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 73 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* (+ n n) PI) (/ 1 2)) 1) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (30 enodes) * [exit]simplify: Simplified to (pow (* PI (+ n n)) (/ 1 2)) * [exit]simplify: Simplified to (pow (* PI (+ n n)) (/ 1 2)) * [enter]simplify: Simplifying (* (pow (* (+ n n) PI) (/ k 2)) (sqrt k)) * * [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) * [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: [ 74 / 86 ] simplifiying candidate # * * * * [misc]progress: [ 75 / 86 ] simplifiying candidate # * * * * [misc]progress: [ 76 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * [exit]simplify: Simplified to (* (* (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (cbrt (/ 1 (sqrt k)))) (cbrt (/ 1 (sqrt k)))) * [exit]simplify: Simplified to (* (* (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (cbrt (/ 1 (sqrt k)))) (cbrt (/ 1 (sqrt k)))) * * * * [misc]progress: [ 77 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 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 (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) * [exit]simplify: Simplified to (* (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) * * * * [misc]progress: [ 78 / 86 ] 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 (19 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) (/ (- 1 k) 2)) * * * * [misc]progress: [ 79 / 86 ] 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 (19 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) (/ (- 1 k) 2)) * * * * [misc]progress: [ 80 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow PI (/ (- 1 k) 2)) (/ 1 (sqrt k))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (23 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: [ 81 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (* (+ n n) PI) (/ (- 1 k) 2))) (/ 1 (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* (+ PI PI) n) (/ (- 1 k) 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (cbrt (pow (* (+ PI PI) n) (/ (- 1 k) 2))) (sqrt k)) * * * * [misc]progress: [ 82 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2))) (/ 1 (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (+ PI PI) n) (/ (- 1 k) 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (pow (* (+ PI PI) n) (/ (- 1 k) 2))) (sqrt k)) * * * * [misc]progress: [ 83 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (/ 1 (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * [exit]simplify: Simplified to (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 84 / 86 ] 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 (19 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* n (+ PI PI)) (/ (- 1 k) 2)) * * * * [misc]progress: [ 85 / 86 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* (+ n n) PI) (/ 1 2)) (/ 1 (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (43 enodes) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) * * * * [misc]progress: [ 86 / 86 ] simplifiying candidate # * * * [misc]progress: adding candidates to table * * [misc]progress: iteration 3 / 3 * * * [misc]progress: picking best candidate * * * * [misc]pick: Picked # * * * [misc]progress: localizing error * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 2 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 / 4 ] 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: [ 3 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (/ (pow (* (+ n n) PI) (/ 1 2)) (* (sqrt k) (pow (* (+ n n) PI) (/ k 2)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (+ n n) PI) (/ 1 2)) (* (sqrt k) (pow (* (+ n n) PI) (/ k 2)))) in k * [misc]taylor: Taking taylor expansion of (pow (* (+ n n) PI) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (+ n n) PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (+ n n) PI))) 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) 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) (pow (* (+ n n) PI) (/ k 2))) in 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]taylor: Taking taylor expansion of (pow (* (+ n n) PI) (/ k 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* (+ n n) PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* (+ n n) PI))) 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) 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 0) into 1 * [misc]backup-simplify: Simplify (* 0 1) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log (* 2 (* n PI)))) 1) 1)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (+ (* 0 (* 1/2 (log (* 2 (* n PI))))) (* +nan.0 1)) 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 2)) (* (sqrt k) (pow (* (+ n n) PI) (/ k 2)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (+ n n) PI) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (+ n n) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (+ n n) PI))) 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) 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 (+ (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]taylor: Taking taylor expansion of (* (sqrt k) (pow (* (+ n n) PI) (/ k 2))) in 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]taylor: Taking taylor expansion of (pow (* (+ n n) PI) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* (+ n n) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* (+ n n) PI))) 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) 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 k) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* (sqrt k) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k))) into (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (+ n n) PI) (/ 1 2)) (* (sqrt k) (pow (* (+ n n) PI) (/ k 2)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (+ n n) PI) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (+ n n) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (+ n n) PI))) 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) 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 (+ (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]taylor: Taking taylor expansion of (* (sqrt k) (pow (* (+ n n) PI) (/ k 2))) in 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]taylor: Taking taylor expansion of (pow (* (+ n n) PI) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* (+ n n) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* (+ n n) PI))) 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) 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 k) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* (sqrt k) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k))) into (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) * [misc]taylor: Taking taylor expansion of (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (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 (+ (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 (+ (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]taylor: Taking taylor expansion of (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* 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 (* k (+ (log (* 2 PI)) (log n))) 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 (* 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 (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 0 (+ (log (* 2 PI)) (log n))) into 0 * [misc]backup-simplify: Simplify (* 1/2 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 (+ (* 0 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 0)) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 1) into (exp (* 1/2 (+ (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 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)) (log n)))) 0) 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 (- (+ (* 1/2 (/ 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 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) 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 2) (+ (* (* 1/2 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 k) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k))) (+ (* (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (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 (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1) 1)))) into (+ (* 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))) 1)))) into (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) +nan.0) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) 0)) 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 (- (+ (* 1/2 (/ 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 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) 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 (/ (+ (* -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 2) (+ (* (* 1/2 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 k) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* 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 (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k))) (+ (* (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)))) (* 0 (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (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 (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.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 (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) 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 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 0))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (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)))) 1)) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) +nan.0) (+ (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) +nan.0) (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) 0))) 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 (- (+ (* 1/2 (/ 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 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (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 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 2) (+ (* (* 1/2 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 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* 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 (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k))) (+ (* (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)))) (* 0 (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)))) (* 0 (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (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 (- (+ (* 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 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 (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (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 (+ (* 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 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 0)))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (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 (+ (* 1/16 (* (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 (- (/ 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)))))) 1)) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) (/ (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) 1)) (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (- (+ (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (log n)))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 3))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 3))) (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow (log n) 2)))))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) +nan.0) (+ (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) +nan.0) (+ (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) +nan.0) (* (- (+ (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (log n)))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 3))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 3))) (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow (log n) 2)))))))) 0)))) 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)))))))))))))) into (- (+ (* +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))))) (- (+ (* +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))))))))))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +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))))) (- (+ (* +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))))))))))))))) (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 2)) (* (sqrt (/ 1 k)) (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ (/ 1 k) 2)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ 1 2)) (* (sqrt (/ 1 k)) (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ (/ 1 k) 2)))) in k * [misc]taylor: Taking taylor expansion of (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (+ (/ 1 n) (/ 1 n)) PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (+ (/ 1 n) (/ 1 n)) PI))) 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)) 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 (* 1/2 (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) 1/2) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ (/ 1 k) 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 (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ (/ 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (+ (/ 1 n) (/ 1 n)) PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (+ (/ 1 n) (/ 1 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 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)) 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 k) 2) (log (* (+ (/ 1 n) (/ 1 n)) PI)))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (* 0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) into (- (* +nan.0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (/ (pow (* 2 (/ PI n)) 1/2) (- (* +nan.0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into (* +nan.0 (* (sqrt (/ (* 2 PI) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ 1 2)) (* (sqrt (/ 1 k)) (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ (/ 1 k) 2)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (+ (/ 1 n) (/ 1 n)) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (+ (/ 1 n) (/ 1 n)) PI))) 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)) 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 (- (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]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ (/ 1 k) 2))) in 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]taylor: Taking taylor expansion of (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (+ (/ 1 n) (/ 1 n)) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (+ (/ 1 n) (/ 1 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 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)) 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 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (/ (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ 1 2)) (* (sqrt (/ 1 k)) (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ (/ 1 k) 2)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (+ (/ 1 n) (/ 1 n)) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (+ (/ 1 n) (/ 1 n)) PI))) 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)) 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 (- (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]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ (/ 1 k) 2))) in 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]taylor: Taking taylor expansion of (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (+ (/ 1 n) (/ 1 n)) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (+ (/ 1 n) (/ 1 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 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)) 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 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (- (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 (- (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 (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (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]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (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 PI)) (log n)) k) in k * [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]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 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) 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)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (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 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 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 (- (+ (* 1/2 (/ 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 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (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 (+ (* 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 2) (+ (* (/ 1/2 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 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (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 (+ (* 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) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [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 (- (+ (* 1/2 (/ 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 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (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 (+ (* 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 2) (+ (* (/ 1/2 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 k) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) 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 (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) (* 0 (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (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 (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.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) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [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 (- (+ (* 1/2 (/ 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 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (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 (/ 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 2) (+ (* (/ 1/2 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 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (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 (- (+ (* (/ 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 (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) (* 0 (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) (* 0 (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (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 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.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) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (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 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* k (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (pow k 3) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (pow k 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))))))) * [misc]approximate: Taking taylor expansion of (/ (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ 1 2)) (* (sqrt (/ 1 (- k))) (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ (/ 1 (- k)) 2)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ 1 2)) (* (sqrt (/ 1 (- k))) (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ (/ 1 (- k)) 2)))) in k * [misc]taylor: Taking taylor expansion of (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI))) 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))) 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 (* 1/2 (log (* -2 (/ PI n))))) into (pow (* -2 (/ PI n)) 1/2) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (- k))) (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ (/ 1 (- k)) 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]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]taylor: Taking taylor expansion of (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ (/ 1 (- k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (+ (/ 1 (- n)) (/ 1 (- 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 (- 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))) 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 (- k)) 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI)))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (* 0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (/ (pow (* -2 (/ PI n)) 1/2) (- (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) into (* +nan.0 (* (sqrt (/ (* PI -2) n)) (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ 1 2)) (* (sqrt (/ 1 (- k))) (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ (/ 1 (- k)) 2)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI))) 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))) 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 (- (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]taylor: Taking taylor expansion of (* (sqrt (/ 1 (- k))) (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ (/ 1 (- k)) 2))) in 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]taylor: Taking taylor expansion of (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (+ (/ 1 (- n)) (/ 1 (- 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 (- 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))) 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 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ 1 2)) (* (sqrt (/ 1 (- k))) (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ (/ 1 (- k)) 2)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI))) 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))) 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 (- (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]taylor: Taking taylor expansion of (* (sqrt (/ 1 (- k))) (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ (/ 1 (- k)) 2))) in 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]taylor: Taking taylor expansion of (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (+ (/ 1 (- n)) (/ 1 (- 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 (- 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))) 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 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (- (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 (- (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 (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (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]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) in k * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (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 PI)) (log n)) k) in k * [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]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 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) 1) 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)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (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 PI)) (log n)) k))) 0) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (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 (+ (* -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 (- (+ (* 1/2 (/ 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 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (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 (+ (* -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 2) (+ (* (/ -1/2 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 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ -1 k)) 0) (* 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) (/ 0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (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 (+ (* -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) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) 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 PI)) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (+ (* (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) 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 (/ 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 (- (+ (* 1/2 (/ 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 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (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 (- 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 2) (+ (* (/ -1/2 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 k) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (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 (+ (* (sqrt (/ -1 k)) 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) (/ 0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))) (* 0 (/ 0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (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 (+ (* -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) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) 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 PI)) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (+ (* (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (* (/ 1 (- k)) 1)) (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) k))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (pow k 2))))))))) * * * * [misc]progress: [ 4 / 4 ] generating series at (2 1) * [misc]approximate: Taking taylor expansion of (pow (* (+ n n) PI) (/ 1 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (+ n n) PI) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (+ n n) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (+ n n) PI))) 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) 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 (+ (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]taylor: Taking taylor expansion of (pow (* (+ n n) PI) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (+ n n) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (+ n n) PI))) 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) 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 (+ (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 (- (+ (* 1/2 (/ 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 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) 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 (/ (+ (* -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 (- (+ (* 1/2 (/ 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 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (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 (+ 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 (- (+ (* 1/2 (/ 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 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (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 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 (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 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 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) 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 (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 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 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (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 (+ 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 (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0 * [misc]backup-simplify: Simplify (- (+ (* 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 (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]approximate: Taking taylor expansion of (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ 1 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (+ (/ 1 n) (/ 1 n)) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (+ (/ 1 n) (/ 1 n)) PI))) 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)) 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 (- (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]taylor: Taking taylor expansion of (pow (* (+ (/ 1 n) (/ 1 n)) PI) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (+ (/ 1 n) (/ 1 n)) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (+ (/ 1 n) (/ 1 n)) PI))) 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)) 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 (- (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 (- (+ (* 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 (- (+ (* 1/2 (/ 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 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) 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 (- (+ (* 1/2 (/ 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 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (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 (- (+ (* 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 (- (+ (* 1/2 (/ 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 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (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 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 (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 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 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) 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 (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 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 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (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 (/ 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 (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0 * [misc]backup-simplify: Simplify (- (+ (* 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 (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]approximate: Taking taylor expansion of (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ 1 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI))) 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))) 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 (- (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]taylor: Taking taylor expansion of (pow (* (+ (/ 1 (- n)) (/ 1 (- n))) PI) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (+ (/ 1 (- n)) (/ 1 (- n))) PI))) 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))) 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 (- (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) 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 (- (+ (* 1/2 (/ 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 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) 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 (- (+ (* 1/2 (/ 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 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (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 (- 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 (- (+ (* 1/2 (/ 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 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (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 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 (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* -2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* -2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* -2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 1)))) 24) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 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 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) 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 (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* -2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* -2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* -2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* -2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* -2 PI) 1)))) 120) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 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 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (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 (- 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 (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* -2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* -2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* -2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* -2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* -2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* -2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* -2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* -2 PI) 1)))) 720) into 0 * [misc]backup-simplify: Simplify (- (+ (* 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 (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * * * [misc]progress: generating rewritten candidates * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2 2 1) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1 1) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 1) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* (+ n n) PI) (/ 1 2)) (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * [exit]simplify: Simplified to (/ (pow (* PI (+ n n)) (/ 1 2)) (* (pow (* PI (+ n n)) (/ k 2)) (sqrt k))) * * * * [misc]progress: [ 2 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* (+ n n) PI) (/ 1 2)) (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * [exit]simplify: Simplified to (/ (pow (* PI (+ n n)) (/ 1 2)) (* (pow (* PI (+ n n)) (/ k 2)) (sqrt k))) * * * * [misc]progress: [ 3 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* (+ n n) PI) (/ 1 2)) (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * [exit]simplify: Simplified to (/ (pow (* PI (+ n n)) (/ 1 2)) (* (pow (* PI (+ n n)) (/ k 2)) (sqrt k))) * * * * [misc]progress: [ 4 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (/ 1 2)) (* (sqrt k) (pow (* (+ n n) PI) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * [exit]simplify: Simplified to (/ (pow (* (+ PI PI) n) (/ 1 2)) (* (pow (* (+ PI PI) n) (/ k 2)) (sqrt k))) * * * * [misc]progress: [ 5 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (/ 1 2)) (* (sqrt k) (pow (* (+ n n) PI) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * [exit]simplify: Simplified to (/ (pow (* (+ PI PI) n) (/ 1 2)) (* (pow (* (+ PI PI) n) (/ k 2)) (sqrt k))) * * * * [misc]progress: [ 6 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (/ 1 2)) (* (sqrt k) (pow (* (+ n n) PI) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (33 enodes) * [exit]simplify: Simplified to (/ (pow (* (+ PI PI) n) (/ 1 2)) (* (pow (* (+ PI PI) n) (/ k 2)) (sqrt k))) * * * * [misc]progress: [ 7 / 88 ] 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: [ 8 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* k (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (pow k 3) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (pow k 2) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))))))) * * * * [misc]progress: [ 9 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) k))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (pow k 2))))))))) * * * * [misc]progress: [ 10 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (sqrt k) (pow (* (+ n n) PI) (/ k 2)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (140 enodes) * * [misc]simplify: iters left: 1 (193 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt n) (sqrt k)) (sqrt (+ PI PI))) (pow (* PI (+ n n)) (/ k 2))) * * * * [misc]progress: [ 11 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (sqrt k) (pow (* (+ n n) PI) (/ k 2)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (62 enodes) * * [misc]simplify: iters left: 1 (83 enodes) * [exit]simplify: Simplified to (/ (pow (exp 1/2) (- (log (+ PI PI)) (log n))) (* (sqrt k) (pow (* (+ PI PI) n) (/ k 2)))) * * * * [misc]progress: [ 12 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (sqrt k) (pow (* (+ n n) PI) (/ k 2)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (65 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (/ (pow (exp 1/2) (- (log (* PI -2)) (log n))) (* (sqrt k) (pow (* (+ PI PI) n) (/ k 2)))) * * * * [misc]progress: [ 13 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 14 / 88 ] 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: [ 15 / 88 ] 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: [ 16 / 88 ] 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: [ 17 / 88 ] 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: [ 18 / 88 ] 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: [ 19 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 20 / 88 ] 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: [ 21 / 88 ] 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: [ 22 / 88 ] 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: [ 23 / 88 ] 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: [ 24 / 88 ] 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: [ 25 / 88 ] 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: [ 26 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 27 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 28 / 88 ] 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: [ 29 / 88 ] 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: [ 30 / 88 ] 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: [ 31 / 88 ] 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: [ 32 / 88 ] 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: [ 33 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 34 / 88 ] 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: [ 35 / 88 ] 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: [ 36 / 88 ] 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: [ 37 / 88 ] 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: [ 38 / 88 ] 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: [ 39 / 88 ] 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: [ 40 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 41 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 42 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* (+ n n) PI)) (/ 1 2)) (+ (log (sqrt k)) (* (log (* (+ n n) PI)) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (116 enodes) * * [misc]simplify: iters left: 2 (180 enodes) * * [misc]simplify: iters left: 1 (300 enodes) * [exit]simplify: Simplified to (+ (/ (log PI) 2) (- (* (log (+ n n)) (- (/ 1 2) (/ k 2))) (+ (log (sqrt k)) (* (/ k 2) (log PI))))) * [exit]simplify: Simplified to (+ (/ (log PI) 2) (- (* (log (+ n n)) (- (/ 1 2) (/ k 2))) (+ (log (sqrt k)) (* (/ k 2) (log PI))))) * * * * [misc]progress: [ 43 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* (+ n n) PI)) (/ 1 2)) (+ (log (sqrt k)) (* (log (* (+ n n) PI)) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (116 enodes) * * [misc]simplify: iters left: 2 (180 enodes) * * [misc]simplify: iters left: 1 (300 enodes) * [exit]simplify: Simplified to (+ (/ (log PI) 2) (- (* (log (+ n n)) (- (/ 1 2) (/ k 2))) (+ (log (sqrt k)) (* (/ k 2) (log PI))))) * [exit]simplify: Simplified to (+ (/ (log PI) 2) (- (* (log (+ n n)) (- (/ 1 2) (/ k 2))) (+ (log (sqrt k)) (* (/ k 2) (log PI))))) * * * * [misc]progress: [ 44 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* (+ n n) PI)) (/ 1 2)) (+ (log (sqrt k)) (log (pow (* (+ n n) PI) (/ k 2))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (214 enodes) * * [misc]simplify: iters left: 1 (336 enodes) * [exit]simplify: Simplified to (- (+ (/ (log (+ n n)) 2) (- (/ (log PI) 2) (log (sqrt k)))) (* (log (* PI (+ n n))) (/ k 2))) * [exit]simplify: Simplified to (- (+ (/ (log (+ n n)) 2) (- (/ (log PI) 2) (log (sqrt k)))) (* (log (* PI (+ n n))) (/ k 2))) * * * * [misc]progress: [ 45 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* (+ n n) PI)) (/ 1 2)) (log (* (sqrt k) (pow (* (+ n n) PI) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (125 enodes) * * [misc]simplify: iters left: 1 (199 enodes) * [exit]simplify: Simplified to (- (+ (- (/ (log PI) 2) (log (sqrt k))) (/ (log (+ n n)) 2)) (* (/ k 2) (log (* PI (+ n n))))) * [exit]simplify: Simplified to (- (+ (- (/ (log PI) 2) (log (sqrt k))) (/ (log (+ n n)) 2)) (* (/ k 2) (log (* PI (+ n n))))) * * * * [misc]progress: [ 46 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* (+ n n) PI)) (/ 1 2)) (+ (log (sqrt k)) (* (log (* (+ n n) PI)) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (116 enodes) * * [misc]simplify: iters left: 2 (180 enodes) * * [misc]simplify: iters left: 1 (300 enodes) * [exit]simplify: Simplified to (+ (/ (log PI) 2) (- (* (log (+ n n)) (- (/ 1 2) (/ k 2))) (+ (log (sqrt k)) (* (/ k 2) (log PI))))) * [exit]simplify: Simplified to (+ (/ (log PI) 2) (- (* (log (+ n n)) (- (/ 1 2) (/ k 2))) (+ (log (sqrt k)) (* (/ k 2) (log PI))))) * * * * [misc]progress: [ 47 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* (+ n n) PI)) (/ 1 2)) (+ (log (sqrt k)) (* (log (* (+ n n) PI)) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (116 enodes) * * [misc]simplify: iters left: 2 (180 enodes) * * [misc]simplify: iters left: 1 (300 enodes) * [exit]simplify: Simplified to (+ (/ (log PI) 2) (- (* (log (+ n n)) (- (/ 1 2) (/ k 2))) (+ (log (sqrt k)) (* (/ k 2) (log PI))))) * [exit]simplify: Simplified to (+ (/ (log PI) 2) (- (* (log (+ n n)) (- (/ 1 2) (/ k 2))) (+ (log (sqrt k)) (* (/ k 2) (log PI))))) * * * * [misc]progress: [ 48 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* (+ n n) PI)) (/ 1 2)) (+ (log (sqrt k)) (log (pow (* (+ n n) PI) (/ k 2))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (214 enodes) * * [misc]simplify: iters left: 1 (336 enodes) * [exit]simplify: Simplified to (- (+ (/ (log (+ n n)) 2) (- (/ (log PI) 2) (log (sqrt k)))) (* (log (* PI (+ n n))) (/ k 2))) * [exit]simplify: Simplified to (- (+ (/ (log (+ n n)) 2) (- (/ (log PI) 2) (log (sqrt k)))) (* (log (* PI (+ n n))) (/ k 2))) * * * * [misc]progress: [ 49 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* (+ n n) PI)) (/ 1 2)) (log (* (sqrt k) (pow (* (+ n n) PI) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (125 enodes) * * [misc]simplify: iters left: 1 (199 enodes) * [exit]simplify: Simplified to (- (+ (- (/ (log PI) 2) (log (sqrt k))) (/ (log (+ n n)) 2)) (* (/ k 2) (log (* PI (+ n n))))) * [exit]simplify: Simplified to (- (+ (- (/ (log PI) 2) (log (sqrt k))) (/ (log (+ n n)) 2)) (* (/ k 2) (log (* PI (+ n n))))) * * * * [misc]progress: [ 50 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* (+ n n) PI) (/ 1 2))) (+ (log (sqrt k)) (* (log (* (+ n n) PI)) (/ k 2)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (312 enodes) * [exit]simplify: Simplified to (- (+ (/ (log (+ n n)) 2) (- (/ (log PI) 2) (log (sqrt k)))) (* (/ k 2) (log (* PI (+ n n))))) * [exit]simplify: Simplified to (- (+ (/ (log (+ n n)) 2) (- (/ (log PI) 2) (log (sqrt k)))) (* (/ k 2) (log (* PI (+ n n))))) * * * * [misc]progress: [ 51 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* (+ n n) PI) (/ 1 2))) (+ (log (sqrt k)) (* (log (* (+ n n) PI)) (/ k 2)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (312 enodes) * [exit]simplify: Simplified to (- (+ (/ (log (+ n n)) 2) (- (/ (log PI) 2) (log (sqrt k)))) (* (/ k 2) (log (* PI (+ n n))))) * [exit]simplify: Simplified to (- (+ (/ (log (+ n n)) 2) (- (/ (log PI) 2) (log (sqrt k)))) (* (/ k 2) (log (* PI (+ n n))))) * * * * [misc]progress: [ 52 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* (+ n n) PI) (/ 1 2))) (+ (log (sqrt k)) (log (pow (* (+ n n) PI) (/ k 2))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (135 enodes) * * [misc]simplify: iters left: 1 (202 enodes) * [exit]simplify: Simplified to (- (/ (log (* n (+ PI PI))) 2) (+ (* (log (+ n n)) (/ k 2)) (+ (* (log PI) (/ k 2)) (log (sqrt k))))) * [exit]simplify: Simplified to (- (/ (log (* n (+ PI PI))) 2) (+ (* (log (+ n n)) (/ k 2)) (+ (* (log PI) (/ k 2)) (log (sqrt k))))) * * * * [misc]progress: [ 53 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* (+ n n) PI) (/ 1 2))) (log (* (sqrt k) (pow (* (+ n n) PI) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (71 enodes) * * [misc]simplify: iters left: 2 (123 enodes) * * [misc]simplify: iters left: 1 (193 enodes) * [exit]simplify: Simplified to (- (- (/ (log PI) 2) (+ (* (/ k 2) (log PI)) (log (sqrt k)))) (- (* (log (+ n n)) (/ k 2)) (/ (log (+ n n)) 2))) * [exit]simplify: Simplified to (- (- (/ (log PI) 2) (+ (* (/ k 2) (log PI)) (log (sqrt k)))) (- (* (log (+ n n)) (/ k 2)) (/ (log (+ n n)) 2))) * * * * [misc]progress: [ 54 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ (pow (* (+ n n) PI) (/ 1 2)) (* (sqrt k) (pow (* (+ n n) PI) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (80 enodes) * * [misc]simplify: iters left: 1 (105 enodes) * [exit]simplify: Simplified to (- (* (- (/ 1 2) (/ k 2)) (log (* n (+ PI PI)))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (- (/ 1 2) (/ k 2)) (log (* n (+ PI PI)))) (log (sqrt k))) * * * * [misc]progress: [ 55 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ (pow (* (+ n n) PI) (/ 1 2)) (* (sqrt k) (pow (* (+ n n) PI) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 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 (exp (/ (pow (* PI (+ n n)) (/ 1 2)) (* (pow (* PI (+ n n)) (/ k 2)) (sqrt k)))) * [exit]simplify: Simplified to (exp (/ (pow (* PI (+ n n)) (/ 1 2)) (* (pow (* PI (+ n n)) (/ k 2)) (sqrt k)))) * * * * [misc]progress: [ 56 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ 1 2))) (pow (* (+ n n) PI) (/ 1 2))) (* (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* (+ n n) PI) (/ k 2)) (pow (* (+ n n) PI) (/ k 2))) (pow (* (+ n n) PI) (/ k 2))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (272 enodes) * [exit]simplify: Simplified to (* (/ (/ (pow (* PI (+ n n)) (/ 1 2)) (pow (* PI (+ n n)) (/ k 2))) (* (sqrt k) k)) (* (/ (pow (* PI (+ n n)) (/ 1 2)) (pow (* PI (+ n n)) (/ k 2))) (/ (pow (* PI (+ n n)) (/ 1 2)) (pow (* PI (+ n n)) (/ k 2))))) * [exit]simplify: Simplified to (* (/ (/ (pow (* PI (+ n n)) (/ 1 2)) (pow (* PI (+ n n)) (/ k 2))) (* (sqrt k) k)) (* (/ (pow (* PI (+ n n)) (/ 1 2)) (pow (* PI (+ n n)) (/ k 2))) (/ (pow (* PI (+ n n)) (/ 1 2)) (pow (* PI (+ n n)) (/ k 2))))) * * * * [misc]progress: [ 57 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ 1 2))) (pow (* (+ n n) PI) (/ 1 2))) (* (* (* (sqrt k) (pow (* (+ n n) PI) (/ k 2))) (* (sqrt k) (pow (* (+ n n) PI) (/ k 2)))) (* (sqrt k) (pow (* (+ n n) PI) (/ k 2))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (148 enodes) * * [misc]simplify: iters left: 2 (303 enodes) * [exit]simplify: Simplified to (/ (/ (* (pow (* PI (+ n n)) (/ 1 2)) (pow (* PI (+ n n)) (/ 1 2))) (/ (pow (* PI (+ n n)) (/ k 2)) (pow (* PI (+ n n)) (/ 1 2)))) (* (* (* (sqrt k) k) (pow (* PI (+ n n)) (/ k 2))) (pow (* PI (+ n n)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (* (pow (* PI (+ n n)) (/ 1 2)) (pow (* PI (+ n n)) (/ 1 2))) (/ (pow (* PI (+ n n)) (/ k 2)) (pow (* PI (+ n n)) (/ 1 2)))) (* (* (* (sqrt k) k) (pow (* PI (+ n n)) (/ k 2))) (pow (* PI (+ n n)) (/ k 2)))) * * * * [misc]progress: [ 58 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (pow (* (+ n n) PI) (/ 1 2)) (* (sqrt k) (pow (* (+ n n) PI) (/ k 2))))) (cbrt (/ (pow (* (+ n n) PI) (/ 1 2)) (* (sqrt k) (pow (* (+ n n) PI) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 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 (* (cbrt (/ (/ (pow (* (+ PI PI) n) (/ 1 2)) (sqrt k)) (pow (* (+ PI PI) n) (/ k 2)))) (cbrt (/ (/ (pow (* (+ PI PI) n) (/ 1 2)) (sqrt k)) (pow (* (+ PI PI) n) (/ k 2))))) * [exit]simplify: Simplified to (* (cbrt (/ (/ (pow (* (+ PI PI) n) (/ 1 2)) (sqrt k)) (pow (* (+ PI PI) n) (/ k 2)))) (cbrt (/ (/ (pow (* (+ PI PI) n) (/ 1 2)) (sqrt k)) (pow (* (+ PI PI) n) (/ k 2))))) * [enter]simplify: Simplifying (cbrt (/ (pow (* (+ n n) PI) (/ 1 2)) (* (sqrt k) (pow (* (+ n n) PI) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 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 (cbrt (/ (pow (* PI (+ n n)) (/ 1 2)) (* (pow (* PI (+ n n)) (/ k 2)) (sqrt k)))) * [exit]simplify: Simplified to (cbrt (/ (pow (* PI (+ n n)) (/ 1 2)) (* (pow (* PI (+ n n)) (/ k 2)) (sqrt k)))) * * * * [misc]progress: [ 59 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (pow (* (+ n n) PI) (/ 1 2)) (* (sqrt k) (pow (* (+ n n) PI) (/ k 2)))) (/ (pow (* (+ n n) PI) (/ 1 2)) (* (sqrt k) (pow (* (+ n n) PI) (/ k 2))))) (/ (pow (* (+ n n) PI) (/ 1 2)) (* (sqrt k) (pow (* (+ n n) PI) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (241 enodes) * [exit]simplify: Simplified to (* (/ (* (pow (* PI (+ n n)) (/ 1 2)) (pow (* PI (+ n n)) (/ 1 2))) (* k (pow (* PI (+ n n)) (/ k 2)))) (/ (/ (pow (* PI (+ n n)) (/ 1 2)) (sqrt k)) (* (pow (* PI (+ n n)) (/ k 2)) (pow (* PI (+ n n)) (/ k 2))))) * [exit]simplify: Simplified to (* (/ (* (pow (* PI (+ n n)) (/ 1 2)) (pow (* PI (+ n n)) (/ 1 2))) (* k (pow (* PI (+ n n)) (/ k 2)))) (/ (/ (pow (* PI (+ n n)) (/ 1 2)) (sqrt k)) (* (pow (* PI (+ n n)) (/ k 2)) (pow (* PI (+ n n)) (/ k 2))))) * * * * [misc]progress: [ 60 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (* (sqrt k) (pow (* (+ n n) PI) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 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 (sqrt (/ (pow (* PI (+ n n)) (/ 1 2)) (* (pow (* PI (+ n n)) (/ k 2)) (sqrt k)))) * [exit]simplify: Simplified to (sqrt (/ (pow (* PI (+ n n)) (/ 1 2)) (* (pow (* PI (+ n n)) (/ k 2)) (sqrt k)))) * [enter]simplify: Simplifying (sqrt (/ (pow (* (+ n n) PI) (/ 1 2)) (* (sqrt k) (pow (* (+ n n) PI) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 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 (sqrt (/ (pow (* PI (+ n n)) (/ 1 2)) (* (pow (* PI (+ n n)) (/ k 2)) (sqrt k)))) * [exit]simplify: Simplified to (sqrt (/ (pow (* PI (+ n n)) (/ 1 2)) (* (pow (* PI (+ n n)) (/ k 2)) (sqrt k)))) * * * * [misc]progress: [ 61 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (- (pow (* (+ n n) PI) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (26 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 (- (* (sqrt k) (pow (* (+ n n) PI) (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * * [misc]simplify: iters left: 2 (34 enodes) * [exit]simplify: Simplified to (* (pow (* (+ PI PI) n) (/ k 2)) (- (sqrt k))) * [exit]simplify: Simplified to (* (pow (* (+ PI PI) n) (/ k 2)) (- (sqrt k))) * * * * [misc]progress: [ 62 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (+ n n) (/ 1 2)) (sqrt k)) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (13 enodes) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (+ n n) (/ 1 2)) (sqrt k)) * [enter]simplify: Simplifying (/ (pow PI (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (30 enodes) * [exit]simplify: Simplified to (/ (pow PI (/ 1 2)) (pow (* PI (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ (pow PI (/ 1 2)) (pow (* PI (+ n n)) (/ k 2))) * * * * [misc]progress: [ 63 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ 1 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (/ (sqrt k) (cbrt (pow (* n (+ PI PI)) (/ 1 2))))) * [exit]simplify: Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (/ (sqrt k) (cbrt (pow (* n (+ PI PI)) (/ 1 2))))) * [enter]simplify: Simplifying (/ (cbrt (pow (* (+ n n) PI) (/ 1 2))) (pow (* (+ n n) PI) (/ k 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (31 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* PI (+ n n)) (/ 1 2))) (pow (* PI (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ (cbrt (pow (* PI (+ n n)) (/ 1 2))) (pow (* PI (+ n n)) (/ k 2))) * * * * [misc]progress: [ 64 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (30 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (+ n n)) (/ 1 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (+ n n)) (/ 1 2))) (sqrt k)) * [enter]simplify: Simplifying (/ (sqrt (pow (* (+ n n) PI) (/ 1 2))) (pow (* (+ n n) PI) (/ k 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (31 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (+ n n)) (/ 1 2))) (pow (* PI (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ (sqrt (pow (* PI (+ n n)) (/ 1 2))) (pow (* PI (+ n n)) (/ k 2))) * * * * [misc]progress: [ 65 / 88 ] 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)) * [enter]simplify: Simplifying (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (30 enodes) * [exit]simplify: Simplified to (/ (pow (* PI (+ n n)) (/ 1 2)) (pow (* PI (+ n n)) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (* PI (+ n n)) (/ 1 2)) (pow (* PI (+ n n)) (/ k 2))) * * * * [misc]progress: [ 66 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 67 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (sqrt k) (pow (* (+ n n) PI) (/ 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 (/ (/ 1 (sqrt k)) (pow (* n (+ PI PI)) (/ k 2))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt k)) (pow (* n (+ PI PI)) (/ k 2))) * * * * [misc]progress: [ 68 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (sqrt k) (pow (* (+ n n) PI) (/ k 2))) (pow (* (+ n n) PI) (/ 1 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * * [misc]simplify: iters left: 1 (43 enodes) * [exit]simplify: Simplified to (* (/ (pow (* (+ PI PI) n) (/ k 2)) (pow (* (+ PI PI) n) (/ 1 2))) (sqrt k)) * [exit]simplify: Simplified to (* (/ (pow (* (+ PI PI) n) (/ k 2)) (pow (* (+ PI PI) n) (/ 1 2))) (sqrt k)) * * * * [misc]progress: [ 69 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* (+ n n) PI) (/ 1 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * * [misc]simplify: iters left: 2 (29 enodes) * [exit]simplify: Simplified to (/ (pow (* PI (+ n n)) (/ 1 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* PI (+ n n)) (/ 1 2)) (sqrt k)) * * * * [misc]progress: [ 70 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (sqrt k) (pow (* (+ n n) PI) (/ k 2))) (pow PI (/ 1 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * * [misc]simplify: iters left: 1 (43 enodes) * [exit]simplify: Simplified to (/ (pow (* (+ PI PI) n) (/ k 2)) (/ (pow PI (/ 1 2)) (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* (+ PI PI) n) (/ k 2)) (/ (pow PI (/ 1 2)) (sqrt k))) * * * * [misc]progress: [ 71 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (sqrt k) (pow (* (+ n n) PI) (/ k 2))) (cbrt (pow (* (+ n n) PI) (/ 1 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (42 enodes) * * [misc]simplify: iters left: 1 (44 enodes) * [exit]simplify: Simplified to (/ (* (sqrt k) (pow (+ (* n PI) (* n PI)) (/ k 2))) (cbrt (pow (+ (* n PI) (* n PI)) (/ 1 2)))) * [exit]simplify: Simplified to (/ (* (sqrt k) (pow (+ (* n PI) (* n PI)) (/ k 2))) (cbrt (pow (+ (* n PI) (* n PI)) (/ 1 2)))) * * * * [misc]progress: [ 72 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (sqrt k) (pow (* (+ n n) PI) (/ k 2))) (sqrt (pow (* (+ n n) PI) (/ 1 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (42 enodes) * * [misc]simplify: iters left: 1 (44 enodes) * [exit]simplify: Simplified to (/ (* (sqrt k) (pow (+ (* n PI) (* n PI)) (/ k 2))) (sqrt (pow (+ (* n PI) (* n PI)) (/ 1 2)))) * [exit]simplify: Simplified to (/ (* (sqrt k) (pow (+ (* n PI) (* n PI)) (/ k 2))) (sqrt (pow (+ (* n PI) (* n PI)) (/ 1 2)))) * * * * [misc]progress: [ 73 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (sqrt k) (pow (* (+ n n) PI) (/ k 2))) (pow (* (+ n n) PI) (/ 1 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * * [misc]simplify: iters left: 1 (43 enodes) * [exit]simplify: Simplified to (* (/ (pow (* (+ PI PI) n) (/ k 2)) (pow (* (+ PI PI) n) (/ 1 2))) (sqrt k)) * [exit]simplify: Simplified to (* (/ (pow (* (+ PI PI) n) (/ k 2)) (pow (* (+ PI PI) n) (/ 1 2))) (sqrt k)) * * * * [misc]progress: [ 74 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* (+ n n) PI)) (/ 1 2)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (89 enodes) * * [misc]simplify: iters left: 1 (117 enodes) * [exit]simplify: Simplified to (/ (log (+ (* n PI) (* n PI))) 2) * [exit]simplify: Simplified to (/ (log (+ (* n PI) (* n PI))) 2) * * * * [misc]progress: [ 75 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* (+ n n) PI)) (/ 1 2)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (89 enodes) * * [misc]simplify: iters left: 1 (117 enodes) * [exit]simplify: Simplified to (/ (log (+ (* n PI) (* n PI))) 2) * [exit]simplify: Simplified to (/ (log (+ (* n PI) (* n PI))) 2) * * * * [misc]progress: [ 76 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (/ 1 2)) * * [misc]simplify: iters left: 4 (4 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * [exit]simplify: Simplified to (/ 1 2) * [exit]simplify: Simplified to (/ 1 2) * * * * [misc]progress: [ 77 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (+ n n) PI) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (27 enodes) * [exit]simplify: Simplified to (pow (* PI (+ n n)) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) * [exit]simplify: Simplified to (pow (* PI (+ n n)) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) * * * * [misc]progress: [ 78 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (+ n n) PI) (sqrt (/ 1 2))) * * [misc]simplify: iters left: 5 (9 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)) (sqrt (/ 1 2))) * [exit]simplify: Simplified to (pow (+ (* n PI) (* n PI)) (sqrt (/ 1 2))) * * * * [misc]progress: [ 79 / 88 ] 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: [ 80 / 88 ] 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: [ 81 / 88 ] 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 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)) * * * * [misc]progress: [ 82 / 88 ] simplifiying candidate # * * * * [misc]progress: [ 83 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (log (pow (* (+ n n) PI) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (80 enodes) * * [misc]simplify: iters left: 1 (114 enodes) * [exit]simplify: Simplified to (/ (log (* n (+ PI PI))) 2) * [exit]simplify: Simplified to (/ (log (* n (+ PI PI))) 2) * * * * [misc]progress: [ 84 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (pow (* (+ n n) PI) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (exp (pow (+ (* n PI) (* n PI)) (/ 1 2))) * [exit]simplify: Simplified to (exp (pow (+ (* n PI) (* n PI)) (/ 1 2))) * * * * [misc]progress: [ 85 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ 1 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (27 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* PI (+ n n)) (/ 1 2))) (cbrt (pow (* PI (+ n n)) (/ 1 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* PI (+ n n)) (/ 1 2))) (cbrt (pow (* PI (+ n n)) (/ 1 2)))) * [enter]simplify: Simplifying (cbrt (pow (* (+ n n) PI) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (cbrt (pow (+ (* n PI) (* n PI)) (/ 1 2))) * [exit]simplify: Simplified to (cbrt (pow (+ (* n PI) (* n PI)) (/ 1 2))) * * * * [misc]progress: [ 86 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ 1 2))) (pow (* (+ n n) PI) (/ 1 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (31 enodes) * [exit]simplify: Simplified to (pow (pow (* PI (+ n n)) (/ 1 2)) 3) * [exit]simplify: Simplified to (pow (pow (* PI (+ n n)) (/ 1 2)) 3) * * * * [misc]progress: [ 87 / 88 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (* (+ n n) PI) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (sqrt (pow (+ (* n PI) (* n PI)) (/ 1 2))) * [exit]simplify: Simplified to (sqrt (pow (+ (* n PI) (* n PI)) (/ 1 2))) * [enter]simplify: Simplifying (sqrt (pow (* (+ n n) PI) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (sqrt (pow (+ (* n PI) (* n PI)) (/ 1 2))) * [exit]simplify: Simplified to (sqrt (pow (+ (* n PI) (* n PI)) (/ 1 2))) * * * * [misc]progress: [ 88 / 88 ] simplifiying candidate # * * * [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 (pow (* (* 2 PI) n) (/ (- 1 k) 2)) +inf.0)) , with alts (#) * [enter]simplify: Simplifying (* (sqrt k) k) * * [misc]simplify: iters left: 3 (3 enodes) * * [misc]simplify: iters left: 2 (4 enodes) * [exit]simplify: Simplified to (* (sqrt k) k) * [exit]simplify: Simplified to (* (sqrt k) k) * [enter]simplify: Simplifying (* (pow (* PI (+ n n)) (/ (- 1 k) 2)) (pow (* PI (+ n n)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (32 enodes) * [exit]simplify: Simplified to (* (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (pow (* (+ PI PI) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (pow (* (+ PI PI) n) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (/ (* k (sqrt k)) (pow (* PI (+ n n)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * * [misc]simplify: iters left: 1 (45 enodes) * [exit]simplify: Simplified to (/ (* (sqrt k) k) (pow (* (+ PI PI) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (/ (* (sqrt k) k) (pow (* (+ PI PI) n) (/ (- 1 k) 2))) * [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) 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)) * [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))) * [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 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))) * [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))) * [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 (* (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))) * [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)