* [misc]progress:  [Phase 1 of 3] Setting up.
* * * [misc]progress:  [1/2] Preparing points
* * * [misc]progress:  [2/2] Setting up program.
* [misc]progress:  [Phase 2 of 3] Improving.
* [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 (42 enodes)
* * [misc]simplify:  iters left: 2 (45 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))
* * [misc]progress:  iteration 1 / 4
* * * [misc]progress:  picking best candidate
* * * * [misc]pick:  Picked  #<alt-delta (λ (k n) (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))>
* * * [misc]progress:  localizing error
* * * [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:  generating series expansions
* * * * [misc]progress:  [ 1 / 3 ] generating series at (2 1)
* [misc]approximate:  Taking taylor expansion of (pow (* n (+ PI PI)) (/ (- 1 k) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* n (+ PI PI)) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (+ PI 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 (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* n (* 2 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 (+ PI PI)) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (+ PI 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 (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 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 (+ PI PI)) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (+ PI 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 (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 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) (+ (* 1 0) (* 0 (* 2 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) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 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) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI 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) (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ 1 n) (* 2 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) (+ PI PI))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI 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) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 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) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI 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) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 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 (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 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 (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 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 (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
* [misc]approximate:  Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI 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)) (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ -1 n) (* 2 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)) (+ PI PI))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI 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)) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 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)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI 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)) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 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 0) 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 (+ (* -1 0) (* 0 (* 2 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 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 (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 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 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
* * * * [misc]progress:  [ 2 / 3 ] generating series at (2 1 1)
* [misc]approximate:  Taking taylor expansion of (* n (+ PI PI)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 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) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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) (+ PI PI)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 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 (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 PI))) 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 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) 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 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) 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 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) 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 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) 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 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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)) (+ PI PI)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 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) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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 (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (pow (* n (+ PI PI)) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (+ PI 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 (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* n (* 2 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 (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (pow (* n (+ PI PI)) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (+ PI 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 (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 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 (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (pow (* n (+ PI PI)) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (+ PI 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 (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 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) (+ (* 1 0) (* 0 (* 2 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) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 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) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI 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) (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ 1 n) (* 2 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) (+ PI 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) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI 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) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 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) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI 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) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 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 (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 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 (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 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 (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)))))))
* [misc]approximate:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI 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)) (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ -1 n) (* 2 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)) (+ PI 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)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI 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)) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 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)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI 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)) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 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 0) 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 (+ (* -1 0) (* 0 (* 2 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 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 (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 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 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))))))))
* * * [misc]progress:  simplifying candidates
* * * * [misc]progress:  [ 1 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (log1p (expm1 (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* * [misc]simplify:  iters left: 2 (34 enodes)
* [exit]simplify:  Simplified to (expm1 (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (expm1 (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 2 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (expm1 (log1p (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* * [misc]simplify:  iters left: 2 (34 enodes)
* [exit]simplify:  Simplified to (log1p (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (log1p (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 3 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (exp (* (log (* n (+ PI PI))) (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* n (+ PI PI))) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (47 enodes)
* * [misc]simplify:  iters left: 3 (79 enodes)
* * [misc]simplify:  iters left: 2 (115 enodes)
* * [misc]simplify:  iters left: 1 (170 enodes)
* [exit]simplify:  Simplified to (/ (log (* n (+ PI PI))) (/ 2 (- 1 k)))
* [exit]simplify:  Simplified to (/ (log (* n (+ PI PI))) (/ 2 (- 1 k)))
* * * * [misc]progress:  [ 4 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (exp (* (log (* n (+ PI PI))) (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* n (+ PI PI))) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (47 enodes)
* * [misc]simplify:  iters left: 3 (79 enodes)
* * [misc]simplify:  iters left: 2 (115 enodes)
* * [misc]simplify:  iters left: 1 (170 enodes)
* [exit]simplify:  Simplified to (/ (log (* n (+ PI PI))) (/ 2 (- 1 k)))
* [exit]simplify:  Simplified to (/ (log (* n (+ PI PI))) (/ 2 (- 1 k)))
* * * * [misc]progress:  [ 5 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n (+ PI PI)) (* 1 (/ (- 1 k) 2))) (sqrt k)))>
* [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:  [ 6 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) (/ 1 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* * [misc]simplify:  iters left: 2 (26 enodes)
* * [misc]simplify:  iters left: 1 (28 enodes)
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) (/ 1 2))
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) (/ 1 2))
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) (/ k 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (21 enodes)
* * [misc]simplify:  iters left: 2 (24 enodes)
* * [misc]simplify:  iters left: 1 (26 enodes)
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) (/ k 2))
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) (/ k 2))
* * * * [misc]progress:  [ 7 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* n (+ PI PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* * [misc]simplify:  iters left: 2 (35 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:  [ 8 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* n (+ PI PI)) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) (sqrt (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* * [misc]simplify:  iters left: 2 (34 enodes)
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) (sqrt (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) (sqrt (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 9 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* n (+ PI PI)) 1) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) 1)
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* * [misc]simplify:  iters left: 2 (25 enodes)
* * [misc]simplify:  iters left: 1 (27 enodes)
* [exit]simplify:  Simplified to (* n (+ PI PI))
* [exit]simplify:  Simplified to (* n (+ PI PI))
* * * * [misc]progress:  [ 10 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* n (+ PI PI)) (- 1 k)) (/ 1 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) (- 1 k))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (27 enodes)
* * [misc]simplify:  iters left: 1 (29 enodes)
* [exit]simplify:  Simplified to (pow (+ (* PI n) (* PI n)) (- 1 k))
* [exit]simplify:  Simplified to (pow (+ (* PI n) (* PI n)) (- 1 k))
* * * * [misc]progress:  [ 11 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow n (/ (- 1 k) 2)) (pow (+ PI PI) (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow n (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* [exit]simplify:  Simplified to (pow n (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow n (/ (- 1 k) 2))
* [enter]simplify:  Simplifying (pow (+ PI PI) (/ (- 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 (+ PI PI) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow (+ PI PI) (/ (- 1 k) 2))
* * * * [misc]progress:  [ 12 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* n (+ PI PI)) (/ (- 1 k) 2)) 1) (sqrt k)))>
* * * * [misc]progress:  [ 13 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (exp (log (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (38 enodes)
* * [misc]simplify:  iters left: 3 (63 enodes)
* * [misc]simplify:  iters left: 2 (101 enodes)
* * [misc]simplify:  iters left: 1 (147 enodes)
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* n (+ PI PI))))
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* n (+ PI PI))))
* * * * [misc]progress:  [ 14 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (log (exp (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* * [misc]simplify:  iters left: 2 (34 enodes)
* [exit]simplify:  Simplified to (exp (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (exp (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 15 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* * [misc]simplify:  iters left: 2 (35 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 (+ PI PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* * [misc]simplify:  iters left: 2 (34 enodes)
* [exit]simplify:  Simplified to (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 16 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (cbrt (* (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (38 enodes)
* [exit]simplify:  Simplified to (pow (pow (* n (+ PI PI)) (/ (- 1 k) 2)) 3)
* [exit]simplify:  Simplified to (pow (pow (* n (+ PI PI)) (/ (- 1 k) 2)) 3)
* * * * [misc]progress:  [ 17 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* * [misc]simplify:  iters left: 2 (34 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* [enter]simplify:  Simplifying (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* * [misc]simplify:  iters left: 2 (34 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 18 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* 1 (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k)))>
* * * * [misc]progress:  [ 19 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (log1p (expm1 (* n (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (expm1 (* n (+ PI PI)))
* [exit]simplify:  Simplified to (expm1 (* n (+ PI PI)))
* * * * [misc]progress:  [ 20 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (expm1 (log1p (* n (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (log1p (* n (+ PI PI)))
* [exit]simplify:  Simplified to (log1p (* n (+ PI PI)))
* * * * [misc]progress:  [ 21 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* n (+ PI PI)) 1) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 22 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (exp (log (* n (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (log (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* * [misc]simplify:  iters left: 1 (43 enodes)
* [exit]simplify:  Simplified to (log (* (+ n n) PI))
* [exit]simplify:  Simplified to (log (* (+ n n) PI))
* * * * [misc]progress:  [ 23 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (log (exp (* n (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* * [misc]simplify:  iters left: 2 (42 enodes)
* * [misc]simplify:  iters left: 1 (47 enodes)
* [exit]simplify:  Simplified to (pow (exp PI) (+ n n))
* [exit]simplify:  Simplified to (pow (exp PI) (+ n n))
* * * * [misc]progress:  [ 24 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI)))) (cbrt (* n (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* * [misc]simplify:  iters left: 2 (25 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI))))
* [exit]simplify:  Simplified to (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI))))
* [enter]simplify:  Simplifying (cbrt (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (cbrt (* n (+ PI PI)))
* [exit]simplify:  Simplified to (cbrt (* n (+ PI PI)))
* * * * [misc]progress:  [ 25 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (cbrt (* (* (* n (+ PI PI)) (* n (+ PI PI))) (* n (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (* n (+ PI PI)) (* n (+ PI PI))) (* n (+ PI PI)))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (54 enodes)
* * [misc]simplify:  iters left: 3 (195 enodes)
* * [misc]simplify:  iters left: 2 (388 enodes)
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) 3)
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) 3)
* * * * [misc]progress:  [ 26 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (sqrt (* n (+ PI PI))) (sqrt (* n (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* [enter]simplify:  Simplifying (sqrt (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* * * * [misc]progress:  [ 27 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* 1 (* n (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 28 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (+ (* n PI) (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
* [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)
* [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:  [ 29 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (+ (* PI n) (* PI n)) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* PI n)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n PI)
* [exit]simplify:  Simplified to (* n PI)
* [enter]simplify:  Simplifying (* PI n)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n PI)
* [exit]simplify:  Simplified to (* n PI)
* * * * [misc]progress:  [ 30 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) (cbrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* [exit]simplify:  Simplified to (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI))))
* [exit]simplify:  Simplified to (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI))))
* * * * [misc]progress:  [ 31 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (sqrt (+ PI 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 (+ PI PI)) n)
* [exit]simplify:  Simplified to (* (sqrt (+ PI PI)) n)
* * * * [misc]progress:  [ 32 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n 1) (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* n 1)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (5 enodes)
* [exit]simplify:  Simplified to n
* [exit]simplify:  Simplified to n
* * * * [misc]progress:  [ 33 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* n 2)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (+ n n)
* [exit]simplify:  Simplified to (+ n n)
* * * * [misc]progress:  [ 34 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (/ (* n (+ (pow PI 3) (pow PI 3))) (+ (* PI PI) (- (* PI PI) (* PI PI)))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (+ (pow PI 3) (pow PI 3)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (52 enodes)
* * [misc]simplify:  iters left: 1 (69 enodes)
* [exit]simplify:  Simplified to (* (+ n n) (pow PI 3))
* [exit]simplify:  Simplified to (* (+ n n) (pow PI 3))
* * * * [misc]progress:  [ 35 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (/ (* n (- (* PI PI) (* PI PI))) (- PI PI)) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (- (* PI PI) (* PI PI)))
* * [misc]simplify:  iters left: 6 (5 enodes)
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* [exit]simplify:  Simplified to 0
* [exit]simplify:  Simplified to 0
* * * * [misc]progress:  [ 36 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 37 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (log1p (expm1 (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (expm1 (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (expm1 (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (expm1 (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 38 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (expm1 (log1p (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (log1p (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (log1p (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (log1p (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 39 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (pow (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) 1))>
* * * * [misc]progress:  [ 40 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (* (log (* n (+ PI PI))) (/ (- 1 k) 2)) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (* (log (* n (+ PI PI))) (/ (- 1 k) 2)) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (52 enodes)
* * [misc]simplify:  iters left: 3 (88 enodes)
* * [misc]simplify:  iters left: 2 (130 enodes)
* * [misc]simplify:  iters left: 1 (192 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* n (+ PI PI))) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* n (+ PI PI))) (- (log (sqrt k))))
* * * * [misc]progress:  [ 41 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (* (log (* n (+ PI PI))) (/ (- 1 k) 2)) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (* (log (* n (+ PI PI))) (/ (- 1 k) 2)) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (52 enodes)
* * [misc]simplify:  iters left: 3 (88 enodes)
* * [misc]simplify:  iters left: 2 (130 enodes)
* * [misc]simplify:  iters left: 1 (192 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* n (+ PI PI))) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* n (+ PI PI))) (- (log (sqrt k))))
* * * * [misc]progress:  [ 42 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (log (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (log (pow (* n (+ PI 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 (43 enodes)
* * [misc]simplify:  iters left: 3 (68 enodes)
* * [misc]simplify:  iters left: 2 (114 enodes)
* * [misc]simplify:  iters left: 1 (180 enodes)
* [exit]simplify:  Simplified to (fma (log (* n (+ PI PI))) (/ (- 1 k) 2) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* n (+ PI PI))) (/ (- 1 k) 2) (- (log (sqrt k))))
* * * * [misc]progress:  [ 43 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (exp (log (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (log (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (54 enodes)
* * [misc]simplify:  iters left: 2 (105 enodes)
* * [misc]simplify:  iters left: 1 (167 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* n (+ PI PI))) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* n (+ PI PI))) (- (log (sqrt k))))
* * * * [misc]progress:  [ 44 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (log (exp (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (exp (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 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:  [ 45 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (/ (* (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (34 enodes)
* * [misc]simplify:  iters left: 4 (60 enodes)
* * [misc]simplify:  iters left: 3 (86 enodes)
* * [misc]simplify:  iters left: 2 (112 enodes)
* * [misc]simplify:  iters left: 1 (127 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:  [ 46 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (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 (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* * [misc]simplify:  iters left: 2 (37 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 (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 47 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (* (* (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (* (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (54 enodes)
* * [misc]simplify:  iters left: 3 (66 enodes)
* * [misc]simplify:  iters left: 2 (82 enodes)
* * [misc]simplify:  iters left: 1 (106 enodes)
* [exit]simplify:  Simplified to (pow (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)) 3)
* [exit]simplify:  Simplified to (pow (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)) 3)
* * * * [misc]progress:  [ 48 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* [enter]simplify:  Simplifying (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 49 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (- (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (- (sqrt k))))>
* [enter]simplify:  Simplifying (- (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* * [misc]simplify:  iters left: 2 (34 enodes)
* [exit]simplify:  Simplified to (- (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (- (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* [enter]simplify:  Simplifying (- (sqrt k))
* * [misc]simplify:  iters left: 3 (3 enodes)
* [exit]simplify:  Simplified to (- (sqrt k))
* [exit]simplify:  Simplified to (- (sqrt k))
* * * * [misc]progress:  [ 50 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (+ PI PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow (+ PI PI) (/ (- 1 k) 2)) (cbrt (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 (+ PI PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (+ PI PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 51 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow n (/ (- 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 n (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (pow (+ PI PI) (/ (- 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 (+ PI PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 52 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) 1) (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow n (/ (- 1 k) 2)) 1)
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) 1)
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) 1)
* [enter]simplify:  Simplifying (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* [exit]simplify:  Simplified to (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))
* [exit]simplify:  Simplified to (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 53 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (47 enodes)
* * [misc]simplify:  iters left: 3 (52 enodes)
* * [misc]simplify:  iters left: 2 (60 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (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))) (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* * [misc]simplify:  iters left: 2 (37 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:  [ 54 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* * [misc]simplify:  iters left: 2 (43 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* * [misc]simplify:  iters left: 2 (37 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:  [ 55 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) 1) (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) 1)
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) 1)
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) 1)
* [enter]simplify:  Simplifying (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k))
* * * * [misc]progress:  [ 56 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* * [misc]simplify:  iters left: 2 (40 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* * [misc]simplify:  iters left: 2 (37 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:  [ 57 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* * [misc]simplify:  iters left: 2 (37 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 (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* * [misc]simplify:  iters left: 2 (37 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:  [ 58 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) 1) (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) 1)
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* * [misc]simplify:  iters left: 2 (35 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 (+ PI PI)) (/ (- 1 k) 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k))
* * * * [misc]progress:  [ 59 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))))>
* [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 (+ PI PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 60 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [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 (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 61 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 1) (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))>
* [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 (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* * [misc]simplify:  iters left: 2 (35 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:  [ 62 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))>
* * * * [misc]progress:  [ 63 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
* [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:  [ 64 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* * [misc]simplify:  iters left: 2 (35 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 65 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* * [misc]simplify:  iters left: 2 (39 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 66 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 67 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) 1) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) 1)
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* * [misc]simplify:  iters left: 2 (34 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) 1)
* [exit]simplify:  Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) 1)
* * * * [misc]progress:  [ 68 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (pow (+ PI PI) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (pow (+ PI PI) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (+ PI PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (+ PI PI) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 69 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (/ (sqrt k) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (cbrt (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (sqrt k) (cbrt (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 70 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (sqrt k) (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 71 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* * [misc]simplify:  iters left: 2 (35 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 72 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (sqrt k) (pow (* n (+ PI PI)) (/ k 2)))))>
* [enter]simplify:  Simplifying (* (sqrt k) (pow (* n (+ PI PI)) (/ k 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (27 enodes)
* * [misc]simplify:  iters left: 2 (29 enodes)
* [exit]simplify:  Simplified to (* (sqrt k) (pow (* PI (+ n n)) (/ k 2)))
* [exit]simplify:  Simplified to (* (sqrt k) (pow (* PI (+ n n)) (/ k 2)))
* * * * [misc]progress:  [ 73 / 81 ] simplifiying candidate #<alt-event (λ (k n) (/ (- (+ (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)))>
* [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 (96 enodes)
* * [misc]simplify:  iters left: 4 (203 enodes)
* * [misc]simplify:  iters left: 3 (419 enodes)
* [exit]simplify:  Simplified to (/ (- (+ (fma (* k k) (* (* 1/8 (* (sqrt (+ PI PI)) (sqrt n))) (+ (* (log (+ PI PI)) (log (+ PI PI))) (* (log n) (log n)))) (* (* 1/4 (* (sqrt (+ PI PI)) (sqrt n))) (* (log (+ PI PI)) (* (* k k) (log n))))) (* (sqrt (+ PI PI)) (sqrt n))) (* (* 1/2 k) (* (* (sqrt (+ PI PI)) (sqrt n)) (+ (log (+ PI PI)) (log n))))) (sqrt k))
* * * * [misc]progress:  [ 74 / 81 ] simplifiying candidate #<alt-event (λ (k n) (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (41 enodes)
* * [misc]simplify:  iters left: 3 (70 enodes)
* * [misc]simplify:  iters left: 2 (148 enodes)
* * [misc]simplify:  iters left: 1 (321 enodes)
* [exit]simplify:  Simplified to (/ (pow (pow (exp 1/2) (- 1 k)) (- (log (+ PI PI)) (- (log n)))) (sqrt k))
* * * * [misc]progress:  [ 75 / 81 ] simplifiying candidate #<alt-event (λ (k n) (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (63 enodes)
* * [misc]simplify:  iters left: 2 (109 enodes)
* * [misc]simplify:  iters left: 1 (174 enodes)
* [exit]simplify:  Simplified to (/ (exp (* (* (- 1 k) 1/2) (- (log (* PI -2)) (log (/ -1 n))))) (sqrt k))
* * * * [misc]progress:  [ 76 / 81 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
* [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 (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 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 77 / 81 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
* [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 (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 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 78 / 81 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
* [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 (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 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 79 / 81 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +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)))))))))))))))))))))))))>
* [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:  [ 80 / 81 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)))))))
* * * * [misc]progress:  [ 81 / 81 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))))))))
* * * [misc]progress:  adding candidates to table
* * [misc]progress:  iteration 2 / 4
* * * [misc]progress:  picking best candidate
* * * * [misc]pick:  Picked  #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 4 ] rewriting at (2 1 1)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2 1 2 1)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2 1 1 1)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2 1 2)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 4 ] generating series at (2 1 1)
* [misc]approximate:  Taking taylor expansion of (pow (* n (+ PI PI)) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* n (+ PI PI)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* n (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* n (+ PI 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 (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 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 (+ PI PI)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* n (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* n (+ PI 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 (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 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) (+ (* 1 0) (* 0 (* 2 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) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 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) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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) (+ PI PI)) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (+ PI 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) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 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) (+ PI PI)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (+ PI 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) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 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 (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 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 (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 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 (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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 (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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 (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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 (- (+ (* 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) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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 (/ 1 n))))) into (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n)))))
* [misc]approximate:  Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI 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)) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 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)) (+ PI PI)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI 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)) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 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) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 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) into 0
* [misc]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 (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 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) into 0
* [misc]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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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) into 0
* [misc]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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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) into 0
* [misc]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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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) into 0
* [misc]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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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 (/ 1 (- n)))))) into (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n)))))
* * * * [misc]progress:  [ 2 / 4 ] generating series at (2 1 2 1)
* [misc]approximate:  Taking taylor expansion of (* n (+ PI PI)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 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) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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) (+ PI PI)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 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 (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 PI))) 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 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) 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 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) 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 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) 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 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) 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 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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)) (+ PI PI)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 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) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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 1 1 1)
* [misc]approximate:  Taking taylor expansion of (* n (+ PI PI)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 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) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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) (+ PI PI)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 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 (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 PI))) 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 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) 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 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) 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 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) 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 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) 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 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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)) (+ PI PI)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 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) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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 1 2)
* [misc]approximate:  Taking taylor expansion of (pow (* n (+ PI PI)) (/ k 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* n (+ PI PI)) (/ k 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* n (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* n (+ PI 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 (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* n (* 2 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]taylor:  Taking taylor expansion of (pow (* n (+ PI PI)) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* n (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* n (+ PI 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 (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 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]taylor:  Taking taylor expansion of (pow (* n (+ PI PI)) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* n (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* n (+ PI 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 (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 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]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 1 into 1
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 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]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 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 (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 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]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 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 (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) 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 (+ (* (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) (pow (* k 1) 2)) (+ (* (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) (* k 1)) 1)) into (+ 1 (+ (* 1/2 (* (log n) k)) (+ (* 1/8 (* (pow (log n) 2) (pow k 2))) (+ (* 1/4 (* (log (* 2 PI)) (* (log n) (pow k 2)))) (+ (* 1/2 (* (log (* 2 PI)) k)) (* 1/8 (* (pow (log (* 2 PI)) 2) (pow k 2))))))))
* [misc]approximate:  Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI 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) (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ 1 n) (* 2 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) (+ PI PI))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI 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) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 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]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (+ PI 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) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 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]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)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 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]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 0) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 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]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 0) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) into (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))
* [misc]approximate:  Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI 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)) (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ -1 n) (* 2 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)) (+ PI PI))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI 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)) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 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]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (+ PI 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)) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 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]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)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (+ 0 0) 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 (+ (* -1 0) (* 0 (* 2 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]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 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 (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 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]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 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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 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]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))) into (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n))))))
* * * [misc]progress:  simplifying candidates
* * * * [misc]progress:  [ 1 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (log1p (expm1 (pow (* n (+ PI PI)) (/ 1 2)))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (pow (* n (+ PI PI)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (27 enodes)
* * [misc]simplify:  iters left: 2 (29 enodes)
* [exit]simplify:  Simplified to (expm1 (pow (+ (* PI n) (* PI n)) (/ 1 2)))
* [exit]simplify:  Simplified to (expm1 (pow (+ (* PI n) (* PI n)) (/ 1 2)))
* * * * [misc]progress:  [ 2 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (expm1 (log1p (pow (* n (+ PI PI)) (/ 1 2)))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (pow (* n (+ PI PI)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (27 enodes)
* * [misc]simplify:  iters left: 2 (29 enodes)
* [exit]simplify:  Simplified to (log1p (pow (+ (* PI n) (* PI n)) (/ 1 2)))
* [exit]simplify:  Simplified to (log1p (pow (+ (* PI n) (* PI n)) (/ 1 2)))
* * * * [misc]progress:  [ 3 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (exp (* (log (* n (+ PI PI))) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* n (+ PI PI))) (/ 1 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (72 enodes)
* * [misc]simplify:  iters left: 2 (104 enodes)
* * [misc]simplify:  iters left: 1 (149 enodes)
* [exit]simplify:  Simplified to (fma (/ 1 2) (log (+ PI PI)) (/ (log n) 2))
* [exit]simplify:  Simplified to (fma (/ 1 2) (log (+ PI PI)) (/ (log n) 2))
* * * * [misc]progress:  [ 4 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (exp (* (log (* n (+ PI PI))) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* n (+ PI PI))) (/ 1 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (72 enodes)
* * [misc]simplify:  iters left: 2 (104 enodes)
* * [misc]simplify:  iters left: 1 (149 enodes)
* [exit]simplify:  Simplified to (fma (/ 1 2) (log (+ PI PI)) (/ (log n) 2))
* [exit]simplify:  Simplified to (fma (/ 1 2) (log (+ PI PI)) (/ (log n) 2))
* * * * [misc]progress:  [ 5 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (* 1 (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [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:  [ 6 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* n (+ PI PI)) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) (cbrt (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) (* (cbrt (/ 1 2)) (cbrt (/ 1 2))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (28 enodes)
* * [misc]simplify:  iters left: 2 (30 enodes)
* [exit]simplify:  Simplified to (pow (* (+ n n) PI) (* (cbrt (/ 1 2)) (cbrt (/ 1 2))))
* [exit]simplify:  Simplified to (pow (* (+ n n) PI) (* (cbrt (/ 1 2)) (cbrt (/ 1 2))))
* * * * [misc]progress:  [ 7 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* n (+ PI PI)) (sqrt (/ 1 2))) (sqrt (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) (sqrt (/ 1 2)))
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (27 enodes)
* * [misc]simplify:  iters left: 1 (29 enodes)
* [exit]simplify:  Simplified to (pow (+ (* PI n) (* PI n)) (sqrt (/ 1 2)))
* [exit]simplify:  Simplified to (pow (+ (* PI n) (* PI n)) (sqrt (/ 1 2)))
* * * * [misc]progress:  [ 8 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* n (+ PI PI)) 1) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) 1)
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* * [misc]simplify:  iters left: 2 (25 enodes)
* * [misc]simplify:  iters left: 1 (27 enodes)
* [exit]simplify:  Simplified to (* n (+ PI PI))
* [exit]simplify:  Simplified to (* n (+ PI PI))
* * * * [misc]progress:  [ 9 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* n (+ PI PI)) 1) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) 1)
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* * [misc]simplify:  iters left: 2 (25 enodes)
* * [misc]simplify:  iters left: 1 (27 enodes)
* [exit]simplify:  Simplified to (* n (+ PI PI))
* [exit]simplify:  Simplified to (* n (+ PI PI))
* * * * [misc]progress:  [ 10 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (pow n (/ 1 2)) (pow (+ PI PI) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow n (/ 1 2))
* * [misc]simplify:  iters left: 3 (5 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (pow n (/ 1 2))
* [exit]simplify:  Simplified to (pow n (/ 1 2))
* [enter]simplify:  Simplifying (pow (+ PI PI) (/ 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 (+ PI PI) (/ 1 2))
* [exit]simplify:  Simplified to (pow (+ PI PI) (/ 1 2))
* * * * [misc]progress:  [ 11 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* n (+ PI PI)) (/ 1 2)) 1) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 12 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (exp (log (pow (* n (+ PI PI)) (/ 1 2)))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (pow (* n (+ PI PI)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (50 enodes)
* * [misc]simplify:  iters left: 2 (81 enodes)
* * [misc]simplify:  iters left: 1 (101 enodes)
* [exit]simplify:  Simplified to (fma (log (+ PI PI)) (/ 1 2) (/ (log n) 2))
* [exit]simplify:  Simplified to (fma (log (+ PI PI)) (/ 1 2) (/ (log n) 2))
* * * * [misc]progress:  [ 13 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (log (exp (pow (* n (+ PI PI)) (/ 1 2)))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (pow (* n (+ PI PI)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (27 enodes)
* * [misc]simplify:  iters left: 2 (29 enodes)
* [exit]simplify:  Simplified to (exp (pow (+ (* PI n) (* PI n)) (/ 1 2)))
* [exit]simplify:  Simplified to (exp (pow (+ (* PI n) (* PI n)) (/ 1 2)))
* * * * [misc]progress:  [ 14 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (28 enodes)
* * [misc]simplify:  iters left: 2 (30 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ 1 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ 1 2))))
* [enter]simplify:  Simplifying (cbrt (pow (* n (+ PI PI)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (27 enodes)
* * [misc]simplify:  iters left: 2 (29 enodes)
* [exit]simplify:  Simplified to (cbrt (pow (+ (* PI n) (* PI n)) (/ 1 2)))
* [exit]simplify:  Simplified to (cbrt (pow (+ (* PI n) (* PI n)) (/ 1 2)))
* * * * [misc]progress:  [ 15 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (cbrt (* (* (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ 1 2)))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (19 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 (pow (* (+ n n) PI) (/ 1 2)) 3)
* [exit]simplify:  Simplified to (pow (pow (* (+ n n) PI) (/ 1 2)) 3)
* * * * [misc]progress:  [ 16 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ 1 2)))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (pow (* n (+ PI PI)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (27 enodes)
* * [misc]simplify:  iters left: 2 (29 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (+ (* PI n) (* PI n)) (/ 1 2)))
* [exit]simplify:  Simplified to (sqrt (pow (+ (* PI n) (* PI n)) (/ 1 2)))
* [enter]simplify:  Simplifying (sqrt (pow (* n (+ PI PI)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (27 enodes)
* * [misc]simplify:  iters left: 2 (29 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (+ (* PI n) (* PI n)) (/ 1 2)))
* [exit]simplify:  Simplified to (sqrt (pow (+ (* PI n) (* PI n)) (/ 1 2)))
* * * * [misc]progress:  [ 17 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* 1 (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 18 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (log1p (expm1 (* n (+ PI PI)))) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (expm1 (* n (+ PI PI)))
* [exit]simplify:  Simplified to (expm1 (* n (+ PI PI)))
* * * * [misc]progress:  [ 19 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (expm1 (log1p (* n (+ PI PI)))) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (log1p (* n (+ PI PI)))
* [exit]simplify:  Simplified to (log1p (* n (+ PI PI)))
* * * * [misc]progress:  [ 20 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (* n (+ PI PI)) 1) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 21 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (exp (log (* n (+ PI PI)))) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* * [misc]simplify:  iters left: 1 (43 enodes)
* [exit]simplify:  Simplified to (log (* (+ n n) PI))
* [exit]simplify:  Simplified to (log (* (+ n n) PI))
* * * * [misc]progress:  [ 22 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (log (exp (* n (+ PI PI)))) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* * [misc]simplify:  iters left: 2 (42 enodes)
* * [misc]simplify:  iters left: 1 (47 enodes)
* [exit]simplify:  Simplified to (pow (exp PI) (+ n n))
* [exit]simplify:  Simplified to (pow (exp PI) (+ n n))
* * * * [misc]progress:  [ 23 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI)))) (cbrt (* n (+ PI PI)))) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* * [misc]simplify:  iters left: 2 (25 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI))))
* [exit]simplify:  Simplified to (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI))))
* [enter]simplify:  Simplifying (cbrt (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (cbrt (* n (+ PI PI)))
* [exit]simplify:  Simplified to (cbrt (* n (+ PI PI)))
* * * * [misc]progress:  [ 24 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (cbrt (* (* (* n (+ PI PI)) (* n (+ PI PI))) (* n (+ PI PI)))) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (* n (+ PI PI)) (* n (+ PI PI))) (* n (+ PI PI)))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (54 enodes)
* * [misc]simplify:  iters left: 3 (195 enodes)
* * [misc]simplify:  iters left: 2 (388 enodes)
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) 3)
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) 3)
* * * * [misc]progress:  [ 25 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* (sqrt (* n (+ PI PI))) (sqrt (* n (+ PI PI)))) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* [enter]simplify:  Simplifying (sqrt (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* * * * [misc]progress:  [ 26 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* 1 (* n (+ PI PI))) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 27 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (+ (* n PI) (* n PI)) (/ k 2))) (sqrt k)))>
* [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)
* [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:  [ 28 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (+ (* PI n) (* PI n)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* PI n)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n PI)
* [exit]simplify:  Simplified to (* n PI)
* [enter]simplify:  Simplifying (* PI n)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n PI)
* [exit]simplify:  Simplified to (* n PI)
* * * * [misc]progress:  [ 29 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) (cbrt (+ PI PI))) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* [exit]simplify:  Simplified to (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI))))
* [exit]simplify:  Simplified to (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI))))
* * * * [misc]progress:  [ 30 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (sqrt (+ PI 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 (+ PI PI)) n)
* [exit]simplify:  Simplified to (* (sqrt (+ PI PI)) n)
* * * * [misc]progress:  [ 31 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* (* n 1) (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n 1)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (5 enodes)
* [exit]simplify:  Simplified to n
* [exit]simplify:  Simplified to n
* * * * [misc]progress:  [ 32 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n 2)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (+ n n)
* [exit]simplify:  Simplified to (+ n n)
* * * * [misc]progress:  [ 33 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (/ (* n (+ (pow PI 3) (pow PI 3))) (+ (* PI PI) (- (* PI PI) (* PI PI)))) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (+ (pow PI 3) (pow PI 3)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (52 enodes)
* * [misc]simplify:  iters left: 1 (69 enodes)
* [exit]simplify:  Simplified to (* (+ n n) (pow PI 3))
* [exit]simplify:  Simplified to (* (+ n n) (pow PI 3))
* * * * [misc]progress:  [ 34 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (/ (* n (- (* PI PI) (* PI PI))) (- PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (- (* PI PI) (* PI PI)))
* * [misc]simplify:  iters left: 6 (5 enodes)
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* [exit]simplify:  Simplified to 0
* [exit]simplify:  Simplified to 0
* * * * [misc]progress:  [ 35 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* (+ PI PI) n) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 36 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (log1p (expm1 (* n (+ PI PI)))) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (expm1 (* n (+ PI PI)))
* [exit]simplify:  Simplified to (expm1 (* n (+ PI PI)))
* * * * [misc]progress:  [ 37 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (expm1 (log1p (* n (+ PI PI)))) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (log1p (* n (+ PI PI)))
* [exit]simplify:  Simplified to (log1p (* n (+ PI PI)))
* * * * [misc]progress:  [ 38 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* n (+ PI PI)) 1) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 39 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (exp (log (* n (+ PI PI)))) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* * [misc]simplify:  iters left: 1 (43 enodes)
* [exit]simplify:  Simplified to (log (* (+ n n) PI))
* [exit]simplify:  Simplified to (log (* (+ n n) PI))
* * * * [misc]progress:  [ 40 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (log (exp (* n (+ PI PI)))) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* * [misc]simplify:  iters left: 2 (42 enodes)
* * [misc]simplify:  iters left: 1 (47 enodes)
* [exit]simplify:  Simplified to (pow (exp PI) (+ n n))
* [exit]simplify:  Simplified to (pow (exp PI) (+ n n))
* * * * [misc]progress:  [ 41 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI)))) (cbrt (* n (+ PI PI)))) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* * [misc]simplify:  iters left: 2 (25 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI))))
* [exit]simplify:  Simplified to (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI))))
* [enter]simplify:  Simplifying (cbrt (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (cbrt (* n (+ PI PI)))
* [exit]simplify:  Simplified to (cbrt (* n (+ PI PI)))
* * * * [misc]progress:  [ 42 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (cbrt (* (* (* n (+ PI PI)) (* n (+ PI PI))) (* n (+ PI PI)))) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (* n (+ PI PI)) (* n (+ PI PI))) (* n (+ PI PI)))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (54 enodes)
* * [misc]simplify:  iters left: 3 (195 enodes)
* * [misc]simplify:  iters left: 2 (388 enodes)
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) 3)
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) 3)
* * * * [misc]progress:  [ 43 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (sqrt (* n (+ PI PI))) (sqrt (* n (+ PI PI)))) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* [enter]simplify:  Simplifying (sqrt (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* * * * [misc]progress:  [ 44 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* 1 (* n (+ PI PI))) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 45 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (+ (* n PI) (* n PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [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)
* [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:  [ 46 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (+ (* PI n) (* PI n)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* PI n)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n PI)
* [exit]simplify:  Simplified to (* n PI)
* [enter]simplify:  Simplifying (* PI n)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n PI)
* [exit]simplify:  Simplified to (* n PI)
* * * * [misc]progress:  [ 47 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) (cbrt (+ PI PI))) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* [exit]simplify:  Simplified to (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI))))
* [exit]simplify:  Simplified to (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI))))
* * * * [misc]progress:  [ 48 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (sqrt (+ PI 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 (+ PI PI)) n)
* [exit]simplify:  Simplified to (* (sqrt (+ PI PI)) n)
* * * * [misc]progress:  [ 49 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n 1) (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n 1)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (5 enodes)
* [exit]simplify:  Simplified to n
* [exit]simplify:  Simplified to n
* * * * [misc]progress:  [ 50 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n 2)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (+ n n)
* [exit]simplify:  Simplified to (+ n n)
* * * * [misc]progress:  [ 51 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (/ (* n (+ (pow PI 3) (pow PI 3))) (+ (* PI PI) (- (* PI PI) (* PI PI)))) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (+ (pow PI 3) (pow PI 3)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (52 enodes)
* * [misc]simplify:  iters left: 1 (69 enodes)
* [exit]simplify:  Simplified to (* (+ n n) (pow PI 3))
* [exit]simplify:  Simplified to (* (+ n n) (pow PI 3))
* * * * [misc]progress:  [ 52 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (/ (* n (- (* PI PI) (* PI PI))) (- PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (- (* PI PI) (* PI PI)))
* * [misc]simplify:  iters left: 6 (5 enodes)
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* [exit]simplify:  Simplified to 0
* [exit]simplify:  Simplified to 0
* * * * [misc]progress:  [ 53 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (+ PI PI) n) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 54 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (log1p (expm1 (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (pow (* n (+ PI PI)) (/ k 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* * [misc]simplify:  iters left: 2 (27 enodes)
* [exit]simplify:  Simplified to (expm1 (pow (* n (+ PI PI)) (/ k 2)))
* [exit]simplify:  Simplified to (expm1 (pow (* n (+ PI PI)) (/ k 2)))
* * * * [misc]progress:  [ 55 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (expm1 (log1p (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (pow (* n (+ PI PI)) (/ k 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* * [misc]simplify:  iters left: 2 (27 enodes)
* [exit]simplify:  Simplified to (log1p (pow (* n (+ PI PI)) (/ k 2)))
* [exit]simplify:  Simplified to (log1p (pow (* n (+ PI PI)) (/ k 2)))
* * * * [misc]progress:  [ 56 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (exp (* (log (* n (+ PI PI))) (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* n (+ PI PI))) (/ k 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (72 enodes)
* * [misc]simplify:  iters left: 2 (105 enodes)
* * [misc]simplify:  iters left: 1 (152 enodes)
* [exit]simplify:  Simplified to (fma (log (* PI n)) (/ k 2) (* (/ k 2) (log 2)))
* [exit]simplify:  Simplified to (fma (log (* PI n)) (/ k 2) (* (/ k 2) (log 2)))
* * * * [misc]progress:  [ 57 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (exp (* (log (* n (+ PI PI))) (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* n (+ PI PI))) (/ k 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (72 enodes)
* * [misc]simplify:  iters left: 2 (105 enodes)
* * [misc]simplify:  iters left: 1 (152 enodes)
* [exit]simplify:  Simplified to (fma (log (* PI n)) (/ k 2) (* (/ k 2) (log 2)))
* [exit]simplify:  Simplified to (fma (log (* PI n)) (/ k 2) (* (/ k 2) (log 2)))
* * * * [misc]progress:  [ 58 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (* 1 (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* 1 (/ k 2))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (10 enodes)
* [exit]simplify:  Simplified to (/ k 2)
* [exit]simplify:  Simplified to (/ k 2)
* * * * [misc]progress:  [ 59 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (* n (+ PI PI)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))) (cbrt (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* * [misc]simplify:  iters left: 2 (28 enodes)
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))
* * * * [misc]progress:  [ 60 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (* n (+ PI PI)) (sqrt (/ k 2))) (sqrt (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) (sqrt (/ k 2)))
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* * [misc]simplify:  iters left: 2 (25 enodes)
* * [misc]simplify:  iters left: 1 (27 enodes)
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) (sqrt (/ k 2)))
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) (sqrt (/ k 2)))
* * * * [misc]progress:  [ 61 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (* n (+ PI PI)) 1) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) 1)
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* * [misc]simplify:  iters left: 2 (25 enodes)
* * [misc]simplify:  iters left: 1 (27 enodes)
* [exit]simplify:  Simplified to (* n (+ PI PI))
* [exit]simplify:  Simplified to (* n (+ PI PI))
* * * * [misc]progress:  [ 62 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) k)
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* * [misc]simplify:  iters left: 2 (23 enodes)
* * [misc]simplify:  iters left: 1 (25 enodes)
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) k)
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) k)
* * * * [misc]progress:  [ 63 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (pow n (/ k 2)) (pow (+ PI PI) (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow n (/ k 2))
* * [misc]simplify:  iters left: 3 (5 enodes)
* [exit]simplify:  Simplified to (pow n (/ k 2))
* [exit]simplify:  Simplified to (pow n (/ k 2))
* [enter]simplify:  Simplifying (pow (+ PI PI) (/ k 2))
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* * [misc]simplify:  iters left: 1 (8 enodes)
* [exit]simplify:  Simplified to (pow (+ PI PI) (/ k 2))
* [exit]simplify:  Simplified to (pow (+ PI PI) (/ k 2))
* * * * [misc]progress:  [ 64 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (* n (+ PI PI)) (/ k 2)) 1)) (sqrt k)))>
* * * * [misc]progress:  [ 65 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (exp (log (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (pow (* n (+ PI PI)) (/ k 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (56 enodes)
* * [misc]simplify:  iters left: 2 (94 enodes)
* * [misc]simplify:  iters left: 1 (137 enodes)
* [exit]simplify:  Simplified to (fma (log (+ PI PI)) (/ k 2) (* (/ k 2) (log n)))
* [exit]simplify:  Simplified to (fma (log (+ PI PI)) (/ k 2) (* (/ k 2) (log n)))
* * * * [misc]progress:  [ 66 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (log (exp (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (pow (* n (+ PI PI)) (/ k 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* * [misc]simplify:  iters left: 2 (27 enodes)
* [exit]simplify:  Simplified to (exp (pow (* n (+ PI PI)) (/ k 2)))
* [exit]simplify:  Simplified to (exp (pow (* n (+ PI PI)) (/ k 2)))
* * * * [misc]progress:  [ 67 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2)))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* * [misc]simplify:  iters left: 2 (28 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* n (+ PI PI)) (/ k 2))) (cbrt (pow (* n (+ PI PI)) (/ k 2))))
* [enter]simplify:  Simplifying (cbrt (pow (* n (+ PI PI)) (/ k 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* * [misc]simplify:  iters left: 2 (27 enodes)
* [exit]simplify:  Simplified to (cbrt (pow (* n (+ PI PI)) (/ k 2)))
* [exit]simplify:  Simplified to (cbrt (pow (* n (+ PI PI)) (/ k 2)))
* * * * [misc]progress:  [ 68 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (cbrt (* (* (pow (* n (+ PI PI)) (/ k 2)) (pow (* n (+ PI PI)) (/ k 2))) (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (pow (* n (+ PI PI)) (/ k 2)) (pow (* n (+ PI PI)) (/ k 2))) (pow (* n (+ PI PI)) (/ k 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (17 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 (pow (* PI (+ n n)) (/ k 2)) 3)
* [exit]simplify:  Simplified to (pow (pow (* PI (+ n n)) (/ k 2)) 3)
* * * * [misc]progress:  [ 69 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (sqrt (pow (* n (+ PI PI)) (/ k 2))) (sqrt (pow (* n (+ PI PI)) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (pow (* n (+ PI PI)) (/ k 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* * [misc]simplify:  iters left: 2 (27 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* n (+ PI PI)) (/ k 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* n (+ PI PI)) (/ k 2)))
* [enter]simplify:  Simplifying (sqrt (pow (* n (+ PI PI)) (/ k 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* * [misc]simplify:  iters left: 2 (27 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* n (+ PI PI)) (/ k 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* n (+ PI PI)) (/ k 2)))
* * * * [misc]progress:  [ 70 / 82 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (* 1 (pow (* n (+ PI PI)) (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 71 / 82 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (39 enodes)
* * [misc]simplify:  iters left: 4 (69 enodes)
* * [misc]simplify:  iters left: 3 (104 enodes)
* * [misc]simplify:  iters left: 2 (158 enodes)
* * [misc]simplify:  iters left: 1 (230 enodes)
* [exit]simplify:  Simplified to (/ (* (sqrt (+ PI PI)) (/ (sqrt n) (sqrt k))) (pow (* PI (+ n n)) (/ k 2)))
* * * * [misc]progress:  [ 72 / 82 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (56 enodes)
* * [misc]simplify:  iters left: 3 (79 enodes)
* * [misc]simplify:  iters left: 2 (117 enodes)
* * [misc]simplify:  iters left: 1 (188 enodes)
* [exit]simplify:  Simplified to (/ (exp (fma (- (log 2) (log 1)) 1/2 (* 1/2 (log PI)))) (* (pow (* n (+ PI PI)) (/ k 2)) (/ (sqrt k) (sqrt n))))
* * * * [misc]progress:  [ 73 / 82 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (21 enodes)
* * [misc]simplify:  iters left: 5 (39 enodes)
* * [misc]simplify:  iters left: 4 (54 enodes)
* * [misc]simplify:  iters left: 3 (76 enodes)
* * [misc]simplify:  iters left: 2 (116 enodes)
* * [misc]simplify:  iters left: 1 (187 enodes)
* [exit]simplify:  Simplified to (/ (exp (fma 1/2 (- (log PI) (log -1)) (* 1/2 (log -2)))) (/ (pow (* PI (+ n n)) (/ k 2)) (/ (sqrt n) (sqrt k))))
* * * * [misc]progress:  [ 74 / 82 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))
* * * * [misc]progress:  [ 75 / 82 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))
* * * * [misc]progress:  [ 76 / 82 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))
* * * * [misc]progress:  [ 77 / 82 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))) (sqrt k))
* * * * [misc]progress:  [ 78 / 82 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))) (sqrt k))
* * * * [misc]progress:  [ 79 / 82 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (+ n n) PI) (/ 1 2)) (pow (* (+ n n) PI) (/ k 2))) (sqrt k))
* * * * [misc]progress:  [ 80 / 82 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (+ 1 (+ (* 1/2 (* (log n) k)) (+ (* 1/8 (* (pow (log n) 2) (pow k 2))) (+ (* 1/4 (* (log (* 2 PI)) (* (log n) (pow k 2)))) (+ (* 1/2 (* (log (* 2 PI)) k)) (* 1/8 (* (pow (log (* 2 PI)) 2) (pow k 2))))))))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (+ 1 (+ (* 1/2 (* (log n) k)) (+ (* 1/8 (* (pow (log n) 2) (pow k 2))) (+ (* 1/4 (* (log (* 2 PI)) (* (log n) (pow k 2)))) (+ (* 1/2 (* (log (* 2 PI)) k)) (* 1/8 (* (pow (log (* 2 PI)) 2) (pow k 2))))))))) (sqrt k))
* * [misc]simplify:  iters left: 6 (37 enodes)
* * [misc]simplify:  iters left: 5 (82 enodes)
* * [misc]simplify:  iters left: 4 (179 enodes)
* * [misc]simplify:  iters left: 3 (414 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (+ n n)) (/ 1 2)) (sqrt k)) (+ (fma (* (* k k) 1/8) (* (log (+ PI PI)) (log (+ PI PI))) (fma (* (* k k) (log n)) (* (log (+ PI PI)) 1/4) (* (* k 1/2) (log (+ PI PI))))) (+ (fma (* k 1/2) (log n) 1) (* (* (* 1/8 k) k) (* (log n) (log n))))))
* * * * [misc]progress:  [ 81 / 82 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))) (sqrt k))
* * [misc]simplify:  iters left: 6 (21 enodes)
* * [misc]simplify:  iters left: 5 (43 enodes)
* * [misc]simplify:  iters left: 4 (62 enodes)
* * [misc]simplify:  iters left: 3 (89 enodes)
* * [misc]simplify:  iters left: 2 (135 enodes)
* * [misc]simplify:  iters left: 1 (239 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (+ n n) PI) (/ 1 2)) (sqrt k)) (exp (* (- (log (+ PI PI)) (- (log n))) (* 1/2 k))))
* * * * [misc]progress:  [ 82 / 82 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n))))))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n))))))) (sqrt k))
* * [misc]simplify:  iters left: 6 (23 enodes)
* * [misc]simplify:  iters left: 5 (45 enodes)
* * [misc]simplify:  iters left: 4 (63 enodes)
* * [misc]simplify:  iters left: 3 (95 enodes)
* * [misc]simplify:  iters left: 2 (183 enodes)
* * [misc]simplify:  iters left: 1 (337 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (exp (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
* * * [misc]progress:  adding candidates to table
* * [misc]progress:  iteration 3 / 4
* * * [misc]progress:  picking best candidate
* * * * [misc]pick:  Picked  #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 4 ] rewriting at (2 1 1)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2 1 2 1 1)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2 1 1 1)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2 1 2 1)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 4 ] generating series at (2 1 1)
* [misc]approximate:  Taking taylor expansion of (pow (* n (+ PI PI)) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* n (+ PI PI)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* n (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* n (+ PI 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 (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 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 (+ PI PI)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* n (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* n (+ PI 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 (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 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) (+ (* 1 0) (* 0 (* 2 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) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 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) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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) (+ PI PI)) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (+ PI 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) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 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) (+ PI PI)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (+ PI 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) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 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 (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 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 (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 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 (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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 (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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 (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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 (- (+ (* 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) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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 (/ 1 n))))) into (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n)))))
* [misc]approximate:  Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI 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)) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 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)) (+ PI PI)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (+ PI 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)) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 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) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 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) into 0
* [misc]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 (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 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) into 0
* [misc]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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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) into 0
* [misc]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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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) into 0
* [misc]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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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) into 0
* [misc]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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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 (/ 1 (- n)))))) into (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n)))))
* * * * [misc]progress:  [ 2 / 4 ] generating series at (2 1 2 1 1)
* [misc]approximate:  Taking taylor expansion of (* n (+ PI PI)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 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) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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) (+ PI PI)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 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 (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 PI))) 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 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) 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 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) 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 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) 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 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) 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 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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)) (+ PI PI)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 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) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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 1 1 1)
* [misc]approximate:  Taking taylor expansion of (* n (+ PI PI)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 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) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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) (+ PI PI)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 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 (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 PI))) 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 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) 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 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) 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 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) 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 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) 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 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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)) (+ PI PI)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 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) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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 1 2 1)
* [misc]approximate:  Taking taylor expansion of (pow (* n (+ PI PI)) k) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* n (+ PI PI)) k) in k
* [misc]taylor:  Taking taylor expansion of (exp (* k (log (* n (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* k (log (* n (+ PI PI)))) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (log (* n (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* n (* 2 PI)) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 0 (log (* 2 (* n PI)))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* n 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (log (* 2 (* n PI))))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (exp 0) into 1
* [misc]taylor:  Taking taylor expansion of (pow (* n (+ PI PI)) k) in n
* [misc]taylor:  Taking taylor expansion of (exp (* k (log (* n (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* k (log (* n (+ PI PI)))) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of (log (* n (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 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 (* k (+ (log (* 2 PI)) (log n))) into (* k (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* k (+ (log (* 2 PI)) (log n)))) into (exp (* k (+ (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* n (+ PI PI)) k) in n
* [misc]taylor:  Taking taylor expansion of (exp (* k (log (* n (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* k (log (* n (+ PI PI)))) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of (log (* n (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 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 (* k (+ (log (* 2 PI)) (log n))) into (* k (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* k (+ (log (* 2 PI)) (log n)))) into (exp (* k (+ (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (exp (* k (+ (log (* 2 PI)) (log n)))) in k
* [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 (+ (* 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 (exp 0) into 1
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* k 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 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 (* (exp 0) (+ (* (/ (pow (+ (log (* 2 PI)) (log n)) 1) 1)))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 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) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* k 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 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 0) (+ (* 1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (log (* 2 PI)) (log n)) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/2 (pow (log (* 2 PI)) 2)) (+ (* (log (* 2 PI)) (log n)) (* 1/2 (pow (log n) 2))))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (pow (log (* 2 PI)) 2)) (+ (* (log (* 2 PI)) (log n)) (* 1/2 (pow (log n) 2)))) into (+ (* 1/2 (pow (log (* 2 PI)) 2)) (+ (* (log (* 2 PI)) (log n)) (* 1/2 (pow (log n) 2))))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/2 (pow (log (* 2 PI)) 2)) (+ (* (log (* 2 PI)) (log n)) (* 1/2 (pow (log n) 2)))) (pow (* k 1) 2)) (+ (* (+ (log (* 2 PI)) (log n)) (* k 1)) 1)) into (+ 1 (+ (* (log n) k) (+ (* 1/2 (* (pow (log n) 2) (pow k 2))) (+ (* (log (* 2 PI)) (* (log n) (pow k 2))) (+ (* (log (* 2 PI)) k) (* 1/2 (* (pow (log (* 2 PI)) 2) (pow k 2))))))))
* [misc]approximate:  Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ 1 k)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 k) (log (* (/ 1 n) (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 k) (log (* (/ 1 n) (+ PI PI)))) 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 (log (* (/ 1 n) (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1 (log (* 2 (/ PI n)))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (exp (* (/ 1 k) (log (* (/ 1 n) (+ PI PI))))) into (exp (/ (log (* 2 (/ PI n))) k))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 k) (log (* (/ 1 n) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 k) (log (* (/ 1 n) (+ PI PI)))) 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 (log (* (/ 1 n) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 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 k) (- (log (* 2 PI)) (log n))) into (/ (- (log (* 2 PI)) (log n)) k)
* [misc]backup-simplify:  Simplify (exp (/ (- (log (* 2 PI)) (log n)) k)) into (exp (/ (- (log (* 2 PI)) (log n)) k))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 k) (log (* (/ 1 n) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 k) (log (* (/ 1 n) (+ PI PI)))) 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 (log (* (/ 1 n) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 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 k) (- (log (* 2 PI)) (log n))) into (/ (- (log (* 2 PI)) (log n)) k)
* [misc]backup-simplify:  Simplify (exp (/ (- (log (* 2 PI)) (log n)) k)) into (exp (/ (- (log (* 2 PI)) (log n)) k))
* [misc]taylor:  Taking taylor expansion of (exp (/ (- (log (* 2 PI)) (log n)) k)) in k
* [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 (exp (/ (- (log (* 2 PI)) (log n)) k)) into (exp (/ (- (log (* 2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (/ (- (log (* 2 PI)) (log n)) k)) into (exp (/ (- (log (* 2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 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 (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (/ (- (log (* 2 PI)) (log n)) k)) (+ (* (/ (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 0) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 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 (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1 k) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (/ (- (log (* 2 PI)) (log n)) k)) (+ (* (/ (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 0) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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 (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (/ (- (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]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 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))) into (exp (* k (- (log (* 2 PI)) (log (/ 1 n)))))
* [misc]approximate:  Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 (- k))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 (- k)) (log (* (/ 1 (- n)) (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- k)) (log (* (/ 1 (- n)) (+ PI PI)))) 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 (log (* (/ 1 (- n)) (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* -1 (log (* -2 (/ PI n)))) into (* -1 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ 1 (- k)) (log (* (/ 1 (- n)) (+ PI PI))))) into (exp (* -1 (/ (log (* -2 (/ PI n))) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 (- k)) (log (* (/ 1 (- n)) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- k)) (log (* (/ 1 (- n)) (+ PI PI)))) 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 (log (* (/ 1 (- n)) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 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 k) (- (log (* -2 PI)) (log n))) into (* -1 (/ (- (log (* -2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* -1 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 (- k)) (log (* (/ 1 (- n)) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- k)) (log (* (/ 1 (- n)) (+ PI PI)))) 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 (log (* (/ 1 (- n)) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 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 k) (- (log (* -2 PI)) (log n))) into (* -1 (/ (- (log (* -2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* -1 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (exp (* -1 (/ (- (log (* -2 PI)) (log n)) k))) in k
* [misc]taylor:  Taking taylor expansion of (* -1 (/ (- (log (* -2 PI)) (log n)) 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 (/ (- (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 (- (log (* -2 PI)) (log n))) into (* -1 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* -1 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (exp (* -1 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (+ 0 0) 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 (+ (* -1 0) (* 0 (* 2 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 (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (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 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 (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 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 (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1 k) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (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 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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 (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1 (/ (- (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]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 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))) into (exp (* k (- (log (* -2 PI)) (log (/ -1 n)))))
* * * [misc]progress:  simplifying candidates
* * * * [misc]progress:  [ 1 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (log1p (expm1 (pow (* n (+ PI PI)) (/ 1 2)))) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (pow (* n (+ PI PI)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (27 enodes)
* * [misc]simplify:  iters left: 2 (29 enodes)
* [exit]simplify:  Simplified to (expm1 (pow (+ (* PI n) (* PI n)) (/ 1 2)))
* [exit]simplify:  Simplified to (expm1 (pow (+ (* PI n) (* PI n)) (/ 1 2)))
* * * * [misc]progress:  [ 2 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (expm1 (log1p (pow (* n (+ PI PI)) (/ 1 2)))) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (pow (* n (+ PI PI)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (27 enodes)
* * [misc]simplify:  iters left: 2 (29 enodes)
* [exit]simplify:  Simplified to (log1p (pow (+ (* PI n) (* PI n)) (/ 1 2)))
* [exit]simplify:  Simplified to (log1p (pow (+ (* PI n) (* PI n)) (/ 1 2)))
* * * * [misc]progress:  [ 3 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (exp (* (log (* n (+ PI PI))) (/ 1 2))) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* n (+ PI PI))) (/ 1 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (72 enodes)
* * [misc]simplify:  iters left: 2 (104 enodes)
* * [misc]simplify:  iters left: 1 (149 enodes)
* [exit]simplify:  Simplified to (fma (/ 1 2) (log (+ PI PI)) (/ (log n) 2))
* [exit]simplify:  Simplified to (fma (/ 1 2) (log (+ PI PI)) (/ (log n) 2))
* * * * [misc]progress:  [ 4 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (exp (* (log (* n (+ PI PI))) (/ 1 2))) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* n (+ PI PI))) (/ 1 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (72 enodes)
* * [misc]simplify:  iters left: 2 (104 enodes)
* * [misc]simplify:  iters left: 1 (149 enodes)
* [exit]simplify:  Simplified to (fma (/ 1 2) (log (+ PI PI)) (/ (log n) 2))
* [exit]simplify:  Simplified to (fma (/ 1 2) (log (+ PI PI)) (/ (log n) 2))
* * * * [misc]progress:  [ 5 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (* 1 (/ 1 2))) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [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:  [ 6 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* n (+ PI PI)) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) (cbrt (/ 1 2))) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) (* (cbrt (/ 1 2)) (cbrt (/ 1 2))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (28 enodes)
* * [misc]simplify:  iters left: 2 (30 enodes)
* [exit]simplify:  Simplified to (pow (* (+ n n) PI) (* (cbrt (/ 1 2)) (cbrt (/ 1 2))))
* [exit]simplify:  Simplified to (pow (* (+ n n) PI) (* (cbrt (/ 1 2)) (cbrt (/ 1 2))))
* * * * [misc]progress:  [ 7 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* n (+ PI PI)) (sqrt (/ 1 2))) (sqrt (/ 1 2))) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) (sqrt (/ 1 2)))
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (27 enodes)
* * [misc]simplify:  iters left: 1 (29 enodes)
* [exit]simplify:  Simplified to (pow (+ (* PI n) (* PI n)) (sqrt (/ 1 2)))
* [exit]simplify:  Simplified to (pow (+ (* PI n) (* PI n)) (sqrt (/ 1 2)))
* * * * [misc]progress:  [ 8 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* n (+ PI PI)) 1) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) 1)
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* * [misc]simplify:  iters left: 2 (25 enodes)
* * [misc]simplify:  iters left: 1 (27 enodes)
* [exit]simplify:  Simplified to (* n (+ PI PI))
* [exit]simplify:  Simplified to (* n (+ PI PI))
* * * * [misc]progress:  [ 9 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* n (+ PI PI)) 1) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) 1)
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* * [misc]simplify:  iters left: 2 (25 enodes)
* * [misc]simplify:  iters left: 1 (27 enodes)
* [exit]simplify:  Simplified to (* n (+ PI PI))
* [exit]simplify:  Simplified to (* n (+ PI PI))
* * * * [misc]progress:  [ 10 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (pow n (/ 1 2)) (pow (+ PI PI) (/ 1 2))) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow n (/ 1 2))
* * [misc]simplify:  iters left: 3 (5 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (pow n (/ 1 2))
* [exit]simplify:  Simplified to (pow n (/ 1 2))
* [enter]simplify:  Simplifying (pow (+ PI PI) (/ 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 (+ PI PI) (/ 1 2))
* [exit]simplify:  Simplified to (pow (+ PI PI) (/ 1 2))
* * * * [misc]progress:  [ 11 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* n (+ PI PI)) (/ 1 2)) 1) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* * * * [misc]progress:  [ 12 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (exp (log (pow (* n (+ PI PI)) (/ 1 2)))) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (pow (* n (+ PI PI)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (50 enodes)
* * [misc]simplify:  iters left: 2 (81 enodes)
* * [misc]simplify:  iters left: 1 (101 enodes)
* [exit]simplify:  Simplified to (fma (log (+ PI PI)) (/ 1 2) (/ (log n) 2))
* [exit]simplify:  Simplified to (fma (log (+ PI PI)) (/ 1 2) (/ (log n) 2))
* * * * [misc]progress:  [ 13 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (log (exp (pow (* n (+ PI PI)) (/ 1 2)))) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (pow (* n (+ PI PI)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (27 enodes)
* * [misc]simplify:  iters left: 2 (29 enodes)
* [exit]simplify:  Simplified to (exp (pow (+ (* PI n) (* PI n)) (/ 1 2)))
* [exit]simplify:  Simplified to (exp (pow (+ (* PI n) (* PI n)) (/ 1 2)))
* * * * [misc]progress:  [ 14 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (cbrt (pow (* n (+ PI PI)) (/ 1 2)))) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (pow (* n (+ PI PI)) (/ 1 2))) (cbrt (pow (* n (+ PI PI)) (/ 1 2))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (28 enodes)
* * [misc]simplify:  iters left: 2 (30 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ 1 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* (+ n n) PI) (/ 1 2))) (cbrt (pow (* (+ n n) PI) (/ 1 2))))
* [enter]simplify:  Simplifying (cbrt (pow (* n (+ PI PI)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (27 enodes)
* * [misc]simplify:  iters left: 2 (29 enodes)
* [exit]simplify:  Simplified to (cbrt (pow (+ (* PI n) (* PI n)) (/ 1 2)))
* [exit]simplify:  Simplified to (cbrt (pow (+ (* PI n) (* PI n)) (/ 1 2)))
* * * * [misc]progress:  [ 15 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (cbrt (* (* (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ 1 2)))) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (19 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 (pow (* (+ n n) PI) (/ 1 2)) 3)
* [exit]simplify:  Simplified to (pow (pow (* (+ n n) PI) (/ 1 2)) 3)
* * * * [misc]progress:  [ 16 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (sqrt (pow (* n (+ PI PI)) (/ 1 2))) (sqrt (pow (* n (+ PI PI)) (/ 1 2)))) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (pow (* n (+ PI PI)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (27 enodes)
* * [misc]simplify:  iters left: 2 (29 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (+ (* PI n) (* PI n)) (/ 1 2)))
* [exit]simplify:  Simplified to (sqrt (pow (+ (* PI n) (* PI n)) (/ 1 2)))
* [enter]simplify:  Simplifying (sqrt (pow (* n (+ PI PI)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (27 enodes)
* * [misc]simplify:  iters left: 2 (29 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (+ (* PI n) (* PI n)) (/ 1 2)))
* [exit]simplify:  Simplified to (sqrt (pow (+ (* PI n) (* PI n)) (/ 1 2)))
* * * * [misc]progress:  [ 17 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* 1 (pow (* n (+ PI PI)) (/ 1 2))) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* * * * [misc]progress:  [ 18 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (log1p (expm1 (* n (+ PI PI)))) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (expm1 (* n (+ PI PI)))
* [exit]simplify:  Simplified to (expm1 (* n (+ PI PI)))
* * * * [misc]progress:  [ 19 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (expm1 (log1p (* n (+ PI PI)))) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (log1p (* n (+ PI PI)))
* [exit]simplify:  Simplified to (log1p (* n (+ PI PI)))
* * * * [misc]progress:  [ 20 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (pow (* n (+ PI PI)) 1) k) (/ 1 2))) (sqrt k)))>
* * * * [misc]progress:  [ 21 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (exp (log (* n (+ PI PI)))) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* * [misc]simplify:  iters left: 1 (43 enodes)
* [exit]simplify:  Simplified to (log (* (+ n n) PI))
* [exit]simplify:  Simplified to (log (* (+ n n) PI))
* * * * [misc]progress:  [ 22 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (log (exp (* n (+ PI PI)))) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* * [misc]simplify:  iters left: 2 (42 enodes)
* * [misc]simplify:  iters left: 1 (47 enodes)
* [exit]simplify:  Simplified to (pow (exp PI) (+ n n))
* [exit]simplify:  Simplified to (pow (exp PI) (+ n n))
* * * * [misc]progress:  [ 23 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (* (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI)))) (cbrt (* n (+ PI PI)))) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* * [misc]simplify:  iters left: 2 (25 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI))))
* [exit]simplify:  Simplified to (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI))))
* [enter]simplify:  Simplifying (cbrt (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (cbrt (* n (+ PI PI)))
* [exit]simplify:  Simplified to (cbrt (* n (+ PI PI)))
* * * * [misc]progress:  [ 24 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (cbrt (* (* (* n (+ PI PI)) (* n (+ PI PI))) (* n (+ PI PI)))) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (* n (+ PI PI)) (* n (+ PI PI))) (* n (+ PI PI)))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (54 enodes)
* * [misc]simplify:  iters left: 3 (195 enodes)
* * [misc]simplify:  iters left: 2 (388 enodes)
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) 3)
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) 3)
* * * * [misc]progress:  [ 25 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (* (sqrt (* n (+ PI PI))) (sqrt (* n (+ PI PI)))) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* [enter]simplify:  Simplifying (sqrt (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* * * * [misc]progress:  [ 26 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (* 1 (* n (+ PI PI))) k) (/ 1 2))) (sqrt k)))>
* * * * [misc]progress:  [ 27 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (+ (* n PI) (* n PI)) k) (/ 1 2))) (sqrt k)))>
* [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)
* [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:  [ 28 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (+ (* PI n) (* PI n)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* PI n)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n PI)
* [exit]simplify:  Simplified to (* n PI)
* [enter]simplify:  Simplifying (* PI n)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n PI)
* [exit]simplify:  Simplified to (* n PI)
* * * * [misc]progress:  [ 29 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (* (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) (cbrt (+ PI PI))) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* [exit]simplify:  Simplified to (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI))))
* [exit]simplify:  Simplified to (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI))))
* * * * [misc]progress:  [ 30 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (sqrt (+ PI 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 (+ PI PI)) n)
* [exit]simplify:  Simplified to (* (sqrt (+ PI PI)) n)
* * * * [misc]progress:  [ 31 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (* (* n 1) (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n 1)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (5 enodes)
* [exit]simplify:  Simplified to n
* [exit]simplify:  Simplified to n
* * * * [misc]progress:  [ 32 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (* (* n 2) PI) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n 2)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (+ n n)
* [exit]simplify:  Simplified to (+ n n)
* * * * [misc]progress:  [ 33 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (/ (* n (+ (pow PI 3) (pow PI 3))) (+ (* PI PI) (- (* PI PI) (* PI PI)))) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (+ (pow PI 3) (pow PI 3)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (52 enodes)
* * [misc]simplify:  iters left: 1 (69 enodes)
* [exit]simplify:  Simplified to (* (+ n n) (pow PI 3))
* [exit]simplify:  Simplified to (* (+ n n) (pow PI 3))
* * * * [misc]progress:  [ 34 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (/ (* n (- (* PI PI) (* PI PI))) (- PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (- (* PI PI) (* PI PI)))
* * [misc]simplify:  iters left: 6 (5 enodes)
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* [exit]simplify:  Simplified to 0
* [exit]simplify:  Simplified to 0
* * * * [misc]progress:  [ 35 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (* (+ PI PI) n) k) (/ 1 2))) (sqrt k)))>
* * * * [misc]progress:  [ 36 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (log1p (expm1 (* n (+ PI PI)))) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (expm1 (* n (+ PI PI)))
* [exit]simplify:  Simplified to (expm1 (* n (+ PI PI)))
* * * * [misc]progress:  [ 37 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (expm1 (log1p (* n (+ PI PI)))) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (log1p (* n (+ PI PI)))
* [exit]simplify:  Simplified to (log1p (* n (+ PI PI)))
* * * * [misc]progress:  [ 38 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* n (+ PI PI)) 1) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* * * * [misc]progress:  [ 39 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (exp (log (* n (+ PI PI)))) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* * [misc]simplify:  iters left: 1 (43 enodes)
* [exit]simplify:  Simplified to (log (* (+ n n) PI))
* [exit]simplify:  Simplified to (log (* (+ n n) PI))
* * * * [misc]progress:  [ 40 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (log (exp (* n (+ PI PI)))) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* * [misc]simplify:  iters left: 2 (42 enodes)
* * [misc]simplify:  iters left: 1 (47 enodes)
* [exit]simplify:  Simplified to (pow (exp PI) (+ n n))
* [exit]simplify:  Simplified to (pow (exp PI) (+ n n))
* * * * [misc]progress:  [ 41 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI)))) (cbrt (* n (+ PI PI)))) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* * [misc]simplify:  iters left: 2 (25 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI))))
* [exit]simplify:  Simplified to (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI))))
* [enter]simplify:  Simplifying (cbrt (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (cbrt (* n (+ PI PI)))
* [exit]simplify:  Simplified to (cbrt (* n (+ PI PI)))
* * * * [misc]progress:  [ 42 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (cbrt (* (* (* n (+ PI PI)) (* n (+ PI PI))) (* n (+ PI PI)))) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (* n (+ PI PI)) (* n (+ PI PI))) (* n (+ PI PI)))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (54 enodes)
* * [misc]simplify:  iters left: 3 (195 enodes)
* * [misc]simplify:  iters left: 2 (388 enodes)
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) 3)
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) 3)
* * * * [misc]progress:  [ 43 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (sqrt (* n (+ PI PI))) (sqrt (* n (+ PI PI)))) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* [enter]simplify:  Simplifying (sqrt (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* * * * [misc]progress:  [ 44 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* 1 (* n (+ PI PI))) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* * * * [misc]progress:  [ 45 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (+ (* n PI) (* n PI)) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [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)
* [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:  [ 46 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (+ (* PI n) (* PI n)) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* PI n)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n PI)
* [exit]simplify:  Simplified to (* n PI)
* [enter]simplify:  Simplifying (* PI n)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n PI)
* [exit]simplify:  Simplified to (* n PI)
* * * * [misc]progress:  [ 47 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) (cbrt (+ PI PI))) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* [exit]simplify:  Simplified to (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI))))
* [exit]simplify:  Simplified to (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI))))
* * * * [misc]progress:  [ 48 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (sqrt (+ PI 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 (+ PI PI)) n)
* [exit]simplify:  Simplified to (* (sqrt (+ PI PI)) n)
* * * * [misc]progress:  [ 49 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n 1) (+ PI PI)) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n 1)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (5 enodes)
* [exit]simplify:  Simplified to n
* [exit]simplify:  Simplified to n
* * * * [misc]progress:  [ 50 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n 2)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (+ n n)
* [exit]simplify:  Simplified to (+ n n)
* * * * [misc]progress:  [ 51 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (/ (* n (+ (pow PI 3) (pow PI 3))) (+ (* PI PI) (- (* PI PI) (* PI PI)))) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (+ (pow PI 3) (pow PI 3)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (52 enodes)
* * [misc]simplify:  iters left: 1 (69 enodes)
* [exit]simplify:  Simplified to (* (+ n n) (pow PI 3))
* [exit]simplify:  Simplified to (* (+ n n) (pow PI 3))
* * * * [misc]progress:  [ 52 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (/ (* n (- (* PI PI) (* PI PI))) (- PI PI)) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (- (* PI PI) (* PI PI)))
* * [misc]simplify:  iters left: 6 (5 enodes)
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* [exit]simplify:  Simplified to 0
* [exit]simplify:  Simplified to 0
* * * * [misc]progress:  [ 53 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (+ PI PI) n) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* * * * [misc]progress:  [ 54 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (log1p (expm1 (pow (* n (+ PI PI)) k))) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (pow (* n (+ PI PI)) k))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (26 enodes)
* [exit]simplify:  Simplified to (expm1 (pow (* n (+ PI PI)) k))
* [exit]simplify:  Simplified to (expm1 (pow (* n (+ PI PI)) k))
* * * * [misc]progress:  [ 55 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (expm1 (log1p (pow (* n (+ PI PI)) k))) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (pow (* n (+ PI PI)) k))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (26 enodes)
* [exit]simplify:  Simplified to (log1p (pow (* n (+ PI PI)) k))
* [exit]simplify:  Simplified to (log1p (pow (* n (+ PI PI)) k))
* * * * [misc]progress:  [ 56 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (exp (* (log (* n (+ PI PI))) k)) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* n (+ PI PI))) k)
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (55 enodes)
* * [misc]simplify:  iters left: 2 (68 enodes)
* * [misc]simplify:  iters left: 1 (86 enodes)
* [exit]simplify:  Simplified to (fma (log (+ n n)) k (* (log PI) k))
* [exit]simplify:  Simplified to (fma (log (+ n n)) k (* (log PI) k))
* * * * [misc]progress:  [ 57 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (exp (* (log (* n (+ PI PI))) k)) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* n (+ PI PI))) k)
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (55 enodes)
* * [misc]simplify:  iters left: 2 (68 enodes)
* * [misc]simplify:  iters left: 1 (86 enodes)
* [exit]simplify:  Simplified to (fma (log (+ n n)) k (* (log PI) k))
* [exit]simplify:  Simplified to (fma (log (+ n n)) k (* (log PI) k))
* * * * [misc]progress:  [ 58 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (* n (+ PI PI)) (* 1 k)) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* 1 k)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (5 enodes)
* [exit]simplify:  Simplified to k
* [exit]simplify:  Simplified to k
* * * * [misc]progress:  [ 59 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* (pow n k) (pow (+ PI PI) k)) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow n k)
* * [misc]simplify:  iters left: 1 (3 enodes)
* [exit]simplify:  Simplified to (pow n k)
* [exit]simplify:  Simplified to (pow n k)
* [enter]simplify:  Simplifying (pow (+ PI PI) k)
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (6 enodes)
* * [misc]simplify:  iters left: 1 (7 enodes)
* [exit]simplify:  Simplified to (pow (+ PI PI) k)
* [exit]simplify:  Simplified to (pow (+ PI PI) k)
* * * * [misc]progress:  [ 60 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (pow (* n (+ PI PI)) k) 1) (/ 1 2))) (sqrt k)))>
* * * * [misc]progress:  [ 61 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (exp (log (pow (* n (+ PI PI)) k))) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (pow (* n (+ PI PI)) k))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* * [misc]simplify:  iters left: 2 (61 enodes)
* * [misc]simplify:  iters left: 1 (83 enodes)
* [exit]simplify:  Simplified to (fma k (log (+ PI PI)) (* k (log n)))
* [exit]simplify:  Simplified to (fma k (log (+ PI PI)) (* k (log n)))
* * * * [misc]progress:  [ 62 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (log (exp (pow (* n (+ PI PI)) k))) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (pow (* n (+ PI PI)) k))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (26 enodes)
* [exit]simplify:  Simplified to (exp (pow (* n (+ PI PI)) k))
* [exit]simplify:  Simplified to (exp (pow (* n (+ PI PI)) k))
* * * * [misc]progress:  [ 63 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* (* (cbrt (pow (* n (+ PI PI)) k)) (cbrt (pow (* n (+ PI PI)) k))) (cbrt (pow (* n (+ PI PI)) k))) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (pow (* n (+ PI PI)) k)) (cbrt (pow (* n (+ PI PI)) k)))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* * [misc]simplify:  iters left: 2 (27 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* n (+ PI PI)) k)) (cbrt (pow (* n (+ PI PI)) k)))
* [exit]simplify:  Simplified to (* (cbrt (pow (* n (+ PI PI)) k)) (cbrt (pow (* n (+ PI PI)) k)))
* [enter]simplify:  Simplifying (cbrt (pow (* n (+ PI PI)) k))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (26 enodes)
* [exit]simplify:  Simplified to (cbrt (pow (* n (+ PI PI)) k))
* [exit]simplify:  Simplified to (cbrt (pow (* n (+ PI PI)) k))
* * * * [misc]progress:  [ 64 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (cbrt (* (* (pow (* n (+ PI PI)) k) (pow (* n (+ PI PI)) k)) (pow (* n (+ PI PI)) k))) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (pow (* n (+ PI PI)) k) (pow (* n (+ PI PI)) k)) (pow (* n (+ PI PI)) k))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (28 enodes)
* * [misc]simplify:  iters left: 2 (30 enodes)
* [exit]simplify:  Simplified to (pow (pow (* (+ n n) PI) k) 3)
* [exit]simplify:  Simplified to (pow (pow (* (+ n n) PI) k) 3)
* * * * [misc]progress:  [ 65 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* (sqrt (pow (* n (+ PI PI)) k)) (sqrt (pow (* n (+ PI PI)) k))) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (pow (* n (+ PI PI)) k))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (26 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* n (+ PI PI)) k))
* [exit]simplify:  Simplified to (sqrt (pow (* n (+ PI PI)) k))
* [enter]simplify:  Simplifying (sqrt (pow (* n (+ PI PI)) k))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (26 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* n (+ PI PI)) k))
* [exit]simplify:  Simplified to (sqrt (pow (* n (+ PI PI)) k))
* * * * [misc]progress:  [ 66 / 78 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* 1 (pow (* n (+ PI PI)) k)) (/ 1 2))) (sqrt k)))>
* * * * [misc]progress:  [ 67 / 78 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (43 enodes)
* * [misc]simplify:  iters left: 4 (73 enodes)
* * [misc]simplify:  iters left: 3 (105 enodes)
* * [misc]simplify:  iters left: 2 (163 enodes)
* * [misc]simplify:  iters left: 1 (235 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (+ PI PI)) (/ (sqrt k) (sqrt n))) (pow (pow (* PI (+ n n)) k) (/ 1 2)))
* * * * [misc]progress:  [ 68 / 78 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (21 enodes)
* * [misc]simplify:  iters left: 5 (41 enodes)
* * [misc]simplify:  iters left: 4 (57 enodes)
* * [misc]simplify:  iters left: 3 (80 enodes)
* * [misc]simplify:  iters left: 2 (118 enodes)
* * [misc]simplify:  iters left: 1 (189 enodes)
* [exit]simplify:  Simplified to (* (/ (sqrt n) (sqrt k)) (/ (exp (fma 1/2 (- (log 2) (log 1)) (* 1/2 (log PI)))) (pow (pow (* (+ n n) PI) k) (/ 1 2))))
* * * * [misc]progress:  [ 69 / 78 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (23 enodes)
* * [misc]simplify:  iters left: 5 (43 enodes)
* * [misc]simplify:  iters left: 4 (58 enodes)
* * [misc]simplify:  iters left: 3 (80 enodes)
* * [misc]simplify:  iters left: 2 (120 enodes)
* * [misc]simplify:  iters left: 1 (191 enodes)
* [exit]simplify:  Simplified to (/ (* (exp (fma 1/2 (- (log -2) (log -1)) (* (log PI) 1/2))) (/ (sqrt n) (sqrt k))) (pow (pow (* n (+ PI PI)) k) (/ 1 2)))
* * * * [misc]progress:  [ 70 / 78 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (* 2 (* n PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (* 2 (* n PI)) k) (/ 1 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (pow (* n (+ PI PI)) k) (/ 1 2)))
* * * * [misc]progress:  [ 71 / 78 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (* 2 (* n PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (* 2 (* n PI)) k) (/ 1 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (pow (* n (+ PI PI)) k) (/ 1 2)))
* * * * [misc]progress:  [ 72 / 78 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (* 2 (* n PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (* 2 (* n PI)) k) (/ 1 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (pow (* n (+ PI PI)) k) (/ 1 2)))
* * * * [misc]progress:  [ 73 / 78 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (+ n n) PI) (/ 1 2)) (sqrt k)) (pow (pow (* (+ n n) PI) k) (/ 1 2)))
* * * * [misc]progress:  [ 74 / 78 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (+ n n) PI) (/ 1 2)) (sqrt k)) (pow (pow (* (+ n n) PI) k) (/ 1 2)))
* * * * [misc]progress:  [ 75 / 78 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (+ n n) PI) (/ 1 2)) (sqrt k)) (pow (pow (* (+ n n) PI) k) (/ 1 2)))
* * * * [misc]progress:  [ 76 / 78 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (+ 1 (+ (* (log n) k) (+ (* 1/2 (* (pow (log n) 2) (pow k 2))) (+ (* (log (* 2 PI)) (* (log n) (pow k 2))) (+ (* (log (* 2 PI)) k) (* 1/2 (* (pow (log (* 2 PI)) 2) (pow k 2)))))))) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (+ 1 (+ (* (log n) k) (+ (* 1/2 (* (pow (log n) 2) (pow k 2))) (+ (* (log (* 2 PI)) (* (log n) (pow k 2))) (+ (* (log (* 2 PI)) k) (* 1/2 (* (pow (log (* 2 PI)) 2) (pow k 2)))))))) (/ 1 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (33 enodes)
* * [misc]simplify:  iters left: 5 (73 enodes)
* * [misc]simplify:  iters left: 4 (144 enodes)
* * [misc]simplify:  iters left: 3 (302 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (+ (+ (fma (log n) k 1) (* (* k (* k 1/2)) (* (log n) (log n)))) (fma (* 1/2 (* k k)) (* (log (+ PI PI)) (log (+ PI PI))) (* (fma (log n) (* k k) k) (log (+ PI PI))))) (/ 1 2)))
* * * * [misc]progress:  [ 77 / 78 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (exp (* k (- (log (* 2 PI)) (log (/ 1 n))))) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (exp (* k (- (log (* 2 PI)) (log (/ 1 n))))) (/ 1 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (56 enodes)
* * [misc]simplify:  iters left: 3 (76 enodes)
* * [misc]simplify:  iters left: 2 (116 enodes)
* * [misc]simplify:  iters left: 1 (163 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (pow (exp k) (- (log (+ PI PI)) (- (log n)))) (/ 1 2)))
* * * * [misc]progress:  [ 78 / 78 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (exp (* k (- (log (* -2 PI)) (log (/ -1 n))))) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (exp (* k (- (log (* -2 PI)) (log (/ -1 n))))) (/ 1 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (22 enodes)
* * [misc]simplify:  iters left: 5 (42 enodes)
* * [misc]simplify:  iters left: 4 (57 enodes)
* * [misc]simplify:  iters left: 3 (79 enodes)
* * [misc]simplify:  iters left: 2 (119 enodes)
* * [misc]simplify:  iters left: 1 (166 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (sqrt k)) (pow (pow (exp k) (- (log (* -2 PI)) (log (/ -1 n)))) (/ 1 2)))
* * * [misc]progress:  adding candidates to table
* * [misc]progress:  iteration 4 / 4
* * * [misc]progress:  picking best candidate
* * * * [misc]pick:  Picked  #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 4 ] rewriting at (2 2 2)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2 2 2 1)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2 2)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 4 ] generating series at (2 2 2)
* [misc]approximate:  Taking taylor expansion of (pow (* n (+ PI PI)) (/ (- 1 k) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* n (+ PI PI)) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (+ PI 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 (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* n (* 2 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 (+ PI PI)) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (+ PI 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 (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 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 (+ PI PI)) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (+ PI 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 (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 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) (+ (* 1 0) (* 0 (* 2 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) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 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) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI 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) (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ 1 n) (* 2 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) (+ PI PI))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI 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) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 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) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI 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) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 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 (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 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 (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 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 (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
* [misc]approximate:  Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI 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)) (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ -1 n) (* 2 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)) (+ PI PI))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI 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)) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 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)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI 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)) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 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 0) 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 (+ (* -1 0) (* 0 (* 2 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 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 (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 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 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
* * * * [misc]progress:  [ 2 / 4 ] generating series at (2 2 2 1)
* [misc]approximate:  Taking taylor expansion of (* n (+ PI PI)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 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) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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) (+ PI PI)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 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 (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 PI))) 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 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) 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 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) 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 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) 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 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) 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 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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)) (+ PI PI)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 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) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 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 2)
* [misc]approximate:  Taking taylor expansion of (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 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 (+ PI PI)) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (+ PI 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 (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 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]backup-simplify:  Simplify (/ (sqrt k) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) into (* (sqrt k) (/ 1 (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))))
* [misc]taylor:  Taking taylor expansion of (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 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 (+ PI PI)) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (+ PI 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 (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* n (* 2 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]backup-simplify:  Simplify (/ +nan.0 (pow (* 2 (* n PI)) 1/2)) into (* +nan.0 (sqrt (/ 1 (* n (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 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 (+ PI PI)) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (+ PI 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 (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* n (* 2 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]backup-simplify:  Simplify (/ +nan.0 (pow (* 2 (* n PI)) 1/2)) into (* +nan.0 (sqrt (/ 1 (* n (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (sqrt (/ 1 (* n (* 2 PI))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (* n (* 2 PI)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (* n (* 2 PI))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* 2 PI)) 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 (* 2 PI) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (/ 1 (* 2 PI)) into (/ 1/2 PI)
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ (/ 1/2 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI)
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (/ +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (/ 1 PI)))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ 1 PI))) into (- (* +nan.0 (/ 1 PI)))
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* n 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (- (/ -1 2) (+ (* 1/2 (/ 0 2)))) into -1/2
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI)))))
* [misc]backup-simplify:  Simplify (- (/ +nan.0 (pow (* 2 (* n PI)) 1/2)) (+ (* (* +nan.0 (sqrt (/ 1 (* n (* 2 PI))))) (/ (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (- (+ (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) (- (* +nan.0 (* (* (log (* 2 (* n PI))) (* (sqrt 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))))))
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) (- (* +nan.0 (* (* (log (* 2 (* n PI))) (* (sqrt 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) (- (* +nan.0 (* (* (log (* 2 (* n PI))) (* (sqrt 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (/ 1 PI) into (/ 1 PI)
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (sqrt 1/2) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]backup-simplify:  Simplify (sqrt 1/2) into (sqrt 1/2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 1/2))) into 0
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (* (* (log (* 2 (* n PI))) (* (sqrt 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (log (* 2 (* n PI))) (* (sqrt 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (log (* 2 (* n PI))) (* (sqrt 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (log (* 2 (* n PI))) (* (sqrt 2) (pow (sqrt 1/2) 2))) in n
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n PI) 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (pow (sqrt 1/2) 2)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (pow (sqrt 1/2) 2) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 2 (log (sqrt 1/2)))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (log (sqrt 1/2))) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (log (sqrt 1/2)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 1/2) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]backup-simplify:  Simplify (sqrt 1/2) into (sqrt 1/2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 1/2))) into 0
* [misc]backup-simplify:  Simplify (log (sqrt 1/2)) into (log (sqrt 1/2))
* [misc]backup-simplify:  Simplify (* 2 (log (sqrt 1/2))) into (* 2 (log (sqrt 1/2)))
* [misc]backup-simplify:  Simplify (exp (* 2 (log (sqrt 1/2)))) into (pow (sqrt 1/2) 2)
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (/ 1 PI) into (/ 1 PI)
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI)
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
* [misc]backup-simplify:  Simplify (* 0 (sqrt 1/2)) into 0
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (sqrt 2) (pow (sqrt 1/2) 2)) into (* (pow (sqrt 1/2) 2) (sqrt 2))
* [misc]backup-simplify:  Simplify (* (+ (log (* 2 PI)) (log n)) (* (pow (sqrt 1/2) 2) (sqrt 2))) into (* (pow (sqrt 1/2) 2) (* (+ (log (* 2 PI)) (log n)) (sqrt 2)))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (sqrt 1/2) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 (log (sqrt 1/2)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 2 (log (sqrt 1/2)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (sqrt 2) 0) (* 0 (pow (sqrt 1/2) 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log (* 2 PI)) (log n)) 0) (* 0 (* (pow (sqrt 1/2) 2) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (pow (sqrt 1/2) 2) (* (+ (log (* 2 PI)) (log n)) (sqrt 2))) (/ +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log (* 2 PI)) (sqrt 2))) PI)) (- (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log n) (sqrt 2))) PI)))))
* [misc]backup-simplify:  Simplify (* (* (pow (sqrt 1/2) 2) (* (+ (log (* 2 PI)) (log n)) (sqrt 2))) 0) into 0
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (- (+ (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log (* 2 PI)) (sqrt 2))) PI)) (- (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log n) (sqrt 2))) PI)))))) (* 0 0)) into (- (+ (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log (* 2 PI)) (sqrt 2))) PI)) (- (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log n) (sqrt 2))) PI)))))
* [misc]backup-simplify:  Simplify (- (- (+ (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log (* 2 PI)) (sqrt 2))) PI)) (- (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log n) (sqrt 2))) PI)))))) into (- (+ (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log (* 2 PI)) (sqrt 2))) PI)) (- (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log n) (sqrt 2))) PI)))))
* [misc]backup-simplify:  Simplify (+ (- (* +nan.0 (/ (sqrt 1/2) PI))) (- (+ (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log (* 2 PI)) (sqrt 2))) PI)) (- (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log n) (sqrt 2))) PI)))))) into (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (+ (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log n) (sqrt 2))) PI)) (- (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log (* 2 PI)) (sqrt 2))) PI)))))))
* [misc]backup-simplify:  Simplify (- (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (+ (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log n) (sqrt 2))) PI)) (- (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log (* 2 PI)) (sqrt 2))) PI)))))))) into (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (+ (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log n) (sqrt 2))) PI)) (- (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log (* 2 PI)) (sqrt 2))) PI)))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (+ (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log n) (sqrt 2))) PI)) (- (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log (* 2 PI)) (sqrt 2))) PI))))))) into (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (+ (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log n) (sqrt 2))) PI)) (- (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log (* 2 PI)) (sqrt 2))) PI)))))))
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1/2 PI) (/ 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (/ +nan.0 (pow PI 2))) (+ (* 0 (/ +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (/ 1 (pow PI 2))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ 1 (pow PI 2)))) into (- (* +nan.0 (/ 1 (pow PI 2))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (/ 1 (pow PI 2)))) (* n k)) (+ (* (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (+ (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log n) (sqrt 2))) PI)) (- (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log (* 2 PI)) (sqrt 2))) PI))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (/ 1 PI))) (* 1 k)))) into (- (+ (* +nan.0 (/ k PI)) (- (+ (* +nan.0 (/ (* n k) (pow PI 2))) (- (+ (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (pow k 2) (* (log n) (sqrt 2)))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log (* 2 PI)) (* (pow k 2) (sqrt 2)))) PI)))))))))))
* [misc]approximate:  Taking taylor expansion of (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 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) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI 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) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 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]backup-simplify:  Simplify (/ (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 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) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI 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) (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ 1 n) (* 2 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) (+ PI PI))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))
* [misc]backup-simplify:  Simplify (/ +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) into (/ +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 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) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI 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) (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ 1 n) (* 2 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) (+ PI PI))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))
* [misc]backup-simplify:  Simplify (/ +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) into (/ +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))
* [misc]taylor:  Taking taylor expansion of (/ +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (log (* 2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [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 (/ PI 1) 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 (- 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]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (* (- (log (* 2 PI)) (log n)) (- 1 (/ 1 k))) into (* (- 1 (/ 1 k)) (- (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]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)))))) into (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
* [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 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) (/ 0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (/ 1 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (log (* 2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [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 (/ PI 1) 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 (- 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]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (* (- (log (* 2 PI)) (log n)) (- 1 (/ 1 k))) into (* (- 1 (/ 1 k)) (- (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]backup-simplify:  Simplify (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (/ 1 (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))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [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 1) (+ (* PI (/ 0 1)))) 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 (+ (* (- (log (* 2 PI)) (log n)) 0) (* 0 (- 1 (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (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 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))) 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 (- (/ +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) (/ 0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))) (/ 0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (/ 1 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (log (* 2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [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 (/ PI 1) 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 (- 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]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (* (- (log (* 2 PI)) (log n)) (- 1 (/ 1 k))) into (* (- 1 (/ 1 k)) (- (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]backup-simplify:  Simplify (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (/ 1 (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))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n))))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n))))))))) (* 1 (/ 1 k))) (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))) (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))) (- (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2)))))))))
* [misc]approximate:  Taking taylor expansion of (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 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)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI 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)) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 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]backup-simplify:  Simplify (/ (sqrt (/ -1 k)) (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (/ (sqrt (/ -1 k)) (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 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)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI 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)) (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ -1 n) (* 2 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)) (+ PI PI))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))
* [misc]backup-simplify:  Simplify (/ +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) into (/ +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 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)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI 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)) (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ -1 n) (* 2 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)) (+ PI PI))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))
* [misc]backup-simplify:  Simplify (/ +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) into (/ +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))
* [misc]taylor:  Taking taylor expansion of (/ +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) 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 (log (* -2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -2 in n
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [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 (/ PI 1) into PI
* [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 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) into (* (+ 1 (/ 1 k)) (- (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]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)))))) 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 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) (/ 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) 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 (log (* -2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -2 in n
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [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 (/ PI 1) into PI
* [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 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) into (* (+ 1 (/ 1 k)) (- (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]backup-simplify:  Simplify (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (/ 1 (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))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) 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 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (+ 1 (/ 1 k)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (* (+ 1 (/ 1 k)) (- (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 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))))) 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 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) (/ 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))) (/ 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) 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 (log (* -2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -2 in n
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [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 (/ PI 1) into PI
* [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 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) into (* (+ 1 (/ 1 k)) (- (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]backup-simplify:  Simplify (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (/ 1 (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))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) (* 1 (/ 1 (- k)))) (/ +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))))
* * * * [misc]progress:  [ 4 / 4 ] generating series at (2)
* [misc]approximate:  Taking taylor expansion of (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 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 (+ PI PI)) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (+ PI 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 (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 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]backup-simplify:  Simplify (/ (sqrt k) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) into (* (sqrt k) (/ 1 (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (/ 1 (* (sqrt k) (/ 1 (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))))) into (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))
* [misc]taylor:  Taking taylor expansion of (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 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 (+ PI PI)) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (+ PI 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 (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* n (* 2 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]backup-simplify:  Simplify (/ +nan.0 (pow (* 2 (* n PI)) 1/2)) into (* +nan.0 (sqrt (/ 1 (* n (* 2 PI)))))
* [misc]backup-simplify:  Simplify (/ 1 (* +nan.0 (sqrt (/ 1 (* n (* 2 PI)))))) into (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2))))
* [misc]taylor:  Taking taylor expansion of (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 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 (+ PI PI)) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (+ PI 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 (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* n (+ PI PI)) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* n (* 2 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]backup-simplify:  Simplify (/ +nan.0 (pow (* 2 (* n PI)) 1/2)) into (* +nan.0 (sqrt (/ 1 (* n (* 2 PI)))))
* [misc]backup-simplify:  Simplify (/ 1 (* +nan.0 (sqrt (/ 1 (* n (* 2 PI)))))) into (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2))))
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (* n PI)) (/ 1 (sqrt 1/2))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt 1/2)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 1/2) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]backup-simplify:  Simplify (sqrt 1/2) into (sqrt 1/2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 1/2))) into 0
* [misc]backup-simplify:  Simplify (/ 1 (sqrt 1/2)) into (/ 1 (sqrt 1/2))
* [misc]backup-simplify:  Simplify (* 0 (/ 1 (sqrt 1/2))) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 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 (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* n 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (- (/ -1 2) (+ (* 1/2 (/ 0 2)))) into -1/2
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI)))))
* [misc]backup-simplify:  Simplify (- (/ +nan.0 (pow (* 2 (* n PI)) 1/2)) (+ (* (* +nan.0 (sqrt (/ 1 (* n (* 2 PI))))) (/ (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (- (+ (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) (- (* +nan.0 (* (* (log (* 2 (* n PI))) (* (sqrt 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))))))
* [misc]backup-simplify:  Simplify (- (+ (* (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))) (/ (- (+ (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) (- (* +nan.0 (* (* (log (* 2 (* n PI))) (* (sqrt 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))))) (* +nan.0 (sqrt (/ 1 (* n (* 2 PI))))))))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))) (- (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))))))
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))) (- (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI))))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))) (- (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (* n PI)) (/ 1 (sqrt 1/2))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt 1/2)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 1/2) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]backup-simplify:  Simplify (sqrt 1/2) into (sqrt 1/2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 1/2))) into 0
* [misc]backup-simplify:  Simplify (/ 1 (sqrt 1/2)) into (/ 1 (sqrt 1/2))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI))))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n PI) 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 0 (/ 1 (sqrt 1/2))) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (sqrt 2) (+ (log (* 2 PI)) (log n))) into (* (+ (log (* 2 PI)) (log n)) (sqrt 2))
* [misc]backup-simplify:  Simplify (* 0 (* (+ (log (* 2 PI)) (log n)) (sqrt 2))) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 (sqrt 1/2)) (/ 0 (sqrt 1/2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* (* +nan.0 PI) (/ 1 (sqrt 1/2)))) into (- (* +nan.0 (/ PI (sqrt 1/2))))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (- (* +nan.0 (/ PI (sqrt 1/2))))) (* 0 0)) into (- (* +nan.0 (/ PI (sqrt 1/2))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ PI (sqrt 1/2)))) into (- (* +nan.0 (/ PI (sqrt 1/2))))
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* n 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* n (* 2 PI))) (pow (log (* 2 (* n PI))) 2)))
* [misc]backup-simplify:  Simplify (- (/ +nan.0 (pow (* 2 (* n PI)) 1/2)) (+ (* (* +nan.0 (sqrt (/ 1 (* n (* 2 PI))))) (/ (* 1/8 (* (sqrt (* n (* 2 PI))) (pow (log (* 2 (* n PI))) 2))) (pow (* 2 (* n PI)) 1/2))) (* (- (+ (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) (- (* +nan.0 (* (* (log (* 2 (* n PI))) (* (sqrt 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))))) (/ (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (- (+ (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) (- (+ (* +nan.0 (* (* (log (* 2 (* n PI))) (* (sqrt 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (* (pow (log (* 2 (* n PI))) 2) (* (sqrt 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (* (pow (log (* 2 (* n PI))) 2) (* (pow (sqrt 2) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))) (/ (- (+ (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) (- (+ (* +nan.0 (* (* (log (* 2 (* n PI))) (* (sqrt 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (* (pow (log (* 2 (* n PI))) 2) (* (sqrt 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (* (pow (log (* 2 (* n PI))) 2) (* (pow (sqrt 2) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI)))))))))))) (* +nan.0 (sqrt (/ 1 (* n (* 2 PI))))))) (* (- (+ (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))) (- (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI))))))))) (/ (- (+ (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) (- (* +nan.0 (* (* (log (* 2 (* n PI))) (* (sqrt 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))))) (* +nan.0 (sqrt (/ 1 (* n (* 2 PI))))))))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))) (- (+ (* +nan.0 (* (* (pow (log (* 2 (* n PI))) 2) (* (pow (sqrt 2) 2) (sqrt 1/2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))))))))))
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))) (- (+ (* +nan.0 (* (* (pow (log (* 2 (* n PI))) 2) (* (pow (sqrt 2) 2) (sqrt 1/2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2))))))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))) (- (+ (* +nan.0 (* (* (pow (log (* 2 (* n PI))) 2) (* (pow (sqrt 2) 2) (sqrt 1/2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (* n PI)) (/ 1 (sqrt 1/2))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt 1/2)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 1/2) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]backup-simplify:  Simplify (sqrt 1/2) into (sqrt 1/2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 1/2))) into 0
* [misc]backup-simplify:  Simplify (/ 1 (sqrt 1/2)) into (/ 1 (sqrt 1/2))
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (log (* 2 (* n PI))) 2) (* (pow (sqrt 2) 2) (sqrt 1/2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2))))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (* (pow (log (* 2 (* n PI))) 2) (* (pow (sqrt 2) 2) (sqrt 1/2))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (pow (log (* 2 (* n PI))) 2) (* (pow (sqrt 2) 2) (sqrt 1/2))) (sqrt (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (pow (log (* 2 (* n PI))) 2) (* (pow (sqrt 2) 2) (sqrt 1/2))) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (pow (log (* 2 (* n PI))) 2) (* (pow (sqrt 2) 2) (sqrt 1/2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 2 (log (log (* 2 (* n PI)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (log (log (* 2 (* n PI))))) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (log (log (* 2 (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n PI) 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 2 PI) (* 0 0)) 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) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (log (+ (log (* 2 PI)) (log n))) into (log (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 2 (log (+ (log (* 2 PI)) (log n)))) into (* 2 (log (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 2 (log (+ (log (* 2 PI)) (log n))))) into (pow (+ (log (* 2 PI)) (log n)) 2)
* [misc]taylor:  Taking taylor expansion of (* (pow (sqrt 2) 2) (sqrt 1/2)) in n
* [misc]taylor:  Taking taylor expansion of (pow (sqrt 2) 2) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 2 (log (sqrt 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (log (sqrt 2))) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (log (sqrt 2)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]backup-simplify:  Simplify (log (sqrt 2)) into (log (sqrt 2))
* [misc]backup-simplify:  Simplify (* 2 (log (sqrt 2))) into (* 2 (log (sqrt 2)))
* [misc]backup-simplify:  Simplify (exp (* 2 (log (sqrt 2)))) into (pow (sqrt 2) 2)
* [misc]taylor:  Taking taylor expansion of (sqrt 1/2) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]backup-simplify:  Simplify (sqrt 1/2) into (sqrt 1/2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 1/2))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI))))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n PI) 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 2 (log (log (* 2 (* n PI)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (log (log (* 2 (* n PI))))) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (log (log (* 2 (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n PI) 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 2 PI) (* 0 0)) 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) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (log (+ (log (* 2 PI)) (log n))) into (log (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 2 (log (+ (log (* 2 PI)) (log n)))) into (* 2 (log (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 2 (log (+ (log (* 2 PI)) (log n))))) into (pow (+ (log (* 2 PI)) (log n)) 2)
* [misc]backup-simplify:  Simplify (* 0 (/ 1 (sqrt 1/2))) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (* (pow (sqrt 2) 2) (sqrt 1/2)) into (* (sqrt 1/2) (pow (sqrt 2) 2))
* [misc]backup-simplify:  Simplify (* (pow (+ (log (* 2 PI)) (log n)) 2) (* (sqrt 1/2) (pow (sqrt 2) 2))) into (* (sqrt 1/2) (* (pow (+ (log (* 2 PI)) (log n)) 2) (pow (sqrt 2) 2)))
* [misc]backup-simplify:  Simplify (* (* (sqrt 1/2) (* (pow (+ (log (* 2 PI)) (log n)) 2) (pow (sqrt 2) 2))) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (sqrt 2) (+ (log (* 2 PI)) (log n))) into (* (+ (log (* 2 PI)) (log n)) (sqrt 2))
* [misc]backup-simplify:  Simplify (* 0 (* (+ (log (* 2 PI)) (log n)) (sqrt 2))) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (* (sqrt 2) (pow (+ (log (* 2 PI)) (log n)) 2)) into (* (pow (+ (log (* 2 PI)) (log n)) 2) (sqrt 2))
* [misc]backup-simplify:  Simplify (* 0 (* (pow (+ (log (* 2 PI)) (log n)) 2) (sqrt 2))) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 (sqrt 1/2)) (/ 0 (sqrt 1/2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* (* +nan.0 PI) (/ 1 (sqrt 1/2)))) into (- (* +nan.0 (/ PI (sqrt 1/2))))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (- (* +nan.0 (/ PI (sqrt 1/2))))) (* 0 0)) into (- (* +nan.0 (/ PI (sqrt 1/2))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* (* +nan.0 PI) (* (+ (log (* 2 PI)) (log n)) (sqrt 2)))) into (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))) (* 0 0)) into (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))
* [misc]backup-simplify:  Simplify (- (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))) into (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))
* [misc]backup-simplify:  Simplify (+ (- (* +nan.0 (/ PI (sqrt 1/2)))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))) into (- (+ (* +nan.0 (/ PI (sqrt 1/2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))))
* [misc]backup-simplify:  Simplify (- (- (+ (* +nan.0 (/ PI (sqrt 1/2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))))) into (- (+ (* +nan.0 (/ PI (sqrt 1/2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ PI (sqrt 1/2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))))) into (- (+ (* +nan.0 (/ PI (sqrt 1/2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))))
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1/2))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 (sqrt 1/2)) (/ 0 (sqrt 1/2))) (* 0 (/ 0 (sqrt 1/2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* (* +nan.0 PI) 0) (* (* +nan.0 (pow PI 2)) (/ 1 (sqrt 1/2))))) into (- (* +nan.0 (/ (pow PI 2) (sqrt 1/2))))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (- (* +nan.0 (/ (pow PI 2) (sqrt 1/2))))) (+ (* 0 (- (* +nan.0 (/ PI (sqrt 1/2))))) (* 0 0))) into (- (* +nan.0 (/ (pow PI 2) (sqrt 1/2))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (pow PI 2) (sqrt 1/2)))) into (- (* +nan.0 (/ (pow PI 2) (sqrt 1/2))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (/ (pow PI 2) (sqrt 1/2)))) (* (pow n 2) (/ 1 k))) (+ (* (- (+ (* +nan.0 (/ PI (sqrt 1/2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))))) (* n 1)) (* (- (* +nan.0 (/ PI (sqrt 1/2)))) (* n (/ 1 k))))) into (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) (* k (sqrt 1/2)))) (- (+ (* +nan.0 (/ (* n PI) (* k (sqrt 1/2)))) (- (+ (* +nan.0 (* n (* PI (* (log n) (sqrt 2))))) (- (+ (* +nan.0 (/ (* n PI) (sqrt 1/2))) (- (* +nan.0 (* n (* PI (* (log (* 2 PI)) (sqrt 2))))))))))))))
* [misc]approximate:  Taking taylor expansion of (/ 1 (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (/ 1 (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 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) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI 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) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 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]backup-simplify:  Simplify (/ (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k)))
* [misc]backup-simplify:  Simplify (/ 1 (* (/ 1 (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 (/ 1 (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 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) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI 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) (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ 1 n) (* 2 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) (+ PI PI))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))
* [misc]backup-simplify:  Simplify (/ +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) into (/ +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))
* [misc]backup-simplify:  Simplify (/ 1 (/ +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) into (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))
* [misc]taylor:  Taking taylor expansion of (/ 1 (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ 1 k)) (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 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) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (+ PI 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) (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (+ PI PI)) 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 (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ 1 n) (* 2 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) (+ PI PI))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))
* [misc]backup-simplify:  Simplify (/ +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) into (/ +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))
* [misc]backup-simplify:  Simplify (/ 1 (/ +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) into (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (log (* 2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [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 (/ PI 1) 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 (- 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]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (* (- (log (* 2 PI)) (log n)) (- 1 (/ 1 k))) into (* (- 1 (/ 1 k)) (- (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]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)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
* [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 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) (/ 0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))))
* [misc]backup-simplify:  Simplify (- (+ (* (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) (/ (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))) (/ +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (log (* 2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [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 (/ PI 1) 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 (- 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]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (* (- (log (* 2 PI)) (log n)) (- 1 (/ 1 k))) into (* (- 1 (/ 1 k)) (- (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]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))))))) 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) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [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 1) (+ (* PI (/ 0 1)))) 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 (+ (* (- (log (* 2 PI)) (log n)) 0) (* 0 (- 1 (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (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 (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) 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 (- (/ +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) (/ 0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))) (/ 0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))))
* [misc]backup-simplify:  Simplify (- (+ (* (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) (/ (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))) (/ +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))) (* (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) (/ (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))) (/ +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (log (* 2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [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 (/ PI 1) 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 (- 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]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (* (- (log (* 2 PI)) (log n)) (- 1 (/ 1 k))) into (* (- 1 (/ 1 k)) (- (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]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))))))) 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 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))) (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)))))))
* [misc]approximate:  Taking taylor expansion of (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 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)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI 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)) (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 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]backup-simplify:  Simplify (/ (sqrt (/ -1 k)) (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (/ (sqrt (/ -1 k)) (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (/ 1 (/ (sqrt (/ -1 k)) (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
* [misc]taylor:  Taking taylor expansion of (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 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)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI 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)) (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ -1 n) (* 2 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)) (+ PI PI))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))
* [misc]backup-simplify:  Simplify (/ +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) into (/ +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))
* [misc]backup-simplify:  Simplify (/ 1 (/ +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))
* [misc]taylor:  Taking taylor expansion of (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 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)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (+ PI 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)) (+ PI PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (+ PI PI)) 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 (+ PI PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ PI PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ -1 n) (* 2 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)) (+ PI PI))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))
* [misc]backup-simplify:  Simplify (/ +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) into (/ +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))
* [misc]backup-simplify:  Simplify (/ 1 (/ +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) 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 (log (* -2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -2 in n
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [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 (/ PI 1) into PI
* [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 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) into (* (+ 1 (/ 1 k)) (- (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]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)))))) 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 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) (/ 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))))
* [misc]backup-simplify:  Simplify (- (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) (/ (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))) (/ +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) 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 (log (* -2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -2 in n
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [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 (/ PI 1) into PI
* [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 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) into (* (+ 1 (/ 1 k)) (- (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]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))))))) 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 1) (+ (* PI (/ 0 1)))) 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 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (+ 1 (/ 1 k)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (* (+ 1 (/ 1 k)) (- (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 (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) 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 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) (/ 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))) (/ 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))))
* [misc]backup-simplify:  Simplify (- (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) (/ (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))) (/ +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))) (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) (/ (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))) (/ +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) 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 (log (* -2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -2 in n
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [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 (/ PI 1) into PI
* [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 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) into (* (+ 1 (/ 1 k)) (- (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]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))))))) 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 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))))))))
* * * [misc]progress:  simplifying candidates
* * * * [misc]progress:  [ 1 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (log1p (expm1 (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (expm1 (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* * [misc]simplify:  iters left: 2 (34 enodes)
* [exit]simplify:  Simplified to (expm1 (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (expm1 (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 2 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (expm1 (log1p (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (log1p (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* * [misc]simplify:  iters left: 2 (34 enodes)
* [exit]simplify:  Simplified to (log1p (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (log1p (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 3 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (exp (* (log (* n (+ PI PI))) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (* (log (* n (+ PI PI))) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (47 enodes)
* * [misc]simplify:  iters left: 3 (79 enodes)
* * [misc]simplify:  iters left: 2 (115 enodes)
* * [misc]simplify:  iters left: 1 (170 enodes)
* [exit]simplify:  Simplified to (/ (log (* n (+ PI PI))) (/ 2 (- 1 k)))
* [exit]simplify:  Simplified to (/ (log (* n (+ PI PI))) (/ 2 (- 1 k)))
* * * * [misc]progress:  [ 4 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (exp (* (log (* n (+ PI PI))) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (* (log (* n (+ PI PI))) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (47 enodes)
* * [misc]simplify:  iters left: 3 (79 enodes)
* * [misc]simplify:  iters left: 2 (115 enodes)
* * [misc]simplify:  iters left: 1 (170 enodes)
* [exit]simplify:  Simplified to (/ (log (* n (+ PI PI))) (/ 2 (- 1 k)))
* [exit]simplify:  Simplified to (/ (log (* n (+ PI PI))) (/ 2 (- 1 k)))
* * * * [misc]progress:  [ 5 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (* 1 (/ (- 1 k) 2))))))>
* [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:  [ 6 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))))))>
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) (/ 1 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* * [misc]simplify:  iters left: 2 (26 enodes)
* * [misc]simplify:  iters left: 1 (28 enodes)
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) (/ 1 2))
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) (/ 1 2))
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) (/ k 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (21 enodes)
* * [misc]simplify:  iters left: 2 (24 enodes)
* * [misc]simplify:  iters left: 1 (26 enodes)
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) (/ k 2))
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) (/ k 2))
* * * * [misc]progress:  [ 7 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (+ PI PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* * [misc]simplify:  iters left: 2 (35 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:  [ 8 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (+ PI PI)) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) (sqrt (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* * [misc]simplify:  iters left: 2 (34 enodes)
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) (sqrt (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) (sqrt (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 9 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (+ PI PI)) 1) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) 1)
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* * [misc]simplify:  iters left: 2 (25 enodes)
* * [misc]simplify:  iters left: 1 (27 enodes)
* [exit]simplify:  Simplified to (* n (+ PI PI))
* [exit]simplify:  Simplified to (* n (+ PI PI))
* * * * [misc]progress:  [ 10 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (+ PI PI)) (- 1 k)) (/ 1 2)))))>
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) (- 1 k))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (27 enodes)
* * [misc]simplify:  iters left: 1 (29 enodes)
* [exit]simplify:  Simplified to (pow (+ (* PI n) (* PI n)) (- 1 k))
* [exit]simplify:  Simplified to (pow (+ (* PI n) (* PI n)) (- 1 k))
* * * * [misc]progress:  [ 11 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (* (pow n (/ (- 1 k) 2)) (pow (+ PI PI) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (pow n (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* [exit]simplify:  Simplified to (pow n (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow n (/ (- 1 k) 2))
* [enter]simplify:  Simplifying (pow (+ PI PI) (/ (- 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 (+ PI PI) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow (+ PI PI) (/ (- 1 k) 2))
* * * * [misc]progress:  [ 12 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (+ PI PI)) (/ (- 1 k) 2)) 1))))>
* * * * [misc]progress:  [ 13 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (exp (log (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (log (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (38 enodes)
* * [misc]simplify:  iters left: 3 (63 enodes)
* * [misc]simplify:  iters left: 2 (101 enodes)
* * [misc]simplify:  iters left: 1 (147 enodes)
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* n (+ PI PI))))
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* n (+ PI PI))))
* * * * [misc]progress:  [ 14 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (log (exp (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (exp (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* * [misc]simplify:  iters left: 2 (34 enodes)
* [exit]simplify:  Simplified to (exp (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (exp (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 15 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (* (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* * [misc]simplify:  iters left: 2 (35 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 (+ PI PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* * [misc]simplify:  iters left: 2 (34 enodes)
* [exit]simplify:  Simplified to (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 16 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (cbrt (* (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (* (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (38 enodes)
* [exit]simplify:  Simplified to (pow (pow (* n (+ PI PI)) (/ (- 1 k) 2)) 3)
* [exit]simplify:  Simplified to (pow (pow (* n (+ PI PI)) (/ (- 1 k) 2)) 3)
* * * * [misc]progress:  [ 17 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (* (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* * [misc]simplify:  iters left: 2 (34 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* [enter]simplify:  Simplifying (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* * [misc]simplify:  iters left: 2 (34 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 18 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (* 1 (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))>
* * * * [misc]progress:  [ 19 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (log1p (expm1 (* n (+ PI PI)))) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (expm1 (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (expm1 (* n (+ PI PI)))
* [exit]simplify:  Simplified to (expm1 (* n (+ PI PI)))
* * * * [misc]progress:  [ 20 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (expm1 (log1p (* n (+ PI PI)))) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (log1p (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (log1p (* n (+ PI PI)))
* [exit]simplify:  Simplified to (log1p (* n (+ PI PI)))
* * * * [misc]progress:  [ 21 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* n (+ PI PI)) 1) (/ (- 1 k) 2)))))>
* * * * [misc]progress:  [ 22 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (exp (log (* n (+ PI PI)))) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (log (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* * [misc]simplify:  iters left: 1 (43 enodes)
* [exit]simplify:  Simplified to (log (* (+ n n) PI))
* [exit]simplify:  Simplified to (log (* (+ n n) PI))
* * * * [misc]progress:  [ 23 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (log (exp (* n (+ PI PI)))) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (exp (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* * [misc]simplify:  iters left: 2 (42 enodes)
* * [misc]simplify:  iters left: 1 (47 enodes)
* [exit]simplify:  Simplified to (pow (exp PI) (+ n n))
* [exit]simplify:  Simplified to (pow (exp PI) (+ n n))
* * * * [misc]progress:  [ 24 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI)))) (cbrt (* n (+ PI PI)))) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* * [misc]simplify:  iters left: 2 (25 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI))))
* [exit]simplify:  Simplified to (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI))))
* [enter]simplify:  Simplifying (cbrt (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (cbrt (* n (+ PI PI)))
* [exit]simplify:  Simplified to (cbrt (* n (+ PI PI)))
* * * * [misc]progress:  [ 25 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (cbrt (* (* (* n (+ PI PI)) (* n (+ PI PI))) (* n (+ PI PI)))) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* (* (* n (+ PI PI)) (* n (+ PI PI))) (* n (+ PI PI)))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (54 enodes)
* * [misc]simplify:  iters left: 3 (195 enodes)
* * [misc]simplify:  iters left: 2 (388 enodes)
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) 3)
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) 3)
* * * * [misc]progress:  [ 26 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (* (sqrt (* n (+ PI PI))) (sqrt (* n (+ PI PI)))) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (sqrt (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* [enter]simplify:  Simplifying (sqrt (* n (+ PI PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* * * * [misc]progress:  [ 27 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (* 1 (* n (+ PI PI))) (/ (- 1 k) 2)))))>
* * * * [misc]progress:  [ 28 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (+ (* n PI) (* n PI)) (/ (- 1 k) 2)))))>
* [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)
* [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:  [ 29 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (+ (* PI n) (* PI n)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* PI n)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n PI)
* [exit]simplify:  Simplified to (* n PI)
* [enter]simplify:  Simplifying (* PI n)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n PI)
* [exit]simplify:  Simplified to (* n PI)
* * * * [misc]progress:  [ 30 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) (cbrt (+ PI PI))) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* [exit]simplify:  Simplified to (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI))))
* [exit]simplify:  Simplified to (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI))))
* * * * [misc]progress:  [ 31 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* n (sqrt (+ PI 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 (+ PI PI)) n)
* [exit]simplify:  Simplified to (* (sqrt (+ PI PI)) n)
* * * * [misc]progress:  [ 32 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 1) (+ PI PI)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* n 1)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (5 enodes)
* [exit]simplify:  Simplified to n
* [exit]simplify:  Simplified to n
* * * * [misc]progress:  [ 33 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* n 2)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (+ n n)
* [exit]simplify:  Simplified to (+ n n)
* * * * [misc]progress:  [ 34 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (/ (* n (+ (pow PI 3) (pow PI 3))) (+ (* PI PI) (- (* PI PI) (* PI PI)))) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* n (+ (pow PI 3) (pow PI 3)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (52 enodes)
* * [misc]simplify:  iters left: 1 (69 enodes)
* [exit]simplify:  Simplified to (* (+ n n) (pow PI 3))
* [exit]simplify:  Simplified to (* (+ n n) (pow PI 3))
* * * * [misc]progress:  [ 35 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (/ (* n (- (* PI PI) (* PI PI))) (- PI PI)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* n (- (* PI PI) (* PI PI)))
* * [misc]simplify:  iters left: 6 (5 enodes)
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* [exit]simplify:  Simplified to 0
* [exit]simplify:  Simplified to 0
* * * * [misc]progress:  [ 36 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (* (+ PI PI) n) (/ (- 1 k) 2)))))>
* * * * [misc]progress:  [ 37 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (log1p (expm1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (expm1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (expm1 (/ (sqrt k) (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (expm1 (/ (sqrt k) (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 38 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (expm1 (log1p (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (log1p (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (log1p (/ (sqrt k) (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (log1p (/ (sqrt k) (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 39 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (pow (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) 1)))>
* * * * [misc]progress:  [ 40 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (exp (- (log (sqrt k)) (* (log (* n (+ PI PI))) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (- (log (sqrt k)) (* (log (* n (+ PI PI))) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (50 enodes)
* * [misc]simplify:  iters left: 3 (86 enodes)
* * [misc]simplify:  iters left: 2 (124 enodes)
* * [misc]simplify:  iters left: 1 (179 enodes)
* [exit]simplify:  Simplified to (- (log (sqrt k)) (* (log (* n (+ PI PI))) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (- (log (sqrt k)) (* (log (* n (+ PI PI))) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 41 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (exp (- (log (sqrt k)) (* (log (* n (+ PI PI))) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (- (log (sqrt k)) (* (log (* n (+ PI PI))) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (50 enodes)
* * [misc]simplify:  iters left: 3 (86 enodes)
* * [misc]simplify:  iters left: 2 (124 enodes)
* * [misc]simplify:  iters left: 1 (179 enodes)
* [exit]simplify:  Simplified to (- (log (sqrt k)) (* (log (* n (+ PI PI))) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (- (log (sqrt k)) (* (log (* n (+ PI PI))) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 42 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (exp (- (log (sqrt k)) (log (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (- (log (sqrt k)) (log (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (41 enodes)
* * [misc]simplify:  iters left: 3 (66 enodes)
* * [misc]simplify:  iters left: 2 (112 enodes)
* * [misc]simplify:  iters left: 1 (163 enodes)
* [exit]simplify:  Simplified to (- (log (sqrt k)) (/ (log (* n (+ PI PI))) (/ 2 (- 1 k))))
* [exit]simplify:  Simplified to (- (log (sqrt k)) (/ (log (* n (+ PI PI))) (/ 2 (- 1 k))))
* * * * [misc]progress:  [ 43 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (exp (log (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (log (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (52 enodes)
* * [misc]simplify:  iters left: 2 (103 enodes)
* * [misc]simplify:  iters left: 1 (165 enodes)
* [exit]simplify:  Simplified to (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* n (+ PI PI)))))
* [exit]simplify:  Simplified to (- (log (sqrt k)) (* (/ (- 1 k) 2) (log (* n (+ PI PI)))))
* * * * [misc]progress:  [ 44 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (log (exp (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (exp (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (exp (/ (sqrt k) (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (exp (/ (sqrt k) (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 45 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (cbrt (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (34 enodes)
* * [misc]simplify:  iters left: 4 (57 enodes)
* * [misc]simplify:  iters left: 3 (82 enodes)
* * [misc]simplify:  iters left: 2 (106 enodes)
* * [misc]simplify:  iters left: 1 (160 enodes)
* [exit]simplify:  Simplified to (/ (/ (* k (sqrt k)) (pow (* (+ n n) PI) (/ (- 1 k) 2))) (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (/ (* k (sqrt k)) (pow (* (+ n n) PI) (/ (- 1 k) 2))) (* (pow (* (+ n n) PI) (/ (- 1 k) 2)) (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 46 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (* (* (cbrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))) (cbrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (* (cbrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* * [misc]simplify:  iters left: 2 (37 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* [exit]simplify:  Simplified to (* (cbrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* [enter]simplify:  Simplifying (cbrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (cbrt (/ (sqrt k) (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (cbrt (/ (sqrt k) (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 47 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (cbrt (* (* (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (* (* (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (54 enodes)
* * [misc]simplify:  iters left: 3 (65 enodes)
* * [misc]simplify:  iters left: 2 (81 enodes)
* * [misc]simplify:  iters left: 1 (98 enodes)
* [exit]simplify:  Simplified to (/ (/ (* (sqrt k) k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (/ (* (sqrt k) k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 48 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (* (sqrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (sqrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (sqrt k) (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (sqrt (/ (sqrt k) (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* [enter]simplify:  Simplifying (sqrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (sqrt k) (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (sqrt (/ (sqrt k) (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 49 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (- (sqrt k)) (- (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (- (sqrt k))
* * [misc]simplify:  iters left: 3 (3 enodes)
* [exit]simplify:  Simplified to (- (sqrt k))
* [exit]simplify:  Simplified to (- (sqrt k))
* [enter]simplify:  Simplifying (- (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* * [misc]simplify:  iters left: 2 (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:  [ 50 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2))) (/ (cbrt (sqrt k)) (pow (+ PI PI) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (21 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2)))
* [enter]simplify:  Simplifying (/ (cbrt (sqrt k)) (pow (+ PI PI) (/ (- 1 k) 2)))
* * [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 (/ (cbrt (sqrt k)) (pow (+ PI PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (cbrt (sqrt k)) (pow (+ PI PI) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 51 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))) (/ (cbrt (sqrt k)) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (47 enodes)
* * [misc]simplify:  iters left: 3 (55 enodes)
* * [misc]simplify:  iters left: 2 (60 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (sqrt k)) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (/ (cbrt (sqrt k)) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* [exit]simplify:  Simplified to (* (/ (cbrt (sqrt k)) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (/ (cbrt (sqrt k)) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* [enter]simplify:  Simplifying (/ (cbrt (sqrt k)) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* * [misc]simplify:  iters left: 2 (37 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (sqrt k)) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (cbrt (sqrt k)) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 52 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (/ (cbrt (sqrt k)) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* * [misc]simplify:  iters left: 2 (43 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* [enter]simplify:  Simplifying (/ (cbrt (sqrt k)) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* * [misc]simplify:  iters left: 2 (37 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (sqrt k)) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (cbrt (sqrt k)) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 53 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (cbrt (sqrt k)) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (13 enodes)
* [exit]simplify:  Simplified to (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) 1))
* [exit]simplify:  Simplified to (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) 1))
* [enter]simplify:  Simplifying (/ (cbrt (sqrt k)) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (sqrt k)) (pow (* (+ n n) PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (cbrt (sqrt k)) (pow (* (+ n n) PI) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 54 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (pow (+ PI PI) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) (pow (+ PI PI) (/ (- 1 k) 2)))
* * [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 (/ (sqrt (sqrt k)) (pow (+ PI PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) (pow (+ PI PI) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 55 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))) (/ (sqrt (sqrt k)) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* * [misc]simplify:  iters left: 2 (40 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (sqrt k)) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (/ (sqrt (sqrt k)) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* * [misc]simplify:  iters left: 2 (37 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 56 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (/ (sqrt (sqrt k)) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* * [misc]simplify:  iters left: 2 (37 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* * [misc]simplify:  iters left: 2 (37 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 57 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) 1) (/ (sqrt (sqrt k)) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) 1)
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) 1)
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) 1)
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) (pow (* (+ n n) PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) (pow (* (+ n n) PI) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 58 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (* (/ 1 (pow n (/ (- 1 k) 2))) (/ (sqrt k) (pow (+ PI PI) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ 1 (pow n (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* [exit]simplify:  Simplified to (/ 1 (pow n (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ 1 (pow n (/ (- 1 k) 2)))
* [enter]simplify:  Simplifying (/ (sqrt k) (pow (+ PI PI) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (+ PI PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (+ PI PI) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 59 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (* (/ 1 (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))) (/ (sqrt k) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (/ 1 (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (38 enodes)
* [exit]simplify:  Simplified to (/ 1 (* (cbrt (pow (* PI (+ n n)) (/ (- 1 k) 2))) (cbrt (pow (* PI (+ n n)) (/ (- 1 k) 2)))))
* [exit]simplify:  Simplified to (/ 1 (* (cbrt (pow (* PI (+ n n)) (/ (- 1 k) 2))) (cbrt (pow (* PI (+ n n)) (/ (- 1 k) 2)))))
* [enter]simplify:  Simplifying (/ (sqrt k) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (cbrt (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (sqrt k) (cbrt (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 60 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (* (/ 1 (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (/ (sqrt k) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* * [misc]simplify:  iters left: 2 (35 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ 1 (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* [enter]simplify:  Simplifying (/ (sqrt k) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (sqrt k) (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 61 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (* (/ 1 1) (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))>
* [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 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* * [misc]simplify:  iters left: 2 (35 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 62 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (* 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))>
* * * * [misc]progress:  [ 63 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (* (sqrt k) (/ 1 (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ 1 (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* * [misc]simplify:  iters left: 2 (34 enodes)
* [exit]simplify:  Simplified to (/ 1 (pow (* (+ n n) PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ 1 (pow (* (+ n n) PI) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 64 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ 1 (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* * [misc]simplify:  iters left: 2 (35 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:  [ 65 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (/ (sqrt k) (pow n (/ (- 1 k) 2))) (pow (+ PI PI) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (pow n (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (pow n (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (sqrt k) (pow n (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 66 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (/ (sqrt k) (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* * [misc]simplify:  iters left: 2 (39 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt k) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (/ (sqrt k) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 67 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (/ (sqrt k) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (sqrt k) (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 68 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (/ (sqrt k) 1) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))>
* [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:  [ 69 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 70 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt (sqrt k)) (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 71 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ 1 (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* * [misc]simplify:  iters left: 2 (35 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:  [ 72 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (* (/ (sqrt k) (pow (* n (+ PI PI)) (/ 1 2))) (pow (* n (+ PI PI)) (/ k 2)))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (pow (* n (+ PI PI)) (/ 1 2)))
* * [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 (29 enodes)
* * [misc]simplify:  iters left: 2 (31 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (* PI (+ n n)) (/ 1 2)))
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (* PI (+ n n)) (/ 1 2)))
* * * * [misc]progress:  [ 73 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (log1p (expm1 (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (expm1 (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (46 enodes)
* * [misc]simplify:  iters left: 2 (48 enodes)
* * [misc]simplify:  iters left: 1 (50 enodes)
* [exit]simplify:  Simplified to (expm1 (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (expm1 (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 74 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (expm1 (log1p (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (log1p (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (46 enodes)
* * [misc]simplify:  iters left: 2 (48 enodes)
* * [misc]simplify:  iters left: 1 (50 enodes)
* [exit]simplify:  Simplified to (log1p (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (log1p (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 75 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (pow (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) -1))>
* * * * [misc]progress:  [ 76 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (pow (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (- 1)))>
* [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:  [ 77 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (pow (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) 1))>
* * * * [misc]progress:  [ 78 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (log (sqrt k)) (* (log (* n (+ PI PI))) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (- (- (log (sqrt k)) (* (log (* n (+ PI PI))) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (51 enodes)
* * [misc]simplify:  iters left: 3 (87 enodes)
* * [misc]simplify:  iters left: 2 (125 enodes)
* * [misc]simplify:  iters left: 1 (180 enodes)
* [exit]simplify:  Simplified to (- (- (log (sqrt k)) (/ (log (* PI (+ n n))) (/ 2 (- 1 k)))))
* [exit]simplify:  Simplified to (- (- (log (sqrt k)) (/ (log (* PI (+ n n))) (/ 2 (- 1 k)))))
* * * * [misc]progress:  [ 79 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (log (sqrt k)) (* (log (* n (+ PI PI))) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (- (- (log (sqrt k)) (* (log (* n (+ PI PI))) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (51 enodes)
* * [misc]simplify:  iters left: 3 (87 enodes)
* * [misc]simplify:  iters left: 2 (125 enodes)
* * [misc]simplify:  iters left: 1 (180 enodes)
* [exit]simplify:  Simplified to (- (- (log (sqrt k)) (/ (log (* PI (+ n n))) (/ 2 (- 1 k)))))
* [exit]simplify:  Simplified to (- (- (log (sqrt k)) (/ (log (* PI (+ n n))) (/ 2 (- 1 k)))))
* * * * [misc]progress:  [ 80 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (log (sqrt k)) (log (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (- (- (log (sqrt k)) (log (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (67 enodes)
* * [misc]simplify:  iters left: 2 (113 enodes)
* * [misc]simplify:  iters left: 1 (164 enodes)
* [exit]simplify:  Simplified to (- (- (log (sqrt k)) (/ (log (* n (+ PI PI))) (/ 2 (- 1 k)))))
* [exit]simplify:  Simplified to (- (- (log (sqrt k)) (/ (log (* n (+ PI PI))) (/ 2 (- 1 k)))))
* * * * [misc]progress:  [ 81 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (log (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (- (log (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (53 enodes)
* * [misc]simplify:  iters left: 2 (104 enodes)
* * [misc]simplify:  iters left: 1 (166 enodes)
* [exit]simplify:  Simplified to (- (- (log (sqrt k)) (/ (log (* n (+ PI PI))) (/ 2 (- 1 k)))))
* [exit]simplify:  Simplified to (- (- (log (sqrt k)) (/ (log (* n (+ PI PI))) (/ 2 (- 1 k)))))
* * * * [misc]progress:  [ 82 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (exp (log (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (log (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (46 enodes)
* * [misc]simplify:  iters left: 3 (60 enodes)
* * [misc]simplify:  iters left: 2 (90 enodes)
* * [misc]simplify:  iters left: 1 (153 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* n (+ PI PI))) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* n (+ PI PI))) (- (log (sqrt k))))
* * * * [misc]progress:  [ 83 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (log (exp (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (exp (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (48 enodes)
* * [misc]simplify:  iters left: 2 (50 enodes)
* * [misc]simplify:  iters left: 1 (55 enodes)
* [exit]simplify:  Simplified to (pow (exp (/ 1 (sqrt k))) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (pow (exp (/ 1 (sqrt k))) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 84 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (cbrt (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))) (cbrt (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))) (cbrt (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (* (cbrt (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))) (cbrt (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (38 enodes)
* * [misc]simplify:  iters left: 3 (47 enodes)
* * [misc]simplify:  iters left: 2 (49 enodes)
* * [misc]simplify:  iters left: 1 (51 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 (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (46 enodes)
* * [misc]simplify:  iters left: 2 (48 enodes)
* * [misc]simplify:  iters left: 1 (50 enodes)
* [exit]simplify:  Simplified to (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 85 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (* (* (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))) (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (* (* (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))) (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (64 enodes)
* * [misc]simplify:  iters left: 2 (87 enodes)
* * [misc]simplify:  iters left: 1 (124 enodes)
* [exit]simplify:  Simplified to (pow (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))) 3)
* [exit]simplify:  Simplified to (pow (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))) 3)
* * * * [misc]progress:  [ 86 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))) (sqrt (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (sqrt (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (46 enodes)
* * [misc]simplify:  iters left: 2 (48 enodes)
* * [misc]simplify:  iters left: 1 (50 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* [enter]simplify:  Simplifying (sqrt (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (46 enodes)
* * [misc]simplify:  iters left: 2 (48 enodes)
* * [misc]simplify:  iters left: 1 (50 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 87 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ (- 1) (- (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))>
* [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) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (38 enodes)
* [exit]simplify:  Simplified to (/ (- (sqrt k)) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (- (sqrt k)) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 88 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))>
* * * * [misc]progress:  [ 89 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (45 enodes)
* * [misc]simplify:  iters left: 2 (47 enodes)
* * [misc]simplify:  iters left: 1 (49 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:  [ 90 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) 1)))>
* [enter]simplify:  Simplifying (/ (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) 1)
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* * [misc]simplify:  iters left: 2 (43 enodes)
* * [misc]simplify:  iters left: 1 (45 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 91 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (* (cbrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))) (cbrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ 1 (* (cbrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* * [misc]simplify:  iters left: 2 (40 enodes)
* [exit]simplify:  Simplified to (/ 1 (* (cbrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))
* [exit]simplify:  Simplified to (/ 1 (* (cbrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))
* * * * [misc]progress:  [ 92 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (sqrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))) (sqrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* * [misc]simplify:  iters left: 2 (37 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* [exit]simplify:  Simplified to (/ 1 (sqrt (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 93 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2)))) (/ (cbrt (sqrt k)) (pow (+ PI PI) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* * [misc]simplify:  iters left: 2 (53 enodes)
* * [misc]simplify:  iters left: 1 (68 enodes)
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 94 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))) (/ (cbrt (sqrt k)) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (34 enodes)
* * [misc]simplify:  iters left: 4 (50 enodes)
* * [misc]simplify:  iters left: 3 (60 enodes)
* * [misc]simplify:  iters left: 2 (69 enodes)
* * [misc]simplify:  iters left: 1 (85 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* PI (+ n n)) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (sqrt k)) (cbrt (pow (* PI (+ n n)) (/ (- 1 k) 2)))))
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* PI (+ n n)) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (sqrt k)) (cbrt (pow (* PI (+ n n)) (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 95 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))) (/ (cbrt (sqrt k)) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (55 enodes)
* * [misc]simplify:  iters left: 2 (75 enodes)
* * [misc]simplify:  iters left: 1 (90 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (+ (* PI n) (* PI n)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (+ (* PI n) (* PI n)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 96 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ (cbrt (sqrt k)) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* * [misc]simplify:  iters left: 2 (29 enodes)
* * [misc]simplify:  iters left: 1 (32 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:  [ 97 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2)))) (/ (sqrt (sqrt k)) (pow (+ PI PI) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ 1 (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (27 enodes)
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 98 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))) (/ (sqrt (sqrt k)) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (51 enodes)
* * [misc]simplify:  iters left: 2 (65 enodes)
* * [misc]simplify:  iters left: 1 (66 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 99 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))) (/ (sqrt (sqrt k)) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (38 enodes)
* * [misc]simplify:  iters left: 3 (47 enodes)
* * [misc]simplify:  iters left: 2 (49 enodes)
* * [misc]simplify:  iters left: 1 (54 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:  [ 100 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) 1)) (/ (sqrt (sqrt k)) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ 1 (/ (sqrt (sqrt k)) 1))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* * [misc]simplify:  iters left: 4 (11 enodes)
* * [misc]simplify:  iters left: 3 (14 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* * * * [misc]progress:  [ 101 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (/ 1 (pow n (/ (- 1 k) 2)))) (/ (sqrt k) (pow (+ PI PI) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ 1 (/ 1 (pow n (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* [exit]simplify:  Simplified to (pow n (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow n (/ (- 1 k) 2))
* * * * [misc]progress:  [ 102 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (/ 1 (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))) (/ (sqrt k) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ 1 (/ 1 (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* * [misc]simplify:  iters left: 2 (51 enodes)
* * [misc]simplify:  iters left: 1 (55 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (+ (* PI n) (* PI n)) (/ (- 1 k) 2))) (cbrt (pow (+ (* PI n) (* PI n)) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (+ (* PI n) (* PI n)) (/ (- 1 k) 2))) (cbrt (pow (+ (* PI n) (* PI n)) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 103 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (/ 1 (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))) (/ (sqrt k) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ 1 (/ 1 (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (43 enodes)
* * [misc]simplify:  iters left: 1 (44 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:  [ 104 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (/ 1 1)) (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ 1 (/ 1 1))
* * [misc]simplify:  iters left: 4 (3 enodes)
* * [misc]simplify:  iters left: 3 (5 enodes)
* [exit]simplify:  Simplified to 1
* [exit]simplify:  Simplified to 1
* * * * [misc]progress:  [ 105 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 1) (/ (sqrt k) (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))>
* [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:  [ 106 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (sqrt k)) (/ 1 (pow (* n (+ PI PI)) (/ (- 1 k) 2)))))>
* [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:  [ 107 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ 1 2)))) (pow (* n (+ PI PI)) (/ k 2))))>
* [enter]simplify:  Simplifying (/ 1 (/ (sqrt k) (pow (* n (+ PI PI)) (/ 1 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* * [misc]simplify:  iters left: 2 (43 enodes)
* * [misc]simplify:  iters left: 1 (45 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:  [ 108 / 120 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (* n (+ PI PI)) (/ (- 1 k) 2))))>
* [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:  [ 109 / 120 ] simplifiying candidate #<alt-event (λ (k n) (/ 1 (/ (sqrt k) (- (+ (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))))))))>
* [enter]simplify:  Simplifying (/ 1 (/ (sqrt k) (- (+ (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]simplify:  iters left: 6 (41 enodes)
* * [misc]simplify:  iters left: 5 (100 enodes)
* * [misc]simplify:  iters left: 4 (216 enodes)
* * [misc]simplify:  iters left: 3 (462 enodes)
* [exit]simplify:  Simplified to (/ (+ (* (sqrt n) (sqrt (+ PI PI))) (- (fma 1/8 (* (* (* k k) (* (sqrt n) (sqrt (+ PI PI)))) (fma (log n) (log n) (* (log (+ PI PI)) (log (+ PI PI))))) (* (* 1/4 (* (* k k) (log n))) (* (* (sqrt n) (sqrt (+ PI PI))) (log (+ PI PI))))) (* (* 1/2 k) (* (* (sqrt n) (sqrt (+ PI PI))) (+ (log n) (log (+ PI PI))))))) (sqrt k))
* * * * [misc]progress:  [ 110 / 120 ] simplifiying candidate #<alt-event (λ (k n) (/ 1 (/ (sqrt k) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))))>
* [enter]simplify:  Simplifying (/ 1 (/ (sqrt k) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (47 enodes)
* * [misc]simplify:  iters left: 3 (72 enodes)
* * [misc]simplify:  iters left: 2 (130 enodes)
* * [misc]simplify:  iters left: 1 (267 enodes)
* [exit]simplify:  Simplified to (/ (pow (/ (+ PI PI) (/ 1 n)) (* 1/2 (- 1 k))) (sqrt k))
* * * * [misc]progress:  [ 111 / 120 ] simplifiying candidate #<alt-event (λ (k n) (/ 1 (/ (sqrt k) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))>
* [enter]simplify:  Simplifying (/ 1 (/ (sqrt k) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (35 enodes)
* * [misc]simplify:  iters left: 4 (46 enodes)
* * [misc]simplify:  iters left: 3 (71 enodes)
* * [misc]simplify:  iters left: 2 (132 enodes)
* * [misc]simplify:  iters left: 1 (269 enodes)
* [exit]simplify:  Simplified to (/ (pow (/ (* PI -2) (/ -1 n)) (* 1/2 (- 1 k))) (sqrt k))
* * * * [misc]progress:  [ 112 / 120 ] simplifiying candidate #<alt-event (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* * [misc]simplify:  iters left: 2 (45 enodes)
* * [misc]simplify:  iters left: 1 (47 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 113 / 120 ] simplifiying candidate #<alt-event (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* * [misc]simplify:  iters left: 2 (45 enodes)
* * [misc]simplify:  iters left: 1 (47 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 114 / 120 ] simplifiying candidate #<alt-event (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* * [misc]simplify:  iters left: 2 (45 enodes)
* * [misc]simplify:  iters left: 1 (47 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 115 / 120 ] simplifiying candidate #<alt-event (λ (k n) (/ 1 (- (+ (* +nan.0 (/ k PI)) (- (+ (* +nan.0 (/ (* n k) (pow PI 2))) (- (+ (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (pow k 2) (* (log n) (sqrt 2)))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log (* 2 PI)) (* (pow k 2) (sqrt 2)))) PI)))))))))))))>
* [enter]simplify:  Simplifying (/ 1 (- (+ (* +nan.0 (/ k PI)) (- (+ (* +nan.0 (/ (* n k) (pow PI 2))) (- (+ (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (pow k 2) (* (log n) (sqrt 2)))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (* +nan.0 (/ (* (pow (sqrt 1/2) 2) (* (log (* 2 PI)) (* (pow k 2) (sqrt 2)))) PI))))))))))))
* * * * [misc]progress:  [ 116 / 120 ] simplifiying candidate #<alt-event (λ (k n) (/ 1 (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))) (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))) (- (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2)))))))))))>
* [enter]simplify:  Simplifying (/ 1 (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))) (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))) (- (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))))))))))
* * * * [misc]progress:  [ 117 / 120 ] simplifiying candidate #<alt-event (λ (k n) (/ 1 (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))))))>
* [enter]simplify:  Simplifying (/ 1 (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))))))))))
* * * * [misc]progress:  [ 118 / 120 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) (* k (sqrt 1/2)))) (- (+ (* +nan.0 (/ (* n PI) (* k (sqrt 1/2)))) (- (+ (* +nan.0 (* n (* PI (* (log n) (sqrt 2))))) (- (+ (* +nan.0 (/ (* n PI) (sqrt 1/2))) (- (* +nan.0 (* n (* PI (* (log (* 2 PI)) (sqrt 2)))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) (* k (sqrt 1/2)))) (- (+ (* +nan.0 (/ (* n PI) (* k (sqrt 1/2)))) (- (+ (* +nan.0 (* n (* PI (* (log n) (sqrt 2))))) (- (+ (* +nan.0 (/ (* n PI) (sqrt 1/2))) (- (* +nan.0 (* n (* PI (* (log (* 2 PI)) (sqrt 2))))))))))))))
* * * * [misc]progress:  [ 119 / 120 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)))))))
* * * * [misc]progress:  [ 120 / 120 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))))))))
* * * [misc]progress:  adding candidates to table
* [misc]progress:  [Phase 3 of 3] Extracting.
* * [misc]regime-changes:  Finding splitpoints for: (#<alt-delta (λ (k n) (/ (- (+ (fma (* k k) (* (* 1/8 (* (sqrt (+ PI PI)) (sqrt n))) (+ (* (log (+ PI PI)) (log (+ PI PI))) (* (log n) (log n)))) (* (* 1/4 (* (sqrt (+ PI PI)) (sqrt n))) (* (log (+ PI PI)) (* (* k k) (log n))))) (* (sqrt (+ PI PI)) (sqrt n))) (* (* 1/2 k) (* (* (sqrt (+ PI PI)) (sqrt n)) (+ (log (+ PI PI)) (log n))))) (sqrt k)))> #<alt-delta (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (pow n (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (pow (+ PI PI) (/ (- 1 k) 2))))))> #<alt-delta (λ (k n) (* (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))> #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))> #<alt-delta (λ (k n) (/ (/ (cbrt (pow (pow (* (+ n n) PI) (/ 1 2)) 3)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))> #<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k)))> #<alt-delta (λ (k n) (/ (exp (* (log (* n (+ PI PI))) (/ (- 1 k) 2))) (sqrt k)))> #<alt-delta (λ (k n) (/ (* (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt k)))> #<alt-event (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))> #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))> #<alt-delta (λ (k n) (* (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) 1) (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k))))> #<alt-delta (λ (k n) (* (* (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))>)
* [misc]regimes:  Found splitpoints: (#s(sp 0 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) +inf.0)) , with alts (#<alt-delta (λ (k n) (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (pow (* n (+ PI PI)) k) (/ 1 2))) (sqrt k)))>)
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) (/ 1 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (13 enodes)
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) (/ 1 2))
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) (/ 1 2))
* [enter]simplify:  Simplifying (pow (* n (+ PI PI)) (/ k 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (11 enodes)
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) (/ k 2))
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) (/ k 2))