* [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 1)
* * * * [misc]progress:  [ 2 / 3 ] rewriting at (2 1)
* * * * [misc]progress:  [ 3 / 3 ] rewriting at (2)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 3 ] generating series at (2 1 1)
* [misc]approximate:  Taking taylor expansion of (* n (+ 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:  [ 2 / 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:  [ 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) (/ (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:  [ 2 / 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:  [ 3 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* n (+ PI PI)) 1) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 4 / 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:  [ 5 / 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:  [ 6 / 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:  [ 7 / 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:  [ 8 / 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:  [ 9 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* 1 (* n (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 10 / 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:  [ 11 / 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:  [ 12 / 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:  [ 13 / 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:  [ 14 / 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:  [ 15 / 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:  [ 16 / 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:  [ 17 / 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:  [ 18 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 19 / 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:  [ 20 / 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:  [ 21 / 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:  [ 22 / 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:  [ 23 / 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:  [ 24 / 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:  [ 25 / 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:  [ 26 / 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:  [ 27 / 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:  [ 28 / 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:  [ 29 / 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:  [ 30 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* n (+ PI PI)) (/ (- 1 k) 2)) 1) (sqrt k)))>
* * * * [misc]progress:  [ 31 / 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:  [ 32 / 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:  [ 33 / 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:  [ 34 / 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:  [ 35 / 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:  [ 36 / 81 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* 1 (pow (* n (+ PI PI)) (/ (- 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) (/ (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:  [ 74 / 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:  [ 75 / 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:  [ 76 / 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:  [ 77 / 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:  [ 78 / 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:  [ 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 (sqrt (+ PI PI))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 4 ] rewriting at (2 1 1 2)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2 1 1 1 2)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2 1 1 1)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2 1 1)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 4 ] generating series at (2 1 1 2)
* * * * [misc]progress:  [ 2 / 4 ] generating series at (2 1 1 1 2)
* * * * [misc]progress:  [ 3 / 4 ] generating series at (2 1 1 1)
* [misc]approximate:  Taking taylor expansion of (* n (sqrt (+ PI PI))) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* n (sqrt (+ 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 (sqrt (+ PI PI)) in n
* [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 (sqrt (* 2 PI)) into (* (sqrt PI) (sqrt 2))
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* 2 PI)))) into 0
* [misc]taylor:  Taking taylor expansion of (* n (sqrt (+ 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 (sqrt (+ PI PI)) in n
* [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 (sqrt (* 2 PI)) into (* (sqrt PI) (sqrt 2))
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (* 0 (* (sqrt PI) (sqrt 2))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* (sqrt PI) (sqrt 2)))) into (* (sqrt PI) (sqrt 2))
* [misc]backup-simplify:  Simplify (* (sqrt PI) (sqrt 2)) into (* (sqrt PI) (sqrt 2))
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* (sqrt PI) (sqrt 2))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2))))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2)))))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* (sqrt PI) (sqrt 2)) n) into (* (* n (sqrt 2)) (sqrt PI))
* [misc]approximate:  Taking taylor expansion of (* (/ 1 n) (sqrt (+ PI PI))) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (sqrt (+ 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 (sqrt (+ PI PI)) in n
* [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 (sqrt (* 2 PI)) into (* (sqrt PI) (sqrt 2))
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* 2 PI)))) into 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (sqrt (+ 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 (sqrt (+ PI PI)) in n
* [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 (sqrt (* 2 PI)) into (* (sqrt PI) (sqrt 2))
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (* 1 (* (sqrt PI) (sqrt 2))) into (* (sqrt PI) (sqrt 2))
* [misc]backup-simplify:  Simplify (* (sqrt PI) (sqrt 2)) into (* (sqrt PI) (sqrt 2))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) 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 (* (sqrt PI) (sqrt 2)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) 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 (* (sqrt PI) (sqrt 2))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) 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 (* (sqrt PI) (sqrt 2)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) 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 (* (sqrt PI) (sqrt 2))))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* (sqrt PI) (sqrt 2)) (/ 1 (/ 1 n))) into (* (* n (sqrt 2)) (sqrt PI))
* [misc]approximate:  Taking taylor expansion of (* (/ 1 (- n)) (sqrt (+ PI PI))) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (sqrt (+ 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 (sqrt (+ PI PI)) in n
* [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 (sqrt (* 2 PI)) into (* (sqrt PI) (sqrt 2))
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* 2 PI)))) into 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (sqrt (+ 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 (sqrt (+ PI PI)) in n
* [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 (sqrt (* 2 PI)) into (* (sqrt PI) (sqrt 2))
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (* -1 (* (sqrt PI) (sqrt 2))) into (* -1 (* (sqrt PI) (sqrt 2)))
* [misc]backup-simplify:  Simplify (* -1 (* (sqrt PI) (sqrt 2))) into (* -1 (* (sqrt PI) (sqrt 2)))
* [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 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (* (sqrt PI) (sqrt 2)))) 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 (* (sqrt PI) (sqrt 2))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) 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 (* (sqrt PI) (sqrt 2)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) 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 (* (sqrt PI) (sqrt 2))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) 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 (* (sqrt PI) (sqrt 2)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) 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 (* (sqrt PI) (sqrt 2))))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* -1 (* (sqrt PI) (sqrt 2))) (/ 1 (/ 1 (- n)))) into (* (* n (sqrt 2)) (sqrt PI))
* * * * [misc]progress:  [ 4 / 4 ] generating series at (2 1 1)
* [misc]approximate:  Taking taylor expansion of (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* n (sqrt (+ 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 (sqrt (+ PI PI)) in n
* [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 (sqrt (* 2 PI)) into (* (sqrt PI) (sqrt 2))
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* 2 PI)))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (+ PI PI)) in n
* [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 (sqrt (* 2 PI)) into (* (sqrt PI) (sqrt 2))
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* 2 PI)))) into 0
* [misc]taylor:  Taking taylor expansion of (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* n (sqrt (+ 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 (sqrt (+ PI PI)) in n
* [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 (sqrt (* 2 PI)) into (* (sqrt PI) (sqrt 2))
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* 2 PI)))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (+ PI PI)) in n
* [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 (sqrt (* 2 PI)) into (* (sqrt PI) (sqrt 2))
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (* 0 (* (sqrt PI) (sqrt 2))) into 0
* [misc]backup-simplify:  Simplify (* 0 (* (sqrt PI) (sqrt 2))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* (sqrt PI) (sqrt 2)))) into (* (sqrt PI) (sqrt 2))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* (* (sqrt PI) (sqrt 2)) (* (sqrt PI) (sqrt 2)))) into (* PI (pow (sqrt 2) 2))
* [misc]backup-simplify:  Simplify (* PI (pow (sqrt 2) 2)) into (* PI (pow (sqrt 2) 2))
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* (sqrt PI) (sqrt 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* (* (sqrt PI) (sqrt 2)) 0) (* 0 (* (sqrt PI) (sqrt 2))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* (* (sqrt PI) (sqrt 2)) 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* (* (sqrt PI) (sqrt 2)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* (* (sqrt PI) (sqrt 2)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2))))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* (* (sqrt PI) (sqrt 2)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2))))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2)))))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* (* (sqrt PI) (sqrt 2)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2)))))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* PI (pow (sqrt 2) 2)) n) into (* n (* PI (pow (sqrt 2) 2)))
* [misc]approximate:  Taking taylor expansion of (* (* (/ 1 n) (sqrt (+ PI PI))) (sqrt (+ PI PI))) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) (sqrt (+ PI PI))) (sqrt (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (sqrt (+ 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 (sqrt (+ PI PI)) in n
* [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 (sqrt (* 2 PI)) into (* (sqrt PI) (sqrt 2))
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* 2 PI)))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (+ PI PI)) in n
* [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 (sqrt (* 2 PI)) into (* (sqrt PI) (sqrt 2))
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* 2 PI)))) into 0
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) (sqrt (+ PI PI))) (sqrt (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (sqrt (+ 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 (sqrt (+ PI PI)) in n
* [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 (sqrt (* 2 PI)) into (* (sqrt PI) (sqrt 2))
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* 2 PI)))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (+ PI PI)) in n
* [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 (sqrt (* 2 PI)) into (* (sqrt PI) (sqrt 2))
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (* 1 (* (sqrt PI) (sqrt 2))) into (* (sqrt PI) (sqrt 2))
* [misc]backup-simplify:  Simplify (* (* (sqrt PI) (sqrt 2)) (* (sqrt PI) (sqrt 2))) into (* PI (pow (sqrt 2) 2))
* [misc]backup-simplify:  Simplify (* PI (pow (sqrt 2) 2)) into (* PI (pow (sqrt 2) 2))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (sqrt PI) (sqrt 2)) 0) (* 0 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (sqrt PI) (sqrt 2)) 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) 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 (* (sqrt PI) (sqrt 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (sqrt PI) (sqrt 2)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) 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 (* (sqrt PI) (sqrt 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (sqrt PI) (sqrt 2)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) 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 (* (sqrt PI) (sqrt 2)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (sqrt PI) (sqrt 2)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) 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 (* (sqrt PI) (sqrt 2))))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (sqrt PI) (sqrt 2)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2))))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* PI (pow (sqrt 2) 2)) (/ 1 (/ 1 n))) into (* n (* PI (pow (sqrt 2) 2)))
* [misc]approximate:  Taking taylor expansion of (* (* (/ 1 (- n)) (sqrt (+ PI PI))) (sqrt (+ PI PI))) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) (sqrt (+ PI PI))) (sqrt (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (sqrt (+ 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 (sqrt (+ PI PI)) in n
* [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 (sqrt (* 2 PI)) into (* (sqrt PI) (sqrt 2))
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* 2 PI)))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (+ PI PI)) in n
* [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 (sqrt (* 2 PI)) into (* (sqrt PI) (sqrt 2))
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* 2 PI)))) into 0
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) (sqrt (+ PI PI))) (sqrt (+ PI PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (sqrt (+ 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 (sqrt (+ PI PI)) in n
* [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 (sqrt (* 2 PI)) into (* (sqrt PI) (sqrt 2))
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* 2 PI)))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (+ PI PI)) in n
* [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 (sqrt (* 2 PI)) into (* (sqrt PI) (sqrt 2))
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (* -1 (* (sqrt PI) (sqrt 2))) into (* -1 (* (sqrt PI) (sqrt 2)))
* [misc]backup-simplify:  Simplify (* (* -1 (* (sqrt PI) (sqrt 2))) (* (sqrt PI) (sqrt 2))) into (* -1 (* PI (pow (sqrt 2) 2)))
* [misc]backup-simplify:  Simplify (* -1 (* PI (pow (sqrt 2) 2))) into (* -1 (* PI (pow (sqrt 2) 2)))
* [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 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* -1 (* (sqrt PI) (sqrt 2))) 0) (* 0 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (* (sqrt PI) (sqrt 2)))) 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 (* (sqrt PI) (sqrt 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* -1 (* (sqrt PI) (sqrt 2))) 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) 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 (* (sqrt PI) (sqrt 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* -1 (* (sqrt PI) (sqrt 2))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) 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 (* (sqrt PI) (sqrt 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* -1 (* (sqrt PI) (sqrt 2))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) 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 (* (sqrt PI) (sqrt 2)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* -1 (* (sqrt PI) (sqrt 2))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (* (sqrt PI) (sqrt 2)))) 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 (* (sqrt PI) (sqrt 2))))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* -1 (* (sqrt PI) (sqrt 2))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt PI) (sqrt 2))))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* -1 (* PI (pow (sqrt 2) 2))) (/ 1 (/ 1 (- n)))) into (* n (* PI (pow (sqrt 2) 2)))
* * * [misc]progress:  simplifying candidates
* * * * [misc]progress:  [ 1 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (sqrt (+ PI PI))) (log1p (expm1 (sqrt (+ PI PI))))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (sqrt (+ PI PI)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (expm1 (sqrt (+ PI PI)))
* [exit]simplify:  Simplified to (expm1 (sqrt (+ PI PI)))
* * * * [misc]progress:  [ 2 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (sqrt (+ PI PI))) (expm1 (log1p (sqrt (+ PI PI))))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (sqrt (+ PI PI)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (log1p (sqrt (+ PI PI)))
* [exit]simplify:  Simplified to (log1p (sqrt (+ PI PI)))
* * * * [misc]progress:  [ 3 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (sqrt (+ PI PI))) (pow (+ PI PI) 1/2)) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 4 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (sqrt (+ PI PI))) (pow (sqrt (+ PI PI)) 1)) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 5 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (sqrt (+ PI PI))) (exp (log (sqrt (+ PI PI))))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (log (sqrt (+ PI PI)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (log (sqrt (+ PI PI)))
* [exit]simplify:  Simplified to (log (sqrt (+ PI PI)))
* * * * [misc]progress:  [ 6 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (sqrt (+ PI PI))) (log (exp (sqrt (+ PI PI))))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (sqrt (+ PI PI)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (exp (sqrt (+ PI PI)))
* [exit]simplify:  Simplified to (exp (sqrt (+ PI PI)))
* * * * [misc]progress:  [ 7 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (sqrt (+ PI PI))) (* (* (cbrt (sqrt (+ PI PI))) (cbrt (sqrt (+ PI PI)))) (cbrt (sqrt (+ PI PI))))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (sqrt (+ PI PI))) (cbrt (sqrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (5 enodes)
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* [exit]simplify:  Simplified to (* (cbrt (sqrt (+ PI PI))) (cbrt (sqrt (+ PI PI))))
* [exit]simplify:  Simplified to (* (cbrt (sqrt (+ PI PI))) (cbrt (sqrt (+ PI PI))))
* [enter]simplify:  Simplifying (cbrt (sqrt (+ PI PI)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (cbrt (sqrt (+ PI PI)))
* [exit]simplify:  Simplified to (cbrt (sqrt (+ PI PI)))
* * * * [misc]progress:  [ 8 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (sqrt (+ PI PI))) (cbrt (* (* (sqrt (+ PI PI)) (sqrt (+ PI PI))) (sqrt (+ PI PI))))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (sqrt (+ PI PI)) (sqrt (+ PI PI))) (sqrt (+ PI PI)))
* * [misc]simplify:  iters left: 6 (5 enodes)
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (* (sqrt (+ PI PI)) (+ PI PI))
* [exit]simplify:  Simplified to (* (sqrt (+ PI PI)) (+ PI PI))
* * * * [misc]progress:  [ 9 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (sqrt (+ PI PI))) (* (sqrt (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) (sqrt (cbrt (+ PI PI))))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (* (cbrt (+ PI PI)) (cbrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (5 enodes)
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (9 enodes)
* [exit]simplify:  Simplified to (fabs (cbrt (+ PI PI)))
* [exit]simplify:  Simplified to (fabs (cbrt (+ PI PI)))
* [enter]simplify:  Simplifying (sqrt (cbrt (+ PI PI)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (sqrt (cbrt (+ PI PI)))
* [exit]simplify:  Simplified to (sqrt (cbrt (+ PI PI)))
* * * * [misc]progress:  [ 10 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (sqrt (+ PI PI))) (* (sqrt (sqrt (+ PI PI))) (sqrt (sqrt (+ PI PI))))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (sqrt (+ PI PI)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (sqrt (sqrt (+ PI PI)))
* [exit]simplify:  Simplified to (sqrt (sqrt (+ PI PI)))
* [enter]simplify:  Simplifying (sqrt (sqrt (+ PI PI)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (sqrt (sqrt (+ PI PI)))
* [exit]simplify:  Simplified to (sqrt (sqrt (+ PI PI)))
* * * * [misc]progress:  [ 11 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (sqrt (+ PI PI))) (* (sqrt 1) (sqrt (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt 1)
* * [misc]simplify:  iters left: 1 (2 enodes)
* [exit]simplify:  Simplified to (sqrt 1)
* [exit]simplify:  Simplified to (sqrt 1)
* [enter]simplify:  Simplifying (sqrt (+ PI PI))
* * [misc]simplify:  iters left: 3 (3 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* * [misc]simplify:  iters left: 1 (6 enodes)
* [exit]simplify:  Simplified to (sqrt (+ PI PI))
* [exit]simplify:  Simplified to (sqrt (+ PI PI))
* * * * [misc]progress:  [ 12 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (sqrt (+ PI PI))) (* (sqrt 2) (sqrt PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt 2)
* * [misc]simplify:  iters left: 1 (2 enodes)
* [exit]simplify:  Simplified to (sqrt 2)
* [exit]simplify:  Simplified to (sqrt 2)
* [enter]simplify:  Simplifying (sqrt PI)
* * [misc]simplify:  iters left: 1 (2 enodes)
* [exit]simplify:  Simplified to (sqrt PI)
* [exit]simplify:  Simplified to (sqrt PI)
* * * * [misc]progress:  [ 13 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (sqrt (+ PI PI))) (/ (sqrt (+ (pow PI 3) (pow PI 3))) (sqrt (+ (* PI PI) (- (* PI PI) (* PI PI)))))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (+ (pow PI 3) (pow PI 3)))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (10 enodes)
* * [misc]simplify:  iters left: 2 (20 enodes)
* * [misc]simplify:  iters left: 1 (23 enodes)
* [exit]simplify:  Simplified to (sqrt (* (+ PI PI) (* PI PI)))
* [exit]simplify:  Simplified to (sqrt (* (+ PI PI) (* PI PI)))
* [enter]simplify:  Simplifying (sqrt (+ (* PI PI) (- (* PI PI) (* PI PI))))
* * [misc]simplify:  iters left: 6 (5 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* * [misc]simplify:  iters left: 2 (24 enodes)
* * [misc]simplify:  iters left: 1 (27 enodes)
* [exit]simplify:  Simplified to (fabs PI)
* [exit]simplify:  Simplified to (fabs PI)
* * * * [misc]progress:  [ 14 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (sqrt (+ PI PI))) (/ (sqrt (- (* PI PI) (* PI PI))) (sqrt (- PI PI)))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (- (* PI PI) (* PI PI)))
* * [misc]simplify:  iters left: 5 (4 enodes)
* * [misc]simplify:  iters left: 4 (7 enodes)
* * [misc]simplify:  iters left: 3 (10 enodes)
* [exit]simplify:  Simplified to (sqrt 0)
* [exit]simplify:  Simplified to (sqrt 0)
* [enter]simplify:  Simplifying (sqrt (- PI PI))
* * [misc]simplify:  iters left: 3 (3 enodes)
* * [misc]simplify:  iters left: 2 (4 enodes)
* [exit]simplify:  Simplified to (sqrt 0)
* [exit]simplify:  Simplified to (sqrt 0)
* * * * [misc]progress:  [ 15 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (sqrt (+ PI PI))) (* (sqrt (sqrt (+ PI PI))) (sqrt (sqrt (+ PI PI))))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (sqrt (+ PI PI)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (sqrt (sqrt (+ PI PI)))
* [exit]simplify:  Simplified to (sqrt (sqrt (+ PI PI)))
* [enter]simplify:  Simplifying (sqrt (sqrt (+ PI PI)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (sqrt (sqrt (+ PI PI)))
* [exit]simplify:  Simplified to (sqrt (sqrt (+ PI PI)))
* * * * [misc]progress:  [ 16 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (sqrt (+ PI PI))) (fabs (sqrt (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 17 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (sqrt (+ PI PI))) (* 1 (sqrt (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 18 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (log1p (expm1 (sqrt (+ PI PI))))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (sqrt (+ PI PI)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (expm1 (sqrt (+ PI PI)))
* [exit]simplify:  Simplified to (expm1 (sqrt (+ PI PI)))
* * * * [misc]progress:  [ 19 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (expm1 (log1p (sqrt (+ PI PI))))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (sqrt (+ PI PI)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (log1p (sqrt (+ PI PI)))
* [exit]simplify:  Simplified to (log1p (sqrt (+ PI PI)))
* * * * [misc]progress:  [ 20 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (pow (+ PI PI) 1/2)) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 21 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (pow (sqrt (+ PI PI)) 1)) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 22 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (exp (log (sqrt (+ PI PI))))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (log (sqrt (+ PI PI)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (log (sqrt (+ PI PI)))
* [exit]simplify:  Simplified to (log (sqrt (+ PI PI)))
* * * * [misc]progress:  [ 23 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (log (exp (sqrt (+ PI PI))))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (sqrt (+ PI PI)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (exp (sqrt (+ PI PI)))
* [exit]simplify:  Simplified to (exp (sqrt (+ PI PI)))
* * * * [misc]progress:  [ 24 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (* (* (cbrt (sqrt (+ PI PI))) (cbrt (sqrt (+ PI PI)))) (cbrt (sqrt (+ PI PI))))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (sqrt (+ PI PI))) (cbrt (sqrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (5 enodes)
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* [exit]simplify:  Simplified to (* (cbrt (sqrt (+ PI PI))) (cbrt (sqrt (+ PI PI))))
* [exit]simplify:  Simplified to (* (cbrt (sqrt (+ PI PI))) (cbrt (sqrt (+ PI PI))))
* [enter]simplify:  Simplifying (cbrt (sqrt (+ PI PI)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (cbrt (sqrt (+ PI PI)))
* [exit]simplify:  Simplified to (cbrt (sqrt (+ PI PI)))
* * * * [misc]progress:  [ 25 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (cbrt (* (* (sqrt (+ PI PI)) (sqrt (+ PI PI))) (sqrt (+ PI PI))))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (sqrt (+ PI PI)) (sqrt (+ PI PI))) (sqrt (+ PI PI)))
* * [misc]simplify:  iters left: 6 (5 enodes)
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (* (sqrt (+ PI PI)) (+ PI PI))
* [exit]simplify:  Simplified to (* (sqrt (+ PI PI)) (+ PI PI))
* * * * [misc]progress:  [ 26 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (* (sqrt (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) (sqrt (cbrt (+ PI PI))))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (* (cbrt (+ PI PI)) (cbrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (5 enodes)
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (9 enodes)
* [exit]simplify:  Simplified to (fabs (cbrt (+ PI PI)))
* [exit]simplify:  Simplified to (fabs (cbrt (+ PI PI)))
* [enter]simplify:  Simplifying (sqrt (cbrt (+ PI PI)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (sqrt (cbrt (+ PI PI)))
* [exit]simplify:  Simplified to (sqrt (cbrt (+ PI PI)))
* * * * [misc]progress:  [ 27 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (* (sqrt (sqrt (+ PI PI))) (sqrt (sqrt (+ PI PI))))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (sqrt (+ PI PI)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (sqrt (sqrt (+ PI PI)))
* [exit]simplify:  Simplified to (sqrt (sqrt (+ PI PI)))
* [enter]simplify:  Simplifying (sqrt (sqrt (+ PI PI)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (sqrt (sqrt (+ PI PI)))
* [exit]simplify:  Simplified to (sqrt (sqrt (+ PI PI)))
* * * * [misc]progress:  [ 28 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (* (sqrt 1) (sqrt (+ PI PI)))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt 1)
* * [misc]simplify:  iters left: 1 (2 enodes)
* [exit]simplify:  Simplified to (sqrt 1)
* [exit]simplify:  Simplified to (sqrt 1)
* [enter]simplify:  Simplifying (sqrt (+ PI PI))
* * [misc]simplify:  iters left: 3 (3 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* * [misc]simplify:  iters left: 1 (6 enodes)
* [exit]simplify:  Simplified to (sqrt (+ PI PI))
* [exit]simplify:  Simplified to (sqrt (+ PI PI))
* * * * [misc]progress:  [ 29 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (* (sqrt 2) (sqrt PI))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt 2)
* * [misc]simplify:  iters left: 1 (2 enodes)
* [exit]simplify:  Simplified to (sqrt 2)
* [exit]simplify:  Simplified to (sqrt 2)
* [enter]simplify:  Simplifying (sqrt PI)
* * [misc]simplify:  iters left: 1 (2 enodes)
* [exit]simplify:  Simplified to (sqrt PI)
* [exit]simplify:  Simplified to (sqrt PI)
* * * * [misc]progress:  [ 30 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (/ (sqrt (+ (pow PI 3) (pow PI 3))) (sqrt (+ (* PI PI) (- (* PI PI) (* PI PI)))))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (+ (pow PI 3) (pow PI 3)))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (10 enodes)
* * [misc]simplify:  iters left: 2 (20 enodes)
* * [misc]simplify:  iters left: 1 (23 enodes)
* [exit]simplify:  Simplified to (sqrt (* (+ PI PI) (* PI PI)))
* [exit]simplify:  Simplified to (sqrt (* (+ PI PI) (* PI PI)))
* [enter]simplify:  Simplifying (sqrt (+ (* PI PI) (- (* PI PI) (* PI PI))))
* * [misc]simplify:  iters left: 6 (5 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* * [misc]simplify:  iters left: 2 (24 enodes)
* * [misc]simplify:  iters left: 1 (27 enodes)
* [exit]simplify:  Simplified to (fabs PI)
* [exit]simplify:  Simplified to (fabs PI)
* * * * [misc]progress:  [ 31 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (/ (sqrt (- (* PI PI) (* PI PI))) (sqrt (- PI PI)))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (- (* PI PI) (* PI PI)))
* * [misc]simplify:  iters left: 5 (4 enodes)
* * [misc]simplify:  iters left: 4 (7 enodes)
* * [misc]simplify:  iters left: 3 (10 enodes)
* [exit]simplify:  Simplified to (sqrt 0)
* [exit]simplify:  Simplified to (sqrt 0)
* [enter]simplify:  Simplifying (sqrt (- PI PI))
* * [misc]simplify:  iters left: 3 (3 enodes)
* * [misc]simplify:  iters left: 2 (4 enodes)
* [exit]simplify:  Simplified to (sqrt 0)
* [exit]simplify:  Simplified to (sqrt 0)
* * * * [misc]progress:  [ 32 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (* (sqrt (sqrt (+ PI PI))) (sqrt (sqrt (+ PI PI))))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (sqrt (+ PI PI)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (sqrt (sqrt (+ PI PI)))
* [exit]simplify:  Simplified to (sqrt (sqrt (+ PI PI)))
* [enter]simplify:  Simplifying (sqrt (sqrt (+ PI PI)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (sqrt (sqrt (+ PI PI)))
* [exit]simplify:  Simplified to (sqrt (sqrt (+ PI PI)))
* * * * [misc]progress:  [ 33 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (fabs (sqrt (+ PI PI)))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 34 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n (* 1 (sqrt (+ PI PI)))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 35 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (log1p (expm1 (* n (sqrt (+ PI PI))))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (* n (sqrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* [exit]simplify:  Simplified to (expm1 (* (sqrt (+ PI PI)) n))
* [exit]simplify:  Simplified to (expm1 (* (sqrt (+ PI PI)) n))
* * * * [misc]progress:  [ 36 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (expm1 (log1p (* n (sqrt (+ PI PI))))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (* n (sqrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* [exit]simplify:  Simplified to (log1p (* (sqrt (+ PI PI)) n))
* [exit]simplify:  Simplified to (log1p (* (sqrt (+ PI PI)) n))
* * * * [misc]progress:  [ 37 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (pow (* n (sqrt (+ PI PI))) 1) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 38 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (exp (log (* n (sqrt (+ PI PI))))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (log (* n (sqrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* [exit]simplify:  Simplified to (log (* (sqrt (+ PI PI)) n))
* [exit]simplify:  Simplified to (log (* (sqrt (+ PI PI)) n))
* * * * [misc]progress:  [ 39 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (log (exp (* n (sqrt (+ PI PI))))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* n (sqrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* [exit]simplify:  Simplified to (pow (exp n) (sqrt (+ PI PI)))
* [exit]simplify:  Simplified to (pow (exp n) (sqrt (+ PI PI)))
* * * * [misc]progress:  [ 40 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* (* (cbrt (* n (sqrt (+ PI PI)))) (cbrt (* n (sqrt (+ PI PI))))) (cbrt (* n (sqrt (+ PI PI))))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (* n (sqrt (+ PI PI)))) (cbrt (* n (sqrt (+ PI PI)))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* * [misc]simplify:  iters left: 4 (11 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* (sqrt (+ PI PI)) n)) (cbrt (* (sqrt (+ PI PI)) n)))
* [exit]simplify:  Simplified to (* (cbrt (* (sqrt (+ PI PI)) n)) (cbrt (* (sqrt (+ PI PI)) n)))
* [enter]simplify:  Simplifying (cbrt (* n (sqrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* [exit]simplify:  Simplified to (cbrt (* (sqrt (+ PI PI)) n))
* [exit]simplify:  Simplified to (cbrt (* (sqrt (+ PI PI)) n))
* * * * [misc]progress:  [ 41 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (cbrt (* (* (* n (sqrt (+ PI PI))) (* n (sqrt (+ PI PI)))) (* n (sqrt (+ PI PI))))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (* n (sqrt (+ PI PI))) (* n (sqrt (+ PI PI)))) (* n (sqrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (63 enodes)
* * [misc]simplify:  iters left: 1 (77 enodes)
* [exit]simplify:  Simplified to (* (sqrt (+ PI PI)) (* (* (+ PI PI) (* n n)) n))
* [exit]simplify:  Simplified to (* (sqrt (+ PI PI)) (* (* (+ PI PI) (* n n)) n))
* * * * [misc]progress:  [ 42 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* (sqrt (* n (sqrt (+ PI PI)))) (sqrt (* n (sqrt (+ PI PI))))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (* n (sqrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* [exit]simplify:  Simplified to (sqrt (* (sqrt (+ PI PI)) n))
* [exit]simplify:  Simplified to (sqrt (* (sqrt (+ PI PI)) n))
* [enter]simplify:  Simplifying (sqrt (* n (sqrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* [exit]simplify:  Simplified to (sqrt (* (sqrt (+ PI PI)) n))
* [exit]simplify:  Simplified to (sqrt (* (sqrt (+ PI PI)) n))
* * * * [misc]progress:  [ 43 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* 1 (* n (sqrt (+ PI PI)))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 44 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* (* n (* (cbrt (sqrt (+ PI PI))) (cbrt (sqrt (+ PI PI))))) (cbrt (sqrt (+ PI PI)))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (* (cbrt (sqrt (+ PI PI))) (cbrt (sqrt (+ PI PI)))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* [exit]simplify:  Simplified to (* (* (cbrt (sqrt (+ PI PI))) (cbrt (sqrt (+ PI PI)))) n)
* [exit]simplify:  Simplified to (* (* (cbrt (sqrt (+ PI PI))) (cbrt (sqrt (+ PI PI)))) n)
* * * * [misc]progress:  [ 45 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* (* n (sqrt (* (cbrt (+ PI PI)) (cbrt (+ PI PI))))) (sqrt (cbrt (+ PI PI)))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (sqrt (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* [exit]simplify:  Simplified to (* (fabs (cbrt (+ PI PI))) n)
* [exit]simplify:  Simplified to (* (fabs (cbrt (+ PI PI))) n)
* * * * [misc]progress:  [ 46 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* (* n (sqrt (sqrt (+ PI PI)))) (sqrt (sqrt (+ PI PI)))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (sqrt (sqrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* [exit]simplify:  Simplified to (* n (sqrt (sqrt (+ PI PI))))
* [exit]simplify:  Simplified to (* n (sqrt (sqrt (+ PI PI))))
* * * * [misc]progress:  [ 47 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* (* n (sqrt 1)) (sqrt (+ PI PI))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (sqrt 1))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (* n (sqrt 1))
* [exit]simplify:  Simplified to (* n (sqrt 1))
* * * * [misc]progress:  [ 48 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* (* n (sqrt 2)) (sqrt PI)) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (sqrt 2))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (* n (sqrt 2))
* [exit]simplify:  Simplified to (* n (sqrt 2))
* * * * [misc]progress:  [ 49 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* (* n (sqrt (sqrt (+ PI PI)))) (sqrt (sqrt (+ PI PI)))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (sqrt (sqrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* [exit]simplify:  Simplified to (* n (sqrt (sqrt (+ PI PI))))
* [exit]simplify:  Simplified to (* n (sqrt (sqrt (+ PI PI))))
* * * * [misc]progress:  [ 50 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* (* n 1) (sqrt (+ PI PI))) (sqrt (+ 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:  [ 51 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (/ (* n (sqrt (+ (pow PI 3) (pow PI 3)))) (sqrt (+ (* PI PI) (- (* PI PI) (* PI PI))))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (sqrt (+ (pow PI 3) (pow PI 3))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* * [misc]simplify:  iters left: 2 (29 enodes)
* [exit]simplify:  Simplified to (* (sqrt (* (* PI PI) (+ PI PI))) n)
* [exit]simplify:  Simplified to (* (sqrt (* (* PI PI) (+ PI PI))) n)
* * * * [misc]progress:  [ 52 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (/ (* n (sqrt (- (* PI PI) (* PI PI)))) (sqrt (- PI PI))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* n (sqrt (- (* PI PI) (* PI PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* [exit]simplify:  Simplified to (* n (sqrt 0))
* [exit]simplify:  Simplified to (* n (sqrt 0))
* * * * [misc]progress:  [ 53 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* (sqrt (+ PI PI)) n) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 54 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (log1p (expm1 (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* * [misc]simplify:  iters left: 2 (30 enodes)
* [exit]simplify:  Simplified to (expm1 (* n (+ PI PI)))
* [exit]simplify:  Simplified to (expm1 (* n (+ PI PI)))
* * * * [misc]progress:  [ 55 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (expm1 (log1p (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* * [misc]simplify:  iters left: 2 (30 enodes)
* [exit]simplify:  Simplified to (log1p (* n (+ PI PI)))
* [exit]simplify:  Simplified to (log1p (* n (+ PI PI)))
* * * * [misc]progress:  [ 56 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) 1) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI)))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (21 enodes)
* * [misc]simplify:  iters left: 2 (29 enodes)
* * [misc]simplify:  iters left: 1 (30 enodes)
* [exit]simplify:  Simplified to (* n (+ PI PI))
* [exit]simplify:  Simplified to (* n (+ PI PI))
* * * * [misc]progress:  [ 57 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) 1) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 58 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (exp (+ (log (* n (sqrt (+ PI PI)))) (log (sqrt (+ PI PI))))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (+ (log (* n (sqrt (+ PI PI)))) (log (sqrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (21 enodes)
* * [misc]simplify:  iters left: 1 (23 enodes)
* [exit]simplify:  Simplified to (fma 2 (log (sqrt (+ PI PI))) (log n))
* [exit]simplify:  Simplified to (fma 2 (log (sqrt (+ PI PI))) (log n))
* * * * [misc]progress:  [ 59 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (exp (log (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (log (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (49 enodes)
* * [misc]simplify:  iters left: 1 (55 enodes)
* [exit]simplify:  Simplified to (log (* (+ n n) PI))
* [exit]simplify:  Simplified to (log (* (+ n n) PI))
* * * * [misc]progress:  [ 60 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (log (exp (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (28 enodes)
* * [misc]simplify:  iters left: 2 (40 enodes)
* * [misc]simplify:  iters left: 1 (50 enodes)
* [exit]simplify:  Simplified to (pow (exp PI) (+ n n))
* [exit]simplify:  Simplified to (pow (exp PI) (+ n n))
* * * * [misc]progress:  [ 61 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (cbrt (* (* (* (* n (sqrt (+ PI PI))) (* n (sqrt (+ PI PI)))) (* n (sqrt (+ PI PI)))) (* (* (sqrt (+ PI PI)) (sqrt (+ PI PI))) (sqrt (+ PI PI))))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (* (* n (sqrt (+ PI PI))) (* n (sqrt (+ PI PI)))) (* n (sqrt (+ PI PI)))) (* (* (sqrt (+ PI PI)) (sqrt (+ PI PI))) (sqrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (49 enodes)
* * [misc]simplify:  iters left: 3 (91 enodes)
* * [misc]simplify:  iters left: 2 (160 enodes)
* * [misc]simplify:  iters left: 1 (229 enodes)
* [exit]simplify:  Simplified to (* (* (* (* n n) (+ PI PI)) (* (+ PI PI) n)) (+ PI PI))
* [exit]simplify:  Simplified to (* (* (* (* n n) (+ PI PI)) (* (+ PI PI) n)) (+ PI PI))
* * * * [misc]progress:  [ 62 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* (cbrt (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI)))) (cbrt (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))))) (cbrt (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI)))) (cbrt (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI)))))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* * [misc]simplify:  iters left: 2 (31 enodes)
* * [misc]simplify:  iters left: 1 (32 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 (sqrt (+ PI PI))) (sqrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* * [misc]simplify:  iters left: 2 (30 enodes)
* [exit]simplify:  Simplified to (cbrt (* n (+ PI PI)))
* [exit]simplify:  Simplified to (cbrt (* n (+ PI PI)))
* * * * [misc]progress:  [ 63 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (cbrt (* (* (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI)))) (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI)))) (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (58 enodes)
* * [misc]simplify:  iters left: 2 (125 enodes)
* * [misc]simplify:  iters left: 1 (336 enodes)
* [exit]simplify:  Simplified to (pow (* (+ n n) PI) 3)
* [exit]simplify:  Simplified to (pow (* (+ n n) PI) 3)
* * * * [misc]progress:  [ 64 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (sqrt (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI)))) (sqrt (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* * [misc]simplify:  iters left: 2 (30 enodes)
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* [enter]simplify:  Simplifying (sqrt (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* * [misc]simplify:  iters left: 2 (30 enodes)
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* [exit]simplify:  Simplified to (sqrt (* n (+ PI PI)))
* * * * [misc]progress:  [ 65 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (/ (* (* n (sqrt (+ (pow PI 3) (pow PI 3)))) (sqrt (+ (pow PI 3) (pow PI 3)))) (* (sqrt (+ (* PI PI) (- (* PI PI) (* PI PI)))) (sqrt (+ (* PI PI) (- (* PI PI) (* PI PI)))))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n (sqrt (+ (pow PI 3) (pow PI 3)))) (sqrt (+ (pow PI 3) (pow PI 3))))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (53 enodes)
* * [misc]simplify:  iters left: 1 (72 enodes)
* [exit]simplify:  Simplified to (* (pow PI 3) (+ n n))
* [exit]simplify:  Simplified to (* (pow PI 3) (+ n n))
* [enter]simplify:  Simplifying (* (sqrt (+ (* PI PI) (- (* PI PI) (* PI PI)))) (sqrt (+ (* PI PI) (- (* PI PI) (* PI PI)))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (30 enodes)
* * [misc]simplify:  iters left: 1 (33 enodes)
* [exit]simplify:  Simplified to (* PI PI)
* [exit]simplify:  Simplified to (* PI PI)
* * * * [misc]progress:  [ 66 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (/ (* (* n (sqrt (+ (pow PI 3) (pow PI 3)))) (sqrt (- (* PI PI) (* PI PI)))) (* (sqrt (+ (* PI PI) (- (* PI PI) (* PI PI)))) (sqrt (- PI PI)))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n (sqrt (+ (pow PI 3) (pow PI 3)))) (sqrt (- (* PI PI) (* PI PI))))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (44 enodes)
* * [misc]simplify:  iters left: 2 (49 enodes)
* [exit]simplify:  Simplified to (* (sqrt (* (* PI PI) (+ PI PI))) (* (sqrt 0) n))
* [exit]simplify:  Simplified to (* (sqrt (* (* PI PI) (+ PI PI))) (* (sqrt 0) n))
* [enter]simplify:  Simplifying (* (sqrt (+ (* PI PI) (- (* PI PI) (* PI PI)))) (sqrt (- PI PI)))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (28 enodes)
* * [misc]simplify:  iters left: 1 (31 enodes)
* [exit]simplify:  Simplified to (* (fabs PI) (sqrt 0))
* [exit]simplify:  Simplified to (* (fabs PI) (sqrt 0))
* * * * [misc]progress:  [ 67 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (/ (* (* n (sqrt (- (* PI PI) (* PI PI)))) (sqrt (+ (pow PI 3) (pow PI 3)))) (* (sqrt (- PI PI)) (sqrt (+ (* PI PI) (- (* PI PI) (* PI PI)))))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n (sqrt (- (* PI PI) (* PI PI)))) (sqrt (+ (pow PI 3) (pow PI 3))))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (44 enodes)
* * [misc]simplify:  iters left: 2 (49 enodes)
* [exit]simplify:  Simplified to (* (sqrt (* (+ PI PI) (* PI PI))) (* n (sqrt 0)))
* [exit]simplify:  Simplified to (* (sqrt (* (+ PI PI) (* PI PI))) (* n (sqrt 0)))
* [enter]simplify:  Simplifying (* (sqrt (- PI PI)) (sqrt (+ (* PI PI) (- (* PI PI) (* PI PI)))))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (28 enodes)
* * [misc]simplify:  iters left: 1 (31 enodes)
* [exit]simplify:  Simplified to (* (sqrt 0) (fabs PI))
* [exit]simplify:  Simplified to (* (sqrt 0) (fabs PI))
* * * * [misc]progress:  [ 68 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (/ (* (* n (sqrt (- (* PI PI) (* PI PI)))) (sqrt (- (* PI PI) (* PI PI)))) (* (sqrt (- PI PI)) (sqrt (- PI PI)))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n (sqrt (- (* PI PI) (* PI PI)))) (sqrt (- (* PI PI) (* PI PI))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* [exit]simplify:  Simplified to 0
* [exit]simplify:  Simplified to 0
* [enter]simplify:  Simplifying (* (sqrt (- PI PI)) (sqrt (- PI PI)))
* * [misc]simplify:  iters left: 5 (4 enodes)
* * [misc]simplify:  iters left: 4 (5 enodes)
* [exit]simplify:  Simplified to 0
* [exit]simplify:  Simplified to 0
* * * * [misc]progress:  [ 69 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* 1 (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 70 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* (* n (sqrt (+ PI PI))) (* (cbrt (sqrt (+ PI PI))) (cbrt (sqrt (+ PI PI))))) (cbrt (sqrt (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n (sqrt (+ PI PI))) (* (cbrt (sqrt (+ PI PI))) (cbrt (sqrt (+ PI PI)))))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* * [misc]simplify:  iters left: 1 (38 enodes)
* [exit]simplify:  Simplified to (* (* (cbrt (sqrt (+ PI PI))) (* (sqrt (+ PI PI)) n)) (cbrt (sqrt (+ PI PI))))
* [exit]simplify:  Simplified to (* (* (cbrt (sqrt (+ PI PI))) (* (sqrt (+ PI PI)) n)) (cbrt (sqrt (+ PI PI))))
* * * * [misc]progress:  [ 71 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* (* n (sqrt (+ PI PI))) (sqrt (* (cbrt (+ PI PI)) (cbrt (+ PI PI))))) (sqrt (cbrt (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n (sqrt (+ PI PI))) (sqrt (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* * [misc]simplify:  iters left: 2 (25 enodes)
* [exit]simplify:  Simplified to (* (fabs (cbrt (+ PI PI))) (* (sqrt (+ PI PI)) n))
* [exit]simplify:  Simplified to (* (fabs (cbrt (+ PI PI))) (* (sqrt (+ PI PI)) n))
* * * * [misc]progress:  [ 72 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* (* n (sqrt (+ PI PI))) (sqrt (sqrt (+ PI PI)))) (sqrt (sqrt (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n (sqrt (+ PI PI))) (sqrt (sqrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* [exit]simplify:  Simplified to (* (sqrt (sqrt (+ PI PI))) (* (sqrt (+ PI PI)) n))
* [exit]simplify:  Simplified to (* (sqrt (sqrt (+ PI PI))) (* (sqrt (+ PI PI)) n))
* * * * [misc]progress:  [ 73 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* (* n (sqrt (+ PI PI))) (sqrt 1)) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n (sqrt (+ PI PI))) (sqrt 1))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* * [misc]simplify:  iters left: 2 (25 enodes)
* [exit]simplify:  Simplified to (* (* n (sqrt 1)) (sqrt (+ PI PI)))
* [exit]simplify:  Simplified to (* (* n (sqrt 1)) (sqrt (+ PI PI)))
* * * * [misc]progress:  [ 74 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* (* n (sqrt (+ PI PI))) (sqrt 2)) (sqrt PI)) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n (sqrt (+ PI PI))) (sqrt 2))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* [exit]simplify:  Simplified to (* (sqrt (+ PI PI)) (* n (sqrt 2)))
* [exit]simplify:  Simplified to (* (sqrt (+ PI PI)) (* n (sqrt 2)))
* * * * [misc]progress:  [ 75 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* (* n (sqrt (+ PI PI))) (sqrt (sqrt (+ PI PI)))) (sqrt (sqrt (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n (sqrt (+ PI PI))) (sqrt (sqrt (+ PI PI))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* [exit]simplify:  Simplified to (* (sqrt (sqrt (+ PI PI))) (* (sqrt (+ PI PI)) n))
* [exit]simplify:  Simplified to (* (sqrt (sqrt (+ PI PI))) (* (sqrt (+ PI PI)) n))
* * * * [misc]progress:  [ 76 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* (* n (sqrt (+ PI PI))) 1) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n (sqrt (+ PI PI))) 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 (17 enodes)
* * [misc]simplify:  iters left: 2 (19 enodes)
* * [misc]simplify:  iters left: 1 (23 enodes)
* [exit]simplify:  Simplified to (* n (sqrt (+ PI PI)))
* [exit]simplify:  Simplified to (* n (sqrt (+ PI PI)))
* * * * [misc]progress:  [ 77 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n (* (sqrt (+ PI PI)) (sqrt (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (sqrt (+ PI PI)) (sqrt (+ PI PI)))
* * [misc]simplify:  iters left: 5 (4 enodes)
* * [misc]simplify:  iters left: 4 (6 enodes)
* * [misc]simplify:  iters left: 3 (8 enodes)
* [exit]simplify:  Simplified to (+ PI PI)
* [exit]simplify:  Simplified to (+ PI PI)
* * * * [misc]progress:  [ 78 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (/ (* (* n (sqrt (+ PI PI))) (sqrt (+ (pow PI 3) (pow PI 3)))) (sqrt (+ (* PI PI) (- (* PI PI) (* PI PI))))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n (sqrt (+ PI PI))) (sqrt (+ (pow PI 3) (pow PI 3))))
* * [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 (38 enodes)
* * [misc]simplify:  iters left: 2 (42 enodes)
* [exit]simplify:  Simplified to (* (sqrt (* (+ PI PI) (* PI PI))) (* (sqrt (+ PI PI)) n))
* [exit]simplify:  Simplified to (* (sqrt (* (+ PI PI) (* PI PI))) (* (sqrt (+ PI PI)) n))
* * * * [misc]progress:  [ 79 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (/ (* (* n (sqrt (+ PI PI))) (sqrt (- (* PI PI) (* PI PI)))) (sqrt (- PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n (sqrt (+ PI PI))) (sqrt (- (* PI PI) (* PI PI))))
* * [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 (28 enodes)
* * [misc]simplify:  iters left: 2 (30 enodes)
* [exit]simplify:  Simplified to (* (* (sqrt 0) n) (sqrt (+ PI PI)))
* [exit]simplify:  Simplified to (* (* (sqrt 0) n) (sqrt (+ PI PI)))
* * * * [misc]progress:  [ 80 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (/ (* (* n (sqrt (+ (pow PI 3) (pow PI 3)))) (sqrt (+ PI PI))) (sqrt (+ (* PI PI) (- (* PI PI) (* PI PI))))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n (sqrt (+ (pow PI 3) (pow PI 3)))) (sqrt (+ PI PI)))
* * [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 (38 enodes)
* * [misc]simplify:  iters left: 2 (42 enodes)
* [exit]simplify:  Simplified to (* (* n (sqrt (+ PI PI))) (sqrt (* (* PI PI) (+ PI PI))))
* [exit]simplify:  Simplified to (* (* n (sqrt (+ PI PI))) (sqrt (* (* PI PI) (+ PI PI))))
* * * * [misc]progress:  [ 81 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (/ (* (* n (sqrt (- (* PI PI) (* PI PI)))) (sqrt (+ PI PI))) (sqrt (- PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n (sqrt (- (* PI PI) (* PI PI)))) (sqrt (+ PI PI)))
* * [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 (28 enodes)
* * [misc]simplify:  iters left: 2 (30 enodes)
* [exit]simplify:  Simplified to (* (* n (sqrt 0)) (sqrt (+ PI PI)))
* [exit]simplify:  Simplified to (* (* n (sqrt 0)) (sqrt (+ PI PI)))
* * * * [misc]progress:  [ 82 / 94 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (sqrt (+ PI PI)) (* n (sqrt (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 83 / 94 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (pow (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 84 / 94 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (pow (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 85 / 94 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (pow (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 86 / 94 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (pow (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 87 / 94 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (pow (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 88 / 94 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (pow (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 89 / 94 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* (* (* n (sqrt 2)) (sqrt PI)) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (pow (* (* (* n (sqrt 2)) (sqrt PI)) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (45 enodes)
* * [misc]simplify:  iters left: 2 (67 enodes)
* * [misc]simplify:  iters left: 1 (74 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* n (sqrt 2)) (* (sqrt (+ PI PI)) (sqrt PI))) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 90 / 94 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* (* (* n (sqrt 2)) (sqrt PI)) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (pow (* (* (* n (sqrt 2)) (sqrt PI)) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (45 enodes)
* * [misc]simplify:  iters left: 2 (67 enodes)
* * [misc]simplify:  iters left: 1 (74 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* n (sqrt 2)) (* (sqrt (+ PI PI)) (sqrt PI))) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 91 / 94 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* (* (* n (sqrt 2)) (sqrt PI)) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (pow (* (* (* n (sqrt 2)) (sqrt PI)) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (45 enodes)
* * [misc]simplify:  iters left: 2 (67 enodes)
* * [misc]simplify:  iters left: 1 (74 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* n (sqrt 2)) (* (sqrt (+ PI PI)) (sqrt PI))) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 92 / 94 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* n (* PI (pow (sqrt 2) 2))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (pow (* n (* PI (pow (sqrt 2) 2))) (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (26 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* * [misc]simplify:  iters left: 2 (33 enodes)
* * [misc]simplify:  iters left: 1 (37 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 93 / 94 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* n (* PI (pow (sqrt 2) 2))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (pow (* n (* PI (pow (sqrt 2) 2))) (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (26 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* * [misc]simplify:  iters left: 2 (33 enodes)
* * [misc]simplify:  iters left: 1 (37 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 94 / 94 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* n (* PI (pow (sqrt 2) 2))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (pow (* n (* PI (pow (sqrt 2) 2))) (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (26 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* * [misc]simplify:  iters left: 2 (33 enodes)
* * [misc]simplify:  iters left: 1 (37 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k))
* * * [misc]progress:  adding candidates to table
* * [misc]progress:  iteration 3 / 4
* * * [misc]progress:  picking best candidate
* * * * [misc]pick:  Picked  #<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)))))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 4 ] rewriting at (2)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2 2 1 1 1)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2 1 1 1 1)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2 2 1 1)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 4 ] generating series at (2)
* [misc]approximate:  Taking taylor expansion of (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) in k
* [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]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ (* +nan.0 (sqrt (* n (* 2 PI)))) (* 2 (sqrt 0))) into (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) in k
* [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]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ (* +nan.0 (sqrt (* n (* 2 PI)))) (* 2 (sqrt 0))) into (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) in 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]backup-simplify:  Simplify (sqrt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) into (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (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]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]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) in 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]backup-simplify:  Simplify (sqrt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) into (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (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]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]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) in 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]backup-simplify:  Simplify (sqrt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) into (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (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]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]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) in 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]backup-simplify:  Simplify (sqrt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) into (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (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]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]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (* (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) (* (pow (/ 1 k) 1/4) (sqrt (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 (* (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 (+ (* (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) 0) (* 0 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [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 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]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) 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 (- 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]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) 0) (+ (* 0 0) (* 0 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))))))) 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 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]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) 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 (- 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]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))))) 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 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 (- 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)) (* 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 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 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 (pow 0 2) (+ (* 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))) (* 0 (/ 0 (sqrt k))))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) 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 (- 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)) (* 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 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 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 (pow 0 2) (+ (* 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))) (* 0 (/ 0 (sqrt k))))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))))))))) 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 (* (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) into (* (sqrt +nan.0) (sqrt (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (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))))))) (* 2 (sqrt (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))))) into (* +nan.0 (* (/ 1 (sqrt +nan.0)) (sqrt (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) into (* (sqrt +nan.0) (sqrt (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (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))))))) (* 2 (sqrt (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))))) into (* +nan.0 (* (/ 1 (sqrt +nan.0)) (sqrt (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))))
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))) into (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4))
* [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]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))) into (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4))
* [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]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))))) into 0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) (sqrt (/ (pow (* (/ 1 n) (+ PI PI)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))) into (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4))
* [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]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))) into (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4))
* [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]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))))) into 0
* [misc]backup-simplify:  Simplify (* (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)) (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)) 0) (* 0 (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)))) 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]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)))) 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]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]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)) 0) (+ (* 0 0) (* 0 (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4))))) 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]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)))) 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]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]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)))))) 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 (* (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) into (* (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (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)))))))) (* 2 (sqrt (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))))) into (* +nan.0 (* (/ 1 (sqrt +nan.0)) (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) into (* (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (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)))))))) (* 2 (sqrt (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))))) into (* +nan.0 (* (/ 1 (sqrt +nan.0)) (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))))
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))) into (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 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) 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]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))) into (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 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) 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]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) (sqrt (/ (pow (* (/ 1 (- n)) (+ PI PI)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))) into (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 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) 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]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))) into (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 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) 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]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))))) into 0
* [misc]backup-simplify:  Simplify (* (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))) (sqrt (/ (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 (+ (* (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))) 0) (* 0 (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (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]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))))) 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]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]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))) 0) (+ (* 0 0) (* 0 (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (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:  [ 2 / 4 ] generating series at (2 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:  [ 3 / 4 ] generating series at (2 1 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 2 1 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:  simplifying candidates
* * * * [misc]progress:  [ 1 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (log1p (expm1 (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (expm1 (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* * [misc]simplify:  iters left: 2 (39 enodes)
* [exit]simplify:  Simplified to (expm1 (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (expm1 (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 2 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (expm1 (log1p (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (log1p (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* * [misc]simplify:  iters left: 2 (39 enodes)
* [exit]simplify:  Simplified to (log1p (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (log1p (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 3 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (pow (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) (+ 1/2 1/2)))>
* [enter]simplify:  Simplifying (+ 1/2 1/2)
* * [misc]simplify:  iters left: 2 (2 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (+ 1/2 1/2)
* [exit]simplify:  Simplified to (+ 1/2 1/2)
* * * * [misc]progress:  [ 4 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (pow (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (+ 1 1)))>
* [enter]simplify:  Simplifying (+ 1 1)
* * [misc]simplify:  iters left: 2 (2 enodes)
* * [misc]simplify:  iters left: 1 (6 enodes)
* [exit]simplify:  Simplified to 2
* [exit]simplify:  Simplified to 2
* * * * [misc]progress:  [ 5 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (pow (* (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) 1/2))>
* [enter]simplify:  Simplifying (* (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (45 enodes)
* * [misc]simplify:  iters left: 2 (54 enodes)
* * [misc]simplify:  iters left: 1 (57 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) k)
* [exit]simplify:  Simplified to (/ (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) k)
* * * * [misc]progress:  [ 6 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (pow (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) 1))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (38 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:  [ 7 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (pow (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) 2))>
* * * * [misc]progress:  [ 8 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (pow (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (+ 1 1)))>
* [enter]simplify:  Simplifying (+ 1 1)
* * [misc]simplify:  iters left: 2 (2 enodes)
* * [misc]simplify:  iters left: 1 (6 enodes)
* [exit]simplify:  Simplified to 2
* [exit]simplify:  Simplified to 2
* * * * [misc]progress:  [ 9 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (pow (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) 1))>
* * * * [misc]progress:  [ 10 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (log (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (log (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (log (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (log (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (27 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 (+ (log (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))) (log (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))))
* [exit]simplify:  Simplified to (+ (log (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))) (log (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))))
* * * * [misc]progress:  [ 11 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (exp (log (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (log (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (46 enodes)
* * [misc]simplify:  iters left: 2 (65 enodes)
* * [misc]simplify:  iters left: 1 (121 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:  [ 12 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (log (exp (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (exp (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* * [misc]simplify:  iters left: 2 (41 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:  [ 13 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (* (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (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))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (49 enodes)
* * [misc]simplify:  iters left: 3 (75 enodes)
* * [misc]simplify:  iters left: 2 (106 enodes)
* * [misc]simplify:  iters left: 1 (127 enodes)
* [exit]simplify:  Simplified to (pow (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) 3)
* [exit]simplify:  Simplified to (pow (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) 3)
* * * * [misc]progress:  [ 14 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (cbrt (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))) (cbrt (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))) (cbrt (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (* (cbrt (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))) (cbrt (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* * [misc]simplify:  iters left: 2 (40 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 (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* * [misc]simplify:  iters left: 2 (39 enodes)
* [exit]simplify:  Simplified to (cbrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (cbrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 15 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (* (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))) (* (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))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (51 enodes)
* * [misc]simplify:  iters left: 3 (72 enodes)
* * [misc]simplify:  iters left: 2 (98 enodes)
* * [misc]simplify:  iters left: 1 (117 enodes)
* [exit]simplify:  Simplified to (pow (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) 3)
* [exit]simplify:  Simplified to (pow (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)) 3)
* * * * [misc]progress:  [ 16 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (sqrt (* (/ (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)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (45 enodes)
* * [misc]simplify:  iters left: 2 (54 enodes)
* * [misc]simplify:  iters left: 1 (57 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) k)
* [exit]simplify:  Simplified to (/ (* (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (pow (* n (+ PI PI)) (/ (- 1 k) 2))) k)
* * * * [misc]progress:  [ 17 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))) (sqrt (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (sqrt (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* * [misc]simplify:  iters left: 2 (40 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))
* [enter]simplify:  Simplifying (sqrt (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* * [misc]simplify:  iters left: 2 (40 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 18 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 19 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (* (sqrt (sqrt k)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (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 (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))
* [exit]simplify:  Simplified to (pow (* n (+ PI PI)) (/ (- 1 k) 2))
* [enter]simplify:  Simplifying (* (sqrt (sqrt k)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* [exit]simplify:  Simplified to (sqrt k)
* [exit]simplify:  Simplified to (sqrt k)
* * * * [misc]progress:  [ 20 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))))>
* * * * [misc]progress:  [ 21 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (* (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))) (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (* (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* * [misc]simplify:  iters left: 2 (44 enodes)
* [exit]simplify:  Simplified to (* (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (* (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))
* [exit]simplify:  Simplified to (* (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (* (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))
* * * * [misc]progress:  [ 22 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))) (sqrt (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* (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 (17 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (42 enodes)
* [exit]simplify:  Simplified to (* (fabs (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (fabs (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 23 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))) (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (15 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 (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 24 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* * [misc]simplify:  iters left: 2 (45 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 25 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))))) (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (42 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 26 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow n (/ (- 1 k) 2)) 1)) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow n (/ (- 1 k) 2)) 1)) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 27 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (* (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 (20 enodes)
* * [misc]simplify:  iters left: 5 (38 enodes)
* * [misc]simplify:  iters left: 4 (53 enodes)
* * [misc]simplify:  iters left: 3 (61 enodes)
* * [misc]simplify:  iters left: 2 (66 enodes)
* [exit]simplify:  Simplified to (* (fabs (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (fabs (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 28 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k))))) (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (46 enodes)
* * [misc]simplify:  iters left: 2 (48 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 29 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) 1))) (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) 1)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (41 enodes)
* * [misc]simplify:  iters left: 3 (45 enodes)
* * [misc]simplify:  iters left: 2 (47 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) 1))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) 1))))
* * * * [misc]progress:  [ 30 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* * [misc]simplify:  iters left: 2 (45 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 31 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))))) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (42 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 32 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) 1))) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) 1)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) 1)) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) 1)) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 33 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ 1 (* (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)) (sqrt k))) (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* * [misc]simplify:  iters left: 2 (44 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 34 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ 1 (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 k))) (sqrt (/ 1 (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 35 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ 1 1))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ 1 1)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* * [misc]simplify:  iters left: 2 (40 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt 1))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt 1))
* * * * [misc]progress:  [ 36 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt 1)) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt 1))
* * [misc]simplify:  iters left: 6 (15 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 1) (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt 1) (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 37 / 127 ] 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 (/ 1 (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (15 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 (pow (* (+ n n) PI) (/ (- 1 k) 2))) (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2))) (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 38 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))) (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (15 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 (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 39 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) 1) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) 1)
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (33 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)) (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 40 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))) (* (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 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 (* (cbrt (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (cbrt (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 41 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (* (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))) (* (sqrt (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* * [misc]simplify:  iters left: 2 (40 enodes)
* [exit]simplify:  Simplified to (* (sqrt (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (cbrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 42 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (* (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 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 (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 43 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (42 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 44 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))) (* (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (42 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 45 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow n (/ (- 1 k) 2)) 1)) (* (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 46 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (42 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 47 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))) (* (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (42 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 48 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (* (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) 1)) (* (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (cbrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k))))
* * * * [misc]progress:  [ 49 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (42 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 50 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (* (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (42 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 51 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) 1)) (* (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k))))
* * * * [misc]progress:  [ 52 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ 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)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 53 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ 1 (sqrt (sqrt k)))) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 54 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ 1 1)) (* (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))) (sqrt (/ (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 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (38 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:  [ 55 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt 1) (* (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))) (sqrt (/ (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 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (38 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:  [ 56 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (* (sqrt (/ 1 (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ 1 (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* * [misc]simplify:  iters left: 2 (40 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ 1 (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ 1 (sqrt k))))
* * * * [misc]progress:  [ 57 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (* (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 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 (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 58 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (* (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))) (sqrt (/ (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 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (38 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:  [ 59 / 127 ] 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 (sqrt k))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (15 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 (pow (* (+ n n) PI) (/ (- 1 k) 2))) (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2))) (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 60 / 127 ] 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)))) (sqrt (sqrt k))))>
* [enter]simplify:  Simplifying (* (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 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 (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))) (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))) (sqrt (pow (* (+ n n) PI) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 61 / 127 ] 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)))))>
* * * * [misc]progress:  [ 62 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 63 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 64 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (pow (* n (+ PI PI)) 1) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 65 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 66 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 67 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 68 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 69 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 70 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 1 (* n (+ PI PI))) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 71 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 72 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 73 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 74 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 75 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 76 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 77 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 78 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 79 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 80 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (log1p (expm1 (* n (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 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:  [ 81 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (expm1 (log1p (* n (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 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:  [ 82 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (pow (* n (+ PI PI)) 1) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 83 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (exp (log (* n (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 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:  [ 84 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (log (exp (* n (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 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:  [ 85 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI)))) (cbrt (* n (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 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:  [ 86 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (cbrt (* (* (* n (+ PI PI)) (* n (+ PI PI))) (* n (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 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:  [ 87 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* (sqrt (* n (+ PI PI))) (sqrt (* n (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 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:  [ 88 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* 1 (* n (+ PI PI))) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 89 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (+ (* n PI) (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI 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:  [ 90 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (+ (* PI n) (* PI n)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 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:  [ 91 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) (cbrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ 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:  [ 92 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ 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:  [ 93 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* (* n 1) (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ 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:  [ 94 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI 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:  [ 95 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (/ (* n (+ (pow PI 3) (pow PI 3))) (+ (* PI PI) (- (* PI PI) (* PI PI)))) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ 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:  [ 96 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (/ (* n (- (* PI PI) (* PI PI))) (- PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ 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:  [ 97 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 98 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 99 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 100 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 101 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 102 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 103 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (/ (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:  [ 104 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 105 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 106 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 107 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 108 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (* (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:  [ 109 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (pow (* n (+ PI PI)) (/ (- 1 k) 2)) 1) (sqrt k)))))>
* * * * [misc]progress:  [ 110 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 111 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 112 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (* (* (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:  [ 113 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 114 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (* (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:  [ 115 / 127 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (* 1 (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k)))))>
* * * * [misc]progress:  [ 116 / 127 ] 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:  [ 117 / 127 ] 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:  [ 118 / 127 ] 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:  [ 119 / 127 ] simplifiying candidate #<alt-event (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 120 / 127 ] simplifiying candidate #<alt-event (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 121 / 127 ] simplifiying candidate #<alt-event (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (+ n n) PI) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 122 / 127 ] simplifiying candidate #<alt-event (λ (k n) (* (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 123 / 127 ] simplifiying candidate #<alt-event (λ (k n) (* (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 124 / 127 ] simplifiying candidate #<alt-event (λ (k n) (* (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 125 / 127 ] simplifiying candidate #<alt-event (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (- (+ (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 (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (- (+ (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 (49 enodes)
* * [misc]simplify:  iters left: 5 (118 enodes)
* * [misc]simplify:  iters left: 4 (236 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (+ (- (fma (* (exp (fma (log (+ PI PI)) 1/2 (* 1/2 (log n)))) 1/8) (* (* k k) (+ (* (log n) (log n)) (* (log (+ PI PI)) (log (+ PI PI))))) (* (* (* (* (* k k) (log n)) (log (+ PI PI))) 1/4) (exp (fma (log (+ PI PI)) 1/2 (* 1/2 (log n)))))) (* 1/2 (* (exp (fma (log (+ PI PI)) 1/2 (* 1/2 (log n)))) (fma k (log (+ PI PI)) (* k (log n)))))) (exp (fma (log (+ PI PI)) 1/2 (* 1/2 (log n))))) (sqrt k))))
* * * * [misc]progress:  [ 126 / 127 ] simplifiying candidate #<alt-event (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k))))
* * [misc]simplify:  iters left: 6 (25 enodes)
* * [misc]simplify:  iters left: 5 (49 enodes)
* * [misc]simplify:  iters left: 4 (65 enodes)
* * [misc]simplify:  iters left: 3 (89 enodes)
* * [misc]simplify:  iters left: 2 (137 enodes)
* * [misc]simplify:  iters left: 1 (202 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (exp (* (- (log (+ PI PI)) (- (log n))) (* 1/2 (- 1 k)))) (sqrt k))))
* * * * [misc]progress:  [ 127 / 127 ] simplifiying candidate #<alt-event (λ (k n) (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k))))
* * [misc]simplify:  iters left: 6 (27 enodes)
* * [misc]simplify:  iters left: 5 (51 enodes)
* * [misc]simplify:  iters left: 4 (66 enodes)
* * [misc]simplify:  iters left: 3 (92 enodes)
* * [misc]simplify:  iters left: 2 (140 enodes)
* * [misc]simplify:  iters left: 1 (205 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (* 1/2 (- 1 k)))) (sqrt k))))
* * * [misc]progress:  adding candidates to table
* * [misc]progress:  iteration 4 / 4
* * * [misc]progress:  picking best candidate
* * * * [misc]pick:  Picked  #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 4 ] rewriting at (2 2 1 1)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2 2 1)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2 1 1 1 1 1)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2 1 1 1 1)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 4 ] generating series at (2 2 1 1)
* [misc]approximate:  Taking taylor expansion of (pow (+ PI PI) (/ (- 1 k) 2)) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (+ PI PI) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (+ PI PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (+ 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 (+ PI PI)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2)
* [misc]taylor:  Taking taylor expansion of (pow (+ PI PI) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (+ PI PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (+ 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 (+ PI PI)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2)
* [misc]backup-simplify:  Simplify (pow (* 2 PI) 1/2) into (pow (* 2 PI) 1/2)
* [misc]backup-simplify:  Simplify (+ 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) 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 PI)))) into (- (* 1/2 (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* 2 PI)) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (* -1/2 (* (sqrt (* 2 PI)) (log (* 2 PI)))) into (* -1/2 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2))))
* [misc]backup-simplify:  Simplify (+ 0 0) 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 (/ 0 2)) (* -1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* 2 PI)) (pow (log (* 2 PI)) 2)))
* [misc]backup-simplify:  Simplify (* 1/8 (* (sqrt (* 2 PI)) (pow (log (* 2 PI)) 2))) into (* 1/8 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (sqrt 2))))
* [misc]backup-simplify:  Simplify (+ (* (* 1/8 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (pow k 2)) (+ (* (* -1/2 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2)))) k) (pow (* 2 PI) 1/2))) into (- (+ (pow (* 2 PI) 1/2) (* 1/8 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (* (pow k 2) (sqrt 2)))))) (* 1/2 (* (sqrt PI) (* (log (* 2 PI)) (* k (sqrt 2))))))
* [misc]approximate:  Taking taylor expansion of (pow (+ PI PI) (/ (- 1 (/ 1 k)) 2)) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (+ PI PI) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (+ PI PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (+ 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 (+ PI PI)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (+ PI PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (pow (+ PI PI) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (+ PI PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (+ 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 (+ PI PI)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (+ PI PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))
* [misc]approximate:  Taking taylor expansion of (pow (+ PI PI) (/ (- 1 (/ 1 (- k))) 2)) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (+ PI PI) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (+ PI PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (+ 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 (+ PI PI)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (+ PI PI)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (pow (+ PI PI) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (+ PI PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (+ 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 (+ PI PI)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (+ PI PI)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))
* * * * [misc]progress:  [ 2 / 4 ] generating series at (2 2 1)
* [misc]approximate:  Taking taylor expansion of (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (pow (+ PI PI) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (+ PI PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (+ 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 (+ PI PI)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 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 PI) 1/2) +nan.0) into (* +nan.0 (sqrt (* 2 PI)))
* [misc]taylor:  Taking taylor expansion of (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (pow (+ PI PI) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (+ PI PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (+ 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 (+ PI PI)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 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 PI) 1/2) +nan.0) into (* +nan.0 (sqrt (* 2 PI)))
* [misc]backup-simplify:  Simplify (* +nan.0 (sqrt (* 2 PI))) into (* +nan.0 (* (sqrt PI) (sqrt 2)))
* [misc]backup-simplify:  Simplify (+ 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) 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 PI)))) into (- (* 1/2 (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* 2 PI)) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ (* -1/2 (* (sqrt (* 2 PI)) (log (* 2 PI)))) +nan.0) (+ (* (* +nan.0 (sqrt (* 2 PI))) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2)))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2))))))) into (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2)))))))
* [misc]backup-simplify:  Simplify (+ 0 0) 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 (/ 0 2)) (* -1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* 2 PI)) (pow (log (* 2 PI)) 2)))
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ (* 1/8 (* (sqrt (* 2 PI)) (pow (log (* 2 PI)) 2))) +nan.0) (+ (* (* +nan.0 (sqrt (* 2 PI))) (/ +nan.0 +nan.0)) (* (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2))))))) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2)))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2))))))))) into (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2)))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2))))))))) k) (+ (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2))))))) (* (* +nan.0 (* (sqrt PI) (sqrt 2))) (/ 1 k)))) into (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (+ (* +nan.0 (* (sqrt PI) (* k (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (* k (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt PI) (/ (sqrt 2) k))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (* k (sqrt 2))))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2)))))))))))))))
* [misc]approximate:  Taking taylor expansion of (/ (pow (+ PI PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (+ PI PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (pow (+ PI PI) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (+ PI PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (+ 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 (+ PI PI)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (+ PI PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]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))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (+ PI PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (pow (+ PI PI) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (+ PI PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (+ 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 (+ PI PI)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (+ PI PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]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))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))))) (pow (/ 1 k) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))))) (/ 1 k)) (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI)))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)))))))
* [misc]approximate:  Taking taylor expansion of (/ (pow (+ PI PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (+ PI PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow (+ PI PI) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (+ PI PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (+ 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 (+ PI PI)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (+ PI PI)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (+ PI PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow (+ PI PI) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (+ PI PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (+ 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 (+ PI PI)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (+ PI PI)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (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)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (log (* 2 PI))))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (log (* 2 PI))))))) (/ 1 (- k))) (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (log (* 2 PI)))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)))))))
* * * * [misc]progress:  [ 3 / 4 ] generating series at (2 1 1 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 1 1 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:  simplifying candidates
* * * * [misc]progress:  [ 1 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (log1p (expm1 (pow (+ PI PI) (/ (- 1 k) 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (expm1 (pow (+ PI PI) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* [exit]simplify:  Simplified to (expm1 (pow (+ PI PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (expm1 (pow (+ PI PI) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 2 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (expm1 (log1p (pow (+ PI PI) (/ (- 1 k) 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (log1p (pow (+ PI PI) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* [exit]simplify:  Simplified to (log1p (pow (+ PI PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (log1p (pow (+ PI PI) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 3 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (exp (* (log (+ PI PI)) (/ (- 1 k) 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (log (+ PI PI)) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* * [misc]simplify:  iters left: 2 (57 enodes)
* * [misc]simplify:  iters left: 1 (70 enodes)
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (+ PI PI)))
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (+ PI PI)))
* * * * [misc]progress:  [ 4 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (exp (* (log (+ PI PI)) (/ (- 1 k) 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (log (+ PI PI)) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* * [misc]simplify:  iters left: 2 (57 enodes)
* * [misc]simplify:  iters left: 1 (70 enodes)
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (+ PI PI)))
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (+ PI PI)))
* * * * [misc]progress:  [ 5 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ 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 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (/ (pow (+ PI PI) (/ 1 2)) (pow (+ PI PI) (/ k 2))) (sqrt k)))))>
* [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))
* [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:  [ 7 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (pow (+ PI PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (pow (+ PI PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* [exit]simplify:  Simplified to (pow (+ PI PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (pow (+ PI PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 8 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (pow (+ PI PI) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (pow (+ PI PI) (sqrt (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* [exit]simplify:  Simplified to (pow (+ PI PI) (sqrt (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (pow (+ PI PI) (sqrt (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 9 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (pow (+ PI PI) 1) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (pow (+ PI PI) 1)
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (8 enodes)
* * [misc]simplify:  iters left: 1 (9 enodes)
* [exit]simplify:  Simplified to (+ PI PI)
* [exit]simplify:  Simplified to (+ PI PI)
* * * * [misc]progress:  [ 10 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (pow (+ PI PI) (- 1 k)) (/ 1 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (pow (+ PI PI) (- 1 k))
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (10 enodes)
* * [misc]simplify:  iters left: 1 (11 enodes)
* [exit]simplify:  Simplified to (pow (+ PI PI) (- 1 k))
* [exit]simplify:  Simplified to (pow (+ PI PI) (- 1 k))
* * * * [misc]progress:  [ 11 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (* (pow (* (cbrt (+ PI PI)) (cbrt (+ PI PI))) (/ (- 1 k) 2)) (pow (cbrt (+ PI PI)) (/ (- 1 k) 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (pow (* (cbrt (+ PI PI)) (cbrt (+ 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 (pow (* (cbrt (+ PI PI)) (cbrt (+ PI PI))) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow (* (cbrt (+ PI PI)) (cbrt (+ PI PI))) (/ (- 1 k) 2))
* [enter]simplify:  Simplifying (pow (cbrt (+ PI PI)) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* [exit]simplify:  Simplified to (pow (cbrt (+ PI PI)) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow (cbrt (+ PI PI)) (/ (- 1 k) 2))
* * * * [misc]progress:  [ 12 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (* (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)) (pow (sqrt (+ PI PI)) (/ (- 1 k) 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (pow (sqrt (+ PI PI)) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* [exit]simplify:  Simplified to (pow (sqrt (+ PI PI)) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow (sqrt (+ PI PI)) (/ (- 1 k) 2))
* [enter]simplify:  Simplifying (pow (sqrt (+ PI PI)) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* [exit]simplify:  Simplified to (pow (sqrt (+ PI PI)) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow (sqrt (+ PI PI)) (/ (- 1 k) 2))
* * * * [misc]progress:  [ 13 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (* (pow 1 (/ (- 1 k) 2)) (pow (+ PI PI) (/ (- 1 k) 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (pow 1 (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (11 enodes)
* [exit]simplify:  Simplified to 1
* [exit]simplify:  Simplified to 1
* [enter]simplify:  Simplifying (pow (+ 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:  [ 14 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (pow 2 (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (11 enodes)
* [exit]simplify:  Simplified to (pow 2 (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow 2 (/ (- 1 k) 2))
* [enter]simplify:  Simplifying (pow PI (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* [exit]simplify:  Simplified to (pow PI (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow PI (/ (- 1 k) 2))
* * * * [misc]progress:  [ 15 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (pow (+ PI PI) (/ (- 1 k) 2)) 1) (sqrt k)))))>
* * * * [misc]progress:  [ 16 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (exp (log (pow (+ PI PI) (/ (- 1 k) 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (log (pow (+ PI PI) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* * [misc]simplify:  iters left: 2 (55 enodes)
* * [misc]simplify:  iters left: 1 (64 enodes)
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (+ PI PI)))
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (+ PI PI)))
* * * * [misc]progress:  [ 17 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (log (exp (pow (+ PI PI) (/ (- 1 k) 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (exp (pow (+ PI PI) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* [exit]simplify:  Simplified to (exp (pow (+ PI PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (exp (pow (+ PI PI) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 18 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (* (* (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (pow (+ PI PI) (/ (- 1 k) 2)))) (cbrt (pow (+ PI PI) (/ (- 1 k) 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (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 (* (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (pow (+ PI PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (pow (+ PI PI) (/ (- 1 k) 2))))
* [enter]simplify:  Simplifying (cbrt (pow (+ PI PI) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* [exit]simplify:  Simplified to (cbrt (pow (+ PI PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (cbrt (pow (+ PI PI) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 19 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (cbrt (* (* (pow (+ PI PI) (/ (- 1 k) 2)) (pow (+ PI PI) (/ (- 1 k) 2))) (pow (+ PI PI) (/ (- 1 k) 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (* (pow (+ PI PI) (/ (- 1 k) 2)) (pow (+ PI PI) (/ (- 1 k) 2))) (pow (+ PI PI) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* [exit]simplify:  Simplified to (pow (pow (+ PI PI) (/ (- 1 k) 2)) 3)
* [exit]simplify:  Simplified to (pow (pow (+ PI PI) (/ (- 1 k) 2)) 3)
* * * * [misc]progress:  [ 20 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (* (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) (sqrt (pow (+ PI PI) (/ (- 1 k) 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (pow (+ PI PI) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (+ PI PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (sqrt (pow (+ PI PI) (/ (- 1 k) 2)))
* [enter]simplify:  Simplifying (sqrt (pow (+ PI PI) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (+ PI PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (sqrt (pow (+ PI PI) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 21 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (* 1 (pow (+ PI PI) (/ (- 1 k) 2))) (sqrt k)))))>
* * * * [misc]progress:  [ 22 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (log1p (expm1 (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (expm1 (/ (pow (+ PI PI) (/ (- 1 k) 2)) (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 (expm1 (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (expm1 (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 23 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (expm1 (log1p (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (log1p (/ (pow (+ PI PI) (/ (- 1 k) 2)) (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 (log1p (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (log1p (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 24 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (pow (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)) 1))))>
* * * * [misc]progress:  [ 25 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (exp (- (* (log (+ PI PI)) (/ (- 1 k) 2)) (log (sqrt k)))))))>
* [enter]simplify:  Simplifying (- (* (log (+ PI PI)) (/ (- 1 k) 2)) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (46 enodes)
* * [misc]simplify:  iters left: 2 (62 enodes)
* * [misc]simplify:  iters left: 1 (78 enodes)
* [exit]simplify:  Simplified to (- (* (/ (- 1 k) 2) (log (+ PI PI))) (log (sqrt k)))
* [exit]simplify:  Simplified to (- (* (/ (- 1 k) 2) (log (+ PI PI))) (log (sqrt k)))
* * * * [misc]progress:  [ 26 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (exp (- (* (log (+ PI PI)) (/ (- 1 k) 2)) (log (sqrt k)))))))>
* [enter]simplify:  Simplifying (- (* (log (+ PI PI)) (/ (- 1 k) 2)) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (46 enodes)
* * [misc]simplify:  iters left: 2 (62 enodes)
* * [misc]simplify:  iters left: 1 (78 enodes)
* [exit]simplify:  Simplified to (- (* (/ (- 1 k) 2) (log (+ PI PI))) (log (sqrt k)))
* [exit]simplify:  Simplified to (- (* (/ (- 1 k) 2) (log (+ PI PI))) (log (sqrt k)))
* * * * [misc]progress:  [ 27 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (exp (- (log (pow (+ PI PI) (/ (- 1 k) 2))) (log (sqrt k)))))))>
* [enter]simplify:  Simplifying (- (log (pow (+ PI PI) (/ (- 1 k) 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (44 enodes)
* * [misc]simplify:  iters left: 2 (60 enodes)
* * [misc]simplify:  iters left: 1 (76 enodes)
* [exit]simplify:  Simplified to (- (* (/ (- 1 k) 2) (log (+ PI PI))) (log (sqrt k)))
* [exit]simplify:  Simplified to (- (* (/ (- 1 k) 2) (log (+ PI PI))) (log (sqrt k)))
* * * * [misc]progress:  [ 28 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (exp (log (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (log (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* * [misc]simplify:  iters left: 2 (50 enodes)
* * [misc]simplify:  iters left: 1 (74 enodes)
* [exit]simplify:  Simplified to (- (/ (log (+ PI PI)) (/ 2 (- 1 k))) (log (sqrt k)))
* [exit]simplify:  Simplified to (- (/ (log (+ PI PI)) (/ 2 (- 1 k))) (log (sqrt k)))
* * * * [misc]progress:  [ 29 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (log (exp (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (exp (/ (pow (+ PI PI) (/ (- 1 k) 2)) (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 (exp (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (exp (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 30 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (cbrt (/ (* (* (pow (+ PI PI) (/ (- 1 k) 2)) (pow (+ PI PI) (/ (- 1 k) 2))) (pow (+ PI PI) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (* (* (pow (+ PI PI) (/ (- 1 k) 2)) (pow (+ PI PI) (/ (- 1 k) 2))) (pow (+ PI PI) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (47 enodes)
* * [misc]simplify:  iters left: 3 (70 enodes)
* * [misc]simplify:  iters left: 2 (97 enodes)
* * [misc]simplify:  iters left: 1 (120 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (+ PI PI) (/ (- 1 k) 2)) (pow (+ PI PI) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (+ PI PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (* (pow (+ PI PI) (/ (- 1 k) 2)) (pow (+ PI PI) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (+ PI PI) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 31 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* (* (cbrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (* (cbrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))))
* [enter]simplify:  Simplifying (cbrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (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 (cbrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (cbrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 32 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (cbrt (* (* (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (* (* (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (41 enodes)
* * [misc]simplify:  iters left: 3 (50 enodes)
* * [misc]simplify:  iters left: 2 (64 enodes)
* * [misc]simplify:  iters left: 1 (88 enodes)
* [exit]simplify:  Simplified to (pow (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)) 3)
* [exit]simplify:  Simplified to (pow (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)) 3)
* * * * [misc]progress:  [ 33 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (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 (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))
* [enter]simplify:  Simplifying (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (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 (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 34 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (- (pow (+ PI PI) (/ (- 1 k) 2))) (- (sqrt k))))))>
* [enter]simplify:  Simplifying (- (pow (+ PI PI) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* [exit]simplify:  Simplified to (- (pow (+ PI PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (- (pow (+ 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:  [ 35 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* (/ (pow (* (cbrt (+ PI PI)) (cbrt (+ PI PI))) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (cbrt (+ PI PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (pow (* (cbrt (+ PI PI)) (cbrt (+ PI PI))) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (cbrt (+ PI PI)) (cbrt (+ PI PI))) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow (* (cbrt (+ PI PI)) (cbrt (+ PI PI))) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow (cbrt (+ PI PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (pow (cbrt (+ PI PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (cbrt (+ PI PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 36 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* (/ (pow (* (cbrt (+ PI PI)) (cbrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (cbrt (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (pow (* (cbrt (+ PI PI)) (cbrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (cbrt (+ PI PI)) (cbrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (* (cbrt (+ PI PI)) (cbrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (pow (cbrt (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (pow (cbrt (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (cbrt (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 37 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* (/ (pow (* (cbrt (+ PI PI)) (cbrt (+ PI PI))) (/ (- 1 k) 2)) 1) (/ (pow (cbrt (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow (* (cbrt (+ PI PI)) (cbrt (+ PI PI))) (/ (- 1 k) 2)) 1)
* * [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 (* (cbrt (+ PI PI)) (cbrt (+ PI PI))) (/ (- 1 k) 2)) 1)
* [exit]simplify:  Simplified to (/ (pow (* (cbrt (+ PI PI)) (cbrt (+ PI PI))) (/ (- 1 k) 2)) 1)
* [enter]simplify:  Simplifying (/ (pow (cbrt (+ PI PI)) (/ (- 1 k) 2)) (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 (cbrt (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))
* [exit]simplify:  Simplified to (/ (pow (cbrt (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 38 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* (/ (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* [exit]simplify:  Simplified to (/ (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 39 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* (/ (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 40 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* (/ (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)) 1) (/ (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)) 1)
* * [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 (sqrt (+ PI PI)) (/ (- 1 k) 2)) 1)
* [exit]simplify:  Simplified to (/ (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)) 1)
* [enter]simplify:  Simplifying (/ (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)) (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 (sqrt (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))
* [exit]simplify:  Simplified to (/ (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 41 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* (/ (pow 1 (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (+ PI PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (pow 1 (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* [exit]simplify:  Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow (+ PI 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:  [ 42 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* (/ (pow 1 (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (pow 1 (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ 1 (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:  [ 43 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* (/ (pow 1 (/ (- 1 k) 2)) 1) (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow 1 (/ (- 1 k) 2)) 1)
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* [exit]simplify:  Simplified to (/ 1 1)
* [exit]simplify:  Simplified to (/ 1 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:  [ 44 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* (/ (pow 2 (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (pow 2 (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 45 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 46 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* (/ (pow 2 (/ (- 1 k) 2)) 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow 2 (/ (- 1 k) 2)) 1)
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) 1)
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) 1)
* [enter]simplify:  Simplifying (/ (pow PI (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt k))
* [exit]simplify:  Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 47 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* (/ (* (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (pow (+ PI PI) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (pow (+ PI PI) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* * [misc]simplify:  iters left: 2 (42 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 48 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* (/ (* (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (pow (+ PI PI) (/ (- 1 k) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (pow (+ PI PI) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (pow (+ PI PI) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (pow (+ PI PI) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 49 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* (/ (* (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (pow (+ PI PI) (/ (- 1 k) 2)))) 1) (/ (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (pow (+ PI PI) (/ (- 1 k) 2)))) 1)
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) 1) (cbrt (pow (+ PI PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) 1) (cbrt (pow (+ PI PI) (/ (- 1 k) 2))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (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 (/ (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (sqrt k))
* [exit]simplify:  Simplified to (/ (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (sqrt k))
* * * * [misc]progress:  [ 50 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* (/ (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 51 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* (/ (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 52 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* (/ (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) 1) (/ (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) 1)
* * [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 (pow (+ PI PI) (/ (- 1 k) 2))) 1)
* [exit]simplify:  Simplified to (/ (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) 1)
* [enter]simplify:  Simplifying (/ (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) (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 (/ (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) (sqrt k))
* [exit]simplify:  Simplified to (/ (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) (sqrt k))
* * * * [misc]progress:  [ 53 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (+ 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 (+ 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:  [ 54 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* (/ 1 (sqrt (sqrt k))) (/ (pow (+ 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 (+ 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:  [ 55 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* (/ 1 1) (/ (pow (+ 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 (+ 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:  [ 56 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* 1 (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))))))>
* * * * [misc]progress:  [ 57 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (* (pow (+ 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:  [ 58 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ 1 (/ (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:  [ 59 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (/ (pow (+ PI PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow (+ PI PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* [exit]simplify:  Simplified to (/ (pow (+ PI PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow (+ PI PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 60 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) (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:  [ 61 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (/ (pow (+ PI PI) (/ (- 1 k) 2)) 1) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (+ PI PI) (/ (- 1 k) 2)) 1)
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* [exit]simplify:  Simplified to (/ (pow (+ PI PI) (/ (- 1 k) 2)) 1)
* [exit]simplify:  Simplified to (/ (pow (+ PI PI) (/ (- 1 k) 2)) 1)
* * * * [misc]progress:  [ 62 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (* (cbrt (+ PI PI)) (cbrt (+ PI PI))) (/ (- 1 k) 2)) (/ (sqrt k) (pow (cbrt (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (pow (cbrt (+ 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 k) (pow (cbrt (+ PI PI)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (cbrt (+ PI PI)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 63 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)) (/ (sqrt k) (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (pow (sqrt (+ 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 k) (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (sqrt (+ PI PI)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 64 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow 1 (/ (- 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:  [ 65 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow 2 (/ (- 1 k) 2)) (/ (sqrt k) (pow PI (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (pow PI (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (pow PI (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (sqrt k) (pow PI (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 66 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (* (cbrt (pow (+ PI PI) (/ (- 1 k) 2))) (cbrt (pow (+ PI PI) (/ (- 1 k) 2)))) (/ (sqrt k) (cbrt (pow (+ PI PI) (/ (- 1 k) 2))))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (cbrt (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 k) (cbrt (pow (+ PI PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (sqrt k) (cbrt (pow (+ PI PI) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 67 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (sqrt (pow (+ PI PI) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (+ PI PI) (/ (- 1 k) 2))))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (sqrt (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 k) (sqrt (pow (+ PI PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (sqrt k) (sqrt (pow (+ PI PI) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 68 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ 1 (/ (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 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ 1 2)) (* (sqrt k) (pow (+ PI PI) (/ k 2)))))))>
* [enter]simplify:  Simplifying (* (sqrt k) (pow (+ 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 (+ PI PI) (/ k 2)) (sqrt k))
* [exit]simplify:  Simplified to (* (pow (+ PI PI) (/ k 2)) (sqrt k))
* * * * [misc]progress:  [ 70 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (log1p (expm1 (* n (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ 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:  [ 71 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (expm1 (log1p (* n (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ 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:  [ 72 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (pow (* n (+ PI PI)) 1) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 73 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (exp (log (* n (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ 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:  [ 74 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (log (exp (* n (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ 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:  [ 75 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* (* (cbrt (* n (+ PI PI))) (cbrt (* n (+ PI PI)))) (cbrt (* n (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ 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:  [ 76 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (cbrt (* (* (* n (+ PI PI)) (* n (+ PI PI))) (* n (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ 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:  [ 77 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* (sqrt (* n (+ PI PI))) (sqrt (* n (+ PI PI)))) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ 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:  [ 78 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* 1 (* n (+ PI PI))) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 79 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (+ (* n PI) (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI 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:  [ 80 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (+ (* PI n) (* PI n)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 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:  [ 81 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* (* n (* (cbrt (+ PI PI)) (cbrt (+ PI PI)))) (cbrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ 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:  [ 82 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* (* n (sqrt (+ PI PI))) (sqrt (+ PI PI))) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ 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:  [ 83 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* (* n 1) (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ 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:  [ 84 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI 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:  [ 85 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (/ (* n (+ (pow PI 3) (pow PI 3))) (+ (* PI PI) (- (* PI PI) (* PI PI)))) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ 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:  [ 86 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (/ (* n (- (* PI PI) (* PI PI))) (- PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ 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:  [ 87 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 88 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (log1p (expm1 (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ 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:  [ 89 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (expm1 (log1p (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ 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:  [ 90 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (exp (* (log (* n (+ PI PI))) (/ (- 1 k) 2))) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ 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:  [ 91 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (exp (* (log (* n (+ PI PI))) (/ (- 1 k) 2))) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ 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:  [ 92 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (* 1 (/ (- 1 k) 2))) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 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:  [ 93 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (/ (pow (* n (+ PI PI)) (/ 1 2)) (pow (* n (+ PI PI)) (/ k 2))) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 1 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:  [ 94 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (pow (* n (+ PI PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 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:  [ 95 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (pow (* n (+ PI PI)) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 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:  [ 96 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (pow (* n (+ PI PI)) 1) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ 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:  [ 97 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (pow (* n (+ PI PI)) (- 1 k)) (/ 1 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 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:  [ 98 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (* (pow n (/ (- 1 k) 2)) (pow (+ PI PI) (/ (- 1 k) 2))) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (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:  [ 99 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (pow (* n (+ PI PI)) (/ (- 1 k) 2)) 1) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 100 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (exp (log (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ 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:  [ 101 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (log (exp (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ 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:  [ 102 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (* (* (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))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ 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:  [ 103 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (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 (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ 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:  [ 104 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (* (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt (pow (* n (+ PI PI)) (/ (- 1 k) 2)))) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ 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:  [ 105 / 117 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (* 1 (pow (* n (+ PI PI)) (/ (- 1 k) 2))) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 106 / 117 ] simplifiying candidate #<alt-event (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (- (+ (pow (* 2 PI) 1/2) (* 1/8 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (* (pow k 2) (sqrt 2)))))) (* 1/2 (* (sqrt PI) (* (log (* 2 PI)) (* k (sqrt 2)))))) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (- (+ (pow (* 2 PI) 1/2) (* 1/8 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (* (pow k 2) (sqrt 2)))))) (* 1/2 (* (sqrt PI) (* (log (* 2 PI)) (* k (sqrt 2)))))) (sqrt k))))
* * [misc]simplify:  iters left: 6 (39 enodes)
* * [misc]simplify:  iters left: 5 (77 enodes)
* * [misc]simplify:  iters left: 4 (127 enodes)
* * [misc]simplify:  iters left: 3 (243 enodes)
* [exit]simplify:  Simplified to (* (* (sqrt (/ (pow n (/ (- 1 k) 2)) 1)) (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (- (* (* (* 1/8 (sqrt PI)) (* (sqrt 2) (* k k))) (* (log (+ PI PI)) (log (+ PI PI)))) (fma (* 1/2 (* (sqrt PI) (sqrt 2))) (* (log (+ PI PI)) k) (- (sqrt (+ PI PI))))) (sqrt k))))
* * * * [misc]progress:  [ 107 / 117 ] simplifiying candidate #<alt-event (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt k))))
* * [misc]simplify:  iters left: 6 (26 enodes)
* * [misc]simplify:  iters left: 5 (48 enodes)
* * [misc]simplify:  iters left: 4 (72 enodes)
* * [misc]simplify:  iters left: 3 (99 enodes)
* * [misc]simplify:  iters left: 2 (165 enodes)
* * [misc]simplify:  iters left: 1 (203 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (sqrt (+ PI PI)) (- 1 k)) (sqrt k))) (* (sqrt (/ (pow n (/ (- 1 k) 2)) 1)) (sqrt (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (sqrt k)))))
* * * * [misc]progress:  [ 108 / 117 ] simplifiying candidate #<alt-event (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt k))))
* * [misc]simplify:  iters left: 6 (26 enodes)
* * [misc]simplify:  iters left: 5 (48 enodes)
* * [misc]simplify:  iters left: 4 (72 enodes)
* * [misc]simplify:  iters left: 3 (99 enodes)
* * [misc]simplify:  iters left: 2 (165 enodes)
* * [misc]simplify:  iters left: 1 (203 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (sqrt (+ PI PI)) (- 1 k)) (sqrt k))) (* (sqrt (/ (pow n (/ (- 1 k) 2)) 1)) (sqrt (/ (pow (* (+ PI PI) n) (/ (- 1 k) 2)) (sqrt k)))))
* * * * [misc]progress:  [ 109 / 117 ] simplifiying candidate #<alt-event (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (+ (* +nan.0 (* (sqrt PI) (* k (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (* k (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt PI) (/ (sqrt 2) k))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (* k (sqrt 2))))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2))))))))))))))))))>
* [enter]simplify:  Simplifying (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (+ (* +nan.0 (* (sqrt PI) (* k (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (* k (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt PI) (/ (sqrt 2) k))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (* k (sqrt 2))))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2)))))))))))))))))
* * * * [misc]progress:  [ 110 / 117 ] simplifiying candidate #<alt-event (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k))))))))))>
* [enter]simplify:  Simplifying (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)))))))))
* * * * [misc]progress:  [ 111 / 117 ] simplifiying candidate #<alt-event (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k))))))))))>
* [enter]simplify:  Simplifying (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)))))))))
* * * * [misc]progress:  [ 112 / 117 ] simplifiying candidate #<alt-event (λ (k n) (* (* (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (* (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (22 enodes)
* * [misc]simplify:  iters left: 5 (35 enodes)
* * [misc]simplify:  iters left: 4 (45 enodes)
* * [misc]simplify:  iters left: 3 (51 enodes)
* * [misc]simplify:  iters left: 2 (53 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))) (* (sqrt (/ (pow n (/ (- 1 k) 2)) 1)) (sqrt (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k)))))
* * * * [misc]progress:  [ 113 / 117 ] simplifiying candidate #<alt-event (λ (k n) (* (* (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (* (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (22 enodes)
* * [misc]simplify:  iters left: 5 (35 enodes)
* * [misc]simplify:  iters left: 4 (45 enodes)
* * [misc]simplify:  iters left: 3 (51 enodes)
* * [misc]simplify:  iters left: 2 (53 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))) (* (sqrt (/ (pow n (/ (- 1 k) 2)) 1)) (sqrt (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k)))))
* * * * [misc]progress:  [ 114 / 117 ] simplifiying candidate #<alt-event (λ (k n) (* (* (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (* (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (22 enodes)
* * [misc]simplify:  iters left: 5 (35 enodes)
* * [misc]simplify:  iters left: 4 (45 enodes)
* * [misc]simplify:  iters left: 3 (51 enodes)
* * [misc]simplify:  iters left: 2 (53 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))) (* (sqrt (/ (pow n (/ (- 1 k) 2)) 1)) (sqrt (/ (pow (* PI (+ n n)) (/ (- 1 k) 2)) (sqrt k)))))
* * * * [misc]progress:  [ 115 / 117 ] simplifiying candidate #<alt-event (λ (k n) (* (* (sqrt (/ (- (+ (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))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (* (sqrt (/ (- (+ (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))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (52 enodes)
* * [misc]simplify:  iters left: 5 (117 enodes)
* * [misc]simplify:  iters left: 4 (229 enodes)
* * [misc]simplify:  iters left: 3 (494 enodes)
* [exit]simplify:  Simplified to (* (* (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (- (fma (* k k) (* (* 1/8 (* (pow (+ PI PI) 1/2) (sqrt n))) (+ (* (log n) (log n)) (* (log (+ PI PI)) (log (+ PI PI))))) (* (* (* (log (+ PI PI)) (* (* k k) (log n))) (* (pow (+ PI PI) 1/2) (sqrt n))) 1/4)) (fma (* (* (pow (+ PI PI) 1/2) (sqrt n)) (fma k (log (+ PI PI)) (* (log n) k))) 1/2 (- (* (pow (+ PI PI) 1/2) (sqrt n))))) (sqrt k))))
* * * * [misc]progress:  [ 116 / 117 ] simplifiying candidate #<alt-event (λ (k n) (* (* (sqrt (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (* (sqrt (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (28 enodes)
* * [misc]simplify:  iters left: 5 (49 enodes)
* * [misc]simplify:  iters left: 4 (60 enodes)
* * [misc]simplify:  iters left: 3 (87 enodes)
* * [misc]simplify:  iters left: 2 (135 enodes)
* * [misc]simplify:  iters left: 1 (239 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (exp (* (* (- 1 k) 1/2) (- (log (+ PI PI)) (- (log n))))) (sqrt k))) (* (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))))
* * * * [misc]progress:  [ 117 / 117 ] simplifiying candidate #<alt-event (λ (k n) (* (* (sqrt (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (* (sqrt (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (30 enodes)
* * [misc]simplify:  iters left: 5 (51 enodes)
* * [misc]simplify:  iters left: 4 (63 enodes)
* * [misc]simplify:  iters left: 3 (90 enodes)
* * [misc]simplify:  iters left: 2 (138 enodes)
* * [misc]simplify:  iters left: 1 (203 enodes)
* [exit]simplify:  Simplified to (* (* (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (exp (* (- (log (* PI -2)) (log (/ -1 n))) (* (- 1 k) 1/2))) (sqrt k))))
* * * [misc]progress:  adding candidates to table
* [misc]progress:  [Phase 3 of 3] Extracting.
* * [misc]regime-changes:  Finding splitpoints for: (#<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-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)))))> #<alt-delta (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (+ 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 (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (+ PI PI) (/ (- 1 k) 2)) (sqrt k)))))> #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k))) (* (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt k)))))) (cbrt (sqrt (/ (pow (* n (+ PI PI)) (/ (- 1 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) (/ (pow (* (* n (sqrt (+ PI PI))) (sqrt (+ 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)))))> #<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)))))> #<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) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))> #<alt-delta (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (+ PI PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))))> #<alt-delta (λ (k n) (/ (pow (* n (+ PI PI)) (/ 1 2)) (* (sqrt k) (pow (* n (+ PI PI)) (/ k 2)))))>)
* [misc]regimes:  Found splitpoints: (#s(sp 0 k +inf.0)) , with alts (#<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)