* [misc]progress:  [Phase 1 of 3] Setting up.
* * * [misc]progress:  [1/2] Preparing points
* * * * [misc]points:  Sampling 256 additional inputs, on iter 0 have 0 / 256
* * * * [misc]points:  Computing exacts on every 16 of 256 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 64
* * * * [misc]points:  Setting MPFR precision to 320
* * * * [misc]points:  Setting MPFR precision to 576
* * * * [misc]points:  Computing exacts on every 8 of 256 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 320
* * * * [misc]points:  Setting MPFR precision to 576
* * * * [misc]points:  Setting MPFR precision to 832
* * * * [misc]points:  Computing exacts on every 4 of 256 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 576
* * * * [misc]points:  Setting MPFR precision to 832
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Computing exacts on every 2 of 256 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 832
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 256 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 208 additional inputs, on iter 1 have 48 / 256
* * * * [misc]points:  Computing exacts on every 13 of 208 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 6 of 208 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 3 of 208 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 208 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 173 additional inputs, on iter 2 have 83 / 256
* * * * [misc]points:  Computing exacts on every 10 of 173 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 5 of 173 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 173 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 173 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 130 additional inputs, on iter 3 have 126 / 256
* * * * [misc]points:  Computing exacts on every 8 of 130 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 4 of 130 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 130 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 130 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 106 additional inputs, on iter 4 have 150 / 256
* * * * [misc]points:  Computing exacts on every 6 of 106 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 3 of 106 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 106 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 85 additional inputs, on iter 5 have 171 / 256
* * * * [misc]points:  Computing exacts on every 5 of 85 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 85 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 85 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 69 additional inputs, on iter 6 have 187 / 256
* * * * [misc]points:  Computing exacts on every 4 of 69 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 69 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 69 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 52 additional inputs, on iter 7 have 204 / 256
* * * * [misc]points:  Computing exacts on every 3 of 52 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 52 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 43 additional inputs, on iter 8 have 213 / 256
* * * * [misc]points:  Computing exacts on every 2 of 43 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 43 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 40 additional inputs, on iter 9 have 216 / 256
* * * * [misc]points:  Computing exacts on every 2 of 40 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 40 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 33 additional inputs, on iter 10 have 223 / 256
* * * * [misc]points:  Computing exacts on every 2 of 33 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 33 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 23 additional inputs, on iter 11 have 233 / 256
* * * * [misc]points:  Computing exacts for 23 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 20 additional inputs, on iter 12 have 236 / 256
* * * * [misc]points:  Computing exacts for 20 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 15 additional inputs, on iter 13 have 241 / 256
* * * * [misc]points:  Computing exacts for 15 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 14 additional inputs, on iter 14 have 242 / 256
* * * * [misc]points:  Computing exacts for 14 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 11 additional inputs, on iter 15 have 245 / 256
* * * * [misc]points:  Computing exacts for 11 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 7 additional inputs, on iter 16 have 249 / 256
* * * * [misc]points:  Computing exacts for 7 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 6 additional inputs, on iter 17 have 250 / 256
* * * * [misc]points:  Computing exacts for 6 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 18 have 253 / 256
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 19 have 254 / 256
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [exit]points:  Sampled 257 points with exact outputs
* * * [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 (27 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (52 enodes)
* * [misc]simplify:  iters left: 2 (56 enodes)
* * [misc]simplify:  iters left: 1 (63 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))
* * [misc]progress:  iteration 1 / 4
* * * [misc]progress:  picking best candidate
* * * * [misc]pick:  Picked  #<alt (λ (k n) (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 3 ] rewriting at (2 1)
* * * * [misc]progress:  [ 2 / 3 ] rewriting at (2)
* * * * [misc]progress:  [ 3 / 3 ] rewriting at (2 1 1)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 3 ] generating series at (2 1)
* [misc]approximate:  Taking taylor expansion of (pow (* (* n 2) PI) (/ (- 1 k) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* n 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* n 2) 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 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* n 2) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [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 (* n 2) into (* 2 n)
* [misc]backup-simplify:  Simplify (* (* 2 n) PI) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* n 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* n 2) 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 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* n 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* n 2) 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 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
* [misc]taylor:  Taking taylor expansion of (- 1 k) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of (log (* 2 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]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
* [misc]backup-simplify:  Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
* [misc]approximate:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 2) 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) 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 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 (* (/ 1 n) 2) into (/ 2 n)
* [misc]backup-simplify:  Simplify (* (/ 2 n) PI) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 2) PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 2) 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) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 2) 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) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 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)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 2) 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)) 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 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 (* (/ -1 n) 2) into (/ -2 n)
* [misc]backup-simplify:  Simplify (* (/ -2 n) PI) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 2) PI)))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 2) 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 k) 1)
* [misc]backup-simplify:  Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1))
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 2) 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 k) 1)
* [misc]backup-simplify:  Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1))
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (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) 1) (- (log (* -2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (+ (/ 1 k) 1) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 1 in k
* [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 (+ 1 0) 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 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (+ (/ 1 k) 1)) (/ 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) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (+ (/ 1 k) 1)) (/ 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) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (+ (/ 1 k) 1)) (/ 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) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
* * * * [misc]progress:  [ 2 / 3 ] generating series at (2)
* [misc]approximate:  Taking taylor expansion of (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* n 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* n 2) 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 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* n 2) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [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 (* n 2) into (* 2 n)
* [misc]backup-simplify:  Simplify (* (* 2 n) PI) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ (pow (* 2 (* n PI)) 1/2) +nan.0) into (* +nan.0 (sqrt (* PI (* n 2))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* n 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* n 2) 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 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt k)) into (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* n 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* n 2) 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 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt k)) into (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
* [misc]taylor:  Taking taylor expansion of (- 1 k) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of (log (* 2 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]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (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 (+ (log n) (log (* 2 PI))))) 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) (/ 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 (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) (/ 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 (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) (/ 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 (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
* [misc]approximate:  Taking taylor expansion of (/ (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 2) 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) 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 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 (* (/ 1 n) 2) into (/ 2 n)
* [misc]backup-simplify:  Simplify (* (/ 2 n) PI) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 2) 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]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 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) 2) PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 2) 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) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) 2) 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) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 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)))))) k)) (- (+ (* +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))))))))
* [misc]approximate:  Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 2) 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)) 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 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 (* (/ -1 n) 2) into (/ -2 n)
* [misc]backup-simplify:  Simplify (* (/ -2 n) PI) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 2) PI)))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
* [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 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 2) 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 k) 1)
* [misc]backup-simplify:  Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1))
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (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 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) 2) 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 k) 1)
* [misc]backup-simplify:  Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1))
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (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 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
* [misc]taylor:  Taking taylor expansion of (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (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) 1) (- (log (* -2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (+ (/ 1 k) 1) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 1 in k
* [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 (+ 1 0) 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 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (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 k) 1) (- (log (* -2 PI)) (log n))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (+ (/ 1 k) 1)) (/ 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) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (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 k) 1) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (+ (/ 1 k) 1)) (/ 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) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (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 k) 1) (- (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 k) 1) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (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)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
* * * * [misc]progress:  [ 3 / 3 ] generating series at (2 1 1)
* [misc]approximate:  Taking taylor expansion of (* (* n 2) PI) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) n) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
* * * [misc]progress:  simplifying candidates
* * * * [misc]progress:  [ 1 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (log1p (expm1 (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 2 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (expm1 (log1p (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 3 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* (* n 2) PI)) (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* (* n 2) PI)) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (58 enodes)
* * [misc]simplify:  iters left: 3 (145 enodes)
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* (* n 2) PI)))
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (exp (* (/ (- 1 k) 2) (log (* (* n 2) PI)))) (sqrt k)))
* * * * [misc]progress:  [ 4 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* (* n 2) PI)) (/ (- 1 k) 2))) (sqrt k)))>
* * * * [misc]progress:  [ 5 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (* 1 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n 2) PI)
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* * [misc]simplify:  iters left: 2 (15 enodes)
* * [misc]simplify:  iters left: 1 (17 enodes)
* [exit]simplify:  Simplified to (* (* n 2) PI)
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (pow (* (* n 2) PI) (* 1 (/ (- 1 k) 2))) (sqrt k)))
* * * * [misc]progress:  [ 6 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* (* n 2) PI) (/ k 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (18 enodes)
* * [misc]simplify:  iters left: 2 (20 enodes)
* [exit]simplify:  Simplified to (pow (* n (* PI 2)) (/ k 2))
* [misc]simplify:  Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 7 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (cbrt (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (cbrt (/ (- 1 k) 2))
* [misc]simplify:  Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* (* n 2) PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))) (sqrt k)))
* * * * [misc]progress:  [ 8 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (- 1 k) 2))
* [misc]simplify:  Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* (* n 2) PI) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (sqrt k)))
* * * * [misc]progress:  [ 9 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (- 1 k) 2)
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (12 enodes)
* * [misc]simplify:  iters left: 2 (15 enodes)
* * [misc]simplify:  iters left: 1 (17 enodes)
* [exit]simplify:  Simplified to (/ (- 1 k) 2)
* [misc]simplify:  Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 10 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) (- 1 k)) (/ 1 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (/ 1 2)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (5 enodes)
* [exit]simplify:  Simplified to (/ 1 2)
* [misc]simplify:  Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* (* n 2) PI) (- 1 k)) (/ 1 2)) (sqrt k)))
* * * * [misc]progress:  [ 11 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n 2) (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n 2) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (21 enodes)
* [exit]simplify:  Simplified to (pow (* n 2) (/ (- 1 k) 2))
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (* (pow (* n 2) (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (sqrt k)))
* * * * [misc]progress:  [ 12 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) (/ (- 1 k) 2)) 1) (sqrt k)))>
* * * * [misc]progress:  [ 13 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 14 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 15 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 16 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 17 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 18 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt k)))>
* * * * [misc]progress:  [ 19 / 74 ] simplifiying candidate #<alt (λ (k n) (log1p (expm1 (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 20 / 74 ] simplifiying candidate #<alt (λ (k n) (expm1 (log1p (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 21 / 74 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) 1))>
* * * * [misc]progress:  [ 22 / 74 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* (* n 2) PI)) (/ (- 1 k) 2)) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (* (log (* (* n 2) PI)) (/ (- 1 k) 2)) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (34 enodes)
* * [misc]simplify:  iters left: 4 (66 enodes)
* * [misc]simplify:  iters left: 3 (166 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 23 / 74 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* (* n 2) PI)) (/ (- 1 k) 2)) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (* (log (* (* n 2) PI)) (/ (- 1 k) 2)) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (34 enodes)
* * [misc]simplify:  iters left: 4 (66 enodes)
* * [misc]simplify:  iters left: 3 (166 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 24 / 74 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (pow (* (* n 2) PI) (/ (- 1 k) 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (log (pow (* (* n 2) PI) (/ (- 1 k) 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (50 enodes)
* * [misc]simplify:  iters left: 3 (98 enodes)
* * [misc]simplify:  iters left: 2 (302 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* (* n 2) PI)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (/ (- 1 k) 2) (log (* (* n 2) PI)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 25 / 74 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 26 / 74 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 27 / 74 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (71 enodes)
* * [misc]simplify:  iters left: 3 (122 enodes)
* * [misc]simplify:  iters left: 2 (191 enodes)
* * [misc]simplify:  iters left: 1 (301 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (* k (sqrt k)) (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (cbrt (/ (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (* k (sqrt k)) (pow (* n (* PI 2)) (/ (- 1 k) 2))))))
* * * * [misc]progress:  [ 28 / 74 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 29 / 74 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 30 / 74 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 31 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (- (pow (* (* n 2) PI) (/ (- 1 k) 2))) (- (sqrt k))))>
* * * * [misc]progress:  [ 32 / 74 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* n 2) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (27 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n 2) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (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 (17 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 33 / 74 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow PI (/ (- 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 (17 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 34 / 74 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) 1) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow (* n 2) (/ (- 1 k) 2)) 1)
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (pow (* n 2) (/ (- 1 k) 2))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (pow (* n 2) (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow PI (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* * [misc]simplify:  iters left: 3 (21 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (pow (* n 2) (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 35 / 74 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) 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 (51 enodes)
* * [misc]simplify:  iters left: 3 (57 enodes)
* * [misc]simplify:  iters left: 2 (60 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* (* n 2) 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 (34 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 36 / 74 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) 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 (39 enodes)
* * [misc]simplify:  iters left: 3 (44 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* (* n 2) 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 (34 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 37 / 74 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) 1) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) 1)
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (41 enodes)
* * [misc]simplify:  iters left: 3 (49 enodes)
* * [misc]simplify:  iters left: 2 (60 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* (* n 2) 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 (33 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt k))))
* * * * [misc]progress:  [ 38 / 74 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* (* n 2) 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 (37 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* (* n 2) 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 (34 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 39 / 74 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* (* n 2) 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 (34 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* (* n 2) 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 (34 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 40 / 74 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) 1) (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) 1)
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* (* n 2) 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 (33 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt k))))
* * * * [misc]progress:  [ 41 / 74 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n 2) 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)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (pow (* (* n 2) 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 (33 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 42 / 74 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n 2) 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)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (pow (* (* n 2) 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 (33 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 43 / 74 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ (pow (* (* n 2) 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
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* 1 (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow (* (* n 2) 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 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 44 / 74 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))))>
* * * * [misc]progress:  [ 45 / 74 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
* * * * [misc]progress:  [ 46 / 74 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))>
* * * * [misc]progress:  [ 47 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
* [enter]simplify:  Simplifying (cbrt (sqrt k))
* * [misc]simplify:  iters left: 2 (3 enodes)
* [exit]simplify:  Simplified to (cbrt (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 48 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k))))>
* [enter]simplify:  Simplifying (sqrt (sqrt k))
* * [misc]simplify:  iters left: 2 (3 enodes)
* [exit]simplify:  Simplified to (sqrt (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 49 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) 1) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt k)
* * [misc]simplify:  iters left: 1 (2 enodes)
* [exit]simplify:  Simplified to (sqrt k)
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) 1) (sqrt k)))
* * * * [misc]progress:  [ 50 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n 2) (/ (- 1 k) 2)) (/ (sqrt k) (pow PI (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (pow (* n 2) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (21 enodes)
* [exit]simplify:  Simplified to (pow (* n 2) (/ (- 1 k) 2))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (pow (* n 2) (/ (- 1 k) 2)) (/ (sqrt k) (pow PI (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 51 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (/ (sqrt k) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (/ (sqrt k) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))))
* * * * [misc]progress:  [ 52 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* 2 (* PI n)) (/ (- 1 k) 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (sqrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))))
* * * * [misc]progress:  [ 53 / 74 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))>
* * * * [misc]progress:  [ 54 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (/ 1 2)) (* (sqrt k) (pow (* (* n 2) PI) (/ k 2)))))>
* [enter]simplify:  Simplifying (pow (* (* n 2) PI) (/ 1 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* [exit]simplify:  Simplified to (pow (* n (* PI 2)) (/ 1 2))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* (* n 2) PI) (/ k 2)))))
* * * * [misc]progress:  [ 55 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log1p (expm1 (* (* n 2) PI))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 56 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (pow (expm1 (log1p (* (* n 2) PI))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 57 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 58 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (log (* (* n 2) PI))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 59 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log (exp (* (* n 2) PI))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 60 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 61 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 62 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 63 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* (* n 2) PI)) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 64 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 65 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 66 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) (sqrt k)))>
* [enter]simplify:  Simplifying (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
* * [misc]simplify:  iters left: 6 (37 enodes)
* * [misc]simplify:  iters left: 5 (108 enodes)
* * [misc]simplify:  iters left: 4 (367 enodes)
* [exit]simplify:  Simplified to (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4)) (* (* k k) (log n)) (- (fma (* (* (log (* PI 2)) 1/8) (* (log (* PI 2)) (* k k))) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)))) (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) 1/2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4)) (* (* k k) (log n)) (- (fma (* (* (log (* PI 2)) 1/8) (* (log (* PI 2)) (* k k))) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)))) (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) 1/2))) (sqrt k)))
* * * * [misc]progress:  [ 67 / 74 ] simplifiying candidate #<alt (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))))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (35 enodes)
* * [misc]simplify:  iters left: 4 (76 enodes)
* * [misc]simplify:  iters left: 3 (274 enodes)
* [exit]simplify:  Simplified to (pow (exp (- 1/2 (* 1/2 k))) (+ (log (* 2 PI)) (log n)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (pow (exp (- 1/2 (* 1/2 k))) (+ (log (* 2 PI)) (log n))) (sqrt k)))
* * * * [misc]progress:  [ 68 / 74 ] simplifiying candidate #<alt (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))))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (35 enodes)
* * [misc]simplify:  iters left: 4 (76 enodes)
* * [misc]simplify:  iters left: 3 (280 enodes)
* [exit]simplify:  Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k)))
* * * * [misc]progress:  [ 69 / 74 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
* [misc]simplify:  Simplified (2) to (λ (k n) +nan.0)
* * * * [misc]progress:  [ 70 / 74 ] simplifiying candidate #<alt (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)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))))>
* [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)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
* [misc]simplify:  Simplified (2) to (λ (k n) +nan.0)
* * * * [misc]progress:  [ 71 / 74 ] simplifiying candidate #<alt (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)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))>
* [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)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
* [misc]simplify:  Simplified (2) to (λ (k n) +nan.0)
* * * * [misc]progress:  [ 72 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* 2 (* n PI))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* * [misc]simplify:  iters left: 2 (15 enodes)
* * [misc]simplify:  iters left: 1 (17 enodes)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 73 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* 2 (* n PI))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* * [misc]simplify:  iters left: 2 (15 enodes)
* * [misc]simplify:  iters left: 1 (17 enodes)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 74 / 74 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* 2 (* n PI))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* * [misc]simplify:  iters left: 2 (15 enodes)
* * [misc]simplify:  iters left: 1 (17 enodes)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))
* * * [misc]progress:  adding candidates to table
* * [misc]progress:  iteration 2 / 4
* * * [misc]progress:  picking best candidate
* * * * [misc]pick:  Picked  #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 4 ] rewriting at (2 1 1)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2 1 2)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2 1 2 1)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 4 ] generating series at (2 1 1)
* [misc]approximate:  Taking taylor expansion of (pow (* (* n 2) PI) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* n 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* n 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* n 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* n 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]approximate:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 n) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 n) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 n) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 n) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n)))))
* [misc]approximate:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 (- n)) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 (- n)) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* -2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* -2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* -2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 1)))) 24) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* -2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* -2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* -2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* -2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* -2 PI) 1)))) 120) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* -2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* -2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* -2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* -2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* -2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* -2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* -2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* -2 PI) 1)))) 720) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n)))))
* * * * [misc]progress:  [ 2 / 4 ] generating series at (2 1 2)
* [misc]approximate:  Taking taylor expansion of (pow (* (* n 2) PI) (/ k 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ k 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* (* n 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* (* n 2) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* n 2) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [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 (* n 2) into (* 2 n)
* [misc]backup-simplify:  Simplify (* (* 2 n) PI) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp 0) into 1
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* (* n 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* (* n 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (* 1/2 k) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (+ (log n) (log (* 2 PI))) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* (* n 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* (* n 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (* 1/2 k) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (+ (log n) (log (* 2 PI))) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ (log n) (log (* 2 PI))) k) in k
* [misc]taylor:  Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of (log (* 2 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 k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (+ (log n) (log (* 2 PI))) 0) into 0
* [misc]backup-simplify:  Simplify (* 1/2 0) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log n) (log (* 2 PI))) 1) (* 0 0)) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (+ (log n) (log (* 2 PI)))) (* 0 0)) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp 0) into 1
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1) 1)))) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (+ (* 0 1) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (+ (log n) (log (* 2 PI)))) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))
* [misc]backup-simplify:  Simplify (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))) into (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))) (pow (* k 1) 2)) (+ (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (* k 1)) 1)) into (+ (* 1/8 (* (pow (log n) 2) (pow k 2))) (+ (* 1/8 (* (pow k 2) (pow (log (* 2 PI)) 2))) (+ (* 1/2 (* k (log (* 2 PI)))) (+ (* 1/4 (* (pow k 2) (* (log n) (log (* 2 PI))))) (+ (* 1/2 (* (log n) k)) 1)))))
* [misc]approximate:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 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 (* (/ 1 n) 2) into (/ 2 n)
* [misc]backup-simplify:  Simplify (* (/ 2 n) PI) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI)))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k
* [misc]taylor:  Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) into (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k)))
* [misc]approximate:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 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 (* (/ -1 n) 2) into (/ -2 n)
* [misc]backup-simplify:  Simplify (* (/ -2 n) PI) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* -2 (/ PI n)))) into (* -1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI)))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k
* [misc]taylor:  Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k
* [misc]taylor:  Taking taylor expansion of -1/2 in k
* [misc]backup-simplify:  Simplify -1/2 into -1/2
* [misc]taylor:  Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k
* [misc]taylor:  Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* -2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* -2 PI) in k
* [misc]taylor:  Taking taylor expansion of -2 in k
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* -1/2 (- (log (* -2 PI)) (log n))) into (* -1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (- 0) 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)) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))) into (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))
* * * * [misc]progress:  [ 3 / 4 ] generating series at (2)
* [misc]approximate:  Taking taylor expansion of (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ 1 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* n 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* n 2) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* n 2) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [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 (* n 2) into (* 2 n)
* [misc]backup-simplify:  Simplify (* (* 2 n) PI) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ k 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* (* n 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* (* n 2) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* n 2) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [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 (* n 2) into (* 2 n)
* [misc]backup-simplify:  Simplify (* (* 2 n) PI) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp 0) into 1
* [misc]backup-simplify:  Simplify (/ (pow (* 2 (* n PI)) 1/2) 1) into (sqrt (* PI (* n 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 (/ (sqrt (* PI (* n 2))) +nan.0) into (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* n 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* n 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* (* n 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* (* n 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (* 1/2 k) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (+ (log n) (log (* 2 PI))) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) into (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))
* [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 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (sqrt k)) into (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (sqrt (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* n 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* n 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* (* n 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* (* n 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (* 1/2 k) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (+ (log n) (log (* 2 PI))) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) into (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))
* [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 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (sqrt k)) into (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (sqrt (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (+ (log n) (log (* 2 PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (+ (log n) (log (* 2 PI)))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of (log (* 2 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]backup-simplify:  Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ (log n) (log (* 2 PI))) k) in k
* [misc]taylor:  Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of (log (* 2 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 k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (+ (log n) (log (* 2 PI))) 0) into 0
* [misc]backup-simplify:  Simplify (* 1/2 0) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log n) (log (* 2 PI))) 1) (* 0 0)) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (+ (log n) (log (* 2 PI)))) (* 0 0)) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp 0) into 1
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1) into (exp (* 1/2 (+ (log n) (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 (+ (log n) (log (* 2 PI))))) 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (+ (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (sqrt (/ 1 k))) (/ 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 (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1) 1)))) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (/ (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1)))) into (- (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (+ (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) (* 0 (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (sqrt (/ 1 k))) (/ 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 (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (+ (* 0 1) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (+ (log n) (log (* 2 PI)))) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (/ (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))) 1)) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))) (/ (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1)))) into (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (+ (* 1/4 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))) +nan.0) (* (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (+ (* 1/4 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (+ (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) (* 0 (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) (* 0 (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (sqrt (/ 1 k))) (/ 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 (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (+ (log n) (log (* 2 PI)))) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 3) 6)) (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3)))))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (/ (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) 1)) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))) (/ (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))) 1)) (* (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (+ (* 1/4 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))))) (/ (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1)))) into (- (+ (* 1/48 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 3))) (+ (* 1/16 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow (log (* 2 PI)) 2)))) (+ (* 1/16 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (log (* 2 PI))))) (* 1/48 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 3)))))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))) +nan.0) (+ (* (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (+ (* 1/4 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))))) +nan.0) (* (- (+ (* 1/48 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 3))) (+ (* 1/16 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow (log (* 2 PI)) 2)))) (+ (* 1/16 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (log (* 2 PI))))) (* 1/48 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 3))))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
* [misc]approximate:  Taking taylor expansion of (/ (/ (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 n) 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 n) 2) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 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 (* (/ 1 n) 2) into (/ 2 n)
* [misc]backup-simplify:  Simplify (* (/ 2 n) PI) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) 1/2)
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 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 (* (/ 1 n) 2) into (/ 2 n)
* [misc]backup-simplify:  Simplify (* (/ 2 n) PI) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI)))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))
* [misc]backup-simplify:  Simplify (/ (pow (* 2 (/ PI n)) 1/2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) into (* (sqrt (/ (* PI 2) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ (* (sqrt (/ (* PI 2) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) +nan.0) into (* +nan.0 (* (/ (sqrt 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) (sqrt (/ PI n))))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 n) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 n) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt (/ 1 k))) into (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 n) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 n) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt (/ 1 k))) into (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (- (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (- (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k
* [misc]taylor:  Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (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 (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 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 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (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 (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 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 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (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 (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (pow k 3)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (pow k 2)))))))))
* [misc]approximate:  Taking taylor expansion of (/ (/ (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 (- n)) 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 (- n)) 2) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 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 (* (/ -1 n) 2) into (/ -2 n)
* [misc]backup-simplify:  Simplify (* (/ -2 n) PI) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* -2 (/ PI n))))) into (pow (* -2 (/ PI n)) 1/2)
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 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 (* (/ -1 n) 2) into (/ -2 n)
* [misc]backup-simplify:  Simplify (* (/ -2 n) PI) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* -2 (/ PI n)))) into (* -1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI)))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))
* [misc]backup-simplify:  Simplify (/ (pow (* -2 (/ PI n)) 1/2) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) into (* (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) (sqrt (/ (* PI -2) 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 (/ (* (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) (sqrt (/ (* PI -2) n))) +nan.0) into (* +nan.0 (/ (sqrt (* -2 (/ PI n))) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 (- n)) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 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 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 (- n)) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 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 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))
* [misc]taylor:  Taking taylor expansion of (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (- (log (* -2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (- (log (* -2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* -2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* -2 PI) in k
* [misc]taylor:  Taking taylor expansion of -2 in k
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ -1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ -1 k) in k
* [misc]taylor:  Taking taylor expansion of -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]taylor:  Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k
* [misc]taylor:  Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k
* [misc]taylor:  Taking taylor expansion of -1/2 in k
* [misc]backup-simplify:  Simplify -1/2 into -1/2
* [misc]taylor:  Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k
* [misc]taylor:  Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* -2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* -2 PI) in k
* [misc]taylor:  Taking taylor expansion of -2 in k
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* -1/2 (- (log (* -2 PI)) (log n))) into (* -1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (* 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) 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 (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))
* [misc]backup-simplify:  Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (+ (* (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (- 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 (- (log (* -2 PI)) (log n)))) (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) 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 (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))
* [misc]backup-simplify:  Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (+ (* (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))))))))))
* * * * [misc]progress:  [ 4 / 4 ] generating series at (2 1 2 1)
* [misc]approximate:  Taking taylor expansion of (* (* n 2) PI) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) n) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
* * * [misc]progress:  simplifying candidates
* * * * [misc]progress:  [ 1 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (log1p (expm1 (pow (* (* n 2) PI) (/ 1 2)))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 2 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (expm1 (log1p (pow (* (* n 2) PI) (/ 1 2)))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 3 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (exp (* (log (* (* n 2) PI)) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* (* n 2) PI)) (/ 1 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (92 enodes)
* * [misc]simplify:  iters left: 2 (180 enodes)
* * [misc]simplify:  iters left: 1 (389 enodes)
* [exit]simplify:  Simplified to (fma (/ 1 2) (log (* n 2)) (/ (log PI) 2))
* [misc]simplify:  Simplified (2 1 1 1) to (λ (k n) (/ (/ (exp (fma (/ 1 2) (log (* n 2)) (/ (log PI) 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 4 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (exp (* (log (* (* n 2) PI)) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 5 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (* 1 (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n 2) PI)
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* * [misc]simplify:  iters left: 2 (15 enodes)
* * [misc]simplify:  iters left: 1 (17 enodes)
* [exit]simplify:  Simplified to (* (* n 2) PI)
* [misc]simplify:  Simplified (2 1 1 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (* 1 (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 6 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) (cbrt (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (cbrt (/ 1 2))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (6 enodes)
* [exit]simplify:  Simplified to (cbrt (/ 1 2))
* [misc]simplify:  Simplified (2 1 1 2) to (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) (cbrt (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 7 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) (sqrt (/ 1 2))) (sqrt (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (/ 1 2))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (6 enodes)
* [exit]simplify:  Simplified to (sqrt (/ 1 2))
* [misc]simplify:  Simplified (2 1 1 2) to (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) (sqrt (/ 1 2))) (sqrt (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 8 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) 1) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ 1 2)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (5 enodes)
* [exit]simplify:  Simplified to (/ 1 2)
* [misc]simplify:  Simplified (2 1 1 2) to (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) 1) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 9 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) 1) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ 1 2)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (5 enodes)
* [exit]simplify:  Simplified to (/ 1 2)
* [misc]simplify:  Simplified (2 1 1 2) to (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) 1) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 10 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (pow (* n 2) (/ 1 2)) (pow PI (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n 2) (/ 1 2))
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (9 enodes)
* [exit]simplify:  Simplified to (pow (* n 2) (/ 1 2))
* [misc]simplify:  Simplified (2 1 1 1) to (λ (k n) (/ (/ (* (pow (* n 2) (/ 1 2)) (pow PI (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 11 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) (/ 1 2)) 1) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 12 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (exp (log (pow (* (* n 2) PI) (/ 1 2)))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 13 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (log (exp (pow (* (* n 2) PI) (/ 1 2)))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 14 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 15 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (cbrt (* (* (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ 1 2)))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 16 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 17 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* 1 (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 18 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (log1p (expm1 (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 19 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (expm1 (log1p (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 20 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (exp (* (log (* (* n 2) PI)) (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* (* n 2) PI)) (/ k 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (82 enodes)
* * [misc]simplify:  iters left: 2 (143 enodes)
* * [misc]simplify:  iters left: 1 (209 enodes)
* [exit]simplify:  Simplified to (fma (/ k 2) (log (* PI 2)) (* (log n) (/ k 2)))
* [misc]simplify:  Simplified (2 1 2 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (exp (fma (/ k 2) (log (* PI 2)) (* (log n) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 21 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (exp (* (log (* (* n 2) PI)) (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 22 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (* 1 (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n 2) PI)
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* * [misc]simplify:  iters left: 2 (15 enodes)
* * [misc]simplify:  iters left: 1 (17 enodes)
* [exit]simplify:  Simplified to (* (* n 2) PI)
* [misc]simplify:  Simplified (2 1 2 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (* 1 (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 23 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (pow (* (* n 2) PI) (* (cbrt (/ k 2)) (cbrt (/ k 2)))) (cbrt (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (cbrt (/ k 2))
* * [misc]simplify:  iters left: 3 (4 enodes)
* [exit]simplify:  Simplified to (cbrt (/ k 2))
* [misc]simplify:  Simplified (2 1 2 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (pow (* (* n 2) PI) (* (cbrt (/ k 2)) (cbrt (/ k 2)))) (cbrt (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 24 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (pow (* (* n 2) PI) (sqrt (/ k 2))) (sqrt (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (/ k 2))
* * [misc]simplify:  iters left: 3 (4 enodes)
* [exit]simplify:  Simplified to (sqrt (/ k 2))
* [misc]simplify:  Simplified (2 1 2 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (pow (* (* n 2) PI) (sqrt (/ k 2))) (sqrt (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 25 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (pow (* (* n 2) PI) 1) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ k 2)
* * [misc]simplify:  iters left: 2 (3 enodes)
* [exit]simplify:  Simplified to (/ k 2)
* [misc]simplify:  Simplified (2 1 2 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (pow (* (* n 2) PI) 1) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 26 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (pow (* (* n 2) PI) k) (/ 1 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ 1 2)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (5 enodes)
* [exit]simplify:  Simplified to (/ 1 2)
* [misc]simplify:  Simplified (2 1 2 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (pow (* (* n 2) PI) k) (/ 1 2))) (sqrt k)))
* * * * [misc]progress:  [ 27 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n 2) (/ k 2))
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (pow (* n 2) (/ k 2))
* [misc]simplify:  Simplified (2 1 2 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 28 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (pow (* (* n 2) PI) (/ k 2)) 1)) (sqrt k)))>
* * * * [misc]progress:  [ 29 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (exp (log (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 30 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (log (exp (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 31 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 32 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (cbrt (* (* (pow (* (* n 2) PI) (/ k 2)) (pow (* (* n 2) PI) (/ k 2))) (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 33 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (sqrt (pow (* (* n 2) PI) (/ k 2))) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 34 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* 1 (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 35 / 165 ] simplifiying candidate #<alt (λ (k n) (log1p (expm1 (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))))>
* * * * [misc]progress:  [ 36 / 165 ] simplifiying candidate #<alt (λ (k n) (expm1 (log1p (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))))>
* * * * [misc]progress:  [ 37 / 165 ] simplifiying candidate #<alt (λ (k n) (pow (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)) 1))>
* * * * [misc]progress:  [ 38 / 165 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (* (log (* (* n 2) PI)) (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (* (log (* (* n 2) PI)) (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (97 enodes)
* * [misc]simplify:  iters left: 3 (306 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 39 / 165 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (* (log (* (* n 2) PI)) (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (* (log (* (* n 2) PI)) (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (97 enodes)
* * [misc]simplify:  iters left: 3 (306 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 40 / 165 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (log (pow (* (* n 2) PI) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (log (pow (* (* n 2) PI) (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (87 enodes)
* * [misc]simplify:  iters left: 3 (281 enodes)
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 41 / 165 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (* (log (* (* n 2) PI)) (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (* (log (* (* n 2) PI)) (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (97 enodes)
* * [misc]simplify:  iters left: 3 (306 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 42 / 165 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (* (log (* (* n 2) PI)) (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (* (log (* (* n 2) PI)) (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (97 enodes)
* * [misc]simplify:  iters left: 3 (306 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 43 / 165 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (log (pow (* (* n 2) PI) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (log (pow (* (* n 2) PI) (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (87 enodes)
* * [misc]simplify:  iters left: 3 (281 enodes)
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 44 / 165 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (log (pow (* (* n 2) PI) (/ 1 2))) (* (log (* (* n 2) PI)) (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (log (pow (* (* n 2) PI) (/ 1 2))) (* (log (* (* n 2) PI)) (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (90 enodes)
* * [misc]simplify:  iters left: 3 (260 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 45 / 165 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (log (pow (* (* n 2) PI) (/ 1 2))) (* (log (* (* n 2) PI)) (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (log (pow (* (* n 2) PI) (/ 1 2))) (* (log (* (* n 2) PI)) (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (90 enodes)
* * [misc]simplify:  iters left: 3 (260 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 46 / 165 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (log (pow (* (* n 2) PI) (/ 1 2))) (log (pow (* (* n 2) PI) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (log (pow (* (* n 2) PI) (/ 1 2))) (log (pow (* (* n 2) PI) (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (70 enodes)
* * [misc]simplify:  iters left: 3 (206 enodes)
* [exit]simplify:  Simplified to (fma (log (* n (* PI 2))) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* n (* PI 2))) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 47 / 165 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (log (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (89 enodes)
* * [misc]simplify:  iters left: 2 (283 enodes)
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 48 / 165 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))))>
* * * * [misc]progress:  [ 49 / 165 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))))>
* * * * [misc]progress:  [ 50 / 165 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (/ (* (* (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ 1 2))) (* (* (pow (* (* n 2) PI) (/ k 2)) (pow (* (* n 2) PI) (/ k 2))) (pow (* (* n 2) PI) (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (* (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ 1 2))) (* (* (pow (* (* n 2) PI) (/ k 2)) (pow (* (* n 2) PI) (/ k 2))) (pow (* (* n 2) PI) (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (113 enodes)
* * [misc]simplify:  iters left: 3 (390 enodes)
* [exit]simplify:  Simplified to (/ (* (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (/ (* k (sqrt k)) (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (cbrt (/ (* (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (/ (* k (sqrt k)) (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))))))
* * * * [misc]progress:  [ 51 / 165 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (* (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (39 enodes)
* * [misc]simplify:  iters left: 4 (96 enodes)
* * [misc]simplify:  iters left: 3 (266 enodes)
* [exit]simplify:  Simplified to (* (* (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (* k (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (cbrt (* (* (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (* k (sqrt k))))))
* * * * [misc]progress:  [ 52 / 165 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k))) (cbrt (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))) (cbrt (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))))>
* * * * [misc]progress:  [ 53 / 165 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))))>
* * * * [misc]progress:  [ 54 / 165 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k))) (sqrt (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))))>
* * * * [misc]progress:  [ 55 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (- (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (- (sqrt k))))>
* * * * [misc]progress:  [ 56 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (45 enodes)
* * [misc]simplify:  iters left: 3 (49 enodes)
* * [misc]simplify:  iters left: 2 (52 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 57 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 58 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) 1) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) 1)
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* * [misc]simplify:  iters left: 2 (52 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 59 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 60 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 61 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) 1) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) 1)
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 62 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* * [misc]simplify:  iters left: 2 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 63 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))) (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))) (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))) (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 64 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) 1) (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) 1)
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* * [misc]simplify:  iters left: 2 (24 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (/ 1 2)) (* (sqrt k) (pow PI (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (/ (pow PI (/ 1 2)) (* (sqrt k) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 65 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow PI (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n 2) (/ 1 2)) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (46 enodes)
* * [misc]simplify:  iters left: 3 (60 enodes)
* * [misc]simplify:  iters left: 2 (72 enodes)
* * [misc]simplify:  iters left: 1 (75 enodes)
* [exit]simplify:  Simplified to (/ (/ (/ (/ (pow (* n 2) (/ 1 2)) (cbrt (sqrt k))) (cbrt (sqrt k))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (pow (* n (* PI 2)) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ (/ (/ (pow (* n 2) (/ 1 2)) (cbrt (sqrt k))) (cbrt (sqrt k))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (pow PI (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow PI (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow PI (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* (* n PI) 2) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow PI (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* (* n PI) 2) (/ k 2))))))
* * * * [misc]progress:  [ 66 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (pow PI (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n 2) (/ 1 2)) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (38 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* * [misc]simplify:  iters left: 2 (48 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n 2) (/ 1 2)) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k)))) (/ (/ (pow PI (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow PI (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow PI (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* (* n PI) 2) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (pow PI (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* (* n PI) 2) (/ k 2))))))
* * * * [misc]progress:  [ 67 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) 1) (/ (/ (pow PI (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n 2) (/ 1 2)) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) 1)
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* * [misc]simplify:  iters left: 2 (47 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n 2) (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (pow (* (* n PI) 2) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (/ (/ (pow PI (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (pow PI (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow PI (/ 1 2)) (sqrt k)) (cbrt (pow (* 2 (* n PI)) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (/ (/ (pow PI (/ 1 2)) (sqrt k)) (cbrt (pow (* 2 (* n PI)) (/ k 2))))))
* * * * [misc]progress:  [ 68 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow PI (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n 2) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (45 enodes)
* * [misc]simplify:  iters left: 2 (46 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n 2) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* 2 (* n PI)) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (pow PI (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow PI (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow PI (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* (* n PI) 2) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow PI (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* (* n PI) 2) (/ k 2))))))
* * * * [misc]progress:  [ 69 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) (/ (/ (pow PI (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n 2) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n 2) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (/ (pow PI (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow PI (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow PI (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* n PI) 2) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) (/ (/ (pow PI (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* n PI) 2) (/ k 2))))))
* * * * [misc]progress:  [ 70 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) 1) (/ (/ (pow PI (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n 2) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) 1)
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (37 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n 2) (/ 1 2)) (sqrt (pow (* 2 (* n PI)) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (pow PI (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (pow PI (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow PI (/ 1 2)) (sqrt k)) (sqrt (pow (* 2 (* n PI)) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (pow PI (/ 1 2)) (sqrt k)) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))
* * * * [misc]progress:  [ 71 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow PI (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n 2) (/ 1 2)) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n 2) (/ 1 2)) (cbrt (sqrt k))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (/ (pow PI (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow PI (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow PI (/ 1 2)) (cbrt (sqrt k))) (pow (* 2 (* n PI)) (/ k 2)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (/ (pow PI (/ 1 2)) (cbrt (sqrt k))) (pow (* 2 (* n PI)) (/ k 2)))))
* * * * [misc]progress:  [ 72 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) 1) (sqrt (sqrt k))) (/ (/ (pow PI (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n 2) (/ 1 2)) 1) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n 2) (/ 1 2)) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (sqrt (sqrt k))) (/ (/ (pow PI (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow PI (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow PI (/ 1 2)) (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ k 2)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (sqrt (sqrt k))) (/ (/ (pow PI (/ 1 2)) (sqrt (sqrt k))) (pow (* 2 (* n PI)) (/ k 2)))))
* * * * [misc]progress:  [ 73 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) 1) 1) (/ (/ (pow PI (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n 2) (/ 1 2)) 1) 1)
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* [exit]simplify:  Simplified to (pow (* n 2) (/ 1 2))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (pow (* n 2) (/ 1 2)) (/ (/ (pow PI (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (pow PI (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow PI (/ 1 2)) (sqrt k)) (pow (* (* n PI) 2) (/ k 2)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (pow (* n 2) (/ 1 2)) (/ (/ (pow PI (/ 1 2)) (sqrt k)) (pow (* (* n PI) 2) (/ k 2)))))
* * * * [misc]progress:  [ 74 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (50 enodes)
* * [misc]simplify:  iters left: 3 (86 enodes)
* * [misc]simplify:  iters left: 2 (125 enodes)
* * [misc]simplify:  iters left: 1 (146 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (/ (* (pow (* n 2) (/ k 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (/ (* (pow (* n 2) (/ k 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (pow (* n (* PI 2)) (/ 1 2))))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (pow PI (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 75 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n 2) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (56 enodes)
* * [misc]simplify:  iters left: 2 (64 enodes)
* * [misc]simplify:  iters left: 1 (67 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (sqrt k))) (/ (pow (* n 2) (/ k 2)) (cbrt (pow (* (* n 2) PI) (/ 1 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (sqrt k))) (/ (pow (* n 2) (/ k 2)) (cbrt (pow (* (* n 2) PI) (/ 1 2))))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (pow PI (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 76 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n 2) (/ k 2))) 1) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n 2) (/ k 2))) 1)
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (65 enodes)
* * [misc]simplify:  iters left: 2 (155 enodes)
* * [misc]simplify:  iters left: 1 (379 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n 2) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n 2) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (* (pow PI (/ k 2)) (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n 2) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (* (pow PI (/ k 2)) (sqrt k)))))
* * * * [misc]progress:  [ 77 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (73 enodes)
* * [misc]simplify:  iters left: 3 (142 enodes)
* * [misc]simplify:  iters left: 2 (253 enodes)
* * [misc]simplify:  iters left: 1 (314 enodes)
* [exit]simplify:  Simplified to (* (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k))) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k))) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ k 2)))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ k 2)))))))
* * * * [misc]progress:  [ 78 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (59 enodes)
* * [misc]simplify:  iters left: 3 (92 enodes)
* * [misc]simplify:  iters left: 2 (126 enodes)
* * [misc]simplify:  iters left: 1 (145 enodes)
* [exit]simplify:  Simplified to (/ (* (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (* (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ k 2)))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ k 2)))))))
* * * * [misc]progress:  [ 79 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) 1) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) 1)
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (56 enodes)
* * [misc]simplify:  iters left: 3 (95 enodes)
* * [misc]simplify:  iters left: 2 (296 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ k 2))))))
* * * * [misc]progress:  [ 80 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (51 enodes)
* * [misc]simplify:  iters left: 3 (87 enodes)
* * [misc]simplify:  iters left: 2 (127 enodes)
* * [misc]simplify:  iters left: 1 (146 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ 1 2))))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ k 2)))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ k 2)))))))
* * * * [misc]progress:  [ 81 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (57 enodes)
* * [misc]simplify:  iters left: 2 (65 enodes)
* * [misc]simplify:  iters left: 1 (68 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (sqrt k)))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ k 2)))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ k 2)))))))
* * * * [misc]progress:  [ 82 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) 1) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) 1)
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (65 enodes)
* * [misc]simplify:  iters left: 2 (161 enodes)
* * [misc]simplify:  iters left: 1 (335 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (sqrt (pow (* (* n 2) PI) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ k 2))))))
* * * * [misc]progress:  [ 83 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (56 enodes)
* * [misc]simplify:  iters left: 3 (102 enodes)
* * [misc]simplify:  iters left: 2 (238 enodes)
* * [misc]simplify:  iters left: 1 (268 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (sqrt k)))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* (* n 2) PI) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* (* n 2) PI) (/ k 2))))))
* * * * [misc]progress:  [ 84 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) 1) (sqrt (sqrt k))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) 1) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (71 enodes)
* * [misc]simplify:  iters left: 2 (138 enodes)
* * [misc]simplify:  iters left: 1 (141 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt (sqrt k))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* (* n 2) PI) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* (* n 2) PI) (/ k 2))))))
* * * * [misc]progress:  [ 85 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) 1) 1) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) 1) 1)
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* * [misc]simplify:  iters left: 2 (50 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (* (pow (* n (* PI 2)) (/ k 2)) (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (* (pow (* n (* PI 2)) (/ k 2)) (sqrt k)))))
* * * * [misc]progress:  [ 86 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (45 enodes)
* * [misc]simplify:  iters left: 2 (46 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (* (pow (* n 2) (/ k 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (* (pow (* n 2) (/ k 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (pow PI (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 87 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (pow PI (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 88 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2))) 1) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2))) 1)
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (37 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (pow (* n 2) (/ k 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (pow (* n 2) (/ k 2))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (pow PI (/ k 2)) (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (pow (* n 2) (/ k 2))) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (pow PI (/ k 2)) (sqrt k)))))
* * * * [misc]progress:  [ 89 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (47 enodes)
* * [misc]simplify:  iters left: 3 (61 enodes)
* * [misc]simplify:  iters left: 2 (73 enodes)
* * [misc]simplify:  iters left: 1 (76 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ k 2)))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ k 2)))))))
* * * * [misc]progress:  [ 90 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* * [misc]simplify:  iters left: 2 (49 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (sqrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (sqrt (sqrt k)))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ k 2)))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ k 2)))))))
* * * * [misc]progress:  [ 91 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) 1) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) 1)
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (26 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 (pow (* 2 (* PI n)) (/ 1 2))) (* (cbrt (pow (* 2 (* PI n)) (/ k 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (* (cbrt (pow (* 2 (* PI n)) (/ k 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (* (cbrt (pow (* 2 (* PI n)) (/ k 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ k 2))))))
* * * * [misc]progress:  [ 92 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (47 enodes)
* * [misc]simplify:  iters left: 2 (48 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* n (* PI 2)) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ k 2)))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ k 2)))))))
* * * * [misc]progress:  [ 93 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ k 2)))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ k 2)))))))
* * * * [misc]progress:  [ 94 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) 1) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) 1)
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* * [misc]simplify:  iters left: 2 (38 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ k 2))))))
* * * * [misc]progress:  [ 95 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (50 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* (* n 2) PI) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* (* n 2) PI) (/ k 2))))))
* * * * [misc]progress:  [ 96 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) 1) (sqrt (sqrt k))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) 1) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (sqrt (sqrt k))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* (* n 2) PI) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* (* n 2) PI) (/ k 2))))))
* * * * [misc]progress:  [ 97 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) 1) 1) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) 1) 1)
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* (* n 2) PI) (/ 1 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (pow (* (* n 2) PI) (/ 1 2))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (pow (* n (* PI 2)) (/ k 2)) (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (sqrt (pow (* (* n 2) PI) (/ 1 2))) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (pow (* n (* PI 2)) (/ k 2)) (sqrt k)))))
* * * * [misc]progress:  [ 98 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow PI (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* * [misc]simplify:  iters left: 2 (31 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (pow (* 2 n) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ 1 (pow (* 2 n) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow PI (/ k 2))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow PI (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* PI 2)) (/ 1 2)) (* (pow PI (/ k 2)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ 1 (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (pow PI (/ k 2)) (cbrt (sqrt k))))))
* * * * [misc]progress:  [ 99 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (pow (* n 2) (/ k 2))) (sqrt (sqrt k))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow PI (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (pow (* n 2) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (pow (* 2 n) (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ 1 (pow (* 2 n) (/ k 2))) (sqrt (sqrt k))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow PI (/ k 2))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow PI (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* PI 2)) (/ 1 2)) (* (pow PI (/ k 2)) (sqrt (sqrt k))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ 1 (pow (* n 2) (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (pow PI (/ k 2)) (sqrt (sqrt k))))))
* * * * [misc]progress:  [ 100 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (pow (* n 2) (/ k 2))) 1) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow PI (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ 1 (pow (* n 2) (/ k 2))) 1)
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* [exit]simplify:  Simplified to (/ 1 (pow (* 2 n) (/ k 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ 1 (pow (* 2 n) (/ k 2))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow PI (/ k 2))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow PI (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* [exit]simplify:  Simplified to (/ (pow (* 2 (* PI n)) (/ 1 2)) (* (sqrt k) (pow PI (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ 1 (pow (* 2 n) (/ k 2))) (/ (pow (* 2 (* PI n)) (/ 1 2)) (* (sqrt k) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 101 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (58 enodes)
* * [misc]simplify:  iters left: 2 (70 enodes)
* * [misc]simplify:  iters left: 1 (73 enodes)
* [exit]simplify:  Simplified to (/ (/ (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (pow (* n (* PI 2)) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* (* n 2) PI) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ 1 (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* (* n 2) PI) (/ k 2))))))
* * * * [misc]progress:  [ 102 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (46 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (pow (* 2 (* n PI)) (/ k 2))) (sqrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ 1 (cbrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (pow (* 2 (* n PI)) (/ k 2))) (sqrt (sqrt k)))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* (* n 2) PI) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ 1 (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* (* n 2) PI) (/ k 2))))))
* * * * [misc]progress:  [ 103 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) 1) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ 1 (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) 1)
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* * [misc]simplify:  iters left: 2 (40 enodes)
* [exit]simplify:  Simplified to (/ 1 (* (cbrt (pow (* 2 (* n PI)) (/ k 2))) (cbrt (pow (* 2 (* n PI)) (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ 1 (* (cbrt (pow (* 2 (* n PI)) (/ k 2))) (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ 1 (* (cbrt (pow (* 2 (* n PI)) (/ k 2))) (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ k 2))))))
* * * * [misc]progress:  [ 104 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* * [misc]simplify:  iters left: 2 (44 enodes)
* [exit]simplify:  Simplified to (/ (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ 1 (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2))))))
* * * * [misc]progress:  [ 105 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* PI 2) n) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ 1 (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2))))))
* * * * [misc]progress:  [ 106 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (pow (* (* n 2) PI) (/ k 2)))) 1) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ 1 (sqrt (pow (* (* n 2) PI) (/ k 2)))) 1)
* * [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 (33 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (pow (* 2 (* n PI)) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ k 2))))))
* * * * [misc]progress:  [ 107 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (cbrt (sqrt k))) (pow (* n (* PI 2)) (/ k 2)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (cbrt (sqrt k))) (pow (* n (* PI 2)) (/ k 2)))))
* * * * [misc]progress:  [ 108 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 1) (sqrt (sqrt k))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 1) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 4 (6 enodes)
* * [misc]simplify:  iters left: 3 (8 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (sqrt k))) (pow (* n (* PI 2)) (/ k 2)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (sqrt k))) (pow (* n (* PI 2)) (/ k 2)))))
* * * * [misc]progress:  [ 109 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 1) 1) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ 1 1) 1)
* * [misc]simplify:  iters left: 4 (3 enodes)
* * [misc]simplify:  iters left: 3 (5 enodes)
* [exit]simplify:  Simplified to 1
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* 1 (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* [exit]simplify:  Simplified to (/ (pow (* 2 (* PI n)) (/ 1 2)) (* (sqrt k) (pow (* 2 (* PI n)) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* 2 (* PI n)) (/ 1 2)) (* (sqrt k) (pow (* 2 (* PI n)) (/ k 2))))))
* * * * [misc]progress:  [ 110 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ 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)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (cbrt (sqrt k))) (pow (* n (* PI 2)) (/ k 2)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (cbrt (sqrt k))) (pow (* n (* PI 2)) (/ k 2)))))
* * * * [misc]progress:  [ 111 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ 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)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (sqrt k))) (pow (* n (* PI 2)) (/ k 2)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (sqrt k))) (pow (* n (* PI 2)) (/ k 2)))))
* * * * [misc]progress:  [ 112 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ 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
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* 1 (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* [exit]simplify:  Simplified to (/ (pow (* 2 (* PI n)) (/ 1 2)) (* (sqrt k) (pow (* 2 (* PI n)) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* 2 (* PI n)) (/ 1 2)) (* (sqrt k) (pow (* 2 (* PI n)) (/ k 2))))))
* * * * [misc]progress:  [ 113 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ 1 (pow (* (* n 2) PI) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* (* n 2) PI) (/ 1 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 (27 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI 2) n) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (pow (* (* PI 2) n) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ 1 (pow (* (* n 2) PI) (/ k 2))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ 1 (pow (* (* n 2) PI) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (31 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (sqrt k))) (pow (* (* n PI) 2) (/ k 2)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (pow (* (* n 2) PI) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ 1 (cbrt (sqrt k))) (pow (* (* n PI) 2) (/ k 2)))))
* * * * [misc]progress:  [ 114 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ 1 2)) (sqrt (sqrt k))) (/ (/ 1 (pow (* (* n 2) PI) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* (* n 2) PI) (/ 1 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (sqrt k))) (/ (/ 1 (pow (* (* n 2) PI) (/ k 2))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ 1 (pow (* (* n 2) PI) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (31 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt (sqrt k))) (pow (* (* n PI) 2) (/ k 2)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (pow (* (* n 2) PI) (/ 1 2)) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt k))) (pow (* (* n PI) 2) (/ k 2)))))
* * * * [misc]progress:  [ 115 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ 1 2)) 1) (/ (/ 1 (pow (* (* n 2) PI) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow (* (* n 2) PI) (/ 1 2)) 1)
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI 2) n) (/ 1 2))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (pow (* (* PI 2) n) (/ 1 2)) (/ (/ 1 (pow (* (* n 2) PI) (/ k 2))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ 1 (pow (* (* n 2) PI) (/ k 2))) (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 (30 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ k 2)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (pow (* (* PI 2) n) (/ 1 2)) (/ (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ k 2)))))
* * * * [misc]progress:  [ 116 / 165 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k))))>
* * * * [misc]progress:  [ 117 / 165 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (/ 1 (sqrt k))))>
* * * * [misc]progress:  [ 118 / 165 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))))>
* * * * [misc]progress:  [ 119 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
* [enter]simplify:  Simplifying (cbrt (sqrt k))
* * [misc]simplify:  iters left: 2 (3 enodes)
* [exit]simplify:  Simplified to (cbrt (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 120 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
* [enter]simplify:  Simplifying (sqrt (sqrt k))
* * [misc]simplify:  iters left: 2 (3 enodes)
* [exit]simplify:  Simplified to (sqrt (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 121 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) 1) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt k)
* * [misc]simplify:  iters left: 1 (2 enodes)
* [exit]simplify:  Simplified to (sqrt k)
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) 1) (sqrt k)))
* * * * [misc]progress:  [ 122 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt k) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))))))>
* [enter]simplify:  Simplifying (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (26 enodes)
* * [misc]simplify:  iters left: 3 (28 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt k) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))))))
* * * * [misc]progress:  [ 123 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt k) (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))))))>
* [enter]simplify:  Simplifying (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* (* PI 2) n) (/ 1 2)) (pow (* (* PI 2) n) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (sqrt (/ (pow (* (* PI 2) n) (/ 1 2)) (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))))))
* * * * [misc]progress:  [ 124 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (/ (sqrt k) (/ (pow PI (/ 1 2)) (pow PI (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2)))
* * [misc]simplify:  iters left: 5 (10 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (/ (sqrt k) (/ (pow PI (/ 1 2)) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 125 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n 2) (/ 1 2)) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt k) (/ (pow PI (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (pow (* n 2) (/ 1 2)) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n 2) (/ 1 2)) (* (cbrt (pow (* 2 (* n PI)) (/ k 2))) (cbrt (pow (* 2 (* n PI)) (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (/ (pow (* n 2) (/ 1 2)) (* (cbrt (pow (* 2 (* n PI)) (/ k 2))) (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (/ (pow PI (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2)))))))
* * * * [misc]progress:  [ 126 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n 2) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt k) (/ (pow PI (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (pow (* n 2) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n 2) (/ 1 2)) (sqrt (pow (* (* PI 2) n) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (/ (pow (* n 2) (/ 1 2)) (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (/ (pow PI (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))))))
* * * * [misc]progress:  [ 127 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n 2) (/ 1 2)) 1) (/ (sqrt k) (/ (pow PI (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (pow (* n 2) (/ 1 2)) 1)
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (12 enodes)
* [exit]simplify:  Simplified to (pow (* n 2) (/ 1 2))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (pow (* n 2) (/ 1 2)) (/ (sqrt k) (/ (pow PI (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))))
* * * * [misc]progress:  [ 128 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n 2) (/ k 2))) (/ (sqrt k) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n 2) (/ k 2)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (pow (* n 2) (/ k 2))) (cbrt (pow (* 2 (* PI n)) (/ 1 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (* (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (pow (* n 2) (/ k 2))) (cbrt (pow (* 2 (* PI n)) (/ 1 2)))) (/ (sqrt k) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 129 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt k) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (48 enodes)
* * [misc]simplify:  iters left: 2 (51 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (* (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt k) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))))))
* * * * [misc]progress:  [ 130 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt k) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (sqrt (pow (* (* n 2) PI) (/ k 2))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt (pow (* n (* PI 2)) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt k) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))))))
* * * * [misc]progress:  [ 131 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) 1) (/ (sqrt k) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) 1)
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* * [misc]simplify:  iters left: 2 (48 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (/ (sqrt k) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))))))
* * * * [misc]progress:  [ 132 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2))) (/ (sqrt k) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI 2) n) (/ 1 2))) (pow (* n 2) (/ k 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (/ (sqrt (pow (* (* PI 2) n) (/ 1 2))) (pow (* n 2) (/ k 2))) (/ (sqrt k) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 133 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt k) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (pow (* n (* PI 2)) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt k) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))))))
* * * * [misc]progress:  [ 134 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt k) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (26 enodes)
* * [misc]simplify:  iters left: 3 (28 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt k) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))))))
* * * * [misc]progress:  [ 135 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) 1) (/ (sqrt k) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) 1)
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (/ (sqrt k) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))))))
* * * * [misc]progress:  [ 136 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (pow (* n 2) (/ k 2))) (/ (sqrt k) (/ (pow (* (* n 2) PI) (/ 1 2)) (pow PI (/ k 2))))))>
* [enter]simplify:  Simplifying (/ 1 (pow (* n 2) (/ k 2)))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (11 enodes)
* [exit]simplify:  Simplified to (/ 1 (pow (* 2 n) (/ k 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (/ 1 (pow (* 2 n) (/ k 2))) (/ (sqrt k) (/ (pow (* (* n 2) PI) (/ 1 2)) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 137 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt k) (/ (pow (* (* n 2) PI) (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ 1 (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (26 enodes)
* * [misc]simplify:  iters left: 3 (27 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (/ (/ 1 (cbrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (/ (pow (* (* n 2) PI) (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2)))))))
* * * * [misc]progress:  [ 138 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt k) (/ (pow (* (* n 2) PI) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt (pow (* (* n 2) PI) (/ k 2))))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (pow (* (* n PI) 2) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (/ 1 (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt k) (/ (pow (* (* n 2) PI) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))))))
* * * * [misc]progress:  [ 139 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 1) (/ (sqrt k) (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ 1 1)
* * [misc]simplify:  iters left: 2 (2 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to 1
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))))
* * * * [misc]progress:  [ 140 / 165 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))))>
* * * * [misc]progress:  [ 141 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (/ 1 2)) (/ (sqrt k) (/ 1 (pow (* (* n 2) PI) (/ k 2))))))>
* [enter]simplify:  Simplifying (pow (* (* n 2) PI) (/ 1 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* [exit]simplify:  Simplified to (pow (* n (* PI 2)) (/ 1 2))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (/ (sqrt k) (/ 1 (pow (* (* n 2) PI) (/ k 2))))))
* * * * [misc]progress:  [ 142 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (/ 1 2)) (* (sqrt k) (pow (* (* n 2) PI) (/ k 2)))))>
* [enter]simplify:  Simplifying (pow (* (* n 2) PI) (/ 1 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* [exit]simplify:  Simplified to (pow (* n (* PI 2)) (/ 1 2))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* (* n 2) PI) (/ k 2)))))
* * * * [misc]progress:  [ 143 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (log1p (expm1 (* (* n 2) PI))) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 144 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (expm1 (log1p (* (* n 2) PI))) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 145 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (pow (* (* n 2) PI) 1) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 146 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (exp (log (* (* n 2) PI))) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 147 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (log (exp (* (* n 2) PI))) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 148 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 149 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (cbrt (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI))) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 150 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI))) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 151 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* 1 (* (* n 2) PI)) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 152 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* n (* 2 PI)) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 153 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 154 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (45 enodes)
* * [misc]simplify:  iters left: 3 (85 enodes)
* * [misc]simplify:  iters left: 2 (144 enodes)
* * [misc]simplify:  iters left: 1 (178 enodes)
* [exit]simplify:  Simplified to (sqrt (* (* n PI) 2))
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (/ (sqrt (* (* n PI) 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 155 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n)))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (89 enodes)
* * [misc]simplify:  iters left: 2 (206 enodes)
* [exit]simplify:  Simplified to (sqrt (* n (* PI 2)))
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (/ (sqrt (* n (* PI 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 156 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n)))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (89 enodes)
* * [misc]simplify:  iters left: 2 (238 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (* PI -2)) (pow (/ -1 n) 1/2))
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (/ (/ (sqrt (* PI -2)) (pow (/ -1 n) 1/2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 157 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (+ (* 1/8 (* (pow (log n) 2) (pow k 2))) (+ (* 1/8 (* (pow k 2) (pow (log (* 2 PI)) 2))) (+ (* 1/2 (* k (log (* 2 PI)))) (+ (* 1/4 (* (pow k 2) (* (log n) (log (* 2 PI))))) (+ (* 1/2 (* (log n) k)) 1)))))) (sqrt k)))>
* [enter]simplify:  Simplifying (+ (* 1/8 (* (pow (log n) 2) (pow k 2))) (+ (* 1/8 (* (pow k 2) (pow (log (* 2 PI)) 2))) (+ (* 1/2 (* k (log (* 2 PI)))) (+ (* 1/4 (* (pow k 2) (* (log n) (log (* 2 PI))))) (+ (* 1/2 (* (log n) k)) 1)))))
* * [misc]simplify:  iters left: 6 (30 enodes)
* * [misc]simplify:  iters left: 5 (80 enodes)
* * [misc]simplify:  iters left: 4 (254 enodes)
* [exit]simplify:  Simplified to (fma 1/8 (* (* k k) (+ (* (log n) (log n)) (* (log (* 2 PI)) (log (* 2 PI))))) (fma (* (log (* 2 PI)) (* 1/4 (* k k))) (log n) (fma (* (log (* 2 PI)) 1/2) k (fma (* (log n) k) 1/2 1))))
* [misc]simplify:  Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (fma 1/8 (* (* k k) (+ (* (log n) (log n)) (* (log (* 2 PI)) (log (* 2 PI))))) (fma (* (log (* 2 PI)) (* 1/4 (* k k))) (log n) (fma (* (log (* 2 PI)) 1/2) k (fma (* (log n) k) 1/2 1))))) (sqrt k)))
* * * * [misc]progress:  [ 158 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k)))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (60 enodes)
* * [misc]simplify:  iters left: 3 (173 enodes)
* [exit]simplify:  Simplified to (exp (fma (log (* PI 2)) (* 1/2 k) (* (* 1/2 k) (log n))))
* [misc]simplify:  Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (exp (fma (log (* PI 2)) (* 1/2 k) (* (* 1/2 k) (log n))))) (sqrt k)))
* * * * [misc]progress:  [ 159 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (57 enodes)
* * [misc]simplify:  iters left: 3 (179 enodes)
* [exit]simplify:  Simplified to (exp (* (- (log (* PI -2)) (log (/ -1 n))) (* 1/2 k)))
* [misc]simplify:  Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (exp (* (- (log (* PI -2)) (log (/ -1 n))) (* 1/2 k)))) (sqrt k)))
* * * * [misc]progress:  [ 160 / 165 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
* [misc]simplify:  Simplified (2) to (λ (k n) +nan.0)
* * * * [misc]progress:  [ 161 / 165 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (pow k 3)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (pow k 2))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (pow k 3)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (pow k 2)))))))))
* [misc]simplify:  Simplified (2) to (λ (k n) +nan.0)
* * * * [misc]progress:  [ 162 / 165 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))))))))))
* [misc]simplify:  Simplified (2) to (λ (k n) +nan.0)
* * * * [misc]progress:  [ 163 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* 2 (* n PI))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* * [misc]simplify:  iters left: 2 (15 enodes)
* * [misc]simplify:  iters left: 1 (17 enodes)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* [misc]simplify:  Simplified (2 1 2 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 164 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* 2 (* n PI))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* * [misc]simplify:  iters left: 2 (15 enodes)
* * [misc]simplify:  iters left: 1 (17 enodes)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* [misc]simplify:  Simplified (2 1 2 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 165 / 165 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* 2 (* n PI))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* * [misc]simplify:  iters left: 2 (15 enodes)
* * [misc]simplify:  iters left: 1 (17 enodes)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* [misc]simplify:  Simplified (2 1 2 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)))
* * * [misc]progress:  adding candidates to table
* * [misc]progress:  iteration 3 / 4
* * * [misc]progress:  picking best candidate
* * * * [misc]pick:  Picked  #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 4 ] rewriting at (2 1 1)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2 1 2 1)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2 1 1 1)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 4 ] generating series at (2 1 1)
* [misc]approximate:  Taking taylor expansion of (pow (* (* n 2) PI) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* n 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* n 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* n 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* n 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]approximate:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 n) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 n) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 n) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 n) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n)))))
* [misc]approximate:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 (- n)) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 (- n)) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* -2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* -2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* -2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 1)))) 24) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* -2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* -2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* -2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* -2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* -2 PI) 1)))) 120) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* -2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* -2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* -2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* -2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* -2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* -2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* -2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* -2 PI) 1)))) 720) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n)))))
* * * * [misc]progress:  [ 2 / 4 ] generating series at (2 1 2 1)
* [misc]approximate:  Taking taylor expansion of (pow (* n 2) (/ k 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* n 2) (/ k 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* n 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* n 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n 2)) in k
* [misc]taylor:  Taking taylor expansion of (* n 2) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* n 2) into (* 2 n)
* [misc]backup-simplify:  Simplify (log (* 2 n)) into (log (* 2 n))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n)))
* [misc]backup-simplify:  Simplify (exp 0) into 1
* [misc]taylor:  Taking taylor expansion of (pow (* n 2) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* n 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* n 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* n 2)) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 k) (+ (log 2) (log n))) into (* 1/2 (* (+ (log 2) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (log 2) (log n)) k))) into (exp (* 1/2 (* (+ (log 2) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* n 2) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* n 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* n 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* n 2)) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 k) (+ (log 2) (log n))) into (* 1/2 (* (+ (log 2) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (log 2) (log n)) k))) into (exp (* 1/2 (* (+ (log 2) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ (log 2) (log n)) k))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ (log 2) (log n)) k)) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ (log 2) (log n)) k) in k
* [misc]taylor:  Taking taylor expansion of (+ (log 2) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (+ (log 2) (log n)) into (+ (log 2) (log n))
* [misc]backup-simplify:  Simplify (* (+ (log 2) (log n)) 0) into 0
* [misc]backup-simplify:  Simplify (* 1/2 0) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log 2) (log n)) 1) (* 0 0)) into (+ (log 2) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (+ (log 2) (log n))) (* 0 0)) into (+ (* 1/2 (log 2)) (* 1/2 (log n)))
* [misc]backup-simplify:  Simplify (exp 0) into 1
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log 2) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log 2)) (* 1/2 (log n))) 1) 1)))) into (+ (* 1/2 (log 2)) (* 1/2 (log n)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (log 2)) (* 1/2 (log n))) into (+ (* 1/2 (log 2)) (* 1/2 (log n)))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 1) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (+ (log 2) (log n))) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log 2)) (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))
* [misc]backup-simplify:  Simplify (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2)))) into (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2)))) (pow (* k 1) 2)) (+ (* (+ (* 1/2 (log 2)) (* 1/2 (log n))) (* k 1)) 1)) into (+ (* 1/8 (* (pow (log n) 2) (pow k 2))) (+ (* 1/4 (* (log 2) (* (log n) (pow k 2)))) (+ (* 1/2 (* (log 2) k)) (+ (* 1/8 (* (pow (log 2) 2) (pow k 2))) (+ (* 1/2 (* (log n) k)) 1)))))
* [misc]approximate:  Taking taylor expansion of (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) 2)) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* (/ 1 n) 2) into (/ 2 n)
* [misc]backup-simplify:  Simplify (log (/ 2 n)) into (log (/ 2 n))
* [misc]backup-simplify:  Simplify (* 1/2 (log (/ 2 n))) into (* 1/2 (log (/ 2 n)))
* [misc]backup-simplify:  Simplify (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2)))) into (exp (* 1/2 (/ (log (/ 2 n)) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n))
* [misc]backup-simplify:  Simplify (* (/ 1/2 k) (- (log 2) (log n))) into (* 1/2 (/ (- (log 2) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log 2) (log n)) k))) into (exp (* 1/2 (/ (- (log 2) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n))
* [misc]backup-simplify:  Simplify (* (/ 1/2 k) (- (log 2) (log n))) into (* 1/2 (/ (- (log 2) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log 2) (log n)) k))) into (exp (* 1/2 (/ (- (log 2) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (/ (- (log 2) (log n)) k))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ (- (log 2) (log n)) k)) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (- (log 2) (log n)) k) in k
* [misc]taylor:  Taking taylor expansion of (- (log 2) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n))
* [misc]backup-simplify:  Simplify (/ (- (log 2) (log n)) 1) into (- (log 2) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log 2) (log n))) into (* 1/2 (- (log 2) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log 2) (log n)) k))) into (exp (* 1/2 (/ (- (log 2) (log n)) k)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log 2) (log n)) k))) into (exp (* 1/2 (/ (- (log 2) (log n)) k)))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log 2) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log 2) (log (/ 1 n))) (/ 1 k)))) into (exp (* 1/2 (* (- (log 2) (log (/ 1 n))) k)))
* [misc]approximate:  Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* (/ -1 n) 2) into (/ -2 n)
* [misc]backup-simplify:  Simplify (log (/ -2 n)) into (log (/ -2 n))
* [misc]backup-simplify:  Simplify (* -1/2 (log (/ -2 n))) into (* -1/2 (log (/ -2 n)))
* [misc]backup-simplify:  Simplify (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2)))) into (exp (* -1/2 (/ (log (/ -2 n)) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (log -2) into (log -2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n))
* [misc]backup-simplify:  Simplify (* (/ -1/2 k) (- (log -2) (log n))) into (* -1/2 (/ (- (log -2) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log -2) (log n)) k))) into (exp (* -1/2 (/ (- (log -2) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (log -2) into (log -2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n))
* [misc]backup-simplify:  Simplify (* (/ -1/2 k) (- (log -2) (log n))) into (* -1/2 (/ (- (log -2) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log -2) (log n)) k))) into (exp (* -1/2 (/ (- (log -2) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (exp (* -1/2 (/ (- (log -2) (log n)) k))) in k
* [misc]taylor:  Taking taylor expansion of (* -1/2 (/ (- (log -2) (log n)) k)) in k
* [misc]taylor:  Taking taylor expansion of -1/2 in k
* [misc]backup-simplify:  Simplify -1/2 into -1/2
* [misc]taylor:  Taking taylor expansion of (/ (- (log -2) (log n)) k) in k
* [misc]taylor:  Taking taylor expansion of (- (log -2) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log -2) in k
* [misc]taylor:  Taking taylor expansion of -2 in k
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]backup-simplify:  Simplify (log -2) into (log -2)
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n))
* [misc]backup-simplify:  Simplify (/ (- (log -2) (log n)) 1) into (- (log -2) (log n))
* [misc]backup-simplify:  Simplify (* -1/2 (- (log -2) (log n))) into (* -1/2 (- (log -2) (log n)))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log -2) (log n)) k))) into (exp (* -1/2 (/ (- (log -2) (log n)) k)))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log -2) (log n)) k))) into (exp (* -1/2 (/ (- (log -2) (log n)) k)))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log -2) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -2 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -2) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log -2) (log (/ 1 (- n)))) (/ 1 (- k))))) into (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k)))
* * * * [misc]progress:  [ 3 / 4 ] generating series at (2)
* [misc]approximate:  Taking taylor expansion of (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ 1 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* n 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* n 2) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* n 2) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [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 (* n 2) into (* 2 n)
* [misc]backup-simplify:  Simplify (* (* 2 n) PI) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
* [misc]taylor:  Taking taylor expansion of (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* n 2) (/ k 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* n 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* n 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n 2)) in k
* [misc]taylor:  Taking taylor expansion of (* n 2) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* n 2) into (* 2 n)
* [misc]backup-simplify:  Simplify (log (* 2 n)) into (log (* 2 n))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n)))
* [misc]backup-simplify:  Simplify (exp 0) into 1
* [misc]taylor:  Taking taylor expansion of (pow PI (/ k 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp 0) into 1
* [misc]backup-simplify:  Simplify (* 1 1) into 1
* [misc]backup-simplify:  Simplify (/ (pow (* 2 (* n PI)) 1/2) 1) into (sqrt (* PI (* n 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 (/ (sqrt (* PI (* n 2))) +nan.0) into (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* n 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* n 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* n 2) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* n 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* n 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* n 2)) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 k) (+ (log 2) (log n))) into (* 1/2 (* (+ (log 2) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (log 2) (log n)) k))) into (exp (* 1/2 (* (+ (log 2) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (pow PI (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log PI)) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (* (* 1/2 k) (log PI)) into (* 1/2 (* (log PI) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (log PI) k))) into (exp (* 1/2 (* (log PI) k)))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k)))) into (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k))))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k))))) into (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k)))))
* [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 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k))))) (sqrt k)) into (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k))))) (sqrt (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* n 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* n 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* n 2) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* n 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* n 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* n 2)) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 k) (+ (log 2) (log n))) into (* 1/2 (* (+ (log 2) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (log 2) (log n)) k))) into (exp (* 1/2 (* (+ (log 2) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (pow PI (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log PI)) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (* (* 1/2 k) (log PI)) into (* 1/2 (* (log PI) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (log PI) k))) into (exp (* 1/2 (* (log PI) k)))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k)))) into (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k))))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k))))) into (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k)))))
* [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 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k))))) (sqrt k)) into (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k))))) (sqrt (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k))))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k))))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (+ (log n) (log (* 2 PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (+ (log n) (log (* 2 PI)))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of (log (* 2 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]backup-simplify:  Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k)))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ (log 2) (log n)) k))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ (log 2) (log n)) k)) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ (log 2) (log n)) k) in k
* [misc]taylor:  Taking taylor expansion of (+ (log 2) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (+ (log 2) (log n)) into (+ (log 2) (log n))
* [misc]backup-simplify:  Simplify (* (+ (log 2) (log n)) 0) into 0
* [misc]backup-simplify:  Simplify (* 1/2 0) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log 2) (log n)) 1) (* 0 0)) into (+ (log 2) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (+ (log 2) (log n))) (* 0 0)) into (+ (* 1/2 (log 2)) (* 1/2 (log n)))
* [misc]backup-simplify:  Simplify (exp 0) into 1
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (log PI) k))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (log PI) k)) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (log PI) k) in k
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (* (log PI) 0) into 0
* [misc]backup-simplify:  Simplify (* 1/2 0) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (log PI) 1) (* 0 0)) into (log PI)
* [misc]backup-simplify:  Simplify (+ (* 1/2 (log PI)) (* 0 0)) into (* 1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp 0) into 1
* [misc]backup-simplify:  Simplify (* 1 1) into 1
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1) into (exp (* 1/2 (+ (log n) (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 (+ (log n) (log (* 2 PI))))) 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (* 0 (log PI))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (log PI) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log 2) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) 0) (* 0 (exp (* 1/2 (* (log PI) k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k))))) (+ (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k))))) (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k)))))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k))))) (sqrt (/ 1 k))) (/ 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 (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log PI)) 1) 1)))) into (* 1/2 (log PI))
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log 2)) (* 1/2 (log n))) 1) 1)))) into (+ (* 1/2 (log 2)) (* 1/2 (log n)))
* [misc]backup-simplify:  Simplify (+ (* 1 (* 1/2 (log PI))) (* (+ (* 1/2 (log 2)) (* 1/2 (log n))) 1)) into (+ (* 1/2 (log 2)) (+ (* 1/2 (log PI)) (* 1/2 (log n))))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (/ (+ (* 1/2 (log 2)) (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 1)))) into (- (+ (* 1/2 (* (log PI) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/2 (* (log 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (- (+ (* 1/2 (* (log PI) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/2 (* (log 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (log PI)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (log PI) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (log PI) k)))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k))))) (+ (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k))))) (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k)))))) (* 0 (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k)))))))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k))))) (sqrt (/ 1 k))) (/ 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 (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ (* (log PI) 0) (+ (* 0 1) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (log PI)) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log PI)) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (pow (log PI) 2))
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 1) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (+ (log 2) (log n))) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log 2)) (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))
* [misc]backup-simplify:  Simplify (+ (* 1 (* 1/8 (pow (log PI) 2))) (+ (* (+ (* 1/2 (log 2)) (* 1/2 (log n))) (* 1/2 (log PI))) (* (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2)))) 1))) into (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log PI))) (+ (* 1/8 (pow (log PI) 2)) (+ (* 1/4 (* (log PI) (log n))) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2)))))))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (/ (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log PI))) (+ (* 1/8 (pow (log PI) 2)) (+ (* 1/4 (* (log PI) (log n))) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))))) 1)) (* (- (+ (* 1/2 (* (log PI) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/2 (* (log 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))) (/ (+ (* 1/2 (log 2)) (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 1)))) into (+ (* 1/8 (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (+ (* 1/4 (* (log PI) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))) (+ (* 1/8 (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/4 (* (log 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))) (* 1/4 (* (log 2) (* (log PI) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))))))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (- (+ (* 1/2 (* (log PI) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/2 (* (log 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))) +nan.0) (* (+ (* 1/8 (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (+ (* 1/4 (* (log PI) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))) (+ (* 1/8 (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/4 (* (log 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))) (* 1/4 (* (log 2) (* (log PI) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))))) 0))) into (- (+ (* +nan.0 (* (log PI) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (log PI) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))) into (- (+ (* +nan.0 (* (log PI) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (log PI) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log 2) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (log PI) k))))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k))))) (+ (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k))))) (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k)))))) (* 0 (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k)))))) (* 0 (/ 0 (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k)))))))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log 2) (log n)) k))) (exp (* 1/2 (* (log PI) k))))) (sqrt (/ 1 k))) (/ 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 (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ (* (log PI) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (log PI)) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log PI)) 3) 6)) (* (/ (pow (* 1/2 (log PI)) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* 1/48 (pow (log PI) 3))
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (+ (log 2) (log n))) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log 2)) (* 1/2 (log n))) 3) 6)) (* (/ (pow (+ (* 1/2 (log 2)) (* 1/2 (log n))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (log 2) (pow (log n) 2))) (+ (* 1/16 (* (pow (log 2) 2) (log n))) (* 1/48 (pow (log 2) 3)))))
* [misc]backup-simplify:  Simplify (+ (* 1 (* 1/48 (pow (log PI) 3))) (+ (* (+ (* 1/2 (log 2)) (* 1/2 (log n))) (* 1/8 (pow (log PI) 2))) (+ (* (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2)))) (* 1/2 (log PI))) (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (log 2) (pow (log n) 2))) (+ (* 1/16 (* (pow (log 2) 2) (log n))) (* 1/48 (pow (log 2) 3))))) 1)))) into (+ (* 1/16 (* (log 2) (pow (log n) 2))) (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log 2) 2) (log PI))) (+ (* 1/16 (* (log 2) (pow (log PI) 2))) (+ (* 1/16 (* (pow (log PI) 2) (log n))) (+ (* 1/16 (* (pow (log 2) 2) (log n))) (+ (* 1/16 (* (log PI) (pow (log n) 2))) (+ (* 1/48 (pow (log PI) 3)) (+ (* 1/8 (* (log 2) (* (log PI) (log n)))) (* 1/48 (pow (log 2) 3)))))))))))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (/ (+ (* 1/16 (* (log 2) (pow (log n) 2))) (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log 2) 2) (log PI))) (+ (* 1/16 (* (log 2) (pow (log PI) 2))) (+ (* 1/16 (* (pow (log PI) 2) (log n))) (+ (* 1/16 (* (pow (log 2) 2) (log n))) (+ (* 1/16 (* (log PI) (pow (log n) 2))) (+ (* 1/48 (pow (log PI) 3)) (+ (* 1/8 (* (log 2) (* (log PI) (log n)))) (* 1/48 (pow (log 2) 3))))))))))) 1)) (* (- (+ (* 1/2 (* (log PI) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/2 (* (log 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))) (/ (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log PI))) (+ (* 1/8 (pow (log PI) 2)) (+ (* 1/4 (* (log PI) (log n))) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))))) 1)) (* (+ (* 1/8 (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (+ (* 1/4 (* (log PI) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))) (+ (* 1/8 (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/4 (* (log 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))) (* 1/4 (* (log 2) (* (log PI) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))))) (/ (+ (* 1/2 (log 2)) (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 1)))) into (- (+ (* 1/16 (* (log PI) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)))) (+ (* 1/16 (* (pow (log 2) 2) (* (log PI) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (+ (* 1/48 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 3))) (+ (* 1/8 (* (log 2) (* (log PI) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))) (+ (* 1/16 (* (log 2) (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (+ (* 1/16 (* (pow (log PI) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))) (+ (* 1/16 (* (log 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)))) (+ (* 1/48 (* (pow (log 2) 3) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/16 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))) (* 1/48 (* (pow (log PI) 3) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))))))))))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (- (+ (* 1/2 (* (log PI) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/2 (* (log 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))) +nan.0) (+ (* (+ (* 1/8 (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (+ (* 1/4 (* (log PI) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))) (+ (* 1/8 (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/4 (* (log 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))) (* 1/4 (* (log 2) (* (log PI) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))))) +nan.0) (* (- (+ (* 1/16 (* (log PI) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)))) (+ (* 1/16 (* (pow (log 2) 2) (* (log PI) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (+ (* 1/48 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 3))) (+ (* 1/8 (* (log 2) (* (log PI) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))) (+ (* 1/16 (* (log 2) (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (+ (* 1/16 (* (pow (log PI) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))) (+ (* 1/16 (* (log 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)))) (+ (* 1/48 (* (pow (log 2) 3) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/16 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))) (* 1/48 (* (pow (log PI) 3) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))))))))) 0)))) into (- (+ (* +nan.0 (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (log PI) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (log PI) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))) (- (* +nan.0 (* (log 2) (* (log PI) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))))))))))))))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (log PI) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (log PI) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))) (- (* +nan.0 (* (log 2) (* (log PI) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))))))))))))))))))) into (- (+ (* +nan.0 (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (log PI) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (log PI) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (- (* +nan.0 (* (log 2) (* (log PI) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))))))))))))))))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (+ (* +nan.0 (* (pow (log 2) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (log PI) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (log PI) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (log PI) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (- (* +nan.0 (* (log 2) (* (log PI) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))))))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (log PI) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (log PI) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (+ (* +nan.0 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (log 2) (* (log PI) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (* (log PI) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (log PI) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (* +nan.0 (* (log PI) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))))))))))))))))))))))))))))))))
* [misc]approximate:  Taking taylor expansion of (/ (/ (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) (* (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)) (pow PI (/ (/ 1 k) 2)))) (sqrt (/ 1 k))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) (* (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)) (pow PI (/ (/ 1 k) 2)))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) (* (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)) (pow PI (/ (/ 1 k) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 n) 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 n) 2) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 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 (* (/ 1 n) 2) into (/ 2 n)
* [misc]backup-simplify:  Simplify (* (/ 2 n) PI) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) 1/2)
* [misc]taylor:  Taking taylor expansion of (* (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)) (pow PI (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) 2)) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* (/ 1 n) 2) into (/ 2 n)
* [misc]backup-simplify:  Simplify (log (/ 2 n)) into (log (/ 2 n))
* [misc]backup-simplify:  Simplify (* 1/2 (log (/ 2 n))) into (* 1/2 (log (/ 2 n)))
* [misc]backup-simplify:  Simplify (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2)))) into (exp (* 1/2 (/ (log (/ 2 n)) k)))
* [misc]taylor:  Taking taylor expansion of (pow PI (/ (/ 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* (/ (/ 1 k) 2) (log PI))) into (exp (* 1/2 (/ (log PI) k)))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (log (/ 2 n)) k))) (exp (* 1/2 (/ (log PI) k)))) into (* (exp (* 1/2 (/ (log (/ 2 n)) k))) (exp (* 1/2 (/ (log PI) k))))
* [misc]backup-simplify:  Simplify (/ (pow (* 2 (/ PI n)) 1/2) (* (exp (* 1/2 (/ (log (/ 2 n)) k))) (exp (* 1/2 (/ (log PI) k))))) into (* (sqrt (/ (* PI 2) n)) (/ 1 (* (exp (* 1/2 (/ (log (/ 2 n)) k))) (exp (* 1/2 (/ (log PI) 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 (/ (* (sqrt (/ (* PI 2) n)) (/ 1 (* (exp (* 1/2 (/ (log (/ 2 n)) k))) (exp (* 1/2 (/ (log PI) k)))))) +nan.0) into (* +nan.0 (* (/ (sqrt 2) (* (exp (* 1/2 (/ (log (/ 2 n)) k))) (exp (* 1/2 (/ (log PI) k))))) (sqrt (/ PI n))))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) (* (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)) (pow PI (/ (/ 1 k) 2)))) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) (* (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)) (pow PI (/ (/ 1 k) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 n) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 n) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (* (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)) (pow PI (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n))
* [misc]backup-simplify:  Simplify (* (/ 1/2 k) (- (log 2) (log n))) into (* 1/2 (/ (- (log 2) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log 2) (log n)) k))) into (exp (* 1/2 (/ (- (log 2) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (pow PI (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log PI)) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (* (/ 1/2 k) (log PI)) into (* 1/2 (/ (log PI) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (log PI) k))) into (exp (* 1/2 (/ (log PI) k)))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))) into (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) (sqrt (/ 1 k))) into (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) (* (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)) (pow PI (/ (/ 1 k) 2)))) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) (* (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)) (pow PI (/ (/ 1 k) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 n) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 n) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (* (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)) (pow PI (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) 2) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n))
* [misc]backup-simplify:  Simplify (* (/ 1/2 k) (- (log 2) (log n))) into (* 1/2 (/ (- (log 2) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log 2) (log n)) k))) into (exp (* 1/2 (/ (- (log 2) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (pow PI (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log PI)) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (* (/ 1/2 k) (log PI)) into (* 1/2 (/ (log PI) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (log PI) k))) into (exp (* 1/2 (/ (log PI) k)))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))) into (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) (sqrt (/ 1 k))) into (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (- (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (- (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (/ (- (log 2) (log n)) k))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ (- (log 2) (log n)) k)) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (- (log 2) (log n)) k) in k
* [misc]taylor:  Taking taylor expansion of (- (log 2) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n))
* [misc]backup-simplify:  Simplify (/ (- (log 2) (log n)) 1) into (- (log 2) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log 2) (log n))) into (* 1/2 (- (log 2) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log 2) (log n)) k))) into (exp (* 1/2 (/ (- (log 2) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (/ (log PI) k))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ (log PI) k)) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (log PI) k) in k
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ (log PI) 1) into (log PI)
* [misc]backup-simplify:  Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (log PI) k))) into (exp (* 1/2 (/ (log PI) k)))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))) into (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (* 0 (log PI))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (log PI) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log 2) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) 0) (* 0 (exp (* 1/2 (/ (log PI) k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) (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 (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) 0) (* 0 (exp (* 1/2 (/ (log PI) k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (log PI)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (log PI) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (/ (log PI) k)))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))))) (* 0 (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))))))) 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 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) (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 (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (/ (log PI) k)))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))))) (* 0 (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))))))
* [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)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (log PI) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (/ (log PI) k))))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))))) (* 0 (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))))) (* 0 (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))))))) 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 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) (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 (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (/ (log PI) k))))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))))) (* 0 (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))))) (* 0 (/ 0 (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (/ (- (log 2) (log n)) k))) (exp (* 1/2 (/ (log PI) k)))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (/ (- (log 2) (log (/ 1 n))) (/ 1 k)))) (exp (* 1/2 (/ (log PI) (/ 1 k)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (/ (- (log 2) (log (/ 1 n))) (/ 1 k)))) (exp (* 1/2 (/ (log PI) (/ 1 k)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (/ (- (log 2) (log (/ 1 n))) (/ 1 k)))) (exp (* 1/2 (/ (log PI) (/ 1 k)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- (log 2) (log (/ 1 n))) k))) (* k (exp (* 1/2 (* (log PI) k))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- (log 2) (log (/ 1 n))) k))) (* (pow k 3) (exp (* 1/2 (* (log PI) k))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- (log 2) (log (/ 1 n))) k))) (* (pow k 2) (exp (* 1/2 (* (log PI) k))))))))))))
* [misc]approximate:  Taking taylor expansion of (/ (/ (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) (* (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)) (pow PI (/ (/ 1 (- k)) 2)))) (sqrt (/ 1 (- k)))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) (* (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)) (pow PI (/ (/ 1 (- k)) 2)))) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) (* (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)) (pow PI (/ (/ 1 (- k)) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 (- n)) 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 (- n)) 2) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 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 (* (/ -1 n) 2) into (/ -2 n)
* [misc]backup-simplify:  Simplify (* (/ -2 n) PI) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* -2 (/ PI n))))) into (pow (* -2 (/ PI n)) 1/2)
* [misc]taylor:  Taking taylor expansion of (* (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)) (pow PI (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* (/ -1 n) 2) into (/ -2 n)
* [misc]backup-simplify:  Simplify (log (/ -2 n)) into (log (/ -2 n))
* [misc]backup-simplify:  Simplify (* -1/2 (log (/ -2 n))) into (* -1/2 (log (/ -2 n)))
* [misc]backup-simplify:  Simplify (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2)))) into (exp (* -1/2 (/ (log (/ -2 n)) k)))
* [misc]taylor:  Taking taylor expansion of (pow PI (/ (/ 1 (- k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (* -1/2 (log PI)) into (* -1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* (/ (/ 1 (- k)) 2) (log PI))) into (exp (* -1/2 (/ (log PI) k)))
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (log (/ -2 n)) k))) (exp (* -1/2 (/ (log PI) k)))) into (* (exp (* -1/2 (/ (log PI) k))) (exp (* -1/2 (/ (log (/ -2 n)) k))))
* [misc]backup-simplify:  Simplify (/ (pow (* -2 (/ PI n)) 1/2) (* (exp (* -1/2 (/ (log PI) k))) (exp (* -1/2 (/ (log (/ -2 n)) k))))) into (* (/ 1 (* (exp (* -1/2 (/ (log (/ -2 n)) k))) (exp (* -1/2 (/ (log PI) k))))) (sqrt (/ (* PI -2) 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 (/ (* (/ 1 (* (exp (* -1/2 (/ (log (/ -2 n)) k))) (exp (* -1/2 (/ (log PI) k))))) (sqrt (/ (* PI -2) n))) +nan.0) into (* +nan.0 (/ (sqrt (* -2 (/ PI n))) (* (exp (* -1/2 (/ (log PI) k))) (exp (* -1/2 (/ (log (/ -2 n)) k))))))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) (* (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)) (pow PI (/ (/ 1 (- k)) 2)))) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) (* (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)) (pow PI (/ (/ 1 (- k)) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 (- n)) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (* (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)) (pow PI (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (log -2) into (log -2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n))
* [misc]backup-simplify:  Simplify (* (/ -1/2 k) (- (log -2) (log n))) into (* -1/2 (/ (- (log -2) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log -2) (log n)) k))) into (exp (* -1/2 (/ (- (log -2) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (pow PI (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log PI)) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (* (/ -1/2 k) (log PI)) into (* -1/2 (/ (log PI) k))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (log PI) k))) into (exp (* -1/2 (/ (log PI) k)))
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))) into (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]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 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (sqrt (/ -1 k)) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) (* (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)) (pow PI (/ (/ 1 (- k)) 2)))) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) (* (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)) (pow PI (/ (/ 1 (- k)) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 (- n)) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (* (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)) (pow PI (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) 2) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (log -2) into (log -2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n))
* [misc]backup-simplify:  Simplify (* (/ -1/2 k) (- (log -2) (log n))) into (* -1/2 (/ (- (log -2) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log -2) (log n)) k))) into (exp (* -1/2 (/ (- (log -2) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (pow PI (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log PI)) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (* (/ -1/2 k) (log PI)) into (* -1/2 (/ (log PI) k))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (log PI) k))) into (exp (* -1/2 (/ (log PI) k)))
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))) into (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]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 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (sqrt (/ -1 k)) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))))
* [misc]taylor:  Taking taylor expansion of (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (sqrt (/ -1 k)) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (- (log (* -2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (- (log (* -2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* -2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* -2 PI) in k
* [misc]taylor:  Taking taylor expansion of -2 in k
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ -1 k)) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ -1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ -1 k) in k
* [misc]taylor:  Taking taylor expansion of -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]taylor:  Taking taylor expansion of (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* -1/2 (/ (- (log -2) (log n)) k))) in k
* [misc]taylor:  Taking taylor expansion of (* -1/2 (/ (- (log -2) (log n)) k)) in k
* [misc]taylor:  Taking taylor expansion of -1/2 in k
* [misc]backup-simplify:  Simplify -1/2 into -1/2
* [misc]taylor:  Taking taylor expansion of (/ (- (log -2) (log n)) k) in k
* [misc]taylor:  Taking taylor expansion of (- (log -2) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log -2) in k
* [misc]taylor:  Taking taylor expansion of -2 in k
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]backup-simplify:  Simplify (log -2) into (log -2)
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n))
* [misc]backup-simplify:  Simplify (/ (- (log -2) (log n)) 1) into (- (log -2) (log n))
* [misc]backup-simplify:  Simplify (* -1/2 (- (log -2) (log n))) into (* -1/2 (- (log -2) (log n)))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log -2) (log n)) k))) into (exp (* -1/2 (/ (- (log -2) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (exp (* -1/2 (/ (log PI) k))) in k
* [misc]taylor:  Taking taylor expansion of (* -1/2 (/ (log PI) k)) in k
* [misc]taylor:  Taking taylor expansion of -1/2 in k
* [misc]backup-simplify:  Simplify -1/2 into -1/2
* [misc]taylor:  Taking taylor expansion of (/ (log PI) k) in k
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ (log PI) 1) into (log PI)
* [misc]backup-simplify:  Simplify (* -1/2 (log PI)) into (* -1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (log PI) k))) into (exp (* -1/2 (/ (log PI) k)))
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))) into (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))
* [misc]backup-simplify:  Simplify (* 0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) 0) (* 0 (exp (* -1/2 (/ (log PI) k))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* +nan.0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (- (* +nan.0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))))) into (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))))) into (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (* 0 (log PI))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (log PI) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log -2) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) 0) (* 0 (exp (* -1/2 (/ (log PI) k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))) (/ 0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (sqrt (/ -1 k)) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) 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 (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (log PI) k)))))) 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 0) (+ (* +nan.0 0) (* +nan.0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))))
* [misc]backup-simplify:  Simplify (- (/ 0 (- (* +nan.0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))))) (+ (* (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))))) (/ (- (* +nan.0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))))) (- (* +nan.0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (* 0 (log PI)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (log PI) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (log PI) k)))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))) (/ 0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))))) (* 0 (/ 0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))))))) 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 (- (log (* -2 PI)) (log n)))) (* (sqrt (/ -1 k)) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) 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 (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (log PI) k))))))) 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 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))))))) into (- (* +nan.0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))))
* [misc]backup-simplify:  Simplify (- (/ 0 (- (* +nan.0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))))) (+ (* (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))))) (/ (- (* +nan.0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))))) (- (* +nan.0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))))))) (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))))) (/ (- (* +nan.0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))))) (- (* +nan.0 (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log -2) (log n)) k))) (exp (* -1/2 (/ (log PI) k)))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (* (exp (* -1/2 (/ (- (log -2) (log (/ 1 (- n)))) (/ 1 (- k))))) (exp (* -1/2 (/ (log PI) (/ 1 (- k))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (* (exp (* -1/2 (/ (- (log -2) (log (/ 1 (- n)))) (/ 1 (- k))))) (exp (* -1/2 (/ (log PI) (/ 1 (- k))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (* (exp (* -1/2 (/ (- (log -2) (log (/ 1 (- n)))) (/ 1 (- k))))) (exp (* -1/2 (/ (log PI) (/ 1 (- k)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k))) (exp (* 1/2 (* (log PI) k)))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k))) (* (exp (* 1/2 (* (log PI) k))) k)))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k))) (* (exp (* 1/2 (* (log PI) k))) (pow k 2))))))))))
* * * * [misc]progress:  [ 4 / 4 ] generating series at (2 1 1 1)
* [misc]approximate:  Taking taylor expansion of (* (* n 2) PI) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) n) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
* * * [misc]progress:  simplifying candidates
* * * * [misc]progress:  [ 1 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (log1p (expm1 (pow (* (* n 2) PI) (/ 1 2)))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 2 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (expm1 (log1p (pow (* (* n 2) PI) (/ 1 2)))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 3 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (exp (* (log (* (* n 2) PI)) (/ 1 2))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* (* n 2) PI)) (/ 1 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (92 enodes)
* * [misc]simplify:  iters left: 2 (180 enodes)
* * [misc]simplify:  iters left: 1 (389 enodes)
* [exit]simplify:  Simplified to (fma (/ 1 2) (log (* n 2)) (/ (log PI) 2))
* [misc]simplify:  Simplified (2 1 1 1) to (λ (k n) (/ (/ (exp (fma (/ 1 2) (log (* n 2)) (/ (log PI) 2))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 4 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (exp (* (log (* (* n 2) PI)) (/ 1 2))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 5 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (* 1 (/ 1 2))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n 2) PI)
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* * [misc]simplify:  iters left: 2 (15 enodes)
* * [misc]simplify:  iters left: 1 (17 enodes)
* [exit]simplify:  Simplified to (* (* n 2) PI)
* [misc]simplify:  Simplified (2 1 1 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (* 1 (/ 1 2))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 6 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) (cbrt (/ 1 2))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (cbrt (/ 1 2))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (6 enodes)
* [exit]simplify:  Simplified to (cbrt (/ 1 2))
* [misc]simplify:  Simplified (2 1 1 2) to (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) (cbrt (/ 1 2))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 7 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) (sqrt (/ 1 2))) (sqrt (/ 1 2))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (/ 1 2))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (6 enodes)
* [exit]simplify:  Simplified to (sqrt (/ 1 2))
* [misc]simplify:  Simplified (2 1 1 2) to (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) (sqrt (/ 1 2))) (sqrt (/ 1 2))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 8 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) 1) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ 1 2)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (5 enodes)
* [exit]simplify:  Simplified to (/ 1 2)
* [misc]simplify:  Simplified (2 1 1 2) to (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) 1) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 9 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) 1) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ 1 2)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (5 enodes)
* [exit]simplify:  Simplified to (/ 1 2)
* [misc]simplify:  Simplified (2 1 1 2) to (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) 1) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 10 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (pow (* n 2) (/ 1 2)) (pow PI (/ 1 2))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n 2) (/ 1 2))
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (9 enodes)
* [exit]simplify:  Simplified to (pow (* n 2) (/ 1 2))
* [misc]simplify:  Simplified (2 1 1 1) to (λ (k n) (/ (/ (* (pow (* n 2) (/ 1 2)) (pow PI (/ 1 2))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 11 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) (/ 1 2)) 1) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 12 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (exp (log (pow (* (* n 2) PI) (/ 1 2)))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 13 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (log (exp (pow (* (* n 2) PI) (/ 1 2)))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 14 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 15 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (cbrt (* (* (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ 1 2)))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 16 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ 1 2)))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 17 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* 1 (pow (* (* n 2) PI) (/ 1 2))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 18 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (log1p (expm1 (pow (* n 2) (/ k 2)))) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 19 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (expm1 (log1p (pow (* n 2) (/ k 2)))) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 20 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (exp (* (log (* n 2)) (/ k 2))) (pow PI (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* n 2)) (/ k 2))
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* * [misc]simplify:  iters left: 2 (43 enodes)
* * [misc]simplify:  iters left: 1 (57 enodes)
* [exit]simplify:  Simplified to (* (log (* n 2)) (/ k 2))
* [misc]simplify:  Simplified (2 1 2 1 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (exp (* (log (* n 2)) (/ k 2))) (pow PI (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 21 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (exp (* (log (* n 2)) (/ k 2))) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 22 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (* 1 (/ k 2))) (pow PI (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n 2)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n 2)
* [misc]simplify:  Simplified (2 1 2 1 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (* 1 (/ k 2))) (pow PI (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 23 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (pow (* n 2) (* (cbrt (/ k 2)) (cbrt (/ k 2)))) (cbrt (/ k 2))) (pow PI (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (cbrt (/ k 2))
* * [misc]simplify:  iters left: 3 (4 enodes)
* [exit]simplify:  Simplified to (cbrt (/ k 2))
* [misc]simplify:  Simplified (2 1 2 1 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (pow (* n 2) (* (cbrt (/ k 2)) (cbrt (/ k 2)))) (cbrt (/ k 2))) (pow PI (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 24 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (pow (* n 2) (sqrt (/ k 2))) (sqrt (/ k 2))) (pow PI (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (/ k 2))
* * [misc]simplify:  iters left: 3 (4 enodes)
* [exit]simplify:  Simplified to (sqrt (/ k 2))
* [misc]simplify:  Simplified (2 1 2 1 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (pow (* n 2) (sqrt (/ k 2))) (sqrt (/ k 2))) (pow PI (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 25 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (pow (* n 2) 1) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ k 2)
* * [misc]simplify:  iters left: 2 (3 enodes)
* [exit]simplify:  Simplified to (/ k 2)
* [misc]simplify:  Simplified (2 1 2 1 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (pow (* n 2) 1) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 26 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (pow (* n 2) k) (/ 1 2)) (pow PI (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ 1 2)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (5 enodes)
* [exit]simplify:  Simplified to (/ 1 2)
* [misc]simplify:  Simplified (2 1 2 1 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (pow (* n 2) k) (/ 1 2)) (pow PI (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 27 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (pow n (/ k 2)) (pow 2 (/ k 2))) (pow PI (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow n (/ k 2))
* * [misc]simplify:  iters left: 3 (5 enodes)
* [exit]simplify:  Simplified to (pow n (/ k 2))
* [misc]simplify:  Simplified (2 1 2 1 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (pow n (/ k 2)) (pow 2 (/ k 2))) (pow PI (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 28 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (pow (* n 2) (/ k 2)) 1) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 29 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (exp (log (pow (* n 2) (/ k 2)))) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 30 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (log (exp (pow (* n 2) (/ k 2)))) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 31 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (* (cbrt (pow (* n 2) (/ k 2))) (cbrt (pow (* n 2) (/ k 2)))) (cbrt (pow (* n 2) (/ k 2)))) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 32 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (cbrt (* (* (pow (* n 2) (/ k 2)) (pow (* n 2) (/ k 2))) (pow (* n 2) (/ k 2)))) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 33 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (sqrt (pow (* n 2) (/ k 2))) (sqrt (pow (* n 2) (/ k 2)))) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 34 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* 1 (pow (* n 2) (/ k 2))) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 35 / 130 ] simplifiying candidate #<alt (λ (k n) (log1p (expm1 (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))))>
* * * * [misc]progress:  [ 36 / 130 ] simplifiying candidate #<alt (λ (k n) (expm1 (log1p (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))))>
* * * * [misc]progress:  [ 37 / 130 ] simplifiying candidate #<alt (λ (k n) (pow (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)) 1))>
* * * * [misc]progress:  [ 38 / 130 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (+ (* (log (* n 2)) (/ k 2)) (* (log PI) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (+ (* (log (* n 2)) (/ k 2)) (* (log PI) (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (51 enodes)
* * [misc]simplify:  iters left: 4 (127 enodes)
* * [misc]simplify:  iters left: 3 (426 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 39 / 130 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (+ (* (log (* n 2)) (/ k 2)) (log (pow PI (/ k 2))))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (+ (* (log (* n 2)) (/ k 2)) (log (pow PI (/ k 2))))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (49 enodes)
* * [misc]simplify:  iters left: 4 (115 enodes)
* * [misc]simplify:  iters left: 3 (373 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI 2) n)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* (* PI 2) n)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 40 / 130 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (+ (* (log (* n 2)) (/ k 2)) (* (log PI) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (+ (* (log (* n 2)) (/ k 2)) (* (log PI) (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (51 enodes)
* * [misc]simplify:  iters left: 4 (127 enodes)
* * [misc]simplify:  iters left: 3 (426 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 41 / 130 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (+ (* (log (* n 2)) (/ k 2)) (log (pow PI (/ k 2))))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (+ (* (log (* n 2)) (/ k 2)) (log (pow PI (/ k 2))))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (49 enodes)
* * [misc]simplify:  iters left: 4 (115 enodes)
* * [misc]simplify:  iters left: 3 (373 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI 2) n)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* (* PI 2) n)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 42 / 130 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (+ (log (pow (* n 2) (/ k 2))) (* (log PI) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (+ (log (pow (* n 2) (/ k 2))) (* (log PI) (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (45 enodes)
* * [misc]simplify:  iters left: 4 (107 enodes)
* * [misc]simplify:  iters left: 3 (320 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI 2) n)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* (* PI 2) n)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 43 / 130 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (+ (log (pow (* n 2) (/ k 2))) (log (pow PI (/ k 2))))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (+ (log (pow (* n 2) (/ k 2))) (log (pow PI (/ k 2))))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (44 enodes)
* * [misc]simplify:  iters left: 4 (104 enodes)
* * [misc]simplify:  iters left: 3 (321 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 44 / 130 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (log (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (log (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (42 enodes)
* * [misc]simplify:  iters left: 4 (86 enodes)
* * [misc]simplify:  iters left: 3 (240 enodes)
* [exit]simplify:  Simplified to (+ (fma (log (* (* PI 2) n)) (/ 1 2) (- (log (sqrt k)))) (* (- (/ k 2)) (log (* (* PI 2) n))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (+ (fma (log (* (* PI 2) n)) (/ 1 2) (- (log (sqrt k)))) (* (- (/ k 2)) (log (* (* PI 2) n))))))
* * * * [misc]progress:  [ 45 / 130 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (+ (* (log (* n 2)) (/ k 2)) (* (log PI) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (+ (* (log (* n 2)) (/ k 2)) (* (log PI) (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (51 enodes)
* * [misc]simplify:  iters left: 4 (127 enodes)
* * [misc]simplify:  iters left: 3 (426 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 46 / 130 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (+ (* (log (* n 2)) (/ k 2)) (log (pow PI (/ k 2))))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (+ (* (log (* n 2)) (/ k 2)) (log (pow PI (/ k 2))))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (49 enodes)
* * [misc]simplify:  iters left: 4 (115 enodes)
* * [misc]simplify:  iters left: 3 (373 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI 2) n)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* (* PI 2) n)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 47 / 130 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (+ (* (log (* n 2)) (/ k 2)) (* (log PI) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (+ (* (log (* n 2)) (/ k 2)) (* (log PI) (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (51 enodes)
* * [misc]simplify:  iters left: 4 (127 enodes)
* * [misc]simplify:  iters left: 3 (426 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 48 / 130 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (+ (* (log (* n 2)) (/ k 2)) (log (pow PI (/ k 2))))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (+ (* (log (* n 2)) (/ k 2)) (log (pow PI (/ k 2))))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (49 enodes)
* * [misc]simplify:  iters left: 4 (115 enodes)
* * [misc]simplify:  iters left: 3 (373 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI 2) n)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* (* PI 2) n)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 49 / 130 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (+ (log (pow (* n 2) (/ k 2))) (* (log PI) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (+ (log (pow (* n 2) (/ k 2))) (* (log PI) (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (45 enodes)
* * [misc]simplify:  iters left: 4 (107 enodes)
* * [misc]simplify:  iters left: 3 (320 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI 2) n)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* (* PI 2) n)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 50 / 130 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (+ (log (pow (* n 2) (/ k 2))) (log (pow PI (/ k 2))))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (+ (log (pow (* n 2) (/ k 2))) (log (pow PI (/ k 2))))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (44 enodes)
* * [misc]simplify:  iters left: 4 (104 enodes)
* * [misc]simplify:  iters left: 3 (321 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 51 / 130 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (log (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n 2) PI)) (/ 1 2)) (log (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (42 enodes)
* * [misc]simplify:  iters left: 4 (86 enodes)
* * [misc]simplify:  iters left: 3 (240 enodes)
* [exit]simplify:  Simplified to (+ (fma (log (* (* PI 2) n)) (/ 1 2) (- (log (sqrt k)))) (* (- (/ k 2)) (log (* (* PI 2) n))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (+ (fma (log (* (* PI 2) n)) (/ 1 2) (- (log (sqrt k)))) (* (- (/ k 2)) (log (* (* PI 2) n))))))
* * * * [misc]progress:  [ 52 / 130 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (log (pow (* (* n 2) PI) (/ 1 2))) (+ (* (log (* n 2)) (/ k 2)) (* (log PI) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (log (pow (* (* n 2) PI) (/ 1 2))) (+ (* (log (* n 2)) (/ k 2)) (* (log PI) (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (49 enodes)
* * [misc]simplify:  iters left: 4 (112 enodes)
* * [misc]simplify:  iters left: 3 (332 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 53 / 130 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (log (pow (* (* n 2) PI) (/ 1 2))) (+ (* (log (* n 2)) (/ k 2)) (log (pow PI (/ k 2))))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (log (pow (* (* n 2) PI) (/ 1 2))) (+ (* (log (* n 2)) (/ k 2)) (log (pow PI (/ k 2))))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (46 enodes)
* * [misc]simplify:  iters left: 4 (103 enodes)
* * [misc]simplify:  iters left: 3 (306 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 54 / 130 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (log (pow (* (* n 2) PI) (/ 1 2))) (+ (* (log (* n 2)) (/ k 2)) (* (log PI) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (log (pow (* (* n 2) PI) (/ 1 2))) (+ (* (log (* n 2)) (/ k 2)) (* (log PI) (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (49 enodes)
* * [misc]simplify:  iters left: 4 (112 enodes)
* * [misc]simplify:  iters left: 3 (332 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 55 / 130 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (log (pow (* (* n 2) PI) (/ 1 2))) (+ (* (log (* n 2)) (/ k 2)) (log (pow PI (/ k 2))))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (log (pow (* (* n 2) PI) (/ 1 2))) (+ (* (log (* n 2)) (/ k 2)) (log (pow PI (/ k 2))))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (46 enodes)
* * [misc]simplify:  iters left: 4 (103 enodes)
* * [misc]simplify:  iters left: 3 (306 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 56 / 130 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (log (pow (* (* n 2) PI) (/ 1 2))) (+ (log (pow (* n 2) (/ k 2))) (* (log PI) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (log (pow (* (* n 2) PI) (/ 1 2))) (+ (log (pow (* n 2) (/ k 2))) (* (log PI) (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (42 enodes)
* * [misc]simplify:  iters left: 4 (97 enodes)
* * [misc]simplify:  iters left: 3 (269 enodes)
* [exit]simplify:  Simplified to (fma (log (* n (* PI 2))) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* n (* PI 2))) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 57 / 130 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (log (pow (* (* n 2) PI) (/ 1 2))) (+ (log (pow (* n 2) (/ k 2))) (log (pow PI (/ k 2))))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (log (pow (* (* n 2) PI) (/ 1 2))) (+ (log (pow (* n 2) (/ k 2))) (log (pow PI (/ k 2))))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (41 enodes)
* * [misc]simplify:  iters left: 4 (94 enodes)
* * [misc]simplify:  iters left: 3 (268 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))))
* * * * [misc]progress:  [ 58 / 130 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (log (pow (* (* n 2) PI) (/ 1 2))) (log (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (log (pow (* (* n 2) PI) (/ 1 2))) (log (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (75 enodes)
* * [misc]simplify:  iters left: 3 (187 enodes)
* [exit]simplify:  Simplified to (- (* (log (* n (* PI 2))) (- (/ 1 2) (/ k 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (log (* n (* PI 2))) (- (/ 1 2) (/ k 2))) (log (sqrt k)))))
* * * * [misc]progress:  [ 59 / 130 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (log (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (51 enodes)
* * [misc]simplify:  iters left: 3 (108 enodes)
* * [misc]simplify:  iters left: 2 (259 enodes)
* [exit]simplify:  Simplified to (- (* (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2))) (log (sqrt k)))))
* * * * [misc]progress:  [ 60 / 130 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))))>
* * * * [misc]progress:  [ 61 / 130 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))))>
* * * * [misc]progress:  [ 62 / 130 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (/ (* (* (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ 1 2))) (* (* (* (pow (* n 2) (/ k 2)) (pow (* n 2) (/ k 2))) (pow (* n 2) (/ k 2))) (* (* (pow PI (/ k 2)) (pow PI (/ k 2))) (pow PI (/ k 2))))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (* (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ 1 2))) (* (* (* (pow (* n 2) (/ k 2)) (pow (* n 2) (/ k 2))) (pow (* n 2) (/ k 2))) (* (* (pow PI (/ k 2)) (pow PI (/ k 2))) (pow PI (/ k 2))))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (24 enodes)
* * [misc]simplify:  iters left: 5 (50 enodes)
* * [misc]simplify:  iters left: 4 (183 enodes)
* [exit]simplify:  Simplified to (* (/ (pow (* (* PI 2) n) (/ 1 2)) (* (* (* (sqrt k) k) (pow (* n 2) (/ k 2))) (* (pow (* n 2) (/ k 2)) (pow (* n 2) (/ k 2))))) (* (/ (pow (* (* PI 2) n) (/ 1 2)) (pow PI (/ k 2))) (/ (pow (* (* PI 2) n) (/ 1 2)) (* (pow PI (/ k 2)) (pow PI (/ k 2))))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (cbrt (* (/ (pow (* (* PI 2) n) (/ 1 2)) (* (* (* (sqrt k) k) (pow (* n 2) (/ k 2))) (* (pow (* n 2) (/ k 2)) (pow (* n 2) (/ k 2))))) (* (/ (pow (* (* PI 2) n) (/ 1 2)) (pow PI (/ k 2))) (/ (pow (* (* PI 2) n) (/ 1 2)) (* (pow PI (/ k 2)) (pow PI (/ k 2))))))))
* * * * [misc]progress:  [ 63 / 130 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (/ (* (* (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ 1 2))) (* (* (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (* (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ 1 2))) (* (* (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (22 enodes)
* * [misc]simplify:  iters left: 5 (49 enodes)
* * [misc]simplify:  iters left: 4 (171 enodes)
* [exit]simplify:  Simplified to (/ (* (/ (pow (* (* PI 2) n) (/ 1 2)) (* (pow PI (/ k 2)) (pow (* n 2) (/ k 2)))) (/ (pow (* (* PI 2) n) (/ 1 2)) (* (pow PI (/ k 2)) (pow (* n 2) (/ k 2))))) (/ (* (sqrt k) k) (/ (pow (* (* PI 2) n) (/ 1 2)) (* (pow PI (/ k 2)) (pow (* n 2) (/ k 2))))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (cbrt (/ (* (/ (pow (* (* PI 2) n) (/ 1 2)) (* (pow PI (/ k 2)) (pow (* n 2) (/ k 2)))) (/ (pow (* (* PI 2) n) (/ 1 2)) (* (pow PI (/ k 2)) (pow (* n 2) (/ k 2))))) (/ (* (sqrt k) k) (/ (pow (* (* PI 2) n) (/ 1 2)) (* (pow PI (/ k 2)) (pow (* n 2) (/ k 2))))))))
* * * * [misc]progress:  [ 64 / 130 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (* (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (44 enodes)
* * [misc]simplify:  iters left: 4 (138 enodes)
* [exit]simplify:  Simplified to (* (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (* k (sqrt k))) (* (/ (pow (* (* PI n) 2) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (/ (pow (* (* PI n) 2) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (cbrt (* (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (* k (sqrt k))) (* (/ (pow (* (* PI n) 2) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (/ (pow (* (* PI n) 2) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))))))
* * * * [misc]progress:  [ 65 / 130 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k))) (cbrt (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))) (cbrt (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))))>
* * * * [misc]progress:  [ 66 / 130 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))))>
* * * * [misc]progress:  [ 67 / 130 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k))) (sqrt (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))))>
* * * * [misc]progress:  [ 68 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (- (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (- (sqrt k))))>
* * * * [misc]progress:  [ 69 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (35 enodes)
* * [misc]simplify:  iters left: 4 (50 enodes)
* * [misc]simplify:  iters left: 3 (55 enodes)
* * [misc]simplify:  iters left: 2 (58 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (sqrt k))) (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (sqrt k))) (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (sqrt k)))) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 70 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))))) (sqrt (sqrt k))) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (38 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt (sqrt k)))) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))))) (sqrt (sqrt k))) (/ (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 71 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))))) 1) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))))) 1)
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (47 enodes)
* * [misc]simplify:  iters left: 2 (57 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))))) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt k))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))))) (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt k))))
* * * * [misc]progress:  [ 72 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 73 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt (sqrt k))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt (sqrt k))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt (sqrt k))) (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 74 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) 1) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) 1)
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt k))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt k))))
* * * * [misc]progress:  [ 75 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* * [misc]simplify:  iters left: 2 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 76 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))) (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))) (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))) (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 77 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) 1) (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) 1)
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* * [misc]simplify:  iters left: 2 (24 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (pow PI (/ 1 2)) (pow PI (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (/ 1 2)) (* (sqrt k) (pow PI (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (/ (pow PI (/ 1 2)) (* (sqrt k) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 78 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (50 enodes)
* * [misc]simplify:  iters left: 3 (86 enodes)
* * [misc]simplify:  iters left: 2 (125 enodes)
* * [misc]simplify:  iters left: 1 (146 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (/ (* (pow (* n 2) (/ k 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (/ (* (pow (* n 2) (/ k 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (pow (* n (* PI 2)) (/ 1 2))))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (pow PI (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 79 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n 2) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (56 enodes)
* * [misc]simplify:  iters left: 2 (64 enodes)
* * [misc]simplify:  iters left: 1 (67 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (sqrt k))) (/ (pow (* n 2) (/ k 2)) (cbrt (pow (* (* n 2) PI) (/ 1 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (sqrt k))) (/ (pow (* n 2) (/ k 2)) (cbrt (pow (* (* n 2) PI) (/ 1 2))))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (pow PI (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 80 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n 2) (/ k 2))) 1) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n 2) (/ k 2))) 1)
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (65 enodes)
* * [misc]simplify:  iters left: 2 (155 enodes)
* * [misc]simplify:  iters left: 1 (379 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n 2) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n 2) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (* (pow PI (/ k 2)) (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n 2) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (* (pow PI (/ k 2)) (sqrt k)))))
* * * * [misc]progress:  [ 81 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (45 enodes)
* * [misc]simplify:  iters left: 2 (46 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (* (pow (* n 2) (/ k 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (* (pow (* n 2) (/ k 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (pow PI (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 82 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2)))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (pow PI (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (sqrt (sqrt k)) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 83 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2))) 1) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2))) 1)
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (37 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (pow (* n 2) (/ k 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (pow (* n 2) (/ k 2))) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (pow PI (/ k 2)) (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (pow (* n 2) (/ k 2))) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (pow PI (/ k 2)) (sqrt k)))))
* * * * [misc]progress:  [ 84 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow PI (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* * [misc]simplify:  iters left: 2 (31 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (pow (* 2 n) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ 1 (pow (* 2 n) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow PI (/ k 2))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow PI (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* PI 2)) (/ 1 2)) (* (pow PI (/ k 2)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ 1 (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (pow PI (/ k 2)) (cbrt (sqrt k))))))
* * * * [misc]progress:  [ 85 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (pow (* n 2) (/ k 2))) (sqrt (sqrt k))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow PI (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (pow (* n 2) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (pow (* 2 n) (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ 1 (pow (* 2 n) (/ k 2))) (sqrt (sqrt k))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow PI (/ k 2))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow PI (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* PI 2)) (/ 1 2)) (* (pow PI (/ k 2)) (sqrt (sqrt k))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ 1 (pow (* n 2) (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (pow PI (/ k 2)) (sqrt (sqrt k))))))
* * * * [misc]progress:  [ 86 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (pow (* n 2) (/ k 2))) 1) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow PI (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ 1 (pow (* n 2) (/ k 2))) 1)
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* [exit]simplify:  Simplified to (/ 1 (pow (* 2 n) (/ k 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ 1 (pow (* 2 n) (/ k 2))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow PI (/ k 2))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow PI (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* [exit]simplify:  Simplified to (/ (pow (* 2 (* PI n)) (/ 1 2)) (* (sqrt k) (pow PI (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ 1 (pow (* 2 n) (/ k 2))) (/ (pow (* 2 (* PI n)) (/ 1 2)) (* (sqrt k) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 87 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ 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)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (41 enodes)
* * [misc]simplify:  iters left: 3 (47 enodes)
* * [misc]simplify:  iters left: 2 (57 enodes)
* * [misc]simplify:  iters left: 1 (59 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* n 2) (/ k 2))) (* (pow PI (/ k 2)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* n 2) (/ k 2))) (* (pow PI (/ k 2)) (cbrt (sqrt k))))))
* * * * [misc]progress:  [ 88 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ 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)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (41 enodes)
* * [misc]simplify:  iters left: 3 (47 enodes)
* * [misc]simplify:  iters left: 2 (57 enodes)
* * [misc]simplify:  iters left: 1 (59 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* n 2) (/ k 2))) (* (pow PI (/ k 2)) (sqrt (sqrt k))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* n 2) (/ k 2))) (* (pow PI (/ k 2)) (sqrt (sqrt k))))))
* * * * [misc]progress:  [ 89 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ 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
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* 1 (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (46 enodes)
* * [misc]simplify:  iters left: 2 (56 enodes)
* * [misc]simplify:  iters left: 1 (58 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (* (sqrt k) (pow PI (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* 1 (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (* (sqrt k) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 90 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ 1 (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* (* n 2) PI) (/ 1 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 (27 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI 2) n) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (pow (* (* PI 2) n) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ 1 (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ 1 (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (44 enodes)
* * [misc]simplify:  iters left: 1 (46 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (pow (* 2 n) (/ k 2))) (* (cbrt (sqrt k)) (pow PI (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (pow (* (* n 2) PI) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ 1 (pow (* 2 n) (/ k 2))) (* (cbrt (sqrt k)) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 91 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ 1 2)) (sqrt (sqrt k))) (/ (/ 1 (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* (* n 2) PI) (/ 1 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (sqrt k))) (/ (/ 1 (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ 1 (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (44 enodes)
* * [misc]simplify:  iters left: 1 (46 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (pow (* 2 n) (/ k 2))) (* (sqrt (sqrt k)) (pow PI (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (pow (* (* n 2) PI) (/ 1 2)) (sqrt (sqrt k))) (/ (/ 1 (pow (* 2 n) (/ k 2))) (* (sqrt (sqrt k)) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 92 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ 1 2)) 1) (/ (/ 1 (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow (* (* n 2) PI) (/ 1 2)) 1)
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI 2) n) (/ 1 2))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (pow (* (* PI 2) n) (/ 1 2)) (/ (/ 1 (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ 1 (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* * [misc]simplify:  iters left: 2 (43 enodes)
* * [misc]simplify:  iters left: 1 (45 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (pow (* 2 n) (/ k 2))) (* (sqrt k) (pow PI (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (pow (* (* PI 2) n) (/ 1 2)) (/ (/ 1 (pow (* 2 n) (/ k 2))) (* (sqrt k) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 93 / 130 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 94 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (/ 1 (sqrt k))))>
* * * * [misc]progress:  [ 95 / 130 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))))))>
* * * * [misc]progress:  [ 96 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
* [enter]simplify:  Simplifying (cbrt (sqrt k))
* * [misc]simplify:  iters left: 2 (3 enodes)
* [exit]simplify:  Simplified to (cbrt (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 97 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
* [enter]simplify:  Simplifying (sqrt (sqrt k))
* * [misc]simplify:  iters left: 2 (3 enodes)
* [exit]simplify:  Simplified to (sqrt (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt (sqrt k))) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 98 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) 1) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt k)
* * [misc]simplify:  iters left: 1 (2 enodes)
* [exit]simplify:  Simplified to (sqrt k)
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) 1) (sqrt k)))
* * * * [misc]progress:  [ 99 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))))) (/ (sqrt k) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))))))>
* [enter]simplify:  Simplifying (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))))) (/ (sqrt k) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))))))
* * * * [misc]progress:  [ 100 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (/ (sqrt k) (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))))))>
* [enter]simplify:  Simplifying (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (/ (sqrt k) (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))))))
* * * * [misc]progress:  [ 101 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (/ (sqrt k) (/ (pow PI (/ 1 2)) (pow PI (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2)))
* * [misc]simplify:  iters left: 5 (10 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2))) (/ (sqrt k) (/ (pow PI (/ 1 2)) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 102 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n 2) (/ k 2))) (/ (sqrt k) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n 2) (/ k 2)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (pow (* n 2) (/ k 2))) (cbrt (pow (* 2 (* PI n)) (/ 1 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (* (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (pow (* n 2) (/ k 2))) (cbrt (pow (* 2 (* PI n)) (/ 1 2)))) (/ (sqrt k) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 103 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2))) (/ (sqrt k) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI 2) n) (/ 1 2))) (pow (* n 2) (/ k 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (/ (sqrt (pow (* (* PI 2) n) (/ 1 2))) (pow (* n 2) (/ k 2))) (/ (sqrt k) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 104 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (pow (* n 2) (/ k 2))) (/ (sqrt k) (/ (pow (* (* n 2) PI) (/ 1 2)) (pow PI (/ k 2))))))>
* [enter]simplify:  Simplifying (/ 1 (pow (* n 2) (/ k 2)))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (11 enodes)
* [exit]simplify:  Simplified to (/ 1 (pow (* 2 n) (/ k 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (/ 1 (pow (* 2 n) (/ k 2))) (/ (sqrt k) (/ (pow (* (* n 2) PI) (/ 1 2)) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 105 / 130 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))))))>
* * * * [misc]progress:  [ 106 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (/ 1 2)) (/ (sqrt k) (/ 1 (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))))))>
* [enter]simplify:  Simplifying (pow (* (* n 2) PI) (/ 1 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* [exit]simplify:  Simplified to (pow (* n (* PI 2)) (/ 1 2))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (/ (sqrt k) (/ 1 (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))))))
* * * * [misc]progress:  [ 107 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (/ 1 2)) (* (sqrt k) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))))>
* [enter]simplify:  Simplifying (pow (* (* n 2) PI) (/ 1 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* [exit]simplify:  Simplified to (pow (* n (* PI 2)) (/ 1 2))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 108 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (log1p (expm1 (* (* n 2) PI))) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 109 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (expm1 (log1p (* (* n 2) PI))) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 110 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) 1) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 111 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (exp (log (* (* n 2) PI))) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 112 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (log (exp (* (* n 2) PI))) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 113 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 114 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (cbrt (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI))) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 115 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI))) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 116 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* 1 (* (* n 2) PI)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 117 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 118 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 119 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (45 enodes)
* * [misc]simplify:  iters left: 3 (85 enodes)
* * [misc]simplify:  iters left: 2 (144 enodes)
* * [misc]simplify:  iters left: 1 (178 enodes)
* [exit]simplify:  Simplified to (sqrt (* (* n PI) 2))
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (/ (sqrt (* (* n PI) 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 120 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n)))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (89 enodes)
* * [misc]simplify:  iters left: 2 (206 enodes)
* [exit]simplify:  Simplified to (sqrt (* n (* PI 2)))
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (/ (sqrt (* n (* PI 2))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 121 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n)))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (89 enodes)
* * [misc]simplify:  iters left: 2 (238 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (* PI -2)) (pow (/ -1 n) 1/2))
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (/ (/ (sqrt (* PI -2)) (pow (/ -1 n) 1/2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 122 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (+ (* 1/8 (* (pow (log n) 2) (pow k 2))) (+ (* 1/4 (* (log 2) (* (log n) (pow k 2)))) (+ (* 1/2 (* (log 2) k)) (+ (* 1/8 (* (pow (log 2) 2) (pow k 2))) (+ (* 1/2 (* (log n) k)) 1))))) (pow PI (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (+ (* 1/8 (* (pow (log n) 2) (pow k 2))) (+ (* 1/4 (* (log 2) (* (log n) (pow k 2)))) (+ (* 1/2 (* (log 2) k)) (+ (* 1/8 (* (pow (log 2) 2) (pow k 2))) (+ (* 1/2 (* (log n) k)) 1)))))
* * [misc]simplify:  iters left: 6 (28 enodes)
* * [misc]simplify:  iters left: 5 (74 enodes)
* * [misc]simplify:  iters left: 4 (212 enodes)
* [exit]simplify:  Simplified to (+ (fma (* (* (log n) k) (* (log n) k)) 1/8 (fma (* (* k k) (log n)) (* 1/4 (log 2)) (* (* 1/2 k) (log 2)))) (fma (* (* (log 2) (* k k)) (log 2)) 1/8 (fma (* (log n) 1/2) k 1)))
* [misc]simplify:  Simplified (2 1 2 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (+ (fma (* (* (log n) k) (* (log n) k)) 1/8 (fma (* (* k k) (log n)) (* 1/4 (log 2)) (* (* 1/2 k) (log 2)))) (fma (* (* (log 2) (* k k)) (log 2)) 1/8 (fma (* (log n) 1/2) k 1))) (pow PI (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 123 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (exp (* 1/2 (* (- (log 2) (log (/ 1 n))) k))) (pow PI (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* 1/2 (* (- (log 2) (log (/ 1 n))) k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (49 enodes)
* * [misc]simplify:  iters left: 3 (113 enodes)
* * [misc]simplify:  iters left: 2 (241 enodes)
* [exit]simplify:  Simplified to (pow (exp (* 1/2 k)) (+ (log n) (log 2)))
* [misc]simplify:  Simplified (2 1 2 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (exp (* 1/2 k)) (+ (log n) (log 2))) (pow PI (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 124 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k))) (pow PI (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (46 enodes)
* * [misc]simplify:  iters left: 3 (117 enodes)
* * [misc]simplify:  iters left: 2 (302 enodes)
* [exit]simplify:  Simplified to (exp (fma (* 1/2 k) (- (log n) (log -1)) (* (* 1/2 k) (log -2))))
* [misc]simplify:  Simplified (2 1 2 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (exp (fma (* 1/2 k) (- (log n) (log -1)) (* (* 1/2 k) (log -2)))) (pow PI (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 125 / 130 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (log PI) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (+ (* +nan.0 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (log 2) (* (log PI) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (* (log PI) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (log PI) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (* +nan.0 (* (log PI) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))))))))))))))))))))))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (log PI) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (+ (* +nan.0 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (log 2) (* (log PI) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (* (log PI) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (log PI) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (* +nan.0 (* (log PI) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))))))))))))))))))))))))))))))))
* [misc]simplify:  Simplified (2) to (λ (k n) +nan.0)
* * * * [misc]progress:  [ 126 / 130 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- (log 2) (log (/ 1 n))) k))) (* k (exp (* 1/2 (* (log PI) k))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- (log 2) (log (/ 1 n))) k))) (* (pow k 3) (exp (* 1/2 (* (log PI) k))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- (log 2) (log (/ 1 n))) k))) (* (pow k 2) (exp (* 1/2 (* (log PI) k)))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- (log 2) (log (/ 1 n))) k))) (* k (exp (* 1/2 (* (log PI) k))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- (log 2) (log (/ 1 n))) k))) (* (pow k 3) (exp (* 1/2 (* (log PI) k))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- (log 2) (log (/ 1 n))) k))) (* (pow k 2) (exp (* 1/2 (* (log PI) k))))))))))))
* [misc]simplify:  Simplified (2) to (λ (k n) +nan.0)
* * * * [misc]progress:  [ 127 / 130 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k))) (exp (* 1/2 (* (log PI) k)))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k))) (* (exp (* 1/2 (* (log PI) k))) k)))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k))) (* (exp (* 1/2 (* (log PI) k))) (pow k 2)))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k))) (exp (* 1/2 (* (log PI) k)))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k))) (* (exp (* 1/2 (* (log PI) k))) k)))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log -2) (log (/ -1 n))) k))) (* (exp (* 1/2 (* (log PI) k))) (pow k 2))))))))))
* [misc]simplify:  Simplified (2) to (λ (k n) +nan.0)
* * * * [misc]progress:  [ 128 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* 2 (* n PI))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* * [misc]simplify:  iters left: 2 (15 enodes)
* * [misc]simplify:  iters left: 1 (17 enodes)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* [misc]simplify:  Simplified (2 1 1 1) to (λ (k n) (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 129 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* 2 (* n PI))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* * [misc]simplify:  iters left: 2 (15 enodes)
* * [misc]simplify:  iters left: 1 (17 enodes)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* [misc]simplify:  Simplified (2 1 1 1) to (λ (k n) (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 130 / 130 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* 2 (* n PI))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* * [misc]simplify:  iters left: 2 (15 enodes)
* * [misc]simplify:  iters left: 1 (17 enodes)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* [misc]simplify:  Simplified (2 1 1 1) to (λ (k n) (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))
* * * [misc]progress:  adding candidates to table
* * [misc]progress:  iteration 4 / 4
* * * [misc]progress:  picking best candidate
* * * * [misc]pick:  Picked  #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 4 ] rewriting at (2 1 1)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2 1 2 2 1)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2 1 2 1 2 1)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2 1 2 1 1 1)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 4 ] generating series at (2 1 1)
* [misc]approximate:  Taking taylor expansion of (pow (* (* n 2) PI) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* n 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* n 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* n 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* n 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]approximate:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 n) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 n) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 n) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 n) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n)))))
* [misc]approximate:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 (- n)) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 (- n)) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* -2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* -2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* -2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 1)))) 24) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* -2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* -2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* -2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* -2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* -2 PI) 1)))) 120) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* -2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* -2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* -2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* -2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* -2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* -2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* -2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* -2 PI) 1)))) 720) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n)))))
* * * * [misc]progress:  [ 2 / 4 ] generating series at (2 1 2 2 1)
* [misc]approximate:  Taking taylor expansion of (pow (* (* n 2) PI) (/ k 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ k 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* (* n 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* (* n 2) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* n 2) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [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 (* n 2) into (* 2 n)
* [misc]backup-simplify:  Simplify (* (* 2 n) PI) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp 0) into 1
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* (* n 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* (* n 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (* 1/2 k) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (+ (log n) (log (* 2 PI))) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* (* n 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* (* n 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (* 1/2 k) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (+ (log n) (log (* 2 PI))) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ (log n) (log (* 2 PI))) k) in k
* [misc]taylor:  Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of (log (* 2 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 k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (+ (log n) (log (* 2 PI))) 0) into 0
* [misc]backup-simplify:  Simplify (* 1/2 0) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log n) (log (* 2 PI))) 1) (* 0 0)) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (+ (log n) (log (* 2 PI)))) (* 0 0)) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp 0) into 1
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1) 1)))) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (+ (* 0 1) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (+ (log n) (log (* 2 PI)))) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))
* [misc]backup-simplify:  Simplify (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))) into (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))) (pow (* k 1) 2)) (+ (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (* k 1)) 1)) into (+ (* 1/8 (* (pow (log n) 2) (pow k 2))) (+ (* 1/8 (* (pow k 2) (pow (log (* 2 PI)) 2))) (+ (* 1/2 (* k (log (* 2 PI)))) (+ (* 1/4 (* (pow k 2) (* (log n) (log (* 2 PI))))) (+ (* 1/2 (* (log n) k)) 1)))))
* [misc]approximate:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 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 (* (/ 1 n) 2) into (/ 2 n)
* [misc]backup-simplify:  Simplify (* (/ 2 n) PI) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI)))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k
* [misc]taylor:  Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) into (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k)))
* [misc]approximate:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 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 (* (/ -1 n) 2) into (/ -2 n)
* [misc]backup-simplify:  Simplify (* (/ -2 n) PI) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* -2 (/ PI n)))) into (* -1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI)))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k
* [misc]taylor:  Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k
* [misc]taylor:  Taking taylor expansion of -1/2 in k
* [misc]backup-simplify:  Simplify -1/2 into -1/2
* [misc]taylor:  Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k
* [misc]taylor:  Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* -2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* -2 PI) in k
* [misc]taylor:  Taking taylor expansion of -2 in k
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* -1/2 (- (log (* -2 PI)) (log n))) into (* -1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (- 0) 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)) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))) into (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))
* * * * [misc]progress:  [ 3 / 4 ] generating series at (2 1 2 1 2 1)
* [misc]approximate:  Taking taylor expansion of (pow (* (* n 2) PI) (/ k 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ k 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* (* n 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* (* n 2) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* n 2) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [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 (* n 2) into (* 2 n)
* [misc]backup-simplify:  Simplify (* (* 2 n) PI) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp 0) into 1
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* (* n 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* (* n 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (* 1/2 k) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (+ (log n) (log (* 2 PI))) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* (* n 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* (* n 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (* 1/2 k) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (+ (log n) (log (* 2 PI))) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ (log n) (log (* 2 PI))) k) in k
* [misc]taylor:  Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of (log (* 2 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 k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (+ (log n) (log (* 2 PI))) 0) into 0
* [misc]backup-simplify:  Simplify (* 1/2 0) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log n) (log (* 2 PI))) 1) (* 0 0)) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (+ (log n) (log (* 2 PI)))) (* 0 0)) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp 0) into 1
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1) 1)))) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (+ (* 0 1) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (+ (log n) (log (* 2 PI)))) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))
* [misc]backup-simplify:  Simplify (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))) into (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))) (pow (* k 1) 2)) (+ (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (* k 1)) 1)) into (+ (* 1/8 (* (pow (log n) 2) (pow k 2))) (+ (* 1/8 (* (pow k 2) (pow (log (* 2 PI)) 2))) (+ (* 1/2 (* k (log (* 2 PI)))) (+ (* 1/4 (* (pow k 2) (* (log n) (log (* 2 PI))))) (+ (* 1/2 (* (log n) k)) 1)))))
* [misc]approximate:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 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 (* (/ 1 n) 2) into (/ 2 n)
* [misc]backup-simplify:  Simplify (* (/ 2 n) PI) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI)))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k
* [misc]taylor:  Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) into (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k)))
* [misc]approximate:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 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 (* (/ -1 n) 2) into (/ -2 n)
* [misc]backup-simplify:  Simplify (* (/ -2 n) PI) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* -2 (/ PI n)))) into (* -1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI)))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k
* [misc]taylor:  Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k
* [misc]taylor:  Taking taylor expansion of -1/2 in k
* [misc]backup-simplify:  Simplify -1/2 into -1/2
* [misc]taylor:  Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k
* [misc]taylor:  Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* -2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* -2 PI) in k
* [misc]taylor:  Taking taylor expansion of -2 in k
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* -1/2 (- (log (* -2 PI)) (log n))) into (* -1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (- 0) 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)) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))) into (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))
* * * * [misc]progress:  [ 4 / 4 ] generating series at (2 1 2 1 1 1)
* [misc]approximate:  Taking taylor expansion of (pow (* (* n 2) PI) (/ k 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ k 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* (* n 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* (* n 2) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* n 2) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [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 (* n 2) into (* 2 n)
* [misc]backup-simplify:  Simplify (* (* 2 n) PI) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp 0) into 1
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* (* n 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* (* n 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (* 1/2 k) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (+ (log n) (log (* 2 PI))) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 2) PI) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* (* n 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* (* n 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* n 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (* 1/2 k) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (+ (log n) (log (* 2 PI))) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ (log n) (log (* 2 PI))) k) in k
* [misc]taylor:  Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of (log (* 2 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 k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (+ (log n) (log (* 2 PI))) 0) into 0
* [misc]backup-simplify:  Simplify (* 1/2 0) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log n) (log (* 2 PI))) 1) (* 0 0)) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (+ (log n) (log (* 2 PI)))) (* 0 0)) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp 0) into 1
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1) 1)))) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 2 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (+ (* 0 1) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (+ (log n) (log (* 2 PI)))) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))
* [misc]backup-simplify:  Simplify (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))) into (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))) (pow (* k 1) 2)) (+ (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (* k 1)) 1)) into (+ (* 1/8 (* (pow (log n) 2) (pow k 2))) (+ (* 1/8 (* (pow k 2) (pow (log (* 2 PI)) 2))) (+ (* 1/2 (* k (log (* 2 PI)))) (+ (* 1/4 (* (pow k 2) (* (log n) (log (* 2 PI))))) (+ (* 1/2 (* (log n) k)) 1)))))
* [misc]approximate:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 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 (* (/ 1 n) 2) into (/ 2 n)
* [misc]backup-simplify:  Simplify (* (/ 2 n) PI) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI)))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 2) PI) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k
* [misc]taylor:  Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) into (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k)))
* [misc]approximate:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 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 (* (/ -1 n) 2) into (/ -2 n)
* [misc]backup-simplify:  Simplify (* (/ -2 n) PI) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* -2 (/ PI n)))) into (* -1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI)))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 2) PI) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) 2) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) 2) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) 2) PI) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k
* [misc]taylor:  Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k
* [misc]taylor:  Taking taylor expansion of -1/2 in k
* [misc]backup-simplify:  Simplify -1/2 into -1/2
* [misc]taylor:  Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k
* [misc]taylor:  Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* -2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* -2 PI) in k
* [misc]taylor:  Taking taylor expansion of -2 in k
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* -1/2 (- (log (* -2 PI)) (log n))) into (* -1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (- 0) 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)) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))) into (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))
* * * [misc]progress:  simplifying candidates
* * * * [misc]progress:  [ 1 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (log1p (expm1 (pow (* (* n 2) PI) (/ 1 2)))) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 2 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (expm1 (log1p (pow (* (* n 2) PI) (/ 1 2)))) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 3 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (exp (* (log (* (* n 2) PI)) (/ 1 2))) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* (* n 2) PI)) (/ 1 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (92 enodes)
* * [misc]simplify:  iters left: 2 (180 enodes)
* * [misc]simplify:  iters left: 1 (389 enodes)
* [exit]simplify:  Simplified to (fma (/ 1 2) (log (* n 2)) (/ (log PI) 2))
* [misc]simplify:  Simplified (2 1 1 1) to (λ (k n) (/ (/ (exp (fma (/ 1 2) (log (* n 2)) (/ (log PI) 2))) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 4 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (exp (* (log (* (* n 2) PI)) (/ 1 2))) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 5 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (* 1 (/ 1 2))) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n 2) PI)
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* * [misc]simplify:  iters left: 2 (15 enodes)
* * [misc]simplify:  iters left: 1 (17 enodes)
* [exit]simplify:  Simplified to (* (* n 2) PI)
* [misc]simplify:  Simplified (2 1 1 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (* 1 (/ 1 2))) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 6 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) (cbrt (/ 1 2))) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (cbrt (/ 1 2))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (6 enodes)
* [exit]simplify:  Simplified to (cbrt (/ 1 2))
* [misc]simplify:  Simplified (2 1 1 2) to (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) (cbrt (/ 1 2))) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 7 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) (sqrt (/ 1 2))) (sqrt (/ 1 2))) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (/ 1 2))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (6 enodes)
* [exit]simplify:  Simplified to (sqrt (/ 1 2))
* [misc]simplify:  Simplified (2 1 1 2) to (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) (sqrt (/ 1 2))) (sqrt (/ 1 2))) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 8 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) 1) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ 1 2)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (5 enodes)
* [exit]simplify:  Simplified to (/ 1 2)
* [misc]simplify:  Simplified (2 1 1 2) to (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) 1) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 9 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) 1) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ 1 2)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (5 enodes)
* [exit]simplify:  Simplified to (/ 1 2)
* [misc]simplify:  Simplified (2 1 1 2) to (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) 1) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 10 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (pow (* n 2) (/ 1 2)) (pow PI (/ 1 2))) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n 2) (/ 1 2))
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (9 enodes)
* [exit]simplify:  Simplified to (pow (* n 2) (/ 1 2))
* [misc]simplify:  Simplified (2 1 1 1) to (λ (k n) (/ (/ (* (pow (* n 2) (/ 1 2)) (pow PI (/ 1 2))) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 11 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) (/ 1 2)) 1) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 12 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (exp (log (pow (* (* n 2) PI) (/ 1 2)))) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 13 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (log (exp (pow (* (* n 2) PI) (/ 1 2)))) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 14 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 15 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (cbrt (* (* (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ 1 2)))) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 16 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ 1 2)))) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 17 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* 1 (pow (* (* n 2) PI) (/ 1 2))) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 18 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (log1p (expm1 (pow (* (* n 2) PI) (/ k 2))))))) (sqrt k)))>
* * * * [misc]progress:  [ 19 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (expm1 (log1p (pow (* (* n 2) PI) (/ k 2))))))) (sqrt k)))>
* * * * [misc]progress:  [ 20 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (exp (* (log (* (* n 2) PI)) (/ k 2)))))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* (* n 2) PI)) (/ k 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (82 enodes)
* * [misc]simplify:  iters left: 2 (143 enodes)
* * [misc]simplify:  iters left: 1 (209 enodes)
* [exit]simplify:  Simplified to (fma (/ k 2) (log (* PI 2)) (* (log n) (/ k 2)))
* [misc]simplify:  Simplified (2 1 2 2 1 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (exp (fma (/ k 2) (log (* PI 2)) (* (log n) (/ k 2))))))) (sqrt k)))
* * * * [misc]progress:  [ 21 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (exp (* (log (* (* n 2) PI)) (/ k 2)))))) (sqrt k)))>
* * * * [misc]progress:  [ 22 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (* 1 (/ k 2)))))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n 2) PI)
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* * [misc]simplify:  iters left: 2 (15 enodes)
* * [misc]simplify:  iters left: 1 (17 enodes)
* [exit]simplify:  Simplified to (* (* n 2) PI)
* [misc]simplify:  Simplified (2 1 2 2 1 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (* 1 (/ k 2)))))) (sqrt k)))
* * * * [misc]progress:  [ 23 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (pow (* (* n 2) PI) (* (cbrt (/ k 2)) (cbrt (/ k 2)))) (cbrt (/ k 2)))))) (sqrt k)))>
* [enter]simplify:  Simplifying (cbrt (/ k 2))
* * [misc]simplify:  iters left: 3 (4 enodes)
* [exit]simplify:  Simplified to (cbrt (/ k 2))
* [misc]simplify:  Simplified (2 1 2 2 1 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (pow (* (* n 2) PI) (* (cbrt (/ k 2)) (cbrt (/ k 2)))) (cbrt (/ k 2)))))) (sqrt k)))
* * * * [misc]progress:  [ 24 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (pow (* (* n 2) PI) (sqrt (/ k 2))) (sqrt (/ k 2)))))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (/ k 2))
* * [misc]simplify:  iters left: 3 (4 enodes)
* [exit]simplify:  Simplified to (sqrt (/ k 2))
* [misc]simplify:  Simplified (2 1 2 2 1 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (pow (* (* n 2) PI) (sqrt (/ k 2))) (sqrt (/ k 2)))))) (sqrt k)))
* * * * [misc]progress:  [ 25 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (pow (* (* n 2) PI) 1) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ k 2)
* * [misc]simplify:  iters left: 2 (3 enodes)
* [exit]simplify:  Simplified to (/ k 2)
* [misc]simplify:  Simplified (2 1 2 2 1 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (pow (* (* n 2) PI) 1) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 26 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (pow (* (* n 2) PI) k) (/ 1 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ 1 2)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (5 enodes)
* [exit]simplify:  Simplified to (/ 1 2)
* [misc]simplify:  Simplified (2 1 2 2 1 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (pow (* (* n 2) PI) k) (/ 1 2))))) (sqrt k)))
* * * * [misc]progress:  [ 27 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n 2) (/ k 2))
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (pow (* n 2) (/ k 2))
* [misc]simplify:  Simplified (2 1 2 2 1 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))))) (sqrt k)))
* * * * [misc]progress:  [ 28 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (pow (* (* n 2) PI) (/ k 2)) 1)))) (sqrt k)))>
* * * * [misc]progress:  [ 29 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (exp (log (pow (* (* n 2) PI) (/ k 2))))))) (sqrt k)))>
* * * * [misc]progress:  [ 30 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (log (exp (pow (* (* n 2) PI) (/ k 2))))))) (sqrt k)))>
* * * * [misc]progress:  [ 31 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))))) (sqrt k)))>
* * * * [misc]progress:  [ 32 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (cbrt (* (* (pow (* (* n 2) PI) (/ k 2)) (pow (* (* n 2) PI) (/ k 2))) (pow (* (* n 2) PI) (/ k 2))))))) (sqrt k)))>
* * * * [misc]progress:  [ 33 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (* (sqrt (pow (* (* n 2) PI) (/ k 2))) (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (sqrt k)))>
* * * * [misc]progress:  [ 34 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (* 1 (pow (* (* n 2) PI) (/ k 2)))))) (sqrt k)))>
* * * * [misc]progress:  [ 35 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (log1p (expm1 (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 36 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (expm1 (log1p (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 37 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (exp (* (log (* (* n 2) PI)) (/ k 2))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* (* n 2) PI)) (/ k 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (82 enodes)
* * [misc]simplify:  iters left: 2 (143 enodes)
* * [misc]simplify:  iters left: 1 (209 enodes)
* [exit]simplify:  Simplified to (fma (/ k 2) (log (* PI 2)) (* (log n) (/ k 2)))
* [misc]simplify:  Simplified (2 1 2 1 2 1 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (exp (fma (/ k 2) (log (* PI 2)) (* (log n) (/ k 2)))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 38 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (exp (* (log (* (* n 2) PI)) (/ k 2))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 39 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (* 1 (/ k 2))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n 2) PI)
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* * [misc]simplify:  iters left: 2 (15 enodes)
* * [misc]simplify:  iters left: 1 (17 enodes)
* [exit]simplify:  Simplified to (* (* n 2) PI)
* [misc]simplify:  Simplified (2 1 2 1 2 1 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (* 1 (/ k 2))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 40 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (pow (* (* n 2) PI) (* (cbrt (/ k 2)) (cbrt (/ k 2)))) (cbrt (/ k 2))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (cbrt (/ k 2))
* * [misc]simplify:  iters left: 3 (4 enodes)
* [exit]simplify:  Simplified to (cbrt (/ k 2))
* [misc]simplify:  Simplified (2 1 2 1 2 1 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (pow (* (* n 2) PI) (* (cbrt (/ k 2)) (cbrt (/ k 2)))) (cbrt (/ k 2))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 41 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (pow (* (* n 2) PI) (sqrt (/ k 2))) (sqrt (/ k 2))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (/ k 2))
* * [misc]simplify:  iters left: 3 (4 enodes)
* [exit]simplify:  Simplified to (sqrt (/ k 2))
* [misc]simplify:  Simplified (2 1 2 1 2 1 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (pow (* (* n 2) PI) (sqrt (/ k 2))) (sqrt (/ k 2))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 42 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (pow (* (* n 2) PI) 1) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ k 2)
* * [misc]simplify:  iters left: 2 (3 enodes)
* [exit]simplify:  Simplified to (/ k 2)
* [misc]simplify:  Simplified (2 1 2 1 2 1 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (pow (* (* n 2) PI) 1) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 43 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (pow (* (* n 2) PI) k) (/ 1 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ 1 2)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (5 enodes)
* [exit]simplify:  Simplified to (/ 1 2)
* [misc]simplify:  Simplified (2 1 2 1 2 1 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (pow (* (* n 2) PI) k) (/ 1 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 44 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n 2) (/ k 2))
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (pow (* n 2) (/ k 2))
* [misc]simplify:  Simplified (2 1 2 1 2 1 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 45 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (pow (* (* n 2) PI) (/ k 2)) 1))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 46 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (exp (log (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 47 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (log (exp (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 48 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 49 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (cbrt (* (* (pow (* (* n 2) PI) (/ k 2)) (pow (* (* n 2) PI) (/ k 2))) (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 50 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (* (sqrt (pow (* (* n 2) PI) (/ k 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 51 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (* 1 (pow (* (* n 2) PI) (/ k 2))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 52 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (log1p (expm1 (pow (* (* n 2) PI) (/ k 2))))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 53 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (expm1 (log1p (pow (* (* n 2) PI) (/ k 2))))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 54 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (exp (* (log (* (* n 2) PI)) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* (* n 2) PI)) (/ k 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (82 enodes)
* * [misc]simplify:  iters left: 2 (143 enodes)
* * [misc]simplify:  iters left: 1 (209 enodes)
* [exit]simplify:  Simplified to (fma (/ k 2) (log (* PI 2)) (* (log n) (/ k 2)))
* [misc]simplify:  Simplified (2 1 2 1 1 1 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (exp (fma (/ k 2) (log (* PI 2)) (* (log n) (/ k 2))))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 55 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (exp (* (log (* (* n 2) PI)) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 56 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (* 1 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n 2) PI)
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* * [misc]simplify:  iters left: 2 (15 enodes)
* * [misc]simplify:  iters left: 1 (17 enodes)
* [exit]simplify:  Simplified to (* (* n 2) PI)
* [misc]simplify:  Simplified (2 1 2 1 1 1 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (* 1 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 57 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (pow (* (* n 2) PI) (* (cbrt (/ k 2)) (cbrt (/ k 2)))) (cbrt (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (cbrt (/ k 2))
* * [misc]simplify:  iters left: 3 (4 enodes)
* [exit]simplify:  Simplified to (cbrt (/ k 2))
* [misc]simplify:  Simplified (2 1 2 1 1 1 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (pow (* (* n 2) PI) (* (cbrt (/ k 2)) (cbrt (/ k 2)))) (cbrt (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 58 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (pow (* (* n 2) PI) (sqrt (/ k 2))) (sqrt (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (/ k 2))
* * [misc]simplify:  iters left: 3 (4 enodes)
* [exit]simplify:  Simplified to (sqrt (/ k 2))
* [misc]simplify:  Simplified (2 1 2 1 1 1 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (pow (* (* n 2) PI) (sqrt (/ k 2))) (sqrt (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 59 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (pow (* (* n 2) PI) 1) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ k 2)
* * [misc]simplify:  iters left: 2 (3 enodes)
* [exit]simplify:  Simplified to (/ k 2)
* [misc]simplify:  Simplified (2 1 2 1 1 1 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (pow (* (* n 2) PI) 1) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 60 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (pow (* (* n 2) PI) k) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ 1 2)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (5 enodes)
* [exit]simplify:  Simplified to (/ 1 2)
* [misc]simplify:  Simplified (2 1 2 1 1 1 2) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (pow (* (* n 2) PI) k) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 61 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n 2) (/ k 2))
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (pow (* n 2) (/ k 2))
* [misc]simplify:  Simplified (2 1 2 1 1 1 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 62 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (pow (* (* n 2) PI) (/ k 2)) 1)) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 63 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (exp (log (pow (* (* n 2) PI) (/ k 2))))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 64 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (log (exp (pow (* (* n 2) PI) (/ k 2))))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 65 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 66 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (cbrt (* (* (pow (* (* n 2) PI) (/ k 2)) (pow (* (* n 2) PI) (/ k 2))) (pow (* (* n 2) PI) (/ k 2))))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 67 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (* (sqrt (pow (* (* n 2) PI) (/ k 2))) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 68 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (* 1 (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 69 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (45 enodes)
* * [misc]simplify:  iters left: 3 (85 enodes)
* * [misc]simplify:  iters left: 2 (144 enodes)
* * [misc]simplify:  iters left: 1 (178 enodes)
* [exit]simplify:  Simplified to (sqrt (* (* n PI) 2))
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (/ (sqrt (* (* n PI) 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 70 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n)))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (89 enodes)
* * [misc]simplify:  iters left: 2 (206 enodes)
* [exit]simplify:  Simplified to (sqrt (* n (* PI 2)))
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (/ (sqrt (* n (* PI 2))) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 71 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n)))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (89 enodes)
* * [misc]simplify:  iters left: 2 (238 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (* PI -2)) (pow (/ -1 n) 1/2))
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (/ (/ (sqrt (* PI -2)) (pow (/ -1 n) 1/2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 72 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (+ (* 1/8 (* (pow (log n) 2) (pow k 2))) (+ (* 1/8 (* (pow k 2) (pow (log (* 2 PI)) 2))) (+ (* 1/2 (* k (log (* 2 PI)))) (+ (* 1/4 (* (pow k 2) (* (log n) (log (* 2 PI))))) (+ (* 1/2 (* (log n) k)) 1)))))))) (sqrt k)))>
* [enter]simplify:  Simplifying (+ (* 1/8 (* (pow (log n) 2) (pow k 2))) (+ (* 1/8 (* (pow k 2) (pow (log (* 2 PI)) 2))) (+ (* 1/2 (* k (log (* 2 PI)))) (+ (* 1/4 (* (pow k 2) (* (log n) (log (* 2 PI))))) (+ (* 1/2 (* (log n) k)) 1)))))
* * [misc]simplify:  iters left: 6 (30 enodes)
* * [misc]simplify:  iters left: 5 (80 enodes)
* * [misc]simplify:  iters left: 4 (254 enodes)
* [exit]simplify:  Simplified to (fma 1/8 (* (* k k) (+ (* (log n) (log n)) (* (log (* 2 PI)) (log (* 2 PI))))) (fma (* (log (* 2 PI)) (* 1/4 (* k k))) (log n) (fma (* (log (* 2 PI)) 1/2) k (fma (* (log n) k) 1/2 1))))
* [misc]simplify:  Simplified (2 1 2 2 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (fma 1/8 (* (* k k) (+ (* (log n) (log n)) (* (log (* 2 PI)) (log (* 2 PI))))) (fma (* (log (* 2 PI)) (* 1/4 (* k k))) (log n) (fma (* (log (* 2 PI)) 1/2) k (fma (* (log n) k) 1/2 1))))))) (sqrt k)))
* * * * [misc]progress:  [ 73 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k)))))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (60 enodes)
* * [misc]simplify:  iters left: 3 (173 enodes)
* [exit]simplify:  Simplified to (exp (fma (log (* PI 2)) (* 1/2 k) (* (* 1/2 k) (log n))))
* [misc]simplify:  Simplified (2 1 2 2 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (exp (fma (log (* PI 2)) (* 1/2 k) (* (* 1/2 k) (log n))))))) (sqrt k)))
* * * * [misc]progress:  [ 74 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (57 enodes)
* * [misc]simplify:  iters left: 3 (179 enodes)
* [exit]simplify:  Simplified to (exp (* (- (log (* PI -2)) (log (/ -1 n))) (* 1/2 k)))
* [misc]simplify:  Simplified (2 1 2 2 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (exp (* (- (log (* PI -2)) (log (/ -1 n))) (* 1/2 k)))))) (sqrt k)))
* * * * [misc]progress:  [ 75 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (+ (* 1/8 (* (pow (log n) 2) (pow k 2))) (+ (* 1/8 (* (pow k 2) (pow (log (* 2 PI)) 2))) (+ (* 1/2 (* k (log (* 2 PI)))) (+ (* 1/4 (* (pow k 2) (* (log n) (log (* 2 PI))))) (+ (* 1/2 (* (log n) k)) 1))))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (+ (* 1/8 (* (pow (log n) 2) (pow k 2))) (+ (* 1/8 (* (pow k 2) (pow (log (* 2 PI)) 2))) (+ (* 1/2 (* k (log (* 2 PI)))) (+ (* 1/4 (* (pow k 2) (* (log n) (log (* 2 PI))))) (+ (* 1/2 (* (log n) k)) 1)))))
* * [misc]simplify:  iters left: 6 (30 enodes)
* * [misc]simplify:  iters left: 5 (80 enodes)
* * [misc]simplify:  iters left: 4 (254 enodes)
* [exit]simplify:  Simplified to (fma 1/8 (* (* k k) (+ (* (log n) (log n)) (* (log (* 2 PI)) (log (* 2 PI))))) (fma (* (log (* 2 PI)) (* 1/4 (* k k))) (log n) (fma (* (log (* 2 PI)) 1/2) k (fma (* (log n) k) 1/2 1))))
* [misc]simplify:  Simplified (2 1 2 1 2 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (fma 1/8 (* (* k k) (+ (* (log n) (log n)) (* (log (* 2 PI)) (log (* 2 PI))))) (fma (* (log (* 2 PI)) (* 1/4 (* k k))) (log n) (fma (* (log (* 2 PI)) 1/2) k (fma (* (log n) k) 1/2 1)))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 76 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (60 enodes)
* * [misc]simplify:  iters left: 3 (173 enodes)
* [exit]simplify:  Simplified to (exp (fma (log (* PI 2)) (* 1/2 k) (* (* 1/2 k) (log n))))
* [misc]simplify:  Simplified (2 1 2 1 2 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (exp (fma (log (* PI 2)) (* 1/2 k) (* (* 1/2 k) (log n)))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 77 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (57 enodes)
* * [misc]simplify:  iters left: 3 (179 enodes)
* [exit]simplify:  Simplified to (exp (* (- (log (* PI -2)) (log (/ -1 n))) (* 1/2 k)))
* [misc]simplify:  Simplified (2 1 2 1 2 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (exp (* (- (log (* PI -2)) (log (/ -1 n))) (* 1/2 k))))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 78 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (+ (* 1/8 (* (pow (log n) 2) (pow k 2))) (+ (* 1/8 (* (pow k 2) (pow (log (* 2 PI)) 2))) (+ (* 1/2 (* k (log (* 2 PI)))) (+ (* 1/4 (* (pow k 2) (* (log n) (log (* 2 PI))))) (+ (* 1/2 (* (log n) k)) 1)))))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (+ (* 1/8 (* (pow (log n) 2) (pow k 2))) (+ (* 1/8 (* (pow k 2) (pow (log (* 2 PI)) 2))) (+ (* 1/2 (* k (log (* 2 PI)))) (+ (* 1/4 (* (pow k 2) (* (log n) (log (* 2 PI))))) (+ (* 1/2 (* (log n) k)) 1)))))
* * [misc]simplify:  iters left: 6 (30 enodes)
* * [misc]simplify:  iters left: 5 (80 enodes)
* * [misc]simplify:  iters left: 4 (254 enodes)
* [exit]simplify:  Simplified to (fma 1/8 (* (* k k) (+ (* (log n) (log n)) (* (log (* 2 PI)) (log (* 2 PI))))) (fma (* (log (* 2 PI)) (* 1/4 (* k k))) (log n) (fma (* (log (* 2 PI)) 1/2) k (fma (* (log n) k) 1/2 1))))
* [misc]simplify:  Simplified (2 1 2 1 1 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (fma 1/8 (* (* k k) (+ (* (log n) (log n)) (* (log (* 2 PI)) (log (* 2 PI))))) (fma (* (log (* 2 PI)) (* 1/4 (* k k))) (log n) (fma (* (log (* 2 PI)) 1/2) k (fma (* (log n) k) 1/2 1))))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 79 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k)))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (60 enodes)
* * [misc]simplify:  iters left: 3 (173 enodes)
* [exit]simplify:  Simplified to (exp (fma (log (* PI 2)) (* 1/2 k) (* (* 1/2 k) (log n))))
* [misc]simplify:  Simplified (2 1 2 1 1 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (exp (fma (log (* PI 2)) (* 1/2 k) (* (* 1/2 k) (log n))))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 80 / 80 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (57 enodes)
* * [misc]simplify:  iters left: 3 (179 enodes)
* [exit]simplify:  Simplified to (exp (* (- (log (* PI -2)) (log (/ -1 n))) (* 1/2 k)))
* [misc]simplify:  Simplified (2 1 2 1 1 1) to (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (exp (* (- (log (* PI -2)) (log (/ -1 n))) (* 1/2 k)))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * [misc]progress:  adding candidates to table
* [misc]progress:  [Phase 3 of 3] Extracting.
* * [misc]regime-changes:  Finding splitpoints for: (#<alt (λ (k n) (* (/ (pow (* n 2) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k)))))> #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (* (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))))) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2))))) (sqrt k))))> #<alt (λ (k n) (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))))> #<alt (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))))> #<alt (λ (k n) (* (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt k))))> #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))> #<alt (λ (k n) (* (/ (/ 1 (pow (* n 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow PI (/ k 2))) (cbrt (sqrt k)))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (pow (* n 2) (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) (sqrt k))))> #<alt (λ (k n) (/ (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4)) (* (* k k) (log n)) (- (fma (* (* (log (* PI 2)) 1/8) (* (log (* PI 2)) (* k k))) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)))) (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) 1/2))) (sqrt k)))> #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>)
* [misc]regimes:  Found splitpoints: (#s(sp 0 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) +nan.0)) , with alts (#<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k)))>)
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* n 2) (/ k 2)) (pow PI (/ k 2)))) (sqrt k))
* * * * [misc]points:  Sampling 8000 additional inputs, on iter 0 have 0 / 8000
* * * * [misc]points:  Computing exacts on every 500 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 250 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 125 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 62 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 31 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 15 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 7 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 3 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 8000 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 6498 additional inputs, on iter 1 have 1502 / 8000
* * * * [misc]points:  Computing exacts on every 406 of 6498 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 203 of 6498 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 101 of 6498 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 50 of 6498 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 25 of 6498 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 12 of 6498 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 6 of 6498 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 3 of 6498 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 6498 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 5292 additional inputs, on iter 2 have 2708 / 8000
* * * * [misc]points:  Computing exacts on every 330 of 5292 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 165 of 5292 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 82 of 5292 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 41 of 5292 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 20 of 5292 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 10 of 5292 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 5 of 5292 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 5292 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 5292 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4324 additional inputs, on iter 3 have 3676 / 8000
* * * * [misc]points:  Computing exacts on every 270 of 4324 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 135 of 4324 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 67 of 4324 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 33 of 4324 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 16 of 4324 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 8 of 4324 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 4 of 4324 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 4324 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 4324 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 3485 additional inputs, on iter 4 have 4515 / 8000
* * * * [misc]points:  Computing exacts on every 217 of 3485 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 108 of 3485 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 54 of 3485 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 27 of 3485 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 13 of 3485 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 6 of 3485 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 3 of 3485 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 3485 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 2842 additional inputs, on iter 5 have 5158 / 8000
* * * * [misc]points:  Computing exacts on every 177 of 2842 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 88 of 2842 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 44 of 2842 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 22 of 2842 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 11 of 2842 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 5 of 2842 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 2842 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 2842 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 2304 additional inputs, on iter 6 have 5696 / 8000
* * * * [misc]points:  Computing exacts on every 144 of 2304 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 72 of 2304 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 36 of 2304 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 18 of 2304 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 9 of 2304 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 4 of 2304 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 2304 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 2304 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 1877 additional inputs, on iter 7 have 6123 / 8000
* * * * [misc]points:  Computing exacts on every 117 of 1877 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 58 of 1877 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 29 of 1877 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 14 of 1877 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 7 of 1877 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 3 of 1877 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1877 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 1530 additional inputs, on iter 8 have 6470 / 8000
* * * * [misc]points:  Computing exacts on every 95 of 1530 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 47 of 1530 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 23 of 1530 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 11 of 1530 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 5 of 1530 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 1530 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1530 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 1255 additional inputs, on iter 9 have 6745 / 8000
* * * * [misc]points:  Computing exacts on every 78 of 1255 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 39 of 1255 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 19 of 1255 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 9 of 1255 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 4 of 1255 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 1255 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1255 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 1021 additional inputs, on iter 10 have 6979 / 8000
* * * * [misc]points:  Computing exacts on every 63 of 1021 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 31 of 1021 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 15 of 1021 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 7 of 1021 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 3 of 1021 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1021 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 823 additional inputs, on iter 11 have 7177 / 8000
* * * * [misc]points:  Computing exacts on every 51 of 823 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 25 of 823 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 12 of 823 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 6 of 823 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 3 of 823 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 823 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 652 additional inputs, on iter 12 have 7348 / 8000
* * * * [misc]points:  Computing exacts on every 40 of 652 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 20 of 652 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 10 of 652 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 5 of 652 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 652 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 652 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 528 additional inputs, on iter 13 have 7472 / 8000
* * * * [misc]points:  Computing exacts on every 33 of 528 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 16 of 528 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 8 of 528 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 4 of 528 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 528 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 528 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 437 additional inputs, on iter 14 have 7563 / 8000
* * * * [misc]points:  Computing exacts on every 27 of 437 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 13 of 437 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 6 of 437 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 3 of 437 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 437 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 363 additional inputs, on iter 15 have 7637 / 8000
* * * * [misc]points:  Computing exacts on every 22 of 363 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 11 of 363 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 5 of 363 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 363 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 363 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 302 additional inputs, on iter 16 have 7698 / 8000
* * * * [misc]points:  Computing exacts on every 18 of 302 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 9 of 302 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 4 of 302 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 302 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 302 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 254 additional inputs, on iter 17 have 7746 / 8000
* * * * [misc]points:  Computing exacts on every 15 of 254 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 7 of 254 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 3 of 254 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 254 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 205 additional inputs, on iter 18 have 7795 / 8000
* * * * [misc]points:  Computing exacts on every 12 of 205 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 6 of 205 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 3 of 205 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 205 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 155 additional inputs, on iter 19 have 7845 / 8000
* * * * [misc]points:  Computing exacts on every 9 of 155 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 4 of 155 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 155 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 155 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 131 additional inputs, on iter 20 have 7869 / 8000
* * * * [misc]points:  Computing exacts on every 8 of 131 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 4 of 131 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 131 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 131 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 111 additional inputs, on iter 21 have 7889 / 8000
* * * * [misc]points:  Computing exacts on every 6 of 111 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 3 of 111 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 111 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 85 additional inputs, on iter 22 have 7915 / 8000
* * * * [misc]points:  Computing exacts on every 5 of 85 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 85 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 85 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 71 additional inputs, on iter 23 have 7929 / 8000
* * * * [misc]points:  Computing exacts on every 4 of 71 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 71 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 71 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 60 additional inputs, on iter 24 have 7940 / 8000
* * * * [misc]points:  Computing exacts on every 3 of 60 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 60 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 50 additional inputs, on iter 25 have 7950 / 8000
* * * * [misc]points:  Computing exacts on every 3 of 50 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 50 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 36 additional inputs, on iter 26 have 7964 / 8000
* * * * [misc]points:  Computing exacts on every 2 of 36 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 36 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 32 additional inputs, on iter 27 have 7968 / 8000
* * * * [misc]points:  Computing exacts on every 2 of 32 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 32 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 26 additional inputs, on iter 28 have 7974 / 8000
* * * * [misc]points:  Computing exacts for 26 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 19 additional inputs, on iter 29 have 7981 / 8000
* * * * [misc]points:  Computing exacts for 19 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 15 additional inputs, on iter 30 have 7985 / 8000
* * * * [misc]points:  Computing exacts for 15 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 11 additional inputs, on iter 31 have 7989 / 8000
* * * * [misc]points:  Computing exacts for 11 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 9 additional inputs, on iter 32 have 7991 / 8000
* * * * [misc]points:  Computing exacts for 9 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 5 additional inputs, on iter 33 have 7995 / 8000
* * * * [misc]points:  Computing exacts for 5 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 34 have 7997 / 8000
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 35 have 7997 / 8000
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 36 have 7998 / 8000
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 37 have 7998 / 8000
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 38 have 7998 / 8000
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 39 have 7998 / 8000
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 40 have 7999 / 8000
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [exit]points:  Sampled 8000 points with exact outputs