* [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:  Computing exacts on every 8 of 256 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 64
* * * * [misc]points:  Setting MPFR precision to 320
* * * * [misc]points:  Computing exacts on every 4 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:  Setting MPFR precision to 832
* * * * [misc]points:  Computing exacts on every 2 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:  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 145 additional inputs, on iter 3 have 111 / 256
* * * * [misc]points:  Computing exacts on every 9 of 145 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 145 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 145 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 145 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 116 additional inputs, on iter 4 have 140 / 256
* * * * [misc]points:  Computing exacts on every 7 of 116 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 116 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 116 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 95 additional inputs, on iter 5 have 161 / 256
* * * * [misc]points:  Computing exacts on every 5 of 95 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 95 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 95 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 81 additional inputs, on iter 6 have 175 / 256
* * * * [misc]points:  Computing exacts on every 5 of 81 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 81 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 81 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 63 additional inputs, on iter 7 have 193 / 256
* * * * [misc]points:  Computing exacts on every 3 of 63 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 63 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 56 additional inputs, on iter 8 have 200 / 256
* * * * [misc]points:  Computing exacts on every 3 of 56 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 56 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 44 additional inputs, on iter 9 have 212 / 256
* * * * [misc]points:  Computing exacts on every 2 of 44 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 44 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 10 have 224 / 256
* * * * [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 28 additional inputs, on iter 11 have 228 / 256
* * * * [misc]points:  Computing exacts for 28 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 22 additional inputs, on iter 12 have 234 / 256
* * * * [misc]points:  Computing exacts for 22 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 18 additional inputs, on iter 13 have 238 / 256
* * * * [misc]points:  Computing exacts for 18 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 14 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 15 additional inputs, on iter 15 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 13 additional inputs, on iter 16 have 243 / 256
* * * * [misc]points:  Computing exacts for 13 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 17 have 247 / 256
* * * * [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 6 additional inputs, on iter 18 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 5 additional inputs, on iter 19 have 251 / 256
* * * * [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 5 additional inputs, on iter 20 have 251 / 256
* * * * [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 21 have 252 / 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 22 have 252 / 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 23 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 24 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
* * * * [misc]points:  Sampling 4 additional inputs, on iter 25 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
* * * * [misc]points:  Sampling 4 additional inputs, on iter 26 have 255 / 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 258 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 (55 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)
* * * * [misc]progress:  [ 2 / 3 ] rewriting at (2 1 1)
* * * * [misc]progress:  [ 3 / 3 ] rewriting at (2 1)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 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:  [ 2 / 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:  [ 3 / 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:  simplifying candidates
* * * * [misc]progress:  [ 1 / 68 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)) 1))>
* * * * [misc]progress:  [ 2 / 68 ] 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 (33 enodes)
* * [misc]simplify:  iters left: 4 (64 enodes)
* * [misc]simplify:  iters left: 3 (159 enodes)
* [exit]simplify:  Simplified to (- (* (/ (- 1 k) 2) (log (* (* PI n) 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (/ (- 1 k) 2) (log (* (* PI n) 2))) (log (sqrt k)))))
* * * * [misc]progress:  [ 3 / 68 ] 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 (33 enodes)
* * [misc]simplify:  iters left: 4 (64 enodes)
* * [misc]simplify:  iters left: 3 (159 enodes)
* [exit]simplify:  Simplified to (- (* (/ (- 1 k) 2) (log (* (* PI n) 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (/ (- 1 k) 2) (log (* (* PI n) 2))) (log (sqrt k)))))
* * * * [misc]progress:  [ 4 / 68 ] 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 (49 enodes)
* * [misc]simplify:  iters left: 3 (96 enodes)
* * [misc]simplify:  iters left: 2 (286 enodes)
* [exit]simplify:  Simplified to (- (/ (log (* (* PI n) 2)) (/ 2 (- 1 k))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (/ (log (* (* PI n) 2)) (/ 2 (- 1 k))) (log (sqrt k)))))
* * * * [misc]progress:  [ 5 / 68 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 6 / 68 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 7 / 68 ] 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 (72 enodes)
* * [misc]simplify:  iters left: 3 (130 enodes)
* * [misc]simplify:  iters left: 2 (204 enodes)
* * [misc]simplify:  iters left: 1 (325 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:  [ 8 / 68 ] 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:  [ 9 / 68 ] 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:  [ 10 / 68 ] 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:  [ 11 / 68 ] simplifiying candidate #<alt (λ (k n) (/ (- (pow (* (* n 2) PI) (/ (- 1 k) 2))) (- (sqrt k))))>
* * * * [misc]progress:  [ 12 / 68 ] 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:  [ 13 / 68 ] 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:  [ 14 / 68 ] 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:  [ 15 / 68 ] 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 (58 enodes)
* * [misc]simplify:  iters left: 2 (61 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 (37 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* 2 (* PI n)) (/ (- 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 (* 2 (* PI n)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 16 / 68 ] 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 (43 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 (37 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* 2 (* PI n)) (/ (- 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 (* 2 (* PI n)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 17 / 68 ] 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 (55 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* [misc]simplify:  Simplified (2 1) to (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))))
* [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 (36 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (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 (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt k))))
* * * * [misc]progress:  [ 18 / 68 ] 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 (40 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 (37 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* 2 (* PI n)) (/ (- 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 (* 2 (* PI n)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 19 / 68 ] 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 (37 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* 2 (* PI n)) (/ (- 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 (37 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* 2 (* PI n)) (/ (- 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 (* 2 (* PI n)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 20 / 68 ] 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 (36 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt k))))
* * * * [misc]progress:  [ 21 / 68 ] 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 (36 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 22 / 68 ] 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 (36 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 23 / 68 ] 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:  [ 24 / 68 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))))>
* * * * [misc]progress:  [ 25 / 68 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
* * * * [misc]progress:  [ 26 / 68 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))>
* * * * [misc]progress:  [ 27 / 68 ] 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:  [ 28 / 68 ] 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:  [ 29 / 68 ] 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:  [ 30 / 68 ] 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:  [ 31 / 68 ] 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:  [ 32 / 68 ] 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 (* (* PI n) 2) (/ (- 1 k) 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))))
* * * * [misc]progress:  [ 33 / 68 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))>
* * * * [misc]progress:  [ 34 / 68 ] 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 (* (* PI n) 2) (/ 1 2))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (pow (* (* PI n) 2) (/ 1 2)) (* (sqrt k) (pow (* (* n 2) PI) (/ k 2)))))
* * * * [misc]progress:  [ 35 / 68 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 36 / 68 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (log (* (* n 2) PI))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 37 / 68 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log (exp (* (* n 2) PI))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 38 / 68 ] 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:  [ 39 / 68 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 40 / 68 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 41 / 68 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* (* n 2) PI)) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 42 / 68 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 43 / 68 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 44 / 68 ] 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 (141 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:  [ 45 / 68 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* (* n 2) PI)) (/ (- 1 k) 2))) (sqrt k)))>
* * * * [misc]progress:  [ 46 / 68 ] 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:  [ 47 / 68 ] 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:  [ 48 / 68 ] 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:  [ 49 / 68 ] 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:  [ 50 / 68 ] 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:  [ 51 / 68 ] 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:  [ 52 / 68 ] 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:  [ 53 / 68 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) (/ (- 1 k) 2)) 1) (sqrt k)))>
* * * * [misc]progress:  [ 54 / 68 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 55 / 68 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 56 / 68 ] 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:  [ 57 / 68 ] 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:  [ 58 / 68 ] 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:  [ 59 / 68 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt k)))>
* * * * [misc]progress:  [ 60 / 68 ] 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:  [ 61 / 68 ] 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:  [ 62 / 68 ] 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:  [ 63 / 68 ] 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:  [ 64 / 68 ] 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:  [ 65 / 68 ] 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:  [ 66 / 68 ] 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 (105 enodes)
* * [misc]simplify:  iters left: 4 (338 enodes)
* [exit]simplify:  Simplified to (+ (+ (* (- 1/2) (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2))))) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (+ (* (* (log (* PI 2)) 1/8) (* (log (* PI 2)) (* k k))) (* (* (log (* PI 2)) 1/4) (* (* k k) (log n))))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (+ (+ (* (- 1/2) (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2))))) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (+ (* (* (log (* PI 2)) 1/8) (* (log (* PI 2)) (* k k))) (* (* (log (* PI 2)) 1/4) (* (* k k) (log n)))))) (sqrt k)))
* * * * [misc]progress:  [ 67 / 68 ] 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 (266 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 / 68 ] 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 (272 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:  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)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2 1 2 1)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2 1 1 1)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2 1 1)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 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:  [ 2 / 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:  [ 3 / 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:  [ 4 / 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:  simplifying candidates
* * * * [misc]progress:  [ 1 / 151 ] simplifiying candidate #<alt (λ (k n) (pow (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)) 1))>
* * * * [misc]progress:  [ 2 / 151 ] 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 (39 enodes)
* * [misc]simplify:  iters left: 4 (89 enodes)
* * [misc]simplify:  iters left: 3 (282 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:  [ 3 / 151 ] 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 (39 enodes)
* * [misc]simplify:  iters left: 4 (89 enodes)
* * [misc]simplify:  iters left: 3 (282 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:  [ 4 / 151 ] 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 (36 enodes)
* * [misc]simplify:  iters left: 4 (81 enodes)
* * [misc]simplify:  iters left: 3 (266 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:  [ 5 / 151 ] 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 (39 enodes)
* * [misc]simplify:  iters left: 4 (89 enodes)
* * [misc]simplify:  iters left: 3 (282 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:  [ 6 / 151 ] 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 (39 enodes)
* * [misc]simplify:  iters left: 4 (89 enodes)
* * [misc]simplify:  iters left: 3 (282 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:  [ 7 / 151 ] 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 (36 enodes)
* * [misc]simplify:  iters left: 4 (81 enodes)
* * [misc]simplify:  iters left: 3 (266 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:  [ 8 / 151 ] 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 (85 enodes)
* * [misc]simplify:  iters left: 3 (238 enodes)
* [exit]simplify:  Simplified to (- (* (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2))) (log (sqrt k)))))
* * * * [misc]progress:  [ 9 / 151 ] 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 (85 enodes)
* * [misc]simplify:  iters left: 3 (238 enodes)
* [exit]simplify:  Simplified to (- (* (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2))) (log (sqrt k)))))
* * * * [misc]progress:  [ 10 / 151 ] 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 (66 enodes)
* * [misc]simplify:  iters left: 3 (186 enodes)
* [exit]simplify:  Simplified to (- (* (- (/ 1 2) (/ k 2)) (log (* n (* PI 2)))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (- (/ 1 2) (/ k 2)) (log (* n (* PI 2)))) (log (sqrt k)))))
* * * * [misc]progress:  [ 11 / 151 ] 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 (84 enodes)
* * [misc]simplify:  iters left: 2 (268 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:  [ 12 / 151 ] 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 / 151 ] 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 / 151 ] 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 (* (* 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) (/ k 2)) (/ (pow (* (* n 2) PI) (/ 1 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) (/ k 2)) (/ (pow (* (* n 2) PI) (/ 1 2)) (* k (sqrt k)))))))
* * * * [misc]progress:  [ 15 / 151 ] 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 (97 enodes)
* * [misc]simplify:  iters left: 3 (268 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)))) (/ (pow (* (* PI n) 2) (/ 1 2)) (* (* k (sqrt k)) (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)))) (/ (pow (* (* PI n) 2) (/ 1 2)) (* (* k (sqrt k)) (pow (* (* PI n) 2) (/ k 2)))))))
* * * * [misc]progress:  [ 16 / 151 ] 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:  [ 17 / 151 ] 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:  [ 18 / 151 ] 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:  [ 19 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (- (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (- (sqrt k))))>
* * * * [misc]progress:  [ 20 / 151 ] 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 (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ 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 (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ 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 (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 21 / 151 ] 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 (35 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ 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 (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ 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 (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 22 / 151 ] 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 (47 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 (28 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:  [ 23 / 151 ] 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 (32 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ 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 (* 2 (* PI n)) (/ 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 (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ 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 (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 24 / 151 ] 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 (* (* PI n) 2) (/ 1 2)) (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)) (pow (* (* PI n) 2) (/ 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 (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ 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 (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 25 / 151 ] 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 (29 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ 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 (28 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 (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 26 / 151 ] 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:  [ 27 / 151 ] 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:  [ 28 / 151 ] 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:  [ 29 / 151 ] 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:  [ 30 / 151 ] 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:  [ 31 / 151 ] 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:  [ 32 / 151 ] 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:  [ 33 / 151 ] 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:  [ 34 / 151 ] 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:  [ 35 / 151 ] 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:  [ 36 / 151 ] 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:  [ 37 / 151 ] 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)
* [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:  [ 38 / 151 ] 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 (87 enodes)
* * [misc]simplify:  iters left: 2 (126 enodes)
* * [misc]simplify:  iters left: 1 (145 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (/ (* (pow (* 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))) (/ (* (pow (* n 2) (/ k 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (pow (* (* PI n) 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 (34 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (* (cbrt (sqrt k)) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 39 / 151 ] 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 (* (* PI n) 2) (/ 1 2))) (sqrt (sqrt k))) (/ (pow (* n 2) (/ k 2)) (cbrt (pow (* (* PI n) 2) (/ 1 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (sqrt k))) (/ (pow (* n 2) (/ k 2)) (cbrt (pow (* (* PI n) 2) (/ 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 (34 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (* (sqrt (sqrt k)) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 40 / 151 ] 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 (66 enodes)
* * [misc]simplify:  iters left: 2 (168 enodes)
* * [misc]simplify:  iters left: 1 (230 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n 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))) (pow (* n 2) (/ k 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))) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n 2) (/ k 2)))) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (* (pow PI (/ k 2)) (sqrt k)))))
* * * * [misc]progress:  [ 41 / 151 ] 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 (143 enodes)
* * [misc]simplify:  iters left: 2 (252 enodes)
* * [misc]simplify:  iters left: 1 (312 enodes)
* [exit]simplify:  Simplified to (* (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (sqrt k))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (sqrt k))) (cbrt (pow (* n (* PI 2)) (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (sqrt k))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (sqrt k))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (/ (/ (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 (35 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (pow (* 2 (* PI n)) (/ 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 (* 2 (* PI n)) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (pow (* 2 (* PI n)) (/ k 2)))))))
* * * * [misc]progress:  [ 42 / 151 ] 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 (144 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 (35 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (* (sqrt (sqrt k)) (cbrt (pow (* 2 (* PI n)) (/ 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 (* 2 (* PI n)) (/ 1 2))) (* (sqrt (sqrt k)) (cbrt (pow (* 2 (* PI n)) (/ k 2)))))))
* * * * [misc]progress:  [ 43 / 151 ] 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 (294 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 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt k)) (cbrt (pow (* (* PI n) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (sqrt k)) (cbrt (pow (* (* PI n) 2) (/ k 2))))))
* * * * [misc]progress:  [ 44 / 151 ] 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 (35 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (* (cbrt (sqrt k)) (sqrt (pow (* 2 (* PI n)) (/ 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 (* 2 (* PI n)) (/ 1 2))) (* (cbrt (sqrt k)) (sqrt (pow (* 2 (* PI n)) (/ k 2)))))))
* * * * [misc]progress:  [ 45 / 151 ] 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 (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 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))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (cbrt (pow (* n (* PI 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 (35 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (* (sqrt (sqrt k)) (sqrt (pow (* 2 (* PI n)) (/ 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 (* 2 (* PI n)) (/ 1 2))) (* (sqrt (sqrt k)) (sqrt (pow (* 2 (* PI n)) (/ k 2)))))))
* * * * [misc]progress:  [ 46 / 151 ] 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 (160 enodes)
* * [misc]simplify:  iters left: 1 (296 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) (sqrt (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) (/ 1 2)))) (sqrt (pow (* (* PI n) 2) (/ 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 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt k)) (sqrt (pow (* (* PI n) 2) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt k)) (sqrt (pow (* (* PI n) 2) (/ k 2))))))
* * * * [misc]progress:  [ 47 / 151 ] 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 (188 enodes)
* * [misc]simplify:  iters left: 1 (216 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 (34 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* (* PI n) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* (* PI n) 2) (/ k 2))))))
* * * * [misc]progress:  [ 48 / 151 ] 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 (70 enodes)
* * [misc]simplify:  iters left: 2 (118 enodes)
* * [misc]simplify:  iters left: 1 (122 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 (34 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* (* PI n) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* (* PI n) 2) (/ k 2))))))
* * * * [misc]progress:  [ 49 / 151 ] 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 (28 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* * [misc]simplify:  iters left: 2 (75 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:  [ 50 / 151 ] 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 (* (* n 2) PI) (/ 1 2))) (* (pow (* n 2) (/ 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)) (* (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 (34 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (* (cbrt (sqrt k)) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 51 / 151 ] 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 (34 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* n 2) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* (* PI n) 2) (/ 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 (34 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (* (sqrt (sqrt k)) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 52 / 151 ] 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 (* (* PI n) 2) (/ 1 2))) (pow (* n 2) (/ k 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* (* PI n) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (pow (* n 2) (/ k 2))) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (pow PI (/ k 2)) (sqrt k)))))
* * * * [misc]progress:  [ 53 / 151 ] 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 (62 enodes)
* * [misc]simplify:  iters left: 2 (74 enodes)
* * [misc]simplify:  iters left: 1 (77 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 (35 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (pow (* 2 (* PI n)) (/ 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 (* 2 (* PI n)) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (pow (* 2 (* PI n)) (/ k 2)))))))
* * * * [misc]progress:  [ 54 / 151 ] 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 (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k))))
* [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 (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 (35 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (* (sqrt (sqrt k)) (cbrt (pow (* 2 (* PI n)) (/ 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 (* 2 (* PI n)) (/ 1 2))) (* (sqrt (sqrt k)) (cbrt (pow (* 2 (* PI n)) (/ k 2)))))))
* * * * [misc]progress:  [ 55 / 151 ] 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 (43 enodes)
* * [misc]simplify:  iters left: 2 (48 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (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 (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)))) (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 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt k)) (cbrt (pow (* (* PI n) 2) (/ 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 (pow (* (* PI n) 2) (/ 1 2))) (sqrt k)) (cbrt (pow (* (* PI n) 2) (/ k 2))))))
* * * * [misc]progress:  [ 56 / 151 ] 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 (46 enodes)
* * [misc]simplify:  iters left: 2 (47 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 (35 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (* (cbrt (sqrt k)) (sqrt (pow (* 2 (* PI n)) (/ 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 (* 2 (* PI n)) (/ 1 2))) (* (cbrt (sqrt k)) (sqrt (pow (* 2 (* PI n)) (/ k 2)))))))
* * * * [misc]progress:  [ 57 / 151 ] 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 (35 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (* (sqrt (sqrt k)) (sqrt (pow (* 2 (* PI n)) (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (* (sqrt (sqrt k)) (sqrt (pow (* 2 (* PI n)) (/ 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 (35 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (* (sqrt (sqrt k)) (sqrt (pow (* 2 (* PI n)) (/ 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 (* 2 (* PI n)) (/ 1 2))) (* (sqrt (sqrt k)) (sqrt (pow (* 2 (* PI n)) (/ k 2)))))))
* * * * [misc]progress:  [ 58 / 151 ] 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 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt k)) (sqrt (pow (* (* PI n) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (sqrt k)) (sqrt (pow (* (* PI n) 2) (/ k 2))))))
* * * * [misc]progress:  [ 59 / 151 ] 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 (49 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 (34 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* (* PI n) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* (* PI n) 2) (/ k 2))))))
* * * * [misc]progress:  [ 60 / 151 ] 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 (* (* PI n) 2) (/ 1 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* (* PI n) 2) (/ 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 (34 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* (* PI n) 2) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* (* PI n) 2) (/ k 2))))))
* * * * [misc]progress:  [ 61 / 151 ] 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 (23 enodes)
* * [misc]simplify:  iters left: 3 (24 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:  [ 62 / 151 ] 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:  [ 63 / 151 ] 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:  [ 64 / 151 ] 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 (* (* PI n) 2) (/ 1 2)) (* (sqrt k) (pow PI (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ 1 (pow (* 2 n) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (* (sqrt k) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 65 / 151 ] 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 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ 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 (* (* PI n) 2) (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ k 2))))))
* * * * [misc]progress:  [ 66 / 151 ] 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 (sqrt (sqrt k))) (cbrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ (/ 1 (sqrt (sqrt k))) (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 (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 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ 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 (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ k 2))))))
* * * * [misc]progress:  [ 67 / 151 ] 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 (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ 1 (* (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)))) (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 (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ k 2))))))
* * * * [misc]progress:  [ 68 / 151 ] 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 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (/ 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 (* (* PI n) 2) (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (/ k 2))))))
* * * * [misc]progress:  [ 69 / 151 ] 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 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (/ 1 (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (/ k 2))))))
* * * * [misc]progress:  [ 70 / 151 ] 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 (* n (* PI 2)) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (pow (* n (* PI 2)) (/ 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 (* n (* PI 2)) (/ k 2)))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ k 2))))))
* * * * [misc]progress:  [ 71 / 151 ] 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:  [ 72 / 151 ] 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:  [ 73 / 151 ] 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 (* (* PI n) 2) (/ 1 2)) (* (sqrt k) (pow (* (* PI n) 2) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* (* PI n) 2) (/ 1 2)) (* (sqrt k) (pow (* (* PI n) 2) (/ k 2))))))
* * * * [misc]progress:  [ 74 / 151 ] 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:  [ 75 / 151 ] 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:  [ 76 / 151 ] 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 (* (* PI n) 2) (/ 1 2)) (* (sqrt k) (pow (* (* PI n) 2) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* (* PI n) 2) (/ 1 2)) (* (sqrt k) (pow (* (* PI n) 2) (/ k 2))))))
* * * * [misc]progress:  [ 77 / 151 ] 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 (28 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 (* (* 2 n) 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 (cbrt (sqrt k))) (pow (* (* 2 n) PI) (/ k 2)))))
* * * * [misc]progress:  [ 78 / 151 ] 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 (* (* 2 n) PI) (/ 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 (* (* 2 n) PI) (/ k 2)))))
* * * * [misc]progress:  [ 79 / 151 ] 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 (* n (* PI 2)) (/ k 2)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (pow (* (* PI 2) n) (/ 1 2)) (/ (/ 1 (sqrt k)) (pow (* n (* PI 2)) (/ k 2)))))
* * * * [misc]progress:  [ 80 / 151 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k))))>
* * * * [misc]progress:  [ 81 / 151 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (/ 1 (sqrt k))))>
* * * * [misc]progress:  [ 82 / 151 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))))>
* * * * [misc]progress:  [ 83 / 151 ] 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:  [ 84 / 151 ] 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:  [ 85 / 151 ] 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:  [ 86 / 151 ] 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 (27 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (* (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt k) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))))))
* * * * [misc]progress:  [ 87 / 151 ] 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:  [ 88 / 151 ] 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:  [ 89 / 151 ] 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:  [ 90 / 151 ] 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:  [ 91 / 151 ] 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:  [ 92 / 151 ] 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 (* (* PI n) 2) (/ 1 2))) (pow (* n 2) (/ k 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (pow (* n 2) (/ k 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) (/ (sqrt k) (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2))))))
* * * * [misc]progress:  [ 93 / 151 ] 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 (47 enodes)
* * [misc]simplify:  iters left: 2 (50 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:  [ 94 / 151 ] 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:  [ 95 / 151 ] 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 (43 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:  [ 96 / 151 ] 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:  [ 97 / 151 ] 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:  [ 98 / 151 ] 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 (27 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (sqrt (pow (* 2 (* PI n)) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt k) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))))))
* * * * [misc]progress:  [ 99 / 151 ] 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 2) n) (/ 1 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (sqrt (pow (* (* PI 2) n) (/ 1 2))) (/ (sqrt k) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))))))
* * * * [misc]progress:  [ 100 / 151 ] 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:  [ 101 / 151 ] 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 (* n (* PI 2)) (/ k 2)))) (cbrt (pow (* n (* PI 2)) (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (/ (/ 1 (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt k) (/ (pow (* (* n 2) PI) (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2)))))))
* * * * [misc]progress:  [ 102 / 151 ] 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:  [ 103 / 151 ] 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:  [ 104 / 151 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))))>
* * * * [misc]progress:  [ 105 / 151 ] 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 (* (* PI n) 2) (/ 1 2))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (pow (* (* PI n) 2) (/ 1 2)) (/ (sqrt k) (/ 1 (pow (* (* n 2) PI) (/ k 2))))))
* * * * [misc]progress:  [ 106 / 151 ] 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 (* (* PI n) 2) (/ 1 2))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (pow (* (* PI n) 2) (/ 1 2)) (* (sqrt k) (pow (* (* n 2) PI) (/ k 2)))))
* * * * [misc]progress:  [ 107 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (pow (* (* n 2) PI) 1) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 108 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (exp (log (* (* n 2) PI))) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 109 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (log (exp (* (* n 2) PI))) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 110 / 151 ] 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:  [ 111 / 151 ] 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:  [ 112 / 151 ] 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:  [ 113 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* 1 (* (* n 2) PI)) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 114 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* n (* 2 PI)) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 115 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 116 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) 1) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 117 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (exp (log (* (* n 2) PI))) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 118 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (log (exp (* (* n 2) PI))) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 119 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 120 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (cbrt (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI))) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 121 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI))) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 122 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* 1 (* (* n 2) PI)) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 123 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 124 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 125 / 151 ] 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 (89 enodes)
* * [misc]simplify:  iters left: 2 (169 enodes)
* * [misc]simplify:  iters left: 1 (333 enodes)
* [exit]simplify:  Simplified to (/ (log (* n (* PI 2))) 2)
* [misc]simplify:  Simplified (2 1 1 1) to (λ (k n) (/ (/ (exp (/ (log (* n (* PI 2))) 2)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 126 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (/ (exp (* (log (* (* n 2) PI)) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 127 / 151 ] 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:  [ 128 / 151 ] 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:  [ 129 / 151 ] 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:  [ 130 / 151 ] 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:  [ 131 / 151 ] 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:  [ 132 / 151 ] 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:  [ 133 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (pow (* (* n 2) PI) (/ 1 2)) 1) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 134 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (/ (exp (log (pow (* (* n 2) PI) (/ 1 2)))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 135 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (/ (log (exp (pow (* (* n 2) PI) (/ 1 2)))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 136 / 151 ] 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:  [ 137 / 151 ] 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:  [ 138 / 151 ] 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:  [ 139 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* 1 (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 140 / 151 ] 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:  [ 141 / 151 ] 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:  [ 142 / 151 ] 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:  [ 143 / 151 ] 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:  [ 144 / 151 ] 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:  [ 145 / 151 ] 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:  [ 146 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* (* n 2) 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) PI) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 147 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* (* n 2) 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) PI) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 148 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* (* n 2) 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) PI) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 149 / 151 ] 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 (43 enodes)
* * [misc]simplify:  iters left: 3 (84 enodes)
* * [misc]simplify:  iters left: 2 (136 enodes)
* * [misc]simplify:  iters left: 1 (169 enodes)
* [exit]simplify:  Simplified to (sqrt (* (* 2 PI) n))
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (/ (sqrt (* (* 2 PI) n)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 150 / 151 ] 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 (87 enodes)
* * [misc]simplify:  iters left: 2 (202 enodes)
* * [misc]simplify:  iters left: 1 (498 enodes)
* [exit]simplify:  Simplified to (sqrt (* (* PI 2) n))
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (/ (sqrt (* (* PI 2) n)) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 151 / 151 ] 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 (87 enodes)
* * [misc]simplify:  iters left: 2 (231 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:  adding candidates to table
* * [misc]progress:  iteration 3 / 4
* * * [misc]progress:  picking best candidate
* * * * [misc]pick:  Picked  #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 4 ] rewriting at (2 2 2 1)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2 2 2)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2 2)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 4 ] generating series at (2 2 2 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:  [ 2 / 4 ] generating series at (2 2 2)
* [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:  [ 3 / 4 ] generating series at (2 2)
* [misc]approximate:  Taking taylor expansion of (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 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]backup-simplify:  Simplify (/ (sqrt k) (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))) into (* (/ 1 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 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]backup-simplify:  Simplify (/ +nan.0 (pow (* 2 (* n PI)) 1/2)) into (* +nan.0 (sqrt (/ 1 (* PI (* n 2)))))
* [misc]taylor:  Taking taylor expansion of (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 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]backup-simplify:  Simplify (/ +nan.0 (pow (* 2 (* n PI)) 1/2)) into (* +nan.0 (sqrt (/ 1 (* PI (* n 2)))))
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (sqrt (/ 1 (* PI (* n 2))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (* PI (* n 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (* PI (* n 2))) in n
* [misc]taylor:  Taking taylor expansion of (* PI (* n 2)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* n 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 (* PI 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* PI 2) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (/ 1 (* 2 PI)) into (/ 1/2 PI)
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ (/ 1/2 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI)
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (/ +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (/ 1 PI)))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ 1 PI))) into (- (* +nan.0 (/ 1 PI)))
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* n 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 n) 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (- (/ -1 2) (+ (* 1/2 (/ 0 2)))) into -1/2
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))
* [misc]backup-simplify:  Simplify (- (/ +nan.0 (pow (* 2 (* n PI)) 1/2)) (+ (* (* +nan.0 (sqrt (/ 1 (* PI (* n 2))))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))))
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2)) in n
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (pow (sqrt 1/2) 2) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 2 (log (sqrt 1/2)))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (log (sqrt 1/2))) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (log (sqrt 1/2)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 1/2) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]backup-simplify:  Simplify (sqrt 1/2) into (sqrt 1/2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 1/2))) into 0
* [misc]backup-simplify:  Simplify (log (sqrt 1/2)) into (log (sqrt 1/2))
* [misc]backup-simplify:  Simplify (* 2 (log (sqrt 1/2))) into (* 2 (log (sqrt 1/2)))
* [misc]backup-simplify:  Simplify (exp (* 2 (log (sqrt 1/2)))) into (pow (sqrt 1/2) 2)
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (/ 1 PI) into (/ 1 PI)
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (/ 1 PI) into (/ 1 PI)
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (sqrt 1/2) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]backup-simplify:  Simplify (sqrt 1/2) into (sqrt 1/2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 1/2))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (+ (log n) (log (* 2 PI))) (pow (sqrt 1/2) 2)) into (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) into (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (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 (/ (* (pow (* 1 0) 1)) (pow (sqrt 1/2) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 (log (sqrt 1/2)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 2 (log (sqrt 1/2)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (* 0 (pow (sqrt 1/2) 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* (sqrt 2) 0) (* 0 (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) (/ +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))
* [misc]backup-simplify:  Simplify (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 0) into 0
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
* [misc]backup-simplify:  Simplify (* 0 (sqrt 1/2)) into 0
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
* [misc]backup-simplify:  Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI)))
* [misc]backup-simplify:  Simplify (+ (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))
* [misc]backup-simplify:  Simplify (- (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 2) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1/2 PI) (/ 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (/ +nan.0 (pow PI 2))) (+ (* 0 (/ +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (/ 1 (pow PI 2))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ 1 (pow PI 2)))) into (- (* +nan.0 (/ 1 (pow PI 2))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (/ 1 (pow PI 2)))) (* n k)) (+ (* (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (/ 1 PI))) (* 1 k)))) into (- (+ (* +nan.0 (/ (* n k) (pow PI 2))) (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (* +nan.0 (/ k PI)))))))))))
* [misc]approximate:  Taking taylor expansion of (/ (sqrt (/ 1 k)) (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ 1 k)) (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 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]backup-simplify:  Simplify (/ (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ 1 k)) (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 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]backup-simplify:  Simplify (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) into (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ 1 k)) (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 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]backup-simplify:  Simplify (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) into (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))
* [misc]taylor:  Taking taylor expansion of (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log (* 2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log (* 2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))) (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log (* 2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n))))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n))))))))) (* 1 (/ 1 k))) (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n))))))))) into (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2)))) (- (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))))
* [misc]approximate:  Taking taylor expansion of (/ (sqrt (/ 1 (- k))) (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ 1 (- k))) (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 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]backup-simplify:  Simplify (/ (sqrt (/ -1 k)) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (/ (sqrt (/ -1 k)) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ 1 (- k))) (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 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]backup-simplify:  Simplify (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) into (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ 1 (- k))) (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 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]backup-simplify:  Simplify (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) into (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
* [misc]taylor:  Taking taylor expansion of (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
* [misc]taylor:  Taking taylor expansion of (log (* -2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -2 in n
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]taylor:  Taking taylor expansion of (+ (/ 1 k) 1) 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 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
* [misc]backup-simplify:  Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (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]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 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 (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ 0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
* [misc]taylor:  Taking taylor expansion of (log (* -2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -2 in n
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]taylor:  Taking taylor expansion of (+ (/ 1 k) 1) 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 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
* [misc]backup-simplify:  Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (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]backup-simplify:  Simplify (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (/ 1 (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 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (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 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ 0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))) (/ 0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
* [misc]taylor:  Taking taylor expansion of (log (* -2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -2 in n
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]taylor:  Taking taylor expansion of (+ (/ 1 k) 1) 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 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
* [misc]backup-simplify:  Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (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]backup-simplify:  Simplify (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (/ 1 (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 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) (* 1 (/ 1 (- k)))) (/ +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))
* * * * [misc]progress:  [ 4 / 4 ] generating series at (2)
* [misc]approximate:  Taking taylor expansion of (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 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]backup-simplify:  Simplify (/ (sqrt k) (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))) into (* (/ 1 (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))) (sqrt k))
* [misc]backup-simplify:  Simplify (/ 1 (* (/ 1 (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 (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 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]backup-simplify:  Simplify (/ +nan.0 (pow (* 2 (* n PI)) 1/2)) into (* +nan.0 (sqrt (/ 1 (* PI (* n 2)))))
* [misc]backup-simplify:  Simplify (/ 1 (* +nan.0 (sqrt (/ 1 (* PI (* n 2)))))) into (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2))))
* [misc]taylor:  Taking taylor expansion of (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (* n 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]backup-simplify:  Simplify (/ +nan.0 (pow (* 2 (* n PI)) 1/2)) into (* +nan.0 (sqrt (/ 1 (* PI (* n 2)))))
* [misc]backup-simplify:  Simplify (/ 1 (* +nan.0 (sqrt (/ 1 (* PI (* n 2)))))) into (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2))))
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (* n PI)) (/ 1 (sqrt 1/2))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt 1/2)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 1/2) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]backup-simplify:  Simplify (sqrt 1/2) into (sqrt 1/2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 1/2))) into 0
* [misc]backup-simplify:  Simplify (/ 1 (sqrt 1/2)) into (/ 1 (sqrt 1/2))
* [misc]backup-simplify:  Simplify (* 0 (/ 1 (sqrt 1/2))) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* n 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 n) 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (- (/ -1 2) (+ (* 1/2 (/ 0 2)))) into -1/2
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))
* [misc]backup-simplify:  Simplify (- (/ +nan.0 (pow (* 2 (* n PI)) 1/2)) (+ (* (* +nan.0 (sqrt (/ 1 (* PI (* n 2))))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))))
* [misc]backup-simplify:  Simplify (- (+ (* (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))) (/ (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) (* +nan.0 (sqrt (/ 1 (* PI (* n 2))))))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))))))
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (* n PI)) (/ 1 (sqrt 1/2))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt 1/2)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 1/2) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]backup-simplify:  Simplify (sqrt 1/2) into (sqrt 1/2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 1/2))) into 0
* [misc]backup-simplify:  Simplify (/ 1 (sqrt 1/2)) into (/ 1 (sqrt 1/2))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (* 0 (/ 1 (sqrt 1/2))) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 (sqrt 1/2)) (/ 0 (sqrt 1/2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* (* +nan.0 PI) (/ 1 (sqrt 1/2)))) into (- (* +nan.0 (/ PI (sqrt 1/2))))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (- (* +nan.0 (/ PI (sqrt 1/2))))) (* 0 0)) into (- (* +nan.0 (/ PI (sqrt 1/2))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ PI (sqrt 1/2)))) into (- (* +nan.0 (/ PI (sqrt 1/2))))
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* n 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 n) 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))
* [misc]backup-simplify:  Simplify (- (/ +nan.0 (pow (* 2 (* n PI)) 1/2)) (+ (* (* +nan.0 (sqrt (/ 1 (* PI (* n 2))))) (/ (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) (pow (* 2 (* n PI)) 1/2))) (* (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) (- (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))) (/ (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (+ (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) (- (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI)))))))))))) (* +nan.0 (sqrt (/ 1 (* PI (* n 2))))))) (* (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2))))))) (/ (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) (* +nan.0 (sqrt (/ 1 (* PI (* n 2))))))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))) (- (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (sqrt 1/2))) (sqrt (* n PI)))))))))))
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))) (- (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (sqrt 1/2))) (sqrt (* n PI))))))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))) (- (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (sqrt 1/2))) (sqrt (* n PI)))))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))) (- (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (sqrt 1/2))) (sqrt (* n PI))))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))) (- (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (sqrt 1/2))) (sqrt (* n PI)))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 2 (log (log (* 2 (* n PI)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (log (log (* 2 (* n PI))))) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (log (log (* 2 (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (log (+ (log n) (log (* 2 PI)))) into (log (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (* 2 (log (+ (log n) (log (* 2 PI))))) into (* 2 (log (+ (log n) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (exp (* 2 (log (+ (log n) (log (* 2 PI)))))) into (pow (+ (log n) (log (* 2 PI))) 2)
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))) (- (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (sqrt 1/2))) (sqrt (* n PI))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))) (- (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (sqrt 1/2))) (sqrt (* n PI)))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (/ 1 (sqrt 1/2)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (* n PI)) (/ 1 (sqrt 1/2))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt 1/2)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 1/2) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]backup-simplify:  Simplify (sqrt 1/2) into (sqrt 1/2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 1/2))) into 0
* [misc]backup-simplify:  Simplify (/ 1 (sqrt 1/2)) into (/ 1 (sqrt 1/2))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (sqrt 1/2))) (sqrt (* n PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (sqrt 1/2))) (sqrt (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (sqrt 1/2))) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (sqrt 1/2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (sqrt 2) 2) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 2 (log (sqrt 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (log (sqrt 2))) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (log (sqrt 2)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]backup-simplify:  Simplify (log (sqrt 2)) into (log (sqrt 2))
* [misc]backup-simplify:  Simplify (* 2 (log (sqrt 2))) into (* 2 (log (sqrt 2)))
* [misc]backup-simplify:  Simplify (exp (* 2 (log (sqrt 2)))) into (pow (sqrt 2) 2)
* [misc]taylor:  Taking taylor expansion of (* (pow (log (* 2 (* n PI))) 2) (sqrt 1/2)) in n
* [misc]taylor:  Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 2 (log (log (* 2 (* n PI)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (log (log (* 2 (* n PI))))) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (log (log (* 2 (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (log (+ (log n) (log (* 2 PI)))) into (log (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (* 2 (log (+ (log n) (log (* 2 PI))))) into (* 2 (log (+ (log n) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (exp (* 2 (log (+ (log n) (log (* 2 PI)))))) into (pow (+ (log n) (log (* 2 PI))) 2)
* [misc]taylor:  Taking taylor expansion of (sqrt 1/2) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]backup-simplify:  Simplify (sqrt 1/2) into (sqrt 1/2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 1/2))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2))
* [misc]backup-simplify:  Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (* 0 (/ 1 (sqrt 1/2))) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (* (pow (+ (log n) (log (* 2 PI))) 2) (sqrt 1/2)) into (* (sqrt 1/2) (pow (+ (log n) (log (* 2 PI))) 2))
* [misc]backup-simplify:  Simplify (* (pow (sqrt 2) 2) (* (sqrt 1/2) (pow (+ (log n) (log (* 2 PI))) 2))) into (* (pow (sqrt 2) 2) (* (sqrt 1/2) (pow (+ (log n) (log (* 2 PI))) 2)))
* [misc]backup-simplify:  Simplify (* (* (pow (sqrt 2) 2) (* (sqrt 1/2) (pow (+ (log n) (log (* 2 PI))) 2))) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 (sqrt 1/2)) (/ 0 (sqrt 1/2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* (* +nan.0 PI) (/ 1 (sqrt 1/2)))) into (- (* +nan.0 (/ PI (sqrt 1/2))))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (- (* +nan.0 (/ PI (sqrt 1/2))))) (* 0 0)) into (- (* +nan.0 (/ PI (sqrt 1/2))))
* [misc]backup-simplify:  Simplify (- (- (* +nan.0 (/ PI (sqrt 1/2))))) into (- (* +nan.0 (/ PI (sqrt 1/2))))
* [misc]backup-simplify:  Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (- (* +nan.0 (/ PI (sqrt 1/2))))) into (- (+ (* +nan.0 (/ PI (sqrt 1/2))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))
* [misc]backup-simplify:  Simplify (- (- (+ (* +nan.0 (/ PI (sqrt 1/2))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (/ PI (sqrt 1/2))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ PI (sqrt 1/2))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))))) into (- (+ (* +nan.0 (/ PI (sqrt 1/2))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1/2))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 (sqrt 1/2)) (/ 0 (sqrt 1/2))) (* 0 (/ 0 (sqrt 1/2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* (* +nan.0 PI) 0) (* (* +nan.0 (pow PI 2)) (/ 1 (sqrt 1/2))))) into (- (* +nan.0 (/ (pow PI 2) (sqrt 1/2))))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (- (* +nan.0 (/ (pow PI 2) (sqrt 1/2))))) (+ (* 0 (- (* +nan.0 (/ PI (sqrt 1/2))))) (* 0 0))) into (- (* +nan.0 (/ (pow PI 2) (sqrt 1/2))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (pow PI 2) (sqrt 1/2)))) into (- (* +nan.0 (/ (pow PI 2) (sqrt 1/2))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (/ (pow PI 2) (sqrt 1/2)))) (* (pow n 2) (/ 1 k))) (+ (* (- (+ (* +nan.0 (/ PI (sqrt 1/2))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))))) (* n 1)) (* (- (* +nan.0 (/ PI (sqrt 1/2)))) (* n (/ 1 k))))) into (- (+ (* +nan.0 (/ (* n PI) (* (sqrt 1/2) k))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (log n))))) (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) (* (sqrt 1/2) k))) (- (+ (* +nan.0 (/ (* n PI) (sqrt 1/2))) (- (* +nan.0 (* (sqrt 2) (* n (* PI (log (* 2 PI)))))))))))))))
* [misc]approximate:  Taking taylor expansion of (/ 1 (/ (sqrt (/ 1 k)) (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (/ 1 (/ (sqrt (/ 1 k)) (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ 1 k)) (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 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]backup-simplify:  Simplify (/ (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k)))
* [misc]backup-simplify:  Simplify (/ 1 (* (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k)))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (/ 1 (/ (sqrt (/ 1 k)) (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ 1 k)) (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 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]backup-simplify:  Simplify (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) into (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))
* [misc]backup-simplify:  Simplify (/ 1 (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))
* [misc]taylor:  Taking taylor expansion of (/ 1 (/ (sqrt (/ 1 k)) (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ 1 k)) (pow (* (* (/ 1 n) 2) PI) (/ (- 1 (/ 1 k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) 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]backup-simplify:  Simplify (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) into (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))
* [misc]backup-simplify:  Simplify (/ 1 (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log (* 2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))))
* [misc]backup-simplify:  Simplify (- (+ (* (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) (/ (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))) (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log (* 2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))) (/ 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))))
* [misc]backup-simplify:  Simplify (- (+ (* (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) (/ (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))) (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) (/ (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))) (/ +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log (* 2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))) (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))))))))
* [misc]approximate:  Taking taylor expansion of (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ 1 (- k))) (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 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]backup-simplify:  Simplify (/ (sqrt (/ -1 k)) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (/ (sqrt (/ -1 k)) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (/ 1 (/ (sqrt (/ -1 k)) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
* [misc]taylor:  Taking taylor expansion of (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ 1 (- k))) (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 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]backup-simplify:  Simplify (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) into (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
* [misc]backup-simplify:  Simplify (/ 1 (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
* [misc]taylor:  Taking taylor expansion of (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ 1 (- k))) (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1 (/ 1 (- k))) 2))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) 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]backup-simplify:  Simplify (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) into (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
* [misc]backup-simplify:  Simplify (/ 1 (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
* [misc]taylor:  Taking taylor expansion of (log (* -2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -2 in n
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]taylor:  Taking taylor expansion of (+ (/ 1 k) 1) 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 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
* [misc]backup-simplify:  Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (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]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 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 (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ 0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))))
* [misc]backup-simplify:  Simplify (- (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))) (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
* [misc]taylor:  Taking taylor expansion of (log (* -2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -2 in n
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]taylor:  Taking taylor expansion of (+ (/ 1 k) 1) 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 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
* [misc]backup-simplify:  Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (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]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 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 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 (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (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 (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (+ (* (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ 0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) (* (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))) (/ 0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))))) into (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))))
* [misc]backup-simplify:  Simplify (- (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))) (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))) (* (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) (/ (- (* +nan.0 (/ 1 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))) (/ +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
* [misc]taylor:  Taking taylor expansion of (log (* -2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -2 in n
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]taylor:  Taking taylor expansion of (+ (/ 1 k) 1) 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 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
* [misc]backup-simplify:  Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (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]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 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 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 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +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:  simplifying candidates
* * * * [misc]progress:  [ 1 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* (* n 2) PI) 1) (/ (- 1 k) 2)))))>
* * * * [misc]progress:  [ 2 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (exp (log (* (* n 2) PI))) (/ (- 1 k) 2)))))>
* * * * [misc]progress:  [ 3 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (log (exp (* (* n 2) PI))) (/ (- 1 k) 2)))))>
* * * * [misc]progress:  [ 4 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (/ (- 1 k) 2)))))>
* * * * [misc]progress:  [ 5 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (cbrt (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI))) (/ (- 1 k) 2)))))>
* * * * [misc]progress:  [ 6 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI))) (/ (- 1 k) 2)))))>
* * * * [misc]progress:  [ 7 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 1 (* (* n 2) PI)) (/ (- 1 k) 2)))))>
* * * * [misc]progress:  [ 8 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
* * * * [misc]progress:  [ 9 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (/ (- 1 k) 2)))))>
* * * * [misc]progress:  [ 10 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* (log (* (* n 2) PI)) (/ (- 1 k) 2))))))>
* [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 (141 enodes)
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* (* n 2) PI)))
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (exp (* (/ (- 1 k) 2) (log (* (* n 2) PI)))))))
* * * * [misc]progress:  [ 11 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* (log (* (* n 2) PI)) (/ (- 1 k) 2))))))>
* * * * [misc]progress:  [ 12 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (* 1 (/ (- 1 k) 2))))))>
* [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 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (* 1 (/ (- 1 k) 2))))))
* * * * [misc]progress:  [ 13 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))))>
* [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 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))))
* * * * [misc]progress:  [ 14 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* (* n 2) PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))))))>
* [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 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* (* n 2) PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))))))
* * * * [misc]progress:  [ 15 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* (* n 2) PI) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))))))>
* [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 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* (* n 2) PI) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))))))
* * * * [misc]progress:  [ 16 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* (* n 2) PI) 1) (/ (- 1 k) 2)))))>
* [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 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* (* n 2) PI) 1) (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 17 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* (* n 2) PI) (- 1 k)) (/ 1 2)))))>
* [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 2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* (* n 2) PI) (- 1 k)) (/ 1 2)))))
* * * * [misc]progress:  [ 18 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* n 2) (/ (- 1 k) 2)) (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 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* n 2) (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))))))
* * * * [misc]progress:  [ 19 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (pow (* (* n 2) PI) (/ (- 1 k) 2)) 1))))>
* * * * [misc]progress:  [ 20 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (log (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))>
* * * * [misc]progress:  [ 21 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (log (exp (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))>
* * * * [misc]progress:  [ 22 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))>
* * * * [misc]progress:  [ 23 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (cbrt (* (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))>
* * * * [misc]progress:  [ 24 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))>
* * * * [misc]progress:  [ 25 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (* 1 (pow (* (* n 2) PI) (/ (- 1 k) 2))))))>
* * * * [misc]progress:  [ 26 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (pow (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))) 1)))>
* * * * [misc]progress:  [ 27 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (log (sqrt k)) (* (log (* (* n 2) PI)) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (- (log (sqrt k)) (* (log (* (* n 2) PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (72 enodes)
* * [misc]simplify:  iters left: 3 (198 enodes)
* [exit]simplify:  Simplified to (- (log (sqrt k)) (/ (log (* (* n PI) 2)) (/ 2 (- 1 k))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (/ 1 (exp (- (log (sqrt k)) (/ (log (* (* n PI) 2)) (/ 2 (- 1 k)))))))
* * * * [misc]progress:  [ 28 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (log (sqrt k)) (* (log (* (* n 2) PI)) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (- (log (sqrt k)) (* (log (* (* n 2) PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (72 enodes)
* * [misc]simplify:  iters left: 3 (198 enodes)
* [exit]simplify:  Simplified to (- (log (sqrt k)) (/ (log (* (* n PI) 2)) (/ 2 (- 1 k))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (/ 1 (exp (- (log (sqrt k)) (/ (log (* (* n PI) 2)) (/ 2 (- 1 k)))))))
* * * * [misc]progress:  [ 29 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (- (log (sqrt k)) (log (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (- (log (sqrt k)) (log (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (53 enodes)
* * [misc]simplify:  iters left: 3 (132 enodes)
* * [misc]simplify:  iters left: 2 (459 enodes)
* [exit]simplify:  Simplified to (+ (log (sqrt k)) (* (log (* (* PI 2) n)) (/ (- k 1) 2)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (/ 1 (exp (+ (log (sqrt k)) (* (log (* (* PI 2) n)) (/ (- k 1) 2))))))
* * * * [misc]progress:  [ 30 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (exp (log (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))>
* * * * [misc]progress:  [ 31 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (log (exp (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))>
* * * * [misc]progress:  [ 32 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (cbrt (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (75 enodes)
* * [misc]simplify:  iters left: 3 (137 enodes)
* * [misc]simplify:  iters left: 2 (213 enodes)
* * [misc]simplify:  iters left: 1 (296 enodes)
* [exit]simplify:  Simplified to (/ (/ (* k (sqrt k)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (/ 1 (cbrt (/ (/ (* k (sqrt k)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2)))))))
* * * * [misc]progress:  [ 33 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (* (cbrt (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))))) (cbrt (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))>
* * * * [misc]progress:  [ 34 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (cbrt (* (* (/ (sqrt k) (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)))))))>
* * * * [misc]progress:  [ 35 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (sqrt (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))>
* * * * [misc]progress:  [ 36 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (- (sqrt k)) (- (pow (* (* n 2) PI) (/ (- 1 k) 2))))))>
* * * * [misc]progress:  [ 37 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n 2) (/ (- 1 k) 2))) (/ (cbrt (sqrt k)) (pow PI (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n 2) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n 2) (/ (- 1 k) 2)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n 2) (/ (- 1 k) 2))) (/ (cbrt (sqrt k)) (pow PI (/ (- 1 k) 2))))))
* [enter]simplify:  Simplifying (/ (cbrt (sqrt k)) (pow PI (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (sqrt k)) (pow PI (/ (- 1 k) 2)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n 2) (/ (- 1 k) 2))) (/ (cbrt (sqrt k)) (pow PI (/ (- 1 k) 2))))))
* * * * [misc]progress:  [ 38 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))))
* * [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 (sqrt k)) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (/ 1 (* (* (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))
* [enter]simplify:  Simplifying (/ (cbrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * [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 (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))) (/ (cbrt (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))))))
* * * * [misc]progress:  [ 39 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (/ (cbrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * [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 (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (/ (cbrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))
* [enter]simplify:  Simplifying (/ (cbrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * [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 (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (/ (cbrt (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))))))
* * * * [misc]progress:  [ 40 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (cbrt (sqrt k)) (pow (* (* n 2) PI) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* * [misc]simplify:  iters left: 3 (21 enodes)
* * [misc]simplify:  iters left: 2 (26 enodes)
* [exit]simplify:  Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (/ 1 (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (cbrt (sqrt k)) (pow (* (* n 2) PI) (/ (- 1 k) 2))))))
* [enter]simplify:  Simplifying (/ (cbrt (sqrt k)) (pow (* (* n 2) PI) (/ (- 1 k) 2)))
* * [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 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (/ 1 (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (cbrt (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))
* * * * [misc]progress:  [ 41 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (pow (* n 2) (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (pow PI (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) (pow (* n 2) (/ (- 1 k) 2)))
* * [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 (/ (sqrt (sqrt k)) (pow (* n 2) (/ (- 1 k) 2)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (pow (* n 2) (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (pow PI (/ (- 1 k) 2))))))
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) (pow PI (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) (pow PI (/ (- 1 k) 2)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (pow (* n 2) (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (pow PI (/ (- 1 k) 2))))))
* * * * [misc]progress:  [ 42 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (* (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)))))))>
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * [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 (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))))))
* * * * [misc]progress:  [ 43 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (/ (sqrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * [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 (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (/ (sqrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * [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 (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))))))
* * * * [misc]progress:  [ 44 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt (sqrt k)) 1) (/ (sqrt (sqrt k)) (pow (* (* n 2) PI) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) 1)
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* * [misc]simplify:  iters left: 2 (9 enodes)
* [exit]simplify:  Simplified to (sqrt (sqrt k))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* (* n 2) PI) (/ (- 1 k) 2))))))
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) (pow (* (* n 2) PI) (/ (- 1 k) 2)))
* * [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 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (/ 1 (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))
* * * * [misc]progress:  [ 45 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (pow (* n 2) (/ (- 1 k) 2))) (/ (sqrt k) (pow PI (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ 1 (pow (* n 2) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (9 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 (/ 1 (pow (* 2 n) (/ (- 1 k) 2)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ 1 (pow (* 2 n) (/ (- 1 k) 2))) (/ (sqrt k) (pow PI (/ (- 1 k) 2))))))
* [enter]simplify:  Simplifying (/ (sqrt k) (pow PI (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* * [misc]simplify:  iters left: 3 (21 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (pow PI (/ (- 1 k) 2)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (pow (* n 2) (/ (- 1 k) 2))) (/ (sqrt k) (pow PI (/ (- 1 k) 2))))))
* * * * [misc]progress:  [ 46 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (* (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 (/ 1 (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (/ 1 (* (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ 1 (* (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)))))))
* [enter]simplify:  Simplifying (/ (sqrt k) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * [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 k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (* (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)))))))
* * * * [misc]progress:  [ 47 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (/ (sqrt k) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt (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 (/ 1 (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (/ 1 (* (/ 1 (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (/ (sqrt k) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))
* [enter]simplify:  Simplifying (/ (sqrt k) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * [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 k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (/ 1 (* (/ 1 (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))))
* * * * [misc]progress:  [ 48 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ 1 1) (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ 1 1)
* * [misc]simplify:  iters left: 2 (2 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to 1
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (/ 1 (* 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))))))
* [enter]simplify:  Simplifying (/ (sqrt k) (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 (36 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (/ 1 (* 1 (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))))
* * * * [misc]progress:  [ 49 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))))))>
* * * * [misc]progress:  [ 50 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (sqrt k) (/ 1 (pow (* (* n 2) PI) (/ (- 1 k) 2))))))>
* * * * [misc]progress:  [ 51 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 52 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* n 2) (/ (- 1 k) 2))) (pow PI (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (pow PI (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (17 enodes)
* * [misc]simplify:  iters left: 2 (19 enodes)
* [exit]simplify:  Simplified to (pow PI (/ (- 1 k) 2))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* n 2) (/ (- 1 k) 2))) (pow PI (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 53 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (cbrt (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 (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))))))
* * * * [misc]progress:  [ 54 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (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 (* (* PI n) 2) (/ (- 1 k) 2)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))))))
* * * * [misc]progress:  [ 55 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) 1) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (pow (* (* n 2) PI) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (10 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* * [misc]simplify:  iters left: 2 (33 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI 2) n) (/ (- 1 k) 2))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (/ 1 (/ (/ (sqrt k) 1) (pow (* (* PI 2) n) (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 56 / 105 ] 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 (* (cbrt (sqrt k)) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* [exit]simplify:  Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (cbrt (sqrt k))))))
* * * * [misc]progress:  [ 57 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt (sqrt k)) (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (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 1) to (λ (k n) (/ 1 (/ (sqrt (sqrt k)) (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt k))))))
* * * * [misc]progress:  [ 58 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ 1 (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 59 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (* (/ (sqrt k) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2)))))>
* [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 2 2) to (λ (k n) (/ 1 (* (/ (sqrt k) (pow (* (* n 2) PI) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2)))))
* * * * [misc]progress:  [ 60 / 105 ] simplifiying candidate #<alt (λ (k n) (pow (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))) -1))>
* * * * [misc]progress:  [ 61 / 105 ] simplifiying candidate #<alt (λ (k n) (pow (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (- 1)))>
* [enter]simplify:  Simplifying (- 1)
* * [misc]simplify:  iters left: 2 (2 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (- 1)
* [misc]simplify:  Simplified (2 2) to (λ (k n) (pow (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (- 1)))
* * * * [misc]progress:  [ 62 / 105 ] simplifiying candidate #<alt (λ (k n) (pow (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))) 1))>
* * * * [misc]progress:  [ 63 / 105 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (log (sqrt k)) (* (log (* (* n 2) PI)) (/ (- 1 k) 2))))))>
* * * * [misc]progress:  [ 64 / 105 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (log (sqrt k)) (* (log (* (* n 2) PI)) (/ (- 1 k) 2))))))>
* * * * [misc]progress:  [ 65 / 105 ] simplifiying candidate #<alt (λ (k n) (exp (- (- (log (sqrt k)) (log (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))>
* * * * [misc]progress:  [ 66 / 105 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))>
* * * * [misc]progress:  [ 67 / 105 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))>
* * * * [misc]progress:  [ 68 / 105 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))>
* * * * [misc]progress:  [ 69 / 105 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))))) (cbrt (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))) (cbrt (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))>
* * * * [misc]progress:  [ 70 / 105 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))))) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))>
* * * * [misc]progress:  [ 71 / 105 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))))) (sqrt (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))))>
* * * * [misc]progress:  [ 72 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (- 1) (- (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))))))>
* * * * [misc]progress:  [ 73 / 105 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))))))>
* * * * [misc]progress:  [ 74 / 105 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))))))>
* * * * [misc]progress:  [ 75 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))) 1)))>
* * * * [misc]progress:  [ 76 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (* (cbrt (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))) (cbrt (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (cbrt (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * [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 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ 1 (* (cbrt (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (cbrt (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))) (cbrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
* * * * [misc]progress:  [ 77 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (sqrt (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))))) (sqrt (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (sqrt (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * [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 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ 1 (sqrt (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))))) (sqrt (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
* * * * [misc]progress:  [ 78 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n 2) (/ (- 1 k) 2)))) (/ (cbrt (sqrt k)) (pow PI (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ (cbrt (sqrt k)) (pow PI (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (sqrt k)) (pow PI (/ (- 1 k) 2)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n 2) (/ (- 1 k) 2)))) (/ (cbrt (sqrt k)) (pow PI (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 79 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (cbrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * [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 (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))))) (/ (cbrt (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))))
* * * * [misc]progress:  [ 80 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))) (/ (cbrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (cbrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * [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 (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))) (/ (cbrt (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))))
* * * * [misc]progress:  [ 81 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ (cbrt (sqrt k)) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ (cbrt (sqrt k)) (pow (* (* n 2) PI) (/ (- 1 k) 2)))
* * [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 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)) (/ (cbrt (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 82 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* n 2) (/ (- 1 k) 2)))) (/ (sqrt (sqrt k)) (pow PI (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) (pow PI (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) (pow PI (/ (- 1 k) 2)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (pow (* n 2) (/ (- 1 k) 2)))) (/ (sqrt (sqrt k)) (pow PI (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 83 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (* (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))))))>
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * [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 (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))))) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))))
* * * * [misc]progress:  [ 84 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))) (/ (sqrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * [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 (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))))
* * * * [misc]progress:  [ 85 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) 1)) (/ (sqrt (sqrt k)) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) (pow (* (* n 2) PI) (/ (- 1 k) 2)))
* * [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 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ 1 (/ (sqrt (sqrt k)) 1)) (/ (sqrt (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 86 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 (pow (* n 2) (/ (- 1 k) 2)))) (/ (sqrt k) (pow PI (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (pow PI (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* * [misc]simplify:  iters left: 3 (21 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (pow PI (/ (- 1 k) 2)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (pow (* n 2) (/ (- 1 k) 2)))) (/ (sqrt k) (pow PI (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 87 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 (* (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 (/ (sqrt k) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * [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 k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (* (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))))))
* * * * [misc]progress:  [ 88 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))) (/ (sqrt k) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * [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 k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))
* * * * [misc]progress:  [ 89 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ 1 1)) (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (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 (36 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ 1 (/ 1 1)) (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 90 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 1) (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (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 (36 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ 1 1) (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 91 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (sqrt k)) (/ 1 (pow (* (* n 2) PI) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ 1 (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 (/ 1 (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ 1 (sqrt k)) (/ 1 (pow (* (* PI 2) n) (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 92 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ 1 2)))) (pow (* (* n 2) PI) (/ k 2))))>
* [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 2) to (λ (k n) (/ (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n (* PI 2)) (/ k 2))))
* * * * [misc]progress:  [ 93 / 105 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* n 2) PI) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (pow (* (* n 2) PI) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (10 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* * [misc]simplify:  iters left: 2 (33 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI 2) n) (/ (- 1 k) 2))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* PI 2) n) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 94 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
* [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 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* PI n) 2) (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 95 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
* [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 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* PI n) 2) (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 96 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))))>
* [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 2 2 1) to (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* PI n) 2) (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 97 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (- (+ (* 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))))))))>
* [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 (105 enodes)
* * [misc]simplify:  iters left: 4 (338 enodes)
* [exit]simplify:  Simplified to (+ (+ (* (- 1/2) (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2))))) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (+ (* (* (log (* PI 2)) 1/8) (* (log (* PI 2)) (* k k))) (* (* (log (* PI 2)) 1/4) (* (* k k) (log n))))))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (+ (+ (* (- 1/2) (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2))))) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (+ (* (* (log (* PI 2)) 1/8) (* (log (* PI 2)) (* k k))) (* (* (log (* PI 2)) 1/4) (* (* k k) (log n)))))))))
* * * * [misc]progress:  [ 98 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))))>
* [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 (266 enodes)
* [exit]simplify:  Simplified to (pow (exp (- 1/2 (* 1/2 k))) (+ (log (* 2 PI)) (log n)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (exp (- 1/2 (* 1/2 k))) (+ (log (* 2 PI)) (log n))))))
* * * * [misc]progress:  [ 99 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))>
* [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 (272 enodes)
* [exit]simplify:  Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n))))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (/ 1 (/ (sqrt k) (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))))))
* * * * [misc]progress:  [ 100 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (- (+ (* +nan.0 (/ (* n k) (pow PI 2))) (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (* +nan.0 (/ k PI)))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (* n k) (pow PI 2))) (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (* +nan.0 (/ k PI)))))))))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ 1 +nan.0))
* * * * [misc]progress:  [ 101 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2)))) (- (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2)))) (- (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ 1 +nan.0))
* * * * [misc]progress:  [ 102 / 105 ] simplifiying candidate #<alt (λ (k n) (/ 1 (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ 1 +nan.0))
* * * * [misc]progress:  [ 103 / 105 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (* n PI) (* (sqrt 1/2) k))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (log n))))) (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) (* (sqrt 1/2) k))) (- (+ (* +nan.0 (/ (* n PI) (sqrt 1/2))) (- (* +nan.0 (* (sqrt 2) (* n (* PI (log (* 2 PI))))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (* n PI) (* (sqrt 1/2) k))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (log n))))) (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) (* (sqrt 1/2) k))) (- (+ (* +nan.0 (/ (* n PI) (sqrt 1/2))) (- (* +nan.0 (* (sqrt 2) (* n (* PI (log (* 2 PI)))))))))))))))
* [misc]simplify:  Simplified (2) to (λ (k n) +nan.0)
* * * * [misc]progress:  [ 104 / 105 ] 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:  [ 105 / 105 ] 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:  adding candidates to table
* * [misc]progress:  iteration 4 / 4
* * * [misc]progress:  picking best candidate
* * * * [misc]pick:  Picked  #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (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)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2 2 1 1 2 1)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2 2 1 1 1 1)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2 1 1 2 1 2)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 4 ] generating series at (2)
* [misc]approximate:  Taking taylor expansion of (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (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 (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* PI n)) (/ 1 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* 2 (* PI n))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* 2 (* PI n)))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* PI n))) in k
* [misc]taylor:  Taking taylor expansion of (* 2 (* PI n)) 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 n) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (* PI n) into (* n PI)
* [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 (* 2 (* PI n)) (/ k 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* 2 (* PI n))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* 2 (* PI n)))) in k
* [misc]taylor:  Taking taylor expansion of (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* PI n))) in k
* [misc]taylor:  Taking taylor expansion of (* 2 (* PI n)) 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 n) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (* PI n) into (* n PI)
* [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]backup-simplify:  Simplify (sqrt (sqrt (* PI (* n 2)))) into (* (sqrt (sqrt 2)) (pow (* n PI) 1/4))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 n)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 (* n PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (log (* 2 (* n PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log (* 2 (* n PI)))) 1) 1)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* (sqrt (* PI (* n 2))) (/ (* 1/2 (log (* 2 (* n PI)))) 1)))) into (- (* 1/2 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))))
* [misc]backup-simplify:  Simplify (/ (- (* 1/2 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))))) (* 2 (sqrt (sqrt (* PI (* n 2)))))) into (* -1/4 (* (sqrt (sqrt 2)) (* (log (* 2 (* n PI))) (pow (* n PI) 1/4))))
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (sqrt (* PI (* n 2)))) into (* (sqrt (sqrt 2)) (pow (* n PI) 1/4))
* [misc]backup-simplify:  Simplify (+ (* n 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 n) 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (log (* 2 (* n PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log (* 2 (* n PI)))) 1) 1)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* (sqrt (* PI (* n 2))) (/ (* 1/2 (log (* 2 (* n PI)))) 1)))) into (- (* 1/2 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))))
* [misc]backup-simplify:  Simplify (/ (- (* 1/2 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))))) (* 2 (sqrt (sqrt (* PI (* n 2)))))) into (* -1/4 (* (sqrt (sqrt 2)) (* (log (* 2 (* n PI))) (pow (* n PI) 1/4))))
* [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 (sqrt 2)) (pow (* n PI) 1/4)) +nan.0) into (* +nan.0 (* (sqrt (sqrt 2)) (pow (* n PI) 1/4)))
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* PI n)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* 2 (* PI n))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* 2 (* PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* PI n)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (* PI 0) into 0
* [misc]backup-simplify:  Simplify (* 2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 1) (* 0 0)) into PI
* [misc]backup-simplify:  Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log 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 (* 2 (* PI n)) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* 2 (* PI n))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* 2 (* PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* PI n)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (* PI 0) into 0
* [misc]backup-simplify:  Simplify (* 2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 1) (* 0 0)) into PI
* [misc]backup-simplify:  Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log 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]backup-simplify:  Simplify (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) into (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 1) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 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 (+ (* PI 0) (+ (* 0 1) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (/ 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 (* 2 (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))))) into 0
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) into (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))))
* [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 (* 2 (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))))) into 0
* [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 (/ (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) (sqrt k)) into (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) k)))
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* PI n)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* 2 (* PI n))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* 2 (* PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* PI n)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (* PI 0) into 0
* [misc]backup-simplify:  Simplify (* 2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 1) (* 0 0)) into PI
* [misc]backup-simplify:  Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log 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 (* 2 (* PI n)) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* 2 (* PI n))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* 2 (* PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* PI n)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (* PI 0) into 0
* [misc]backup-simplify:  Simplify (* 2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 1) (* 0 0)) into PI
* [misc]backup-simplify:  Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log 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]backup-simplify:  Simplify (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) into (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 1) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 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 (+ (* PI 0) (+ (* 0 1) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (/ 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 (* 2 (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))))) into 0
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) into (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))))
* [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 (* 2 (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))))) into 0
* [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 (/ (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) (sqrt k)) into (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) k)))
* [misc]backup-simplify:  Simplify (* (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) 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 (sqrt k)) (+ (* (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) k))) (/ 0 (sqrt k))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) 0) (* 0 (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) 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 (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (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)) (+ (* (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) k))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 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 (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) 0) (+ (* 0 0) (* 0 (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) 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 (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (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)) (+ (* (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) k))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) 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 (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) 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 (* (sqrt (/ (pow (* 2 (* PI (/ 1 n))) (/ 1 2)) (pow (* 2 (* PI (/ 1 n))) (/ (/ 1 k) 2)))) (/ (sqrt (/ (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 (* (sqrt (/ (pow (* 2 (* PI (/ 1 n))) (/ 1 2)) (pow (* 2 (* PI (/ 1 n))) (/ (/ 1 k) 2)))) (/ (sqrt (/ (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 (sqrt (/ (pow (* 2 (* PI (/ 1 n))) (/ 1 2)) (pow (* 2 (* PI (/ 1 n))) (/ (/ 1 k) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (pow (* 2 (* PI (/ 1 n))) (/ 1 2)) (pow (* 2 (* PI (/ 1 n))) (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* PI (/ 1 n))) (/ 1 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* 2 (* PI (/ 1 n)))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* 2 (* PI (/ 1 n))))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* PI (/ 1 n)))) in k
* [misc]taylor:  Taking taylor expansion of (* 2 (* PI (/ 1 n))) 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 (/ 1 n)) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (/ 1 n) into (/ 1 n)
* [misc]backup-simplify:  Simplify (* PI (/ 1 n)) into (/ PI n)
* [misc]backup-simplify:  Simplify (* 2 (/ PI n)) 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 (* 2 (* PI (/ 1 n))) (/ (/ 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* 2 (* PI (/ 1 n)))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* 2 (* PI (/ 1 n))))) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* PI (/ 1 n)))) in k
* [misc]taylor:  Taking taylor expansion of (* 2 (* PI (/ 1 n))) 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 (/ 1 n)) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (/ 1 n) into (/ 1 n)
* [misc]backup-simplify:  Simplify (* PI (/ 1 n)) into (/ PI n)
* [misc]backup-simplify:  Simplify (* 2 (/ PI n)) 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 (* 2 (* PI (/ 1 n)))))) 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]backup-simplify:  Simplify (sqrt (* (sqrt (/ (* PI 2) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into (* (sqrt (/ (sqrt 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) (pow (/ PI n) 1/4))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 n) (/ 0 n)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 (/ 1 n))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 (/ PI n))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (/ PI n)) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (log (* 2 (/ PI n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 (/ PI n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) (+ (* (* (sqrt (/ (* PI 2) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) (/ 0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* (sqrt (/ (* PI 2) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))))) into 0
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ (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 (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (* (sqrt (/ (* PI 2) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into (* (sqrt (/ (sqrt 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) (pow (/ PI n) 1/4))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 n) (/ 0 n)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ 1 n) 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ 2 n) 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (/ PI n)) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (log (* 2 (/ PI n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 (/ PI n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) (+ (* (* (sqrt (/ (* PI 2) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) (/ 0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* (sqrt (/ (* PI 2) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))))) into 0
* [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 (/ (sqrt 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) (pow (/ PI n) 1/4)) +nan.0) into (* +nan.0 (* (sqrt (/ (sqrt 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) (pow (/ PI n) 1/4)))
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ (pow (* 2 (* PI (/ 1 n))) (/ 1 2)) (pow (* 2 (* PI (/ 1 n))) (/ (/ 1 k) 2)))) (/ (sqrt (/ (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 (sqrt (/ (pow (* 2 (* PI (/ 1 n))) (/ 1 2)) (pow (* 2 (* PI (/ 1 n))) (/ (/ 1 k) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* 2 (* PI (/ 1 n))) (/ 1 2)) (pow (* 2 (* PI (/ 1 n))) (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* PI (/ 1 n))) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* 2 (* PI (/ 1 n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* 2 (* PI (/ 1 n))))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* PI (/ 1 n)))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* PI (/ 1 n))) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* PI (/ 1 n)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (* PI 1) into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (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 (* 2 (* PI (/ 1 n))) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* 2 (* PI (/ 1 n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* 2 (* PI (/ 1 n))))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* PI (/ 1 n)))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* PI (/ 1 n))) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* PI (/ 1 n)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (* PI 1) into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (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]backup-simplify:  Simplify (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 1)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 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 (+ (* PI 0) (* 0 1)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 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 (* 2 (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ (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 (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (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 (- (+ (* 1/2 (/ 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 (* 2 (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [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 (/ (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (sqrt (/ 1 k))) into (sqrt (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ (pow (* 2 (* PI (/ 1 n))) (/ 1 2)) (pow (* 2 (* PI (/ 1 n))) (/ (/ 1 k) 2)))) (/ (sqrt (/ (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 (sqrt (/ (pow (* 2 (* PI (/ 1 n))) (/ 1 2)) (pow (* 2 (* PI (/ 1 n))) (/ (/ 1 k) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* 2 (* PI (/ 1 n))) (/ 1 2)) (pow (* 2 (* PI (/ 1 n))) (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* PI (/ 1 n))) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* 2 (* PI (/ 1 n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* 2 (* PI (/ 1 n))))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* PI (/ 1 n)))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* PI (/ 1 n))) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* PI (/ 1 n)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (* PI 1) into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (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 (* 2 (* PI (/ 1 n))) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* 2 (* PI (/ 1 n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* 2 (* PI (/ 1 n))))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* PI (/ 1 n)))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* PI (/ 1 n))) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* PI (/ 1 n)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (* PI 1) into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (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]backup-simplify:  Simplify (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 1)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 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 (+ (* PI 0) (* 0 1)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 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 (* 2 (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ (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 (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (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 (- (+ (* 1/2 (/ 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 (* 2 (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [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 (/ (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (sqrt (/ 1 k))) into (sqrt (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))
* [misc]backup-simplify:  Simplify (* (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (sqrt (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (- (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (- (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k
* [misc]taylor:  Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (sqrt (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 0) (* 0 (sqrt (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 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 (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (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))) (+ (* (sqrt (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 1))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 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 (+ (* PI 0) (+ (* 0 0) (* 0 1))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 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 (pow 0 2) (+)) (* 2 (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 0) (+ (* 0 0) (* 0 (sqrt (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 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 (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (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))) (+ (* (sqrt (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 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 (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (sqrt (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) k) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 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 (* (sqrt (/ (pow (* 2 (* PI (/ 1 (- n)))) (/ 1 2)) (pow (* 2 (* PI (/ 1 (- n)))) (/ (/ 1 (- k)) 2)))) (/ (sqrt (/ (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 (* (sqrt (/ (pow (* 2 (* PI (/ 1 (- n)))) (/ 1 2)) (pow (* 2 (* PI (/ 1 (- n)))) (/ (/ 1 (- k)) 2)))) (/ (sqrt (/ (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 (sqrt (/ (pow (* 2 (* PI (/ 1 (- n)))) (/ 1 2)) (pow (* 2 (* PI (/ 1 (- n)))) (/ (/ 1 (- k)) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (pow (* 2 (* PI (/ 1 (- n)))) (/ 1 2)) (pow (* 2 (* PI (/ 1 (- n)))) (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* PI (/ 1 (- n)))) (/ 1 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* 2 (* PI (/ 1 (- n))))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* 2 (* PI (/ 1 (- n)))))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* PI (/ 1 (- n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 2 (* PI (/ 1 (- n)))) 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 (/ 1 (- n))) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in k
* [misc]taylor:  Taking taylor expansion of (- n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (/ 1 (- n)) into (/ -1 n)
* [misc]backup-simplify:  Simplify (* PI (/ -1 n)) into (* -1 (/ PI n))
* [misc]backup-simplify:  Simplify (* 2 (* -1 (/ PI n))) 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 (* 2 (* PI (/ 1 (- n)))) (/ (/ 1 (- k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* 2 (* PI (/ 1 (- n))))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* 2 (* PI (/ 1 (- n)))))) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* PI (/ 1 (- n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 2 (* PI (/ 1 (- n)))) 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 (/ 1 (- n))) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in k
* [misc]taylor:  Taking taylor expansion of (- n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (/ 1 (- n)) into (/ -1 n)
* [misc]backup-simplify:  Simplify (* PI (/ -1 n)) into (* -1 (/ PI n))
* [misc]backup-simplify:  Simplify (* 2 (* -1 (/ PI n))) 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 (* 2 (* PI (/ 1 (- n))))))) 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]backup-simplify:  Simplify (sqrt (* (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) (sqrt (/ (* PI -2) n)))) into (sqrt (/ (sqrt (* -2 (/ PI n))) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 n) (/ 0 (- n))))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 (/ -1 n))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 (* -1 (/ PI n)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 (/ PI n)) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (log (* -2 (/ PI n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* -2 (/ PI n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) (+ (* (* (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) (sqrt (/ (* PI -2) n))) (/ 0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) (sqrt (/ (* PI -2) n)))))) into 0
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ (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 (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (* (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) (sqrt (/ (* PI -2) n)))) into (sqrt (/ (sqrt (* -2 (/ PI n))) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 n) (/ 0 (- n))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ -1 n) 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ -2 n) 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 (/ PI n)) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (log (* -2 (/ PI n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* -2 (/ PI n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) (+ (* (* (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) (sqrt (/ (* PI -2) n))) (/ 0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) (sqrt (/ (* PI -2) n)))))) into 0
* [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 (/ (sqrt (/ (sqrt (* -2 (/ PI n))) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) +nan.0) into (* +nan.0 (sqrt (/ (sqrt (* -2 (/ PI n))) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ (pow (* 2 (* PI (/ 1 (- n)))) (/ 1 2)) (pow (* 2 (* PI (/ 1 (- n)))) (/ (/ 1 (- k)) 2)))) (/ (sqrt (/ (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 (sqrt (/ (pow (* 2 (* PI (/ 1 (- n)))) (/ 1 2)) (pow (* 2 (* PI (/ 1 (- n)))) (/ (/ 1 (- k)) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* 2 (* PI (/ 1 (- n)))) (/ 1 2)) (pow (* 2 (* PI (/ 1 (- n)))) (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* PI (/ 1 (- n)))) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* 2 (* PI (/ 1 (- n))))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* 2 (* PI (/ 1 (- n)))))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* PI (/ 1 (- n))))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* PI (/ 1 (- n)))) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* PI (/ 1 (- n))) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (* PI -1) into (* -1 PI)
* [misc]backup-simplify:  Simplify (* 2 (* -1 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 (* 2 (* PI (/ 1 (- n)))) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* 2 (* PI (/ 1 (- n))))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* 2 (* PI (/ 1 (- n)))))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* PI (/ 1 (- n))))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* PI (/ 1 (- n)))) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* PI (/ 1 (- n))) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (* PI -1) into (* -1 PI)
* [misc]backup-simplify:  Simplify (* 2 (* -1 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]backup-simplify:  Simplify (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (sqrt (/ (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 (+ (* PI 0) (* 0 -1)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 (* -1 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 (+ (* PI 0) (* 0 -1)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 (* -1 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 (* 2 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ (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 (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (sqrt (/ (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 (* 2 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0
* [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 (/ (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (sqrt (/ -1 k))) into (* (/ 1 (sqrt (/ -1 k))) (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ (pow (* 2 (* PI (/ 1 (- n)))) (/ 1 2)) (pow (* 2 (* PI (/ 1 (- n)))) (/ (/ 1 (- k)) 2)))) (/ (sqrt (/ (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 (sqrt (/ (pow (* 2 (* PI (/ 1 (- n)))) (/ 1 2)) (pow (* 2 (* PI (/ 1 (- n)))) (/ (/ 1 (- k)) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* 2 (* PI (/ 1 (- n)))) (/ 1 2)) (pow (* 2 (* PI (/ 1 (- n)))) (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* PI (/ 1 (- n)))) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* 2 (* PI (/ 1 (- n))))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* 2 (* PI (/ 1 (- n)))))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* PI (/ 1 (- n))))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* PI (/ 1 (- n)))) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* PI (/ 1 (- n))) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (* PI -1) into (* -1 PI)
* [misc]backup-simplify:  Simplify (* 2 (* -1 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 (* 2 (* PI (/ 1 (- n)))) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* 2 (* PI (/ 1 (- n))))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* 2 (* PI (/ 1 (- n)))))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* PI (/ 1 (- n))))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* PI (/ 1 (- n)))) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* PI (/ 1 (- n))) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (* PI -1) into (* -1 PI)
* [misc]backup-simplify:  Simplify (* 2 (* -1 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]backup-simplify:  Simplify (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (sqrt (/ (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 (+ (* PI 0) (* 0 -1)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 (* -1 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 (+ (* PI 0) (* 0 -1)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 (* -1 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 (* 2 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0
* [misc]taylor:  Taking taylor expansion of (/ (sqrt (/ (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 (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (sqrt (/ (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 (* 2 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0
* [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 (/ (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (sqrt (/ -1 k))) into (* (/ 1 (sqrt (/ -1 k))) (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (* (/ 1 (sqrt (/ -1 k))) (sqrt (/ (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)))) (* (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 (sqrt (/ -1 k))) (+ (* (* (/ 1 (sqrt (/ -1 k))) (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (/ 0 (sqrt (/ -1 k)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 0) (* 0 (* (/ 1 (sqrt (/ -1 k))) (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 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 (pow 0 2) (+)) (* 2 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (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))) (+ (* (* (/ 1 (sqrt (/ -1 k))) (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 -1))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* -1 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 (+ (* PI 0) (+ (* 0 0) (* 0 -1))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* -1 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 (pow 0 2) (+)) (* 2 (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) 0) (+ (* 0 0) (* 0 (* (/ 1 (sqrt (/ -1 k))) (sqrt (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* -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:  [ 2 / 4 ] generating series at (2 2 1 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:  [ 3 / 4 ] generating series at (2 2 1 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:  [ 4 / 4 ] generating series at (2 1 1 2 1 2)
* [misc]approximate:  Taking taylor expansion of (* PI n) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (* PI 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 1) (* 0 0)) into PI
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 1) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* PI n) into (* n PI)
* [misc]approximate:  Taking taylor expansion of (* PI (/ 1 n)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* PI (/ 1 n)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of (* PI (/ 1 n)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (* PI 1) into PI
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 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 (+ (* PI 0) (+ (* 0 0) (* 0 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* PI (/ 1 (/ 1 n))) into (* n PI)
* [misc]approximate:  Taking taylor expansion of (* PI (/ 1 (- n))) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* PI (/ 1 (- n))) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of (* PI (/ 1 (- n))) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (* PI -1) into (* -1 PI)
* [misc]backup-simplify:  Simplify (* -1 PI) into (* -1 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 (+ (* PI 0) (* 0 -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 (+ (* PI 0) (+ (* 0 0) (* 0 -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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 -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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI)
* * * [misc]progress:  simplifying candidates
* * * * [misc]progress:  [ 1 / 151 ] simplifiying candidate #<alt (λ (k n) (pow (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))) 1))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (22 enodes)
* * [misc]simplify:  iters left: 5 (34 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (pow (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) 1))
* * * * [misc]progress:  [ 2 / 151 ] simplifiying candidate #<alt (λ (k n) (pow (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))) 1))>
* * * * [misc]progress:  [ 3 / 151 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (- (log (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (log (sqrt k))))))>
* [enter]simplify:  Simplifying (+ (log (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (- (log (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (log (sqrt k))))
* * [misc]simplify:  iters left: 6 (25 enodes)
* * [misc]simplify:  iters left: 5 (39 enodes)
* * [misc]simplify:  iters left: 4 (48 enodes)
* * [misc]simplify:  iters left: 3 (57 enodes)
* * [misc]simplify:  iters left: 2 (68 enodes)
* * [misc]simplify:  iters left: 1 (82 enodes)
* [exit]simplify:  Simplified to (+ (log (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))) (- (log (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))) (log (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (+ (log (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))) (- (log (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))) (log (sqrt k))))))
* * * * [misc]progress:  [ 4 / 151 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (log (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))))>
* [enter]simplify:  Simplifying (+ (log (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (log (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))
* * [misc]simplify:  iters left: 6 (24 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (46 enodes)
* * [misc]simplify:  iters left: 3 (62 enodes)
* * [misc]simplify:  iters left: 2 (72 enodes)
* * [misc]simplify:  iters left: 1 (82 enodes)
* [exit]simplify:  Simplified to (+ (log (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))) (log (/ (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (+ (log (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))) (log (/ (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (sqrt k))))))
* * * * [misc]progress:  [ 5 / 151 ] simplifiying candidate #<alt (λ (k n) (exp (log (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))))>
* * * * [misc]progress:  [ 6 / 151 ] simplifiying candidate #<alt (λ (k n) (log (exp (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))))>
* * * * [misc]progress:  [ 7 / 151 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (/ (* (* (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 (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (* (* (sqrt k) (sqrt k)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (/ (* (* (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 (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (* (* (sqrt k) (sqrt k)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (28 enodes)
* * [misc]simplify:  iters left: 5 (52 enodes)
* * [misc]simplify:  iters left: 4 (140 enodes)
* [exit]simplify:  Simplified to (* (/ (pow (* (* n PI) 2) (/ 1 2)) (* (* k (sqrt k)) (pow (* (* n PI) 2) (/ k 2)))) (* (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (/ (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)) (* (* k (sqrt k)) (pow (* (* n PI) 2) (/ k 2)))) (* (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))))))
* * * * [misc]progress:  [ 8 / 151 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (* (* (/ (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))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (* (* (/ (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))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))
* * [misc]simplify:  iters left: 6 (26 enodes)
* * [misc]simplify:  iters left: 5 (48 enodes)
* * [misc]simplify:  iters left: 4 (122 enodes)
* * [misc]simplify:  iters left: 3 (362 enodes)
* [exit]simplify:  Simplified to (* (* (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (cbrt (* (* (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))))
* * * * [misc]progress:  [ 9 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))) (cbrt (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))) (cbrt (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))))>
* * * * [misc]progress:  [ 10 / 151 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))))>
* * * * [misc]progress:  [ 11 / 151 ] simplifiying candidate #<alt (λ (k n) (sqrt (* (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) k))))>
* [enter]simplify:  Simplifying (* (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))) (/ (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))) k))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (35 enodes)
* * [misc]simplify:  iters left: 4 (64 enodes)
* * [misc]simplify:  iters left: 3 (154 enodes)
* * [misc]simplify:  iters left: 2 (314 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (/ k (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (sqrt (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (/ k (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))))))
* * * * [misc]progress:  [ 12 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))) (sqrt (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))))>
* * * * [misc]progress:  [ 13 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (* (sqrt (pow (* 2 (* PI n)) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (* (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* [exit]simplify:  Simplified to (* (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (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) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))) (* (sqrt (pow (* 2 (* PI n)) (/ k 2))) (sqrt k))))
* [enter]simplify:  Simplifying (* (sqrt (pow (* 2 (* PI n)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (* (sqrt k) (sqrt (pow (* (* 2 n) PI) (/ k 2))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (* (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (* (sqrt k) (sqrt (pow (* (* 2 n) PI) (/ k 2))))))
* * * * [misc]progress:  [ 14 / 151 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* * * * [misc]progress:  [ 15 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (* (cbrt (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))) (cbrt (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))) (cbrt (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (cbrt (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (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 (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (* (cbrt (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))) (cbrt (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))) (cbrt (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 16 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))) (sqrt (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (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 (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))) (sqrt (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 17 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (* (cbrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (cbrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 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 (/ (cbrt (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 (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (* (cbrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 18 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (* (cbrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))))) (sqrt (sqrt k)))) (/ (cbrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (cbrt (sqrt (/ (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 (23 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (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 (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (* (cbrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))))) (sqrt (sqrt k)))) (/ (cbrt (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 19 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (* (cbrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))))) 1)) (/ (cbrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (cbrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (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 (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (* (cbrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))))) 1)) (/ (cbrt (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))) (sqrt k))))
* * * * [misc]progress:  [ 20 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (* (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))))) (/ (sqrt (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 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 (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) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (* (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))))) (/ (sqrt (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 21 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (* (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)))) (/ (sqrt (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (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 (23 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (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) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (* (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)))) (/ (sqrt (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 22 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (* (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)) (/ (sqrt (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (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 (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (* (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)) (/ (sqrt (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))) (sqrt k))))
* * * * [misc]progress:  [ 23 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 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 (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 (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 24 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))) (/ (sqrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (sqrt (/ (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 (23 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (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 (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))) (/ (sqrt (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 25 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) 1)) (/ (sqrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (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 (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) 1)) (/ (sqrt (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))) (sqrt k))))
* * * * [misc]progress:  [ 26 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ (pow PI (/ 1 2)) (pow PI (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow PI (/ 1 2)) (pow PI (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow PI (/ 1 2)) (pow PI (/ k 2)))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ (pow PI (/ 1 2)) (pow PI (/ k 2)))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 27 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt (/ (pow PI (/ 1 2)) (pow PI (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow PI (/ 1 2)) (pow PI (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow PI (/ 1 2)) (pow PI (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt (/ (pow PI (/ 1 2)) (pow PI (/ k 2)))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 28 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2)))) 1)) (/ (sqrt (/ (pow PI (/ 1 2)) (pow PI (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow PI (/ 1 2)) (pow PI (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow PI (/ 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 (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* n 2) (/ 1 2)) (pow (* n 2) (/ k 2)))) 1)) (/ (sqrt (/ (pow PI (/ 1 2)) (pow PI (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 29 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (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))))) (/ (sqrt (/ (pow PI (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow 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 (23 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow PI (/ 1 2)) (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (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))))) (/ (sqrt (/ (pow PI (/ 1 2)) (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 30 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* n 2) (/ 1 2)) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))))) (sqrt (sqrt k)))) (/ (sqrt (/ (pow PI (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow 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 (23 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow PI (/ 1 2)) (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* n 2) (/ 1 2)) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))))) (sqrt (sqrt k)))) (/ (sqrt (/ (pow PI (/ 1 2)) (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 31 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* n 2) (/ 1 2)) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))))) 1)) (/ (sqrt (/ (pow PI (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow PI (/ 1 2)) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (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 (30 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow PI (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* n 2) (/ 1 2)) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))))) 1)) (/ (sqrt (/ (pow PI (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt k))))
* * * * [misc]progress:  [ 32 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* n 2) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ (pow PI (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow 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 (23 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow PI (/ 1 2)) (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* n 2) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ (pow PI (/ 1 2)) (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 33 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* n 2) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))) (/ (sqrt (/ (pow PI (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow 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 (23 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow PI (/ 1 2)) (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* n 2) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))) (/ (sqrt (/ (pow PI (/ 1 2)) (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 34 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* n 2) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2))))) 1)) (/ (sqrt (/ (pow PI (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow PI (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (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 (30 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow PI (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* n 2) (/ 1 2)) (sqrt (pow (* (* n 2) PI) (/ k 2))))) 1)) (/ (sqrt (/ (pow PI (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt k))))
* * * * [misc]progress:  [ 35 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* n 2) (/ 1 2)) 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ (pow PI (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow 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 (30 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow PI (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* n 2) (/ 1 2)) 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ (pow PI (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 36 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* n 2) (/ 1 2)) 1)) (sqrt (sqrt k)))) (/ (sqrt (/ (pow PI (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow 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 (30 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow PI (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* n 2) (/ 1 2)) 1)) (sqrt (sqrt k)))) (/ (sqrt (/ (pow PI (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 37 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* n 2) (/ 1 2)) 1)) 1)) (/ (sqrt (/ (pow PI (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow 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 (28 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow PI (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* n 2) (/ 1 2)) 1)) 1)) (/ (sqrt (/ (pow PI (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 38 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (* (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))))) (/ (sqrt (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 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 (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (pow PI (/ k 2)))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (* (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))))) (/ (sqrt (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (pow PI (/ k 2)))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 39 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n 2) (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 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 (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (pow PI (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n 2) (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (pow PI (/ k 2)))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 40 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n 2) (/ k 2)))) 1)) (/ (sqrt (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2)))) (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 (/ (cbrt (pow (* (* PI n) 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 (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (pow (* n 2) (/ k 2)))) 1)) (/ (sqrt (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (pow PI (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 41 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (* (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))))) (/ (sqrt (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (31 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2))))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (* (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))))) (/ (sqrt (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2))))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 42 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (* (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)))) (/ (sqrt (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (31 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (* (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)))) (/ (sqrt (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 43 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (* (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)) (/ (sqrt (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k))
* * [misc]simplify:  iters left: 6 (17 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 (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (* (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)) (/ (sqrt (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt k))))
* * * * [misc]progress:  [ 44 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (* (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))))) (/ (sqrt (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (31 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (pow (* (* PI n) 2) (/ k 2))))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (* (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))))) (/ (sqrt (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (pow (* (* PI n) 2) (/ k 2))))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 45 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))) (/ (sqrt (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (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 (24 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (31 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))) (/ (sqrt (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 46 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (sqrt (pow (* (* n 2) PI) (/ k 2))))) 1)) (/ (sqrt (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k))
* * [misc]simplify:  iters left: 6 (17 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 (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) (sqrt (pow (* (* n 2) PI) (/ k 2))))) 1)) (/ (sqrt (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt k))))
* * * * [misc]progress:  [ 47 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 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 (/ (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) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 48 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) 1)) (sqrt (sqrt k)))) (/ (sqrt (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (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 (23 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (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) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) 1)) (sqrt (sqrt k)))) (/ (sqrt (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 49 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) 1)) 1)) (/ (sqrt (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2)))) (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 (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) 1)) 1)) (/ (sqrt (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 50 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 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 (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (pow PI (/ k 2)))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (pow PI (/ k 2)))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 51 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 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 (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (pow PI (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (pow PI (/ k 2)))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 52 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2)))) 1)) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow PI (/ k 2)))) (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 (/ (sqrt (pow (* (* PI n) 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 (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* n 2) (/ k 2)))) 1)) (/ (sqrt (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (pow PI (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 53 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (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 (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (31 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2))))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (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 (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2))))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 54 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (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 (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (31 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (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 (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 55 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))))) 1)) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k))
* * [misc]simplify:  iters left: 6 (17 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 (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))))) 1)) (/ (sqrt (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt k))))
* * * * [misc]progress:  [ 56 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (31 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (pow (* (* PI n) 2) (/ k 2))))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (pow (* (* PI n) 2) (/ k 2))))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 57 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (sqrt (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 (24 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (31 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))) (/ (sqrt (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 58 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2))))) 1)) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt k))
* * [misc]simplify:  iters left: 6 (17 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 (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2))))) 1)) (/ (sqrt (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt k))))
* * * * [misc]progress:  [ 59 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 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 (/ (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 (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 60 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) 1)) (sqrt (sqrt k)))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (sqrt (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 (23 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (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 (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) 1)) (sqrt (sqrt k)))) (/ (sqrt (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 61 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) 1)) 1)) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2)))) (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 (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) 1)) 1)) (/ (sqrt (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 62 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ 1 (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 (22 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow PI (/ k 2)))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ 1 (pow (* n 2) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow PI (/ k 2)))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 63 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ 1 (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 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 (* (* PI n) 2) (/ 1 2)) (pow PI (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ 1 (pow (* n 2) (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow PI (/ k 2)))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 64 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ 1 (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 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 (28 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 (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ 1 (pow (* n 2) (/ k 2)))) 1)) (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow PI (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 65 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ 1 (* (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 (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 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 (* 2 (* PI n)) (/ 1 2)) (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ 1 (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 66 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ 1 (* (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))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 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 (* 2 (* PI n)) (/ 1 2)) (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ 1 (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))))) (sqrt (sqrt k)))) (/ (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 67 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ 1 (* (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))))) (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 (* (* PI n) 2) (/ 1 2)) (cbrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ 1 (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))))) 1)) (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (cbrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt k))))
* * * * [misc]progress:  [ 68 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ 1 (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)))
* * [misc]simplify:  iters left: 6 (17 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 (* 2 (* PI n)) (/ 1 2)) (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ 1 (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 69 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ 1 (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 (23 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ 1 (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))) (/ (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 70 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ 1 (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))))) (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 (* (* PI n) 2) (/ 1 2)) (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ 1 (sqrt (pow (* (* n 2) PI) (/ k 2))))) 1)) (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt k))))
* * * * [misc]progress:  [ 71 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ 1 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)) (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 (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ 1 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 72 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ 1 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)) (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 (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ 1 1)) (sqrt (sqrt k)))) (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 73 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ 1 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)) (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 (28 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 (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ 1 1)) 1)) (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 74 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt 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)) (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 (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 75 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt 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)) (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 (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt 1) (sqrt (sqrt k)))) (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 76 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt 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)) (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 (28 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 (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt 1) 1)) (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 77 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ 1 (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ 1 (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * [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 (27 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ 1 (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ 1 (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 78 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (sqrt k)))) (/ (sqrt (/ 1 (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ 1 (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * [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 (27 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ 1 (pow (* (* PI 2) n) (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (sqrt k)))) (/ (sqrt (/ 1 (pow (* (* PI 2) n) (/ k 2)))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 79 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) 1)) (/ (sqrt (/ 1 (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ 1 (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))
* * [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 (/ 1 (pow (* (* n PI) 2) (/ k 2)))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) 1)) (/ (sqrt (/ 1 (pow (* (* n PI) 2) (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 80 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 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 (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 (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 81 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))) (/ (sqrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (sqrt (/ (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 (23 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (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 (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))) (/ (sqrt (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 82 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) 1)) (/ (sqrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (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 (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) 1)) (/ (sqrt (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))) (sqrt k))))
* * * * [misc]progress:  [ 83 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 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)) (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 (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 84 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 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)) (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 (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ 1 (sqrt (sqrt k)))) (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 85 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 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)) (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 (28 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 (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ 1 1)) (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 86 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ 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)))) (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 (28 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 (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 87 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (/ 1 (sqrt k))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt k))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (6 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (/ 1 (sqrt k))))
* * * * [misc]progress:  [ 88 / 151 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))))) (* (cbrt (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (cbrt (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))))
* * [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 (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (cbrt (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))))) (* (cbrt (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 89 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (* (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))))) (* (sqrt (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (* (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))))
* * [misc]simplify:  iters left: 6 (15 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 (fabs (cbrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (fabs (cbrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))) (* (sqrt (cbrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 90 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (* (sqrt (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ 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 (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))) (* (sqrt (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 91 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow 2 (/ 1 2)) (pow 2 (/ k 2)))) (* (sqrt (/ (pow (* PI n) (/ 1 2)) (pow (* PI n) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ (pow 2 (/ 1 2)) (pow 2 (/ k 2))))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow 2 (/ 1 2)) (pow 2 (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (/ (pow 2 (/ 1 2)) (pow 2 (/ k 2)))) (* (sqrt (/ (pow (* PI n) (/ 1 2)) (pow (* PI n) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 92 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow 2 (/ 1 2)) (* (cbrt (pow (* 2 (* PI n)) (/ k 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))))) (* (sqrt (/ (pow (* PI n) (/ 1 2)) (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ (pow 2 (/ 1 2)) (* (cbrt (pow (* 2 (* PI n)) (/ k 2))) (cbrt (pow (* 2 (* PI n)) (/ 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 2 (/ 1 2)) (* (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 2 (/ 1 2)) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))))) (* (sqrt (/ (pow (* PI n) (/ 1 2)) (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 93 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow 2 (/ 1 2)) (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (* (sqrt (/ (pow (* PI n) (/ 1 2)) (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ (pow 2 (/ 1 2)) (sqrt (pow (* 2 (* PI n)) (/ 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 2 (/ 1 2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (/ (pow 2 (/ 1 2)) (sqrt (pow (* PI (* n 2)) (/ k 2))))) (* (sqrt (/ (pow (* PI n) (/ 1 2)) (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 94 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow 2 (/ 1 2)) 1)) (* (sqrt (/ (pow (* PI n) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ (pow 2 (/ 1 2)) 1))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* [exit]simplify:  Simplified to (sqrt (pow 2 (/ 1 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (pow 2 (/ 1 2))) (* (sqrt (/ (pow (* PI n) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 95 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ 1 2)))) (pow 2 (/ k 2)))) (* (sqrt (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (pow (* PI n) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ (* (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ 1 2)))) (pow 2 (/ 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 (sqrt (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow 2 (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow 2 (/ k 2))))) (* (sqrt (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (pow (* PI n) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 96 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ 1 2)))) (* (cbrt (pow (* 2 (* PI n)) (/ k 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))))) (* (sqrt (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ (* (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ 1 2)))) (* (cbrt (pow (* 2 (* PI n)) (/ k 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2))))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (29 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 (fabs (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (fabs (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) (* (sqrt (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 97 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ 1 2)))) (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (* (sqrt (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ (* (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ 1 2)))) (sqrt (pow (* 2 (* PI n)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (* (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) (* (sqrt (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (sqrt (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 98 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ 1 2)))) 1)) (* (sqrt (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ (* (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ 1 2)))) 1))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (46 enodes)
* [exit]simplify:  Simplified to (fabs (cbrt (pow (* (* n PI) 2) (/ 1 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (fabs (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (* (sqrt (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 99 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (pow 2 (/ k 2)))) (* (sqrt (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (pow (* PI n) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (pow 2 (/ 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 (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow 2 (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow 2 (/ k 2)))) (* (sqrt (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (pow (* PI n) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 100 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (* (cbrt (pow (* 2 (* PI n)) (/ k 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))))) (* (sqrt (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (* (cbrt (pow (* 2 (* PI n)) (/ k 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2))))))
* * [misc]simplify:  iters left: 6 (16 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 (/ (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 (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (* (sqrt (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 101 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (* (sqrt (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (sqrt (pow (* 2 (* PI n)) (/ k 2)))))
* * [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 (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (sqrt (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 102 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) 1)) (* (sqrt (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) 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 (sqrt (pow (* (* n PI) 2) (/ 1 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (sqrt (pow (* (* n PI) 2) (/ 1 2)))) (* (sqrt (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 103 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (pow 2 (/ k 2)))) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* PI n) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ 1 (pow 2 (/ k 2))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (9 enodes)
* [exit]simplify:  Simplified to (sqrt (/ 1 (pow 2 (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (/ 1 (pow 2 (/ k 2)))) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* PI n) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 104 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (* (cbrt (pow (* 2 (* PI n)) (/ k 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))))) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ 1 (* (cbrt (pow (* 2 (* PI n)) (/ k 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2))))))
* * [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 (28 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (/ 1 (cbrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (pow (* (* PI 2) n) (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (/ (/ 1 (cbrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (pow (* (* PI 2) n) (/ k 2))))) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 105 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ 1 (sqrt (pow (* 2 (* PI n)) (/ k 2)))))
* * [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 (sqrt (/ 1 (sqrt (pow (* (* PI 2) n) (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (/ 1 (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 106 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 1)) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ 1 1))
* * [misc]simplify:  iters left: 3 (3 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (sqrt 1)
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt 1) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 107 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt 1) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt 1)
* * [misc]simplify:  iters left: 1 (2 enodes)
* [exit]simplify:  Simplified to (sqrt 1)
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt 1) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 108 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (* (sqrt (/ 1 (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (pow (* 2 (* PI n)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* (* 2 PI) n) (/ 1 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (pow (* (* 2 PI) n) (/ 1 2))) (* (sqrt (/ 1 (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 109 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (* (sqrt (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ 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 (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))) (* (sqrt (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 110 / 151 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))))>
* * * * [misc]progress:  [ 111 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (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) (/ (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 112 / 151 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))) (sqrt (pow (* 2 (* PI n)) (/ k 2)))))>
* [enter]simplify:  Simplifying (* (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* * [misc]simplify:  iters left: 2 (43 enodes)
* * [misc]simplify:  iters left: 1 (44 enodes)
* [exit]simplify:  Simplified to (* (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt k)) (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (* (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt k)) (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))) (sqrt (pow (* 2 (* PI n)) (/ k 2)))))
* * * * [misc]progress:  [ 113 / 151 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k)) (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2))))))>
* * * * [misc]progress:  [ 114 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (pow (* (* n 2) PI) 1) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 115 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (exp (log (* (* n 2) PI))) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 116 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (log (exp (* (* n 2) PI))) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 117 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (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:  [ 118 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (cbrt (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI))) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 119 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI))) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 120 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* 1 (* (* n 2) PI)) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 121 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* n (* 2 PI)) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 122 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 123 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (pow (* (* n 2) PI) 1) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 124 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (exp (log (* (* n 2) PI))) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 125 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (log (exp (* (* n 2) PI))) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 126 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 127 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (cbrt (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI))) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 128 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI))) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 129 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* 1 (* (* n 2) PI)) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 130 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* n (* 2 PI)) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 131 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 132 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (pow (* PI n) 1)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 133 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (exp (log (* PI n)))) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 134 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (log (exp (* PI n)))) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 135 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* (* (cbrt (* PI n)) (cbrt (* PI n))) (cbrt (* PI n)))) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 136 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (cbrt (* (* (* PI n) (* PI n)) (* PI n)))) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 137 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* (sqrt (* PI n)) (sqrt (* PI n)))) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 138 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* 1 (* PI n))) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 139 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 140 / 151 ] 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:  [ 141 / 151 ] 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:  [ 142 / 151 ] 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:  [ 143 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (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 2 1 1 2 1) to (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 144 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (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 2 1 1 2 1) to (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 145 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (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 2 1 1 2 1) to (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 146 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* (* n 2) 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 2 1 1 1 1) to (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 147 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* (* n 2) 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 2 1 1 1 1) to (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 148 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* (* n 2) 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 2 1 1 1 1) to (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 149 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (* n PI)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n PI)
* [misc]simplify:  Simplified (2 1 1 2 1 2) to (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 150 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (* n PI)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n PI)
* [misc]simplify:  Simplified (2 1 1 2 1 2) to (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 151 / 151 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (* n PI)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n PI)
* [misc]simplify:  Simplified (2 1 1 2 1 2) to (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))
* * * [misc]progress:  adding candidates to table
* [misc]progress:  [Phase 3 of 3] Extracting.
* * [misc]regime:  Finding splitpoints for: (#<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n 2) (/ (- 1 k) 2))) (/ (cbrt (sqrt k)) (pow PI (/ (- 1 k) 2))))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<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)))))> #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))> #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))> #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))))> #<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)))))> #<alt (λ (k n) (/ (+ (+ (* (- 1/2) (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2))))) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (+ (* (* (log (* PI 2)) 1/8) (* (log (* PI 2)) (* k k))) (* (* (log (* PI 2)) 1/4) (* (* k k) (log n)))))) (sqrt k)))> #<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))))> #<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)))))>)
* * * [misc]regime-changes:  Trying 4 branch expressions: (n (* (* 2 PI) n) k (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * * * [misc]regimes:  Trying to branch on n from (#<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n 2) (/ (- 1 k) 2))) (/ (cbrt (sqrt k)) (pow PI (/ (- 1 k) 2))))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<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)))))> #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))> #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))> #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))))> #<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)))))> #<alt (λ (k n) (/ (+ (+ (* (- 1/2) (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2))))) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (+ (* (* (log (* PI 2)) 1/8) (* (log (* PI 2)) (* k k))) (* (* (log (* PI 2)) 1/4) (* (* k k) (log n)))))) (sqrt k)))> #<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))))> #<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)))))>)
* * * * [misc]regimes:  Trying to branch on (* (* 2 PI) n) from (#<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n 2) (/ (- 1 k) 2))) (/ (cbrt (sqrt k)) (pow PI (/ (- 1 k) 2))))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<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)))))> #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))> #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))> #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))))> #<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)))))> #<alt (λ (k n) (/ (+ (+ (* (- 1/2) (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2))))) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (+ (* (* (log (* PI 2)) 1/8) (* (log (* PI 2)) (* k k))) (* (* (log (* PI 2)) 1/4) (* (* k k) (log n)))))) (sqrt k)))> #<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))))> #<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)))))>)
* * * * [misc]regimes:  Trying to branch on k from (#<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n 2) (/ (- 1 k) 2))) (/ (cbrt (sqrt k)) (pow PI (/ (- 1 k) 2))))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<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)))))> #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))> #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))> #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))))> #<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)))))> #<alt (λ (k n) (/ (+ (+ (* (- 1/2) (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2))))) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (+ (* (* (log (* PI 2)) 1/8) (* (log (* PI 2)) (* k k))) (* (* (log (* PI 2)) 1/4) (* (* k k) (log n)))))) (sqrt k)))> #<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))))> #<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)))))>)
* * * * [misc]regimes:  Trying to branch on (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) from (#<alt (λ (k n) (/ 1 (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n 2) (/ (- 1 k) 2))) (/ (cbrt (sqrt k)) (pow PI (/ (- 1 k) 2))))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<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)))))> #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* PI n)) (/ 1 2)) (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt k))))> #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))> #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))))> #<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)))))> #<alt (λ (k n) (/ (+ (+ (* (- 1/2) (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2))))) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (+ (* (* (log (* PI 2)) 1/8) (* (log (* PI 2)) (* k k))) (* (* (log (* PI 2)) 1/4) (* (* k k) (log n)))))) (sqrt k)))> #<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))))> #<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)))))>)
* * * [misc]regime:  Found split indices: #<option (#s(si 4 256))>
* [enter]simplify:  Simplifying (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* [exit]simplify:  Simplified to (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * * * [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 6515 additional inputs, on iter 1 have 1485 / 8000
* * * * [misc]points:  Computing exacts on every 407 of 6515 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 6515 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 6515 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 6515 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 6515 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 6515 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 6515 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 6515 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 6515 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 5306 additional inputs, on iter 2 have 2694 / 8000
* * * * [misc]points:  Computing exacts on every 331 of 5306 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 5306 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 5306 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 5306 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 5306 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 5306 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 5306 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 5306 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 5306 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 4247 additional inputs, on iter 3 have 3753 / 8000
* * * * [misc]points:  Computing exacts on every 265 of 4247 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 132 of 4247 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 66 of 4247 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 4247 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 4247 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 4247 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 4247 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 4247 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 4247 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 3405 additional inputs, on iter 4 have 4595 / 8000
* * * * [misc]points:  Computing exacts on every 212 of 3405 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 106 of 3405 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 53 of 3405 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 26 of 3405 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 3405 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 3405 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 3405 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 3405 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 2709 additional inputs, on iter 5 have 5291 / 8000
* * * * [misc]points:  Computing exacts on every 169 of 2709 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 84 of 2709 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 42 of 2709 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 21 of 2709 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 2709 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 2709 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 2709 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 2709 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 2219 additional inputs, on iter 6 have 5781 / 8000
* * * * [misc]points:  Computing exacts on every 138 of 2219 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 69 of 2219 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 34 of 2219 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 17 of 2219 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 2219 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 2219 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 2219 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 2219 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 1803 additional inputs, on iter 7 have 6197 / 8000
* * * * [misc]points:  Computing exacts on every 112 of 1803 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 56 of 1803 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 28 of 1803 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 1803 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 1803 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 1803 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1803 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 1464 additional inputs, on iter 8 have 6536 / 8000
* * * * [misc]points:  Computing exacts on every 91 of 1464 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 45 of 1464 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 1464 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 1464 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 1464 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 1464 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1464 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 1177 additional inputs, on iter 9 have 6823 / 8000
* * * * [misc]points:  Computing exacts on every 73 of 1177 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 1177 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 1177 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 1177 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 1177 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 1177 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1177 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 961 additional inputs, on iter 10 have 7039 / 8000
* * * * [misc]points:  Computing exacts on every 60 of 961 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 30 of 961 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 961 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 961 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 961 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 961 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 794 additional inputs, on iter 11 have 7206 / 8000
* * * * [misc]points:  Computing exacts on every 49 of 794 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 24 of 794 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 794 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 794 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 794 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 794 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 645 additional inputs, on iter 12 have 7355 / 8000
* * * * [misc]points:  Computing exacts on every 40 of 645 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 645 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 645 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 645 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 645 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 645 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 513 additional inputs, on iter 13 have 7487 / 8000
* * * * [misc]points:  Computing exacts on every 32 of 513 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 513 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 513 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 513 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 513 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 513 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 405 additional inputs, on iter 14 have 7595 / 8000
* * * * [misc]points:  Computing exacts on every 25 of 405 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 405 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 405 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 405 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 405 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 324 additional inputs, on iter 15 have 7676 / 8000
* * * * [misc]points:  Computing exacts on every 20 of 324 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 324 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 324 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 324 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 324 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 248 additional inputs, on iter 16 have 7752 / 8000
* * * * [misc]points:  Computing exacts on every 15 of 248 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 248 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 248 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 248 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 203 additional inputs, on iter 17 have 7797 / 8000
* * * * [misc]points:  Computing exacts on every 12 of 203 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 203 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 203 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 203 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 150 additional inputs, on iter 18 have 7850 / 8000
* * * * [misc]points:  Computing exacts on every 9 of 150 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 150 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 150 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 150 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 126 additional inputs, on iter 19 have 7874 / 8000
* * * * [misc]points:  Computing exacts on every 7 of 126 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 126 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 126 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 102 additional inputs, on iter 20 have 7898 / 8000
* * * * [misc]points:  Computing exacts on every 6 of 102 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 102 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 102 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 84 additional inputs, on iter 21 have 7916 / 8000
* * * * [misc]points:  Computing exacts on every 5 of 84 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 84 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 84 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 22 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 48 additional inputs, on iter 23 have 7952 / 8000
* * * * [misc]points:  Computing exacts on every 3 of 48 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 48 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 42 additional inputs, on iter 24 have 7958 / 8000
* * * * [misc]points:  Computing exacts on every 2 of 42 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 42 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 25 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 27 additional inputs, on iter 26 have 7973 / 8000
* * * * [misc]points:  Computing exacts for 27 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 22 additional inputs, on iter 27 have 7978 / 8000
* * * * [misc]points:  Computing exacts for 22 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 28 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 16 additional inputs, on iter 29 have 7984 / 8000
* * * * [misc]points:  Computing exacts for 16 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 30 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 4 additional inputs, on iter 31 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 32 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 33 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 34 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
* * * * [exit]points:  Sampled 8000 points with exact outputs