* [misc]progress:  [Phase 1 of 3] Setting up.
* * * [misc]progress:  [1/2] Preparing points
* * * * [misc]points:  Sampling 256 additional inputs, on iter 0 have 0 / 256
* * * * [misc]points:  Computing exacts on every 16 of 256 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 64
* * * * [misc]points:  Setting MPFR precision to 320
* * * * [misc]points:  Setting MPFR precision to 576
* * * * [misc]points:  Computing exacts on every 8 of 256 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 320
* * * * [misc]points:  Setting MPFR precision to 576
* * * * [misc]points:  Computing exacts on every 4 of 256 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 320
* * * * [misc]points:  Setting MPFR precision to 576
* * * * [misc]points:  Setting MPFR precision to 832
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 256 points to ramp up precision
* * * * [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 216 additional inputs, on iter 1 have 40 / 256
* * * * [misc]points:  Computing exacts on every 13 of 216 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 216 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 216 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 216 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 166 additional inputs, on iter 2 have 90 / 256
* * * * [misc]points:  Computing exacts on every 10 of 166 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 166 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 166 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 166 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 133 additional inputs, on iter 3 have 123 / 256
* * * * [misc]points:  Computing exacts on every 8 of 133 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 133 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 133 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 133 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 111 additional inputs, on iter 4 have 145 / 256
* * * * [misc]points:  Computing exacts on every 6 of 111 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 3 of 111 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 111 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 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 74 additional inputs, on iter 6 have 182 / 256
* * * * [misc]points:  Computing exacts on every 4 of 74 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 74 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 74 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 59 additional inputs, on iter 7 have 197 / 256
* * * * [misc]points:  Computing exacts on every 3 of 59 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 59 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 50 additional inputs, on iter 8 have 206 / 256
* * * * [misc]points:  Computing exacts on every 3 of 50 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 50 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 42 additional inputs, on iter 9 have 214 / 256
* * * * [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 33 additional inputs, on iter 10 have 223 / 256
* * * * [misc]points:  Computing exacts on every 2 of 33 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 33 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 25 additional inputs, on iter 11 have 231 / 256
* * * * [misc]points:  Computing exacts for 25 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 20 additional inputs, on iter 12 have 236 / 256
* * * * [misc]points:  Computing exacts for 20 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 14 additional inputs, on iter 13 have 242 / 256
* * * * [misc]points:  Computing exacts for 14 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 12 additional inputs, on iter 14 have 244 / 256
* * * * [misc]points:  Computing exacts for 12 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 11 additional inputs, on iter 15 have 245 / 256
* * * * [misc]points:  Computing exacts for 11 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 9 additional inputs, on iter 16 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 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 7 additional inputs, on iter 18 have 249 / 256
* * * * [misc]points:  Computing exacts for 7 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 6 additional inputs, on iter 19 have 250 / 256
* * * * [misc]points:  Computing exacts for 6 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 20 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 21 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 22 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 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 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 256 points with exact outputs
* * * [misc]progress:  [2/2] Setting up program.
* [misc]progress:  [Phase 2 of 3] Improving.
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (52 enodes)
* * [misc]simplify:  iters left: 2 (56 enodes)
* * [misc]simplify:  iters left: 1 (63 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))
* * [misc]progress:  iteration 1 / 4
* * * [misc]progress:  picking best candidate
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(k n) (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))"}* * * * [misc]pick:  Picked  #<alt-delta (λ (k n) (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 3 ] rewriting at (2 1)
* * * * [misc]progress:  [ 2 / 3 ] rewriting at (2 1 1 1)
* * * * [misc]progress:  [ 3 / 3 ] rewriting at (2)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 3 ] generating series at (2 1)
* [misc]approximate:  Taking taylor expansion of (pow (* (* n PI) 2) (/ (- 1 k) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* n PI) 2) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* n PI) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* n PI) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 k) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* n PI) 2)) in k
* [misc]taylor:  Taking taylor expansion of (* (* n PI) 2) in k
* [misc]taylor:  Taking taylor expansion of (* n PI) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* n PI) into (* n PI)
* [misc]backup-simplify:  Simplify (* (* n PI) 2) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
* [misc]taylor:  Taking taylor expansion of (pow (* (* n PI) 2) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* n PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* n PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (+ 1 (- k)) into (- 1 k)
* [misc]backup-simplify:  Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k))
* [misc]taylor:  Taking taylor expansion of (log (* (* n PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n PI) 2) 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]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* PI 2)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k)))) into (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* n PI) 2) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* n PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* n PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (+ 1 (- k)) into (- 1 k)
* [misc]backup-simplify:  Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k))
* [misc]taylor:  Taking taylor expansion of (log (* (* n PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n PI) 2) 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]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* PI 2)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k)))) into (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 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)) (- 1 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 (- 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 (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (* (+ (log (* 2 PI)) (log n)) 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)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* PI 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log (* 2 PI)) (log n)) -1) (* 0 1)) into (- (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))
* [misc]backup-simplify:  Simplify (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* PI 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log (* 2 PI)) (log n)) 0) (+ (* 0 -1) (* 0 1))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log (* 2 PI)) 2)))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (+ (* 1/8 (pow (log n) 2)) (* 1/8 (pow (log (* 2 PI)) 2)))))
* [misc]backup-simplify:  Simplify (+ (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (+ (* 1/8 (pow (log n) 2)) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (+ (* 1/4 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))) (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))) (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 1/2 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (* 1/2 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))))))
* [misc]approximate:  Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ (- 1 (/ 1 k)) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) PI) 2) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (/ 1 n) into (/ 1 n)
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* (/ 1 n) PI) into (/ PI n)
* [misc]backup-simplify:  Simplify (* (/ PI n) 2) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) PI) 2) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) PI) 2) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 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 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) 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 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) 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 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) 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 (* (- (log (* 2 PI)) (log (/ 1 n))) (- 1 k))))
* [misc]approximate:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ (- 1 (/ 1 (- k))) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- -1) into 1
* [misc]backup-simplify:  Simplify (+ 0 1) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) PI) 2)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in k
* [misc]taylor:  Taking taylor expansion of (- n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (/ 1 (- n)) into (/ -1 n)
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* (/ -1 n) PI) into (* -1 (/ PI n))
* [misc]backup-simplify:  Simplify (* (* -1 (/ PI n)) 2) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* -2 (/ PI n))))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2))) 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)) PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* -1 PI) into (* -1 PI)
* [misc]backup-simplify:  Simplify (* (* -1 PI) 2) into (* -2 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)) PI) 2) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2))) 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)) PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* -1 PI) into (* -1 PI)
* [misc]backup-simplify:  Simplify (* (* -1 PI) 2) into (* -2 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 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* -1 PI) 0) (* 0 2)) 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 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* -1 PI) 0) (+ (* 0 0) (* 0 2))) 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 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* -1 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) 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 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k))))
* * * * [misc]progress:  [ 2 / 3 ] generating series at (2 1 1 1)
* [misc]approximate:  Taking taylor expansion of (* n PI) in (n) around 0
* [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]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 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 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 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 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 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 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* PI n) into (* n PI)
* [misc]approximate:  Taking taylor expansion of (* (/ 1 n) PI) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 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 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 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 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 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 PI))))))) 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 (* (/ 1 (- n)) PI) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 PI) 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 (+ (* -1 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 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 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 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 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 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI)
* * * * [misc]progress:  [ 3 / 3 ] generating series at (2)
* [misc]approximate:  Taking taylor expansion of (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (* n PI) 2) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* n PI) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* n PI) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 k) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* n PI) 2)) in k
* [misc]taylor:  Taking taylor expansion of (* (* n PI) 2) in k
* [misc]taylor:  Taking taylor expansion of (* n PI) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* n PI) into (* n PI)
* [misc]backup-simplify:  Simplify (* (* n PI) 2) 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 PI) 2) (/ (- 1 k) 2)) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* n PI) 2) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* n PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* n PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (+ 1 (- k)) into (- 1 k)
* [misc]backup-simplify:  Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k))
* [misc]taylor:  Taking taylor expansion of (log (* (* n PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n PI) 2) 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]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* PI 2)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k)))) into (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 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 (* 2 PI)) (log n)) (- 1 k)))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k)))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* n PI) 2) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* n PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* n PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (+ 1 (- k)) into (- 1 k)
* [misc]backup-simplify:  Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k))
* [misc]taylor:  Taking taylor expansion of (log (* (* n PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n PI) 2) 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]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* PI 2)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k)))) into (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 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 (* 2 PI)) (log n)) (- 1 k)))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k)))))
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k))))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 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)) (- 1 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 (- 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 (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (* (+ (log (* 2 PI)) (log n)) 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)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (* 0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* PI 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 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) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log (* 2 PI)) (log n)) -1) (* 0 1)) into (- (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))
* [misc]backup-simplify:  Simplify (+ (* 0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* PI 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log (* 2 PI)) (log n)) 0) (+ (* 0 -1) (* 0 1))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log (* 2 PI)) 2)))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* 0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log (* 2 PI)) 2)))))) (+ (* +nan.0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))))))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log (* 2 PI)) (log n)) 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2)))))) (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* 0 (* -1 (* (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2)))))) (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))) (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log (* 2 PI)) 2)))))) (+ (* +nan.0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))))))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))))))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))))) into (- (+ (* +nan.0 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* k (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2)))) (- (+ (* +nan.0 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))) (- (+ (* +nan.0 (* (pow k 2) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))) (- (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))))))))))))
* [misc]approximate:  Taking taylor expansion of (/ (pow (* (* (/ 1 n) PI) 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 n) PI) 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) PI) 2) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (/ 1 n) into (/ 1 n)
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* (/ 1 n) PI) into (/ PI n)
* [misc]backup-simplify:  Simplify (* (/ PI n) 2) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2)))) 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) PI) 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) PI) 2) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 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 (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 n) PI) 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) PI) 2) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 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 (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
* [misc]taylor:  Taking taylor expansion of (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) 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 (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 (* 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)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) 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))) (+ (* (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (/ 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 0) (* +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)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) 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))) (+ (* (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (/ 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 (+ (* 0 0) (+ (* +nan.0 0) (* +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)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) 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))) (+ (* (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (/ 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 (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +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 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 (* (- (log (* 2 PI)) (log (/ 1 n))) (- 1 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) (- 1 k)))) k)) (- (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) (- 1 k)))) (pow k 2))))))))
* [misc]approximate:  Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) PI) 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) PI) 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- -1) into 1
* [misc]backup-simplify:  Simplify (+ 0 1) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) PI) 2)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in k
* [misc]taylor:  Taking taylor expansion of (- n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (/ 1 (- n)) into (/ -1 n)
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* (/ -1 n) PI) into (* -1 (/ PI n))
* [misc]backup-simplify:  Simplify (* (* -1 (/ PI n)) 2) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* -2 (/ PI n))))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* -2 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* -2 (/ PI n)))))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) PI) 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2))) 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)) PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* -1 PI) into (* -1 PI)
* [misc]backup-simplify:  Simplify (* (* -1 PI) 2) into (* -2 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)) PI) 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2))) 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)) PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* -1 PI) into (* -1 PI)
* [misc]backup-simplify:  Simplify (* (* -1 PI) 2) into (* -2 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 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* -1 PI) 0) (* 0 2)) 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 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* -1 PI) 0) (+ (* 0 0) (* 0 2))) 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 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)))) k)))))))
* * * [misc]progress:  simplifying candidates
* * * * [misc]progress:  [ 1 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (log1p (expm1 (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (pow (* (* n PI) 2) (/ (- 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 (expm1 (pow (* (* PI n) 2) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (expm1 (pow (* (* PI n) 2) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 2 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (expm1 (log1p (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (pow (* (* n PI) 2) (/ (- 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 (log1p (pow (* (* PI n) 2) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (log1p (pow (* (* PI n) 2) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 3 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (exp (* (log (* (* n PI) 2)) (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* (* n PI) 2)) (/ (- 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 (144 enodes)
* [exit]simplify:  Simplified to (/ (log (* (* PI n) 2)) (/ 2 (- 1 k)))
* [exit]simplify:  Simplified to (/ (log (* (* PI n) 2)) (/ 2 (- 1 k)))
* * * * [misc]progress:  [ 4 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (exp (* (log (* (* n PI) 2)) (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* (* n PI) 2)) (/ (- 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 (144 enodes)
* [exit]simplify:  Simplified to (/ (log (* (* PI n) 2)) (/ 2 (- 1 k)))
* [exit]simplify:  Simplified to (/ (log (* (* PI n) 2)) (/ 2 (- 1 k)))
* * * * [misc]progress:  [ 5 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n PI) 2) (* 1 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* 1 (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (51 enodes)
* * [misc]simplify:  iters left: 2 (79 enodes)
* * [misc]simplify:  iters left: 1 (117 enodes)
* [exit]simplify:  Simplified to (/ (- 1 k) 2)
* [exit]simplify:  Simplified to (/ (- 1 k) 2)
* * * * [misc]progress:  [ 6 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* (* n PI) 2) (/ 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))
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (/ 1 2))
* [enter]simplify:  Simplifying (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ k 2))
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (/ k 2))
* * * * [misc]progress:  [ 7 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* (* n PI) 2) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* (* n PI) 2) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 8 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* (* n PI) 2) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* (* n PI) 2) (sqrt (/ (- 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 (pow (* (* PI n) 2) (sqrt (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (sqrt (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 9 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* (* n PI) 2) 1) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* (* n PI) 2) 1)
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (21 enodes)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* * * * [misc]progress:  [ 10 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* (* n PI) 2) (- 1 k)) (/ 1 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* (* n PI) 2) (- 1 k))
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (25 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (- 1 k))
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (- 1 k))
* * * * [misc]progress:  [ 11 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n PI) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* [exit]simplify:  Simplified to (pow (* PI n) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow (* PI n) (/ (- 1 k) 2))
* [enter]simplify:  Simplifying (pow 2 (/ (- 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 (pow 2 (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow 2 (/ (- 1 k) 2))
* * * * [misc]progress:  [ 12 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* (* n PI) 2) (/ (- 1 k) 2)) 1) (sqrt k)))>
* * * * [misc]progress:  [ 13 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (exp (log (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (pow (* (* n PI) 2) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (90 enodes)
* * [misc]simplify:  iters left: 2 (246 enodes)
* [exit]simplify:  Simplified to (/ (log (* (* PI n) 2)) (/ 2 (- 1 k)))
* [exit]simplify:  Simplified to (/ (log (* (* PI n) 2)) (/ 2 (- 1 k)))
* * * * [misc]progress:  [ 14 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (log (exp (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (pow (* (* n PI) 2) (/ (- 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 (exp (pow (* (* PI n) 2) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (exp (pow (* (* PI n) 2) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 15 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (* (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* n PI) 2) (/ (- 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 (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))))
* [enter]simplify:  Simplifying (cbrt (pow (* (* n PI) 2) (/ (- 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)))
* [exit]simplify:  Simplified to (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 16 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (cbrt (* (* (pow (* (* n PI) 2) (/ (- 1 k) 2)) (pow (* (* n PI) 2) (/ (- 1 k) 2))) (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (pow (* (* n PI) 2) (/ (- 1 k) 2)) (pow (* (* n PI) 2) (/ (- 1 k) 2))) (pow (* (* n PI) 2) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (pow (pow (* (* PI n) 2) (/ (- 1 k) 2)) 3)
* [exit]simplify:  Simplified to (pow (pow (* (* PI n) 2) (/ (- 1 k) 2)) 3)
* * * * [misc]progress:  [ 17 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (pow (* (* n PI) 2) (/ (- 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)))
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))
* [enter]simplify:  Simplifying (sqrt (pow (* (* n PI) 2) (/ (- 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)))
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 18 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* 1 (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt k)))>
* * * * [misc]progress:  [ 19 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (log1p (expm1 (* n PI))) 2) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (expm1 (* PI n))
* [exit]simplify:  Simplified to (expm1 (* PI n))
* * * * [misc]progress:  [ 20 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (expm1 (log1p (* n PI))) 2) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (log1p (* PI n))
* [exit]simplify:  Simplified to (log1p (* PI n))
* * * * [misc]progress:  [ 21 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (pow (* n PI) 1) 2) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 22 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (exp (log (* n PI))) 2) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (log (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (8 enodes)
* * [misc]simplify:  iters left: 1 (9 enodes)
* [exit]simplify:  Simplified to (log (* PI n))
* [exit]simplify:  Simplified to (log (* PI n))
* * * * [misc]progress:  [ 23 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (log (exp (* n PI))) 2) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (exp (* PI n))
* [exit]simplify:  Simplified to (exp (* PI n))
* * * * [misc]progress:  [ 24 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI))) 2) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (* n PI)) (cbrt (* n PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (6 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* PI n)) (cbrt (* PI n)))
* [exit]simplify:  Simplified to (* (cbrt (* PI n)) (cbrt (* PI n)))
* [enter]simplify:  Simplifying (cbrt (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (cbrt (* PI n))
* [exit]simplify:  Simplified to (cbrt (* PI n))
* * * * [misc]progress:  [ 25 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (cbrt (* (* (* n PI) (* n PI)) (* n PI))) 2) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (* n PI) (* n PI)) (* n PI))
* * [misc]simplify:  iters left: 6 (5 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (55 enodes)
* * [misc]simplify:  iters left: 2 (86 enodes)
* * [misc]simplify:  iters left: 1 (89 enodes)
* [exit]simplify:  Simplified to (pow (* PI n) 3)
* [exit]simplify:  Simplified to (pow (* PI n) 3)
* * * * [misc]progress:  [ 26 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [enter]simplify:  Simplifying (sqrt (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [exit]simplify:  Simplified to (sqrt (* PI n))
* * * * [misc]progress:  [ 27 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* 1 (* n PI)) 2) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 28 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 29 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (log1p (expm1 (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (expm1 (/ (pow (* (* n PI) 2) (/ (- 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 (expm1 (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (expm1 (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 30 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (expm1 (log1p (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (log1p (/ (pow (* (* n PI) 2) (/ (- 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 (log1p (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (log1p (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 31 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (pow (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)) 1))>
* * * * [misc]progress:  [ 32 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (* (log (* (* n PI) 2)) (/ (- 1 k) 2)) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (* (log (* (* n PI) 2)) (/ (- 1 k) 2)) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (34 enodes)
* * [misc]simplify:  iters left: 4 (66 enodes)
* * [misc]simplify:  iters left: 3 (165 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (/ (- 1 k) 2) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (/ (- 1 k) 2) (- (log (sqrt k))))
* * * * [misc]progress:  [ 33 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (* (log (* (* n PI) 2)) (/ (- 1 k) 2)) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (* (log (* (* n PI) 2)) (/ (- 1 k) 2)) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (34 enodes)
* * [misc]simplify:  iters left: 4 (66 enodes)
* * [misc]simplify:  iters left: 3 (165 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (/ (- 1 k) 2) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (/ (- 1 k) 2) (- (log (sqrt k))))
* * * * [misc]progress:  [ 34 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (log (pow (* (* n PI) 2) (/ (- 1 k) 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (log (pow (* (* n PI) 2) (/ (- 1 k) 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (50 enodes)
* * [misc]simplify:  iters left: 3 (98 enodes)
* * [misc]simplify:  iters left: 2 (302 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* (* PI n) 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* (* PI n) 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 35 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (exp (log (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (log (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (62 enodes)
* * [misc]simplify:  iters left: 2 (139 enodes)
* * [misc]simplify:  iters left: 1 (418 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (/ (- 1 k) 2) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (/ (- 1 k) 2) (- (log (sqrt k))))
* * * * [misc]progress:  [ 36 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (log (exp (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (exp (/ (pow (* (* n PI) 2) (/ (- 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 (exp (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (exp (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 37 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (/ (* (* (pow (* (* n PI) 2) (/ (- 1 k) 2)) (pow (* (* n PI) 2) (/ (- 1 k) 2))) (pow (* (* n PI) 2) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (* (pow (* (* n PI) 2) (/ (- 1 k) 2)) (pow (* (* n PI) 2) (/ (- 1 k) 2))) (pow (* (* n PI) 2) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (71 enodes)
* * [misc]simplify:  iters left: 3 (123 enodes)
* * [misc]simplify:  iters left: 2 (192 enodes)
* * [misc]simplify:  iters left: 1 (302 enodes)
* [exit]simplify:  Simplified to (* (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (* k (sqrt k))) (* (pow (* (* PI n) 2) (/ (- 1 k) 2)) (pow (* (* PI n) 2) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (* (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (* k (sqrt k))) (* (pow (* (* PI n) 2) (/ (- 1 k) 2)) (pow (* (* PI n) 2) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 38 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (cbrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (cbrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (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 (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))))
* [enter]simplify:  Simplifying (cbrt (/ (pow (* (* n PI) 2) (/ (- 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)))
* [exit]simplify:  Simplified to (cbrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 39 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (* (* (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (* (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (57 enodes)
* * [misc]simplify:  iters left: 3 (86 enodes)
* * [misc]simplify:  iters left: 2 (121 enodes)
* * [misc]simplify:  iters left: 1 (152 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* (* PI n) 2) (/ (- 1 k) 2)) (pow (* (* PI n) 2) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (* PI n) 2) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (* (pow (* (* PI n) 2) (/ (- 1 k) 2)) (pow (* (* PI n) 2) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (* PI n) 2) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 40 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ (pow (* (* n PI) 2) (/ (- 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)))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))
* [enter]simplify:  Simplifying (sqrt (/ (pow (* (* n PI) 2) (/ (- 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)))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 41 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (- (pow (* (* n PI) 2) (/ (- 1 k) 2))) (- (sqrt k))))>
* [enter]simplify:  Simplifying (- (pow (* (* n PI) 2) (/ (- 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 (- (pow (* (* PI n) 2) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (- (pow (* (* PI n) 2) (/ (- 1 k) 2)))
* [enter]simplify:  Simplifying (- (sqrt k))
* * [misc]simplify:  iters left: 3 (3 enodes)
* [exit]simplify:  Simplified to (- (sqrt k))
* [exit]simplify:  Simplified to (- (sqrt k))
* * * * [misc]progress:  [ 42 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow (* n PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow 2 (/ (- 1 k) 2)) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* n PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (26 enodes)
* * [misc]simplify:  iters left: 3 (28 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow (* PI n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow 2 (/ (- 1 k) 2)) (cbrt (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 2 (/ (- 1 k) 2)) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 43 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow (* n PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* n PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (* PI n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* * [misc]simplify:  iters left: 3 (21 enodes)
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 44 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow (* n PI) (/ (- 1 k) 2)) 1) (/ (pow 2 (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow (* n PI) (/ (- 1 k) 2)) 1)
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (pow (* PI n) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow (* PI n) (/ (- 1 k) 2))
* [enter]simplify:  Simplifying (/ (pow 2 (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt k))
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 45 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (* (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* n PI) 2) (/ (- 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 (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* (* n PI) 2) (/ (- 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 (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 46 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (* (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* n PI) 2) (/ (- 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 (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* (* n PI) 2) (/ (- 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 (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 47 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (* (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) 1) (/ (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) 1)
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (41 enodes)
* * [misc]simplify:  iters left: 3 (49 enodes)
* * [misc]simplify:  iters left: 2 (60 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* (* n PI) 2) (/ (- 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))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt k))
* * * * [misc]progress:  [ 48 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* (* n PI) 2) (/ (- 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 (* (* PI n) 2) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* (* n PI) 2) (/ (- 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 (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 49 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* (* n PI) 2) (/ (- 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 (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* (* n PI) 2) (/ (- 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 (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 50 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) 1) (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* (* n PI) 2) (/ (- 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 (* (* PI n) 2) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* (* n PI) 2) (/ (- 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))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt k))
* * * * [misc]progress:  [ 51 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (pow (* (* n PI) 2) (/ (- 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)))
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 52 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (pow (* (* n PI) 2) (/ (- 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)))
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 53 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 1) (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (/ 1 1)
* * [misc]simplify:  iters left: 2 (2 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to 1
* [exit]simplify:  Simplified to 1
* [enter]simplify:  Simplifying (/ (pow (* (* n PI) 2) (/ (- 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 (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 54 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))))>
* * * * [misc]progress:  [ 55 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow (* (* n PI) 2) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt k))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (6 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt k))
* [exit]simplify:  Simplified to (/ 1 (sqrt k))
* * * * [misc]progress:  [ 56 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n PI) 2) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (pow (* (* n PI) 2) (/ (- 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 (* (* PI 2) n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 57 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 58 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow (* (* n PI) 2) (/ (- 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)))
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 59 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) 1) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) 1)
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 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))
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (/ (- 1 k) 2))
* * * * [misc]progress:  [ 60 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n PI) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 61 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (/ (sqrt k) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (cbrt (pow (* (* n PI) 2) (/ (- 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 (* PI (* 2 n)) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (sqrt k) (cbrt (pow (* PI (* 2 n)) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 62 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (sqrt (pow (* (* n PI) 2) (/ (- 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 (* PI (* 2 n)) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (sqrt k) (sqrt (pow (* PI (* 2 n)) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 63 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n PI) 2) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (pow (* (* n PI) 2) (/ (- 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 (* (* PI 2) n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 64 / 73 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n PI) 2) (/ 1 2)) (* (sqrt k) (pow (* (* n PI) 2) (/ k 2)))))>
* [enter]simplify:  Simplifying (* (sqrt k) (pow (* (* n PI) 2) (/ k 2)))
* * [misc]simplify:  iters left: 6 (10 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 (* (pow (* n (* PI 2)) (/ k 2)) (sqrt k))
* [exit]simplify:  Simplified to (* (pow (* n (* PI 2)) (/ k 2)) (sqrt k))
* * * * [misc]progress:  [ 65 / 73 ] simplifiying candidate #<alt-event (λ (k n) (/ (- (+ (* 1/4 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))) (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))) (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 1/2 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (* 1/2 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (- (+ (* 1/4 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))) (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))) (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 1/2 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (* 1/2 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))))) (sqrt k))
* * [misc]simplify:  iters left: 6 (39 enodes)
* * [misc]simplify:  iters left: 5 (112 enodes)
* * [misc]simplify:  iters left: 4 (387 enodes)
* [exit]simplify:  Simplified to (/ (fma (- 1/2) (* (+ (log n) (log (* PI 2))) (* (pow (* PI 2) 1/2) (* (pow n 1/2) k))) (fma (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) (* k k))) (fma (log (* PI 2)) (log (* PI 2)) (* (log n) (log n)))) 1/8 (fma (* (pow (* PI 2) 1/2) (* (pow n 1/2) (* k k))) (* (log (* PI 2)) (* (log n) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2))))) (sqrt k))
* * * * [misc]progress:  [ 66 / 73 ] simplifiying candidate #<alt-event (λ (k n) (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) (- 1 k)))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) (- 1 k)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (78 enodes)
* * [misc]simplify:  iters left: 3 (301 enodes)
* [exit]simplify:  Simplified to (/ (pow (exp (* (- 1 k) 1/2)) (+ (log n) (log (* PI 2)))) (sqrt k))
* * * * [misc]progress:  [ 67 / 73 ] simplifiying candidate #<alt-event (λ (k n) (/ (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (78 enodes)
* * [misc]simplify:  iters left: 3 (316 enodes)
* [exit]simplify:  Simplified to (/ (pow (exp (* 1/2 (- 1 k))) (- (log (* PI -2)) (log (/ -1 n)))) (sqrt k))
* * * * [misc]progress:  [ 68 / 73 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (pow (* (* n PI) 2) (/ (- 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 (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 69 / 73 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (pow (* (* n PI) 2) (/ (- 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 (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 70 / 73 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (pow (* (* n PI) 2) (/ (- 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 (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 71 / 73 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* k (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2)))) (- (+ (* +nan.0 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))) (- (+ (* +nan.0 (* (pow k 2) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))) (- (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))))))))))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* k (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2)))) (- (+ (* +nan.0 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))) (- (+ (* +nan.0 (* (pow k 2) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))) (- (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))))))))))))
* * * * [misc]progress:  [ 72 / 73 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) (- 1 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) (- 1 k)))) k)) (- (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) (- 1 k)))) (pow k 2)))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) (- 1 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) (- 1 k)))) k)) (- (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) (- 1 k)))) (pow k 2))))))))
* * * * [misc]progress:  [ 73 / 73 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)))) k))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)))) k)))))))
* * * [misc]progress:  adding candidates to table
* * [misc]progress:  iteration 2 / 4
* * * [misc]progress:  picking best candidate
"ALT DATA: "{"all-alts":["#<alt-delta (λ (k n) (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>","#<alt-delta (λ (k n) (/ (* (* (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (sqrt k)))>","#<alt-delta (λ (k n) (* (* (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))) (/ (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt k))))>","#<alt-delta (λ (k n) (* (sqrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))))>","#<alt-delta (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>","#<alt-event (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>","#<alt-delta (λ (k n) (* (/ (* (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (sqrt k)))))>","#<alt-delta (λ (k n) (* (pow (* PI n) (/ (- 1 k) 2)) (/ (pow 2 (/ (- 1 k) 2)) (sqrt k))))>","#<alt-delta (λ (k n) (* (/ (pow (* n PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt 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(k n) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))"}* * * * [misc]pick:  Picked  #<alt-delta (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 4 ] rewriting at (2 1 2 1 1)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2 1 1 1 1)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2 1 1)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 4 ] generating series at (2 1 2 1 1)
* [misc]approximate:  Taking taylor expansion of (* n PI) in (n) around 0
* [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]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 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 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 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 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 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 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* PI n) into (* n PI)
* [misc]approximate:  Taking taylor expansion of (* (/ 1 n) PI) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 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 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 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 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 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 PI))))))) 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 (* (/ 1 (- n)) PI) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 PI) 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 (+ (* -1 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 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 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 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 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 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI)
* * * * [misc]progress:  [ 2 / 4 ] generating series at (2 1 1 1 1)
* [misc]approximate:  Taking taylor expansion of (* n PI) in (n) around 0
* [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]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 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 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 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 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 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 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* PI n) into (* n PI)
* [misc]approximate:  Taking taylor expansion of (* (/ 1 n) PI) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 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 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 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 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 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 PI))))))) 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 (* (/ 1 (- n)) PI) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 PI) 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 (+ (* -1 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 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 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 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 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 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI)
* * * * [misc]progress:  [ 3 / 4 ] generating series at (2)
* [misc]approximate:  Taking taylor expansion of (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (* n PI) 2) (/ 1 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* n PI) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* n PI) 2))) 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 PI) 2)) in k
* [misc]taylor:  Taking taylor expansion of (* (* n PI) 2) in k
* [misc]taylor:  Taking taylor expansion of (* n PI) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* n PI) into (* n PI)
* [misc]backup-simplify:  Simplify (* (* n PI) 2) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
* [misc]taylor:  Taking taylor expansion of (pow (* (* n PI) 2) (/ k 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* (* n PI) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* (* n PI) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* n PI) 2)) in k
* [misc]taylor:  Taking taylor expansion of (* (* n PI) 2) in k
* [misc]taylor:  Taking taylor expansion of (* n PI) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* n PI) into (* n PI)
* [misc]backup-simplify:  Simplify (* (* n PI) 2) 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 PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* n PI) 2) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* n PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* n PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* n PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n PI) 2) 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]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* PI 2)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* n PI) 2) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* (* n PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* (* n PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* n PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n PI) 2) 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]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* PI 2)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 k) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* k (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (/ (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt k)) into (* (sqrt (/ 1 k)) (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* n PI) 2) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* n PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* n PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* n PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n PI) 2) 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]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* PI 2)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* n PI) 2) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* (* n PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* (* n PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* n PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n PI) 2) 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]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* PI 2)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 k) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* k (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (/ (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt k)) into (* (sqrt (/ 1 k)) (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))))
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ 1 k)) (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]taylor:  Taking taylor expansion of (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (+ (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* k (+ (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 0 (+ (log (* 2 PI)) (log n))) into 0
* [misc]backup-simplify:  Simplify (* 1/2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (+ (log (* 2 PI)) (log n)))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (+ (log (* 2 PI)) (log n))) (* 0 0)) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))
* [misc]backup-simplify:  Simplify (exp 0) into 1
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 1) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (* 0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* PI 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* PI 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (/ 0 (sqrt k))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1) 1)))) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))))
* [misc]backup-simplify:  Simplify (+ (* 0 (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))))) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* PI 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* PI 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (+ (log (* 2 PI)) (log n))) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log (* 2 PI)) 2))))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log (* 2 PI)) 2)))) 1)) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (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 (+ (* 0 (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))) (+ (* +nan.0 (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))))) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))))))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (+ (log (* 2 PI)) (log n))) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 3) 6)) (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2))))))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2)))))) 1)) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))))) (/ (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log (* 2 PI)) 2)))) 1)) (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (- (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 3))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 3))) (+ (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (log n)))) (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow (log n) 2))))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* 0 (- (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 3))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 3))) (+ (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (log n)))) (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow (log n) 2))))))))) (+ (* +nan.0 (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))) (+ (* +nan.0 (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))))) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))))))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))))))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))))) into (- (+ (* +nan.0 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* k (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2)))) (- (+ (* +nan.0 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))) (- (+ (* +nan.0 (* (pow k 2) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))) (- (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))))))))))))
* [misc]approximate:  Taking taylor expansion of (/ (/ (pow (* (* (/ 1 n) PI) 2) (/ 1 2)) (pow (* (* (/ 1 n) PI) 2) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (* (/ 1 n) PI) 2) (/ 1 2)) (pow (* (* (/ 1 n) PI) 2) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 n) PI) 2) (/ 1 2)) (pow (* (* (/ 1 n) PI) 2) (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ 1 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 n) PI) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 n) PI) 2))) 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) PI) 2)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) PI) 2) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (/ 1 n) into (/ 1 n)
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* (/ 1 n) PI) into (/ PI n)
* [misc]backup-simplify:  Simplify (* (/ PI n) 2) 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) PI) 2) (/ (/ 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) PI) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) PI) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) PI) 2) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (/ 1 n) into (/ 1 n)
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* (/ 1 n) PI) into (/ PI n)
* [misc]backup-simplify:  Simplify (* (/ PI n) 2) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) PI) 2)))) 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) PI) 2) (/ 1 2)) (pow (* (* (/ 1 n) PI) 2) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 n) PI) 2) (/ 1 2)) (pow (* (* (/ 1 n) PI) 2) (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 n) PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 n) PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) PI) 2) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) PI) 2) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 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 (* (sqrt k) (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (* (/ 1 n) PI) 2) (/ 1 2)) (pow (* (* (/ 1 n) PI) 2) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 n) PI) 2) (/ 1 2)) (pow (* (* (/ 1 n) PI) 2) (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 n) PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 n) PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) PI) 2) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) PI) 2) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 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 (* (sqrt k) (/ (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) (/ (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 (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 (/ (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]backup-simplify:  Simplify (* 0 (/ (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 (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) 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 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) 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))) (+ (* (* (sqrt k) (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (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 (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 0) (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) 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 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) 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 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) 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))) (+ (* (* (sqrt k) (/ (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]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 (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 +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)))) (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 (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) 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 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) 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))) (+ (* (* (sqrt k) (/ (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)))) (* 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 (+ (* 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 (/ (- 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)))) (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) 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))))) (* k (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 3) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))))))))
* [misc]approximate:  Taking taylor expansion of (/ (/ (pow (* (* (/ 1 (- n)) PI) 2) (/ 1 2)) (pow (* (* (/ 1 (- n)) PI) 2) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (* (/ 1 (- n)) PI) 2) (/ 1 2)) (pow (* (* (/ 1 (- n)) PI) 2) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) PI) 2) (/ 1 2)) (pow (* (* (/ 1 (- n)) PI) 2) (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ 1 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 (- n)) PI) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 (- n)) PI) 2))) 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)) PI) 2)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in k
* [misc]taylor:  Taking taylor expansion of (- n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (/ 1 (- n)) into (/ -1 n)
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* (/ -1 n) PI) into (* -1 (/ PI n))
* [misc]backup-simplify:  Simplify (* (* -1 (/ PI n)) 2) 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)) PI) 2) (/ (/ 1 (- k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) PI) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) PI) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) PI) 2)) in k
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in k
* [misc]taylor:  Taking taylor expansion of (- n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (/ 1 (- n)) into (/ -1 n)
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* (/ -1 n) PI) into (* -1 (/ PI n))
* [misc]backup-simplify:  Simplify (* (* -1 (/ PI n)) 2) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* -2 (/ PI n)))) into (* -1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) PI) 2)))) 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)) PI) 2) (/ 1 2)) (pow (* (* (/ 1 (- n)) PI) 2) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) PI) 2) (/ 1 2)) (pow (* (* (/ 1 (- n)) PI) 2) (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 (- n)) PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 (- n)) PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* -1 PI) into (* -1 PI)
* [misc]backup-simplify:  Simplify (* (* -1 PI) 2) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* -1 PI) into (* -1 PI)
* [misc]backup-simplify:  Simplify (* (* -1 PI) 2) into (* -2 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)) PI) 2) (/ 1 2)) (pow (* (* (/ 1 (- n)) PI) 2) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) PI) 2) (/ 1 2)) (pow (* (* (/ 1 (- n)) PI) 2) (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 (- n)) PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 (- n)) PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* -1 PI) into (* -1 PI)
* [misc]backup-simplify:  Simplify (* (* -1 PI) 2) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* -1 PI) into (* -1 PI)
* [misc]backup-simplify:  Simplify (* (* -1 PI) 2) into (* -2 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 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* -1 PI) 0) (* 0 2)) 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 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* -1 PI) 0) (* 0 2)) 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 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* -1 PI) 0) (+ (* 0 0) (* 0 2))) 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 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* -1 PI) 0) (+ (* 0 0) (* 0 2))) 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 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* k (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n))))))))))))))
* * * * [misc]progress:  [ 4 / 4 ] generating series at (2 1 1)
* [misc]approximate:  Taking taylor expansion of (pow (* (* n PI) 2) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* n PI) 2) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* n PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* n PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* n PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n PI) 2) 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]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* PI 2)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* n PI) 2) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* n PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* n PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* n PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* n PI) 2) 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]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* PI 2)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* PI 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* PI 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]approximate:  Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 n) PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 n) PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) PI) 2) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 n) PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 n) PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 n) PI) 2) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 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 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) 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 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) 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 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) 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 PI))))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) 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 PI)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) 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 PI))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n)))))
* [misc]approximate:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 (- n)) PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 (- n)) PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* -1 PI) into (* -1 PI)
* [misc]backup-simplify:  Simplify (* (* -1 PI) 2) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 (- n)) PI) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 (- n)) PI) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* (/ 1 (- n)) PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* -1 PI) into (* -1 PI)
* [misc]backup-simplify:  Simplify (* (* -1 PI) 2) into (* -2 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 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* -1 PI) 0) (* 0 2)) 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 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* -1 PI) 0) (+ (* 0 0) (* 0 2))) 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 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* -1 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) 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 PI))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* -1 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) 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 PI)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* -1 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) 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 PI))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* -1 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) 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 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (log1p (expm1 (* n PI))) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (expm1 (* PI n))
* [exit]simplify:  Simplified to (expm1 (* PI n))
* * * * [misc]progress:  [ 2 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (expm1 (log1p (* n PI))) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (log1p (* PI n))
* [exit]simplify:  Simplified to (log1p (* PI n))
* * * * [misc]progress:  [ 3 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (pow (* n PI) 1) 2) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 4 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (exp (log (* n PI))) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (8 enodes)
* * [misc]simplify:  iters left: 1 (9 enodes)
* [exit]simplify:  Simplified to (log (* PI n))
* [exit]simplify:  Simplified to (log (* PI n))
* * * * [misc]progress:  [ 5 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (log (exp (* n PI))) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (exp (* PI n))
* [exit]simplify:  Simplified to (exp (* PI n))
* * * * [misc]progress:  [ 6 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI))) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (* n PI)) (cbrt (* n PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (6 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* PI n)) (cbrt (* PI n)))
* [exit]simplify:  Simplified to (* (cbrt (* PI n)) (cbrt (* PI n)))
* [enter]simplify:  Simplifying (cbrt (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (cbrt (* PI n))
* [exit]simplify:  Simplified to (cbrt (* PI n))
* * * * [misc]progress:  [ 7 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (cbrt (* (* (* n PI) (* n PI)) (* n PI))) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (* n PI) (* n PI)) (* n PI))
* * [misc]simplify:  iters left: 6 (5 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (55 enodes)
* * [misc]simplify:  iters left: 2 (86 enodes)
* * [misc]simplify:  iters left: 1 (89 enodes)
* [exit]simplify:  Simplified to (pow (* PI n) 3)
* [exit]simplify:  Simplified to (pow (* PI n) 3)
* * * * [misc]progress:  [ 8 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [enter]simplify:  Simplifying (sqrt (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [exit]simplify:  Simplified to (sqrt (* PI n))
* * * * [misc]progress:  [ 9 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* 1 (* n PI)) 2) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 10 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 11 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (log1p (expm1 (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (expm1 (* PI n))
* [exit]simplify:  Simplified to (expm1 (* PI n))
* * * * [misc]progress:  [ 12 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (expm1 (log1p (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (log1p (* PI n))
* [exit]simplify:  Simplified to (log1p (* PI n))
* * * * [misc]progress:  [ 13 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (pow (* n PI) 1) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 14 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (exp (log (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (8 enodes)
* * [misc]simplify:  iters left: 1 (9 enodes)
* [exit]simplify:  Simplified to (log (* PI n))
* [exit]simplify:  Simplified to (log (* PI n))
* * * * [misc]progress:  [ 15 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (log (exp (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (exp (* PI n))
* [exit]simplify:  Simplified to (exp (* PI n))
* * * * [misc]progress:  [ 16 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (* n PI)) (cbrt (* n PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (6 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* PI n)) (cbrt (* PI n)))
* [exit]simplify:  Simplified to (* (cbrt (* PI n)) (cbrt (* PI n)))
* [enter]simplify:  Simplifying (cbrt (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (cbrt (* PI n))
* [exit]simplify:  Simplified to (cbrt (* PI n))
* * * * [misc]progress:  [ 17 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (cbrt (* (* (* n PI) (* n PI)) (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (* n PI) (* n PI)) (* n PI))
* * [misc]simplify:  iters left: 6 (5 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (55 enodes)
* * [misc]simplify:  iters left: 2 (86 enodes)
* * [misc]simplify:  iters left: 1 (89 enodes)
* [exit]simplify:  Simplified to (pow (* PI n) 3)
* [exit]simplify:  Simplified to (pow (* PI n) 3)
* * * * [misc]progress:  [ 18 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [enter]simplify:  Simplifying (sqrt (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [exit]simplify:  Simplified to (sqrt (* PI n))
* * * * [misc]progress:  [ 19 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* 1 (* n PI)) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 20 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 21 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (log1p (expm1 (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (expm1 (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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 (expm1 (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)))
* [exit]simplify:  Simplified to (expm1 (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 22 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (expm1 (log1p (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (log1p (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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 (log1p (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)))
* [exit]simplify:  Simplified to (log1p (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 23 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (pow (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) 1))>
* * * * [misc]progress:  [ 24 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (* (log (* (* n PI) 2)) (/ 1 2)) (* (log (* (* n PI) 2)) (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n PI) 2)) (/ 1 2)) (* (log (* (* n PI) 2)) (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (97 enodes)
* * [misc]simplify:  iters left: 3 (303 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 25 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (* (log (* (* n PI) 2)) (/ 1 2)) (* (log (* (* n PI) 2)) (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n PI) 2)) (/ 1 2)) (* (log (* (* n PI) 2)) (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (97 enodes)
* * [misc]simplify:  iters left: 3 (303 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 26 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (* (log (* (* n PI) 2)) (/ 1 2)) (log (pow (* (* n PI) 2) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n PI) 2)) (/ 1 2)) (log (pow (* (* n PI) 2) (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (87 enodes)
* * [misc]simplify:  iters left: 3 (286 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 27 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (* (log (* (* n PI) 2)) (/ 1 2)) (* (log (* (* n PI) 2)) (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n PI) 2)) (/ 1 2)) (* (log (* (* n PI) 2)) (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (97 enodes)
* * [misc]simplify:  iters left: 3 (303 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 28 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (* (log (* (* n PI) 2)) (/ 1 2)) (* (log (* (* n PI) 2)) (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n PI) 2)) (/ 1 2)) (* (log (* (* n PI) 2)) (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (97 enodes)
* * [misc]simplify:  iters left: 3 (303 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 29 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (* (log (* (* n PI) 2)) (/ 1 2)) (log (pow (* (* n PI) 2) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* (* n PI) 2)) (/ 1 2)) (log (pow (* (* n PI) 2) (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (87 enodes)
* * [misc]simplify:  iters left: 3 (286 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 30 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (log (pow (* (* n PI) 2) (/ 1 2))) (* (log (* (* n PI) 2)) (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (log (pow (* (* n PI) 2) (/ 1 2))) (* (log (* (* n PI) 2)) (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (90 enodes)
* * [misc]simplify:  iters left: 3 (263 enodes)
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 31 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (log (pow (* (* n PI) 2) (/ 1 2))) (* (log (* (* n PI) 2)) (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (log (pow (* (* n PI) 2) (/ 1 2))) (* (log (* (* n PI) 2)) (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (90 enodes)
* * [misc]simplify:  iters left: 3 (263 enodes)
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 32 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (log (pow (* (* n PI) 2) (/ 1 2))) (log (pow (* (* n PI) 2) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (log (pow (* (* n PI) 2) (/ 1 2))) (log (pow (* (* n PI) 2) (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (70 enodes)
* * [misc]simplify:  iters left: 3 (205 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 33 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (log (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (log (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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 (90 enodes)
* * [misc]simplify:  iters left: 2 (285 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 34 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (exp (log (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (log (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (55 enodes)
* * [misc]simplify:  iters left: 2 (103 enodes)
* * [misc]simplify:  iters left: 1 (295 enodes)
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 35 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (log (exp (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (exp (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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 (exp (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)))
* [exit]simplify:  Simplified to (exp (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 36 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (/ (/ (* (* (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ 1 2))) (* (* (pow (* (* n PI) 2) (/ k 2)) (pow (* (* n PI) 2) (/ k 2))) (pow (* (* n PI) 2) (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (* (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ 1 2))) (* (* (pow (* (* n PI) 2) (/ k 2)) (pow (* (* n PI) 2) (/ k 2))) (pow (* (* n PI) 2) (/ 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 (389 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)))) (* (* (sqrt k) k) (/ (pow (* (* PI n) 2) (/ k 2)) (pow (* (* PI n) 2) (/ 1 2)))))
* [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)))) (* (* (sqrt k) k) (/ (pow (* (* PI n) 2) (/ k 2)) (pow (* (* PI n) 2) (/ 1 2)))))
* * * * [misc]progress:  [ 37 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (/ (* (* (/ (pow (* (* n PI) 2) (/ 1 2)) (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)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (* (/ (pow (* (* n PI) 2) (/ 1 2)) (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)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (39 enodes)
* * [misc]simplify:  iters left: 4 (96 enodes)
* * [misc]simplify:  iters left: 3 (267 enodes)
* [exit]simplify:  Simplified to (* (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (* (sqrt k) k)) (* (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))))
* [exit]simplify:  Simplified to (* (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (* (sqrt k) k)) (* (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))))
* * * * [misc]progress:  [ 38 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (cbrt (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))) (cbrt (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))) (cbrt (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (cbrt (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))) (cbrt (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))) (cbrt (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))))
* [exit]simplify:  Simplified to (* (cbrt (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))) (cbrt (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))))
* [enter]simplify:  Simplifying (cbrt (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)))
* [exit]simplify:  Simplified to (cbrt (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 39 / 157 ] simplifiying candidate #<alt-delta (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)))))>
* [enter]simplify:  Simplifying (* (* (/ (/ (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:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (73 enodes)
* * [misc]simplify:  iters left: 3 (201 enodes)
* [exit]simplify:  Simplified to (/ (* (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k))) (/ (* k (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))))
* [exit]simplify:  Simplified to (/ (* (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k))) (/ (* k (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))))
* * * * [misc]progress:  [ 40 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))) (sqrt (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)))
* [enter]simplify:  Simplifying (sqrt (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 41 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (- (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (- (sqrt k))))>
* [enter]simplify:  Simplifying (- (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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 (- (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))
* [exit]simplify:  Simplified to (- (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))
* [enter]simplify:  Simplifying (- (sqrt k))
* * [misc]simplify:  iters left: 3 (3 enodes)
* [exit]simplify:  Simplified to (- (sqrt k))
* [exit]simplify:  Simplified to (- (sqrt k))
* * * * [misc]progress:  [ 42 / 157 ] simplifiying candidate #<alt-delta (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 (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (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 (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))))
* [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))))
* [enter]simplify:  Simplifying (/ (cbrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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)))
* [exit]simplify:  Simplified to (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 43 / 157 ] simplifiying candidate #<alt-delta (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))))) (sqrt (sqrt k))) (/ (cbrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (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 (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 (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (* (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (cbrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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)))
* [exit]simplify:  Simplified to (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 44 / 157 ] simplifiying candidate #<alt-delta (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))))) 1) (/ (cbrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (* (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))))) 1)
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* * [misc]simplify:  iters left: 2 (52 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))))
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))))
* [enter]simplify:  Simplifying (/ (cbrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k))
* [exit]simplify:  Simplified to (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k))
* * * * [misc]progress:  [ 45 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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)))
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 46 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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)))
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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)))
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 47 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) 1) (/ (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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 n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k))
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k))
* * * * [misc]progress:  [ 48 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow (* n PI) (/ 1 2)) (pow (* n PI) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow 2 (/ 1 2)) (pow 2 (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n PI) (/ 1 2)) (pow (* n PI) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [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 (33 enodes)
* * [misc]simplify:  iters left: 2 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI n) (/ 1 2)) (pow (* PI n) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI n) (/ 1 2)) (pow (* PI n) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (pow 2 (/ 1 2)) (pow 2 (/ k 2))) (cbrt (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 2 (/ 1 2)) (pow 2 (/ k 2))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (pow 2 (/ 1 2)) (pow 2 (/ k 2))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 49 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow (* n PI) (/ 1 2)) (pow (* n PI) (/ k 2))) (sqrt (sqrt k))) (/ (/ (pow 2 (/ 1 2)) (pow 2 (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n PI) (/ 1 2)) (pow (* n PI) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI n) (/ 1 2)) (pow (* PI n) (/ k 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI n) (/ 1 2)) (pow (* PI n) (/ k 2))) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ (pow 2 (/ 1 2)) (pow 2 (/ k 2))) (sqrt (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 2 (/ 1 2)) (pow 2 (/ k 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (pow 2 (/ 1 2)) (pow 2 (/ k 2))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 50 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow (* n PI) (/ 1 2)) (pow (* n PI) (/ k 2))) 1) (/ (/ (pow 2 (/ 1 2)) (pow 2 (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n PI) (/ 1 2)) (pow (* n PI) (/ k 2))) 1)
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (25 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI n) (/ 1 2)) (pow (* PI n) (/ k 2)))
* [exit]simplify:  Simplified to (/ (pow (* PI n) (/ 1 2)) (pow (* PI n) (/ k 2)))
* [enter]simplify:  Simplifying (/ (/ (pow 2 (/ 1 2)) (pow 2 (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* [exit]simplify:  Simplified to (/ (pow 2 (/ 1 2)) (* (sqrt k) (pow 2 (/ k 2))))
* [exit]simplify:  Simplified to (/ (pow 2 (/ 1 2)) (* (sqrt k) (pow 2 (/ k 2))))
* * * * [misc]progress:  [ 51 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow (* n PI) (/ 1 2)) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow 2 (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n PI) (/ 1 2)) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 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 (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 (* PI n) (/ 1 2)) (cbrt (sqrt k))) (cbrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (/ (/ (pow (* PI n) (/ 1 2)) (cbrt (sqrt k))) (cbrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow 2 (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ 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 2 (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow 2 (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ k 2))))
* * * * [misc]progress:  [ 52 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow (* n PI) (/ 1 2)) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (pow 2 (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n PI) (/ 1 2)) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 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 (38 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* * [misc]simplify:  iters left: 2 (48 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI n) (/ 1 2)) (sqrt (sqrt k))) (* (cbrt (pow (* (* 2 PI) n) (/ k 2))) (cbrt (pow (* (* 2 PI) n) (/ k 2)))))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI n) (/ 1 2)) (sqrt (sqrt k))) (* (cbrt (pow (* (* 2 PI) n) (/ k 2))) (cbrt (pow (* (* 2 PI) n) (/ k 2)))))
* [enter]simplify:  Simplifying (/ (/ (pow 2 (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow 2 (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow 2 (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ k 2))))
* * * * [misc]progress:  [ 53 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow (* n PI) (/ 1 2)) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) 1) (/ (/ (pow 2 (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n PI) (/ 1 2)) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ 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 (* PI n) (/ 1 2)) (cbrt (pow (* PI (* 2 n)) (/ k 2)))) (cbrt (pow (* PI (* 2 n)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI n) (/ 1 2)) (cbrt (pow (* PI (* 2 n)) (/ k 2)))) (cbrt (pow (* PI (* 2 n)) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow 2 (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ 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 2 (/ 1 2)) (sqrt k)) (cbrt (pow (* (* PI n) 2) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow 2 (/ 1 2)) (sqrt k)) (cbrt (pow (* (* PI n) 2) (/ k 2))))
* * * * [misc]progress:  [ 54 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow (* n PI) (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow 2 (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n PI) (/ 1 2)) (sqrt (pow (* (* n PI) 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 (/ (/ (pow (* PI n) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* (* 2 PI) n) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI n) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* (* 2 PI) n) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow 2 (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ 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 2 (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow 2 (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (/ k 2))))
* * * * [misc]progress:  [ 55 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow (* n PI) (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k))) (/ (/ (pow 2 (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n PI) (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI n) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI n) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow 2 (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow 2 (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow 2 (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (/ k 2))))
* * * * [misc]progress:  [ 56 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow (* n PI) (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))) 1) (/ (/ (pow 2 (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n PI) (/ 1 2)) (sqrt (pow (* (* n PI) 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 (37 enodes)
* * [misc]simplify:  iters left: 2 (38 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI n) (/ 1 2)) (sqrt (pow (* (* 2 n) PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (pow (* PI n) (/ 1 2)) (sqrt (pow (* (* 2 n) PI) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow 2 (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ 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 2 (/ 1 2)) (sqrt k)) (sqrt (pow (* (* PI n) 2) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow 2 (/ 1 2)) (sqrt k)) (sqrt (pow (* (* PI n) 2) (/ k 2))))
* * * * [misc]progress:  [ 57 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow (* n PI) (/ 1 2)) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow 2 (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n PI) (/ 1 2)) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI n) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow (* PI n) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (pow 2 (/ 1 2)) (pow (* (* n PI) 2) (/ 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 2 (/ 1 2)) (cbrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ (pow 2 (/ 1 2)) (cbrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 58 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow (* n PI) (/ 1 2)) 1) (sqrt (sqrt k))) (/ (/ (pow 2 (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n PI) (/ 1 2)) 1) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI n) (/ 1 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (* PI n) (/ 1 2)) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ (pow 2 (/ 1 2)) (pow (* (* n PI) 2) (/ 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 2 (/ 1 2)) (sqrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ (pow 2 (/ 1 2)) (sqrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 59 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow (* n PI) (/ 1 2)) 1) 1) (/ (/ (pow 2 (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n PI) (/ 1 2)) 1) 1)
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* [exit]simplify:  Simplified to (pow (* PI n) (/ 1 2))
* [exit]simplify:  Simplified to (pow (* PI n) (/ 1 2))
* [enter]simplify:  Simplifying (/ (/ (pow 2 (/ 1 2)) (pow (* (* n PI) 2) (/ 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 2 (/ 1 2)) (sqrt k)) (pow (* (* PI n) 2) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ (pow 2 (/ 1 2)) (sqrt k)) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 60 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (pow (* n PI) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow 2 (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (pow (* n 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 (50 enodes)
* * [misc]simplify:  iters left: 3 (87 enodes)
* * [misc]simplify:  iters left: 2 (125 enodes)
* * [misc]simplify:  iters left: 1 (144 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) (* (pow (* PI n) (/ k 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) (* (pow (* PI n) (/ k 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow 2 (/ 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))) (* (pow 2 (/ k 2)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow 2 (/ k 2)) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 61 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (pow (* n PI) (/ k 2))) (sqrt (sqrt k))) (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow 2 (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (pow (* n 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 (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))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) (* (pow (* PI n) (/ k 2)) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) (* (pow (* PI n) (/ k 2)) (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow 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 (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow 2 (/ k 2)) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow 2 (/ k 2)) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 62 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (pow (* n PI) (/ k 2))) 1) (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow 2 (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (pow (* n PI) (/ 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 (165 enodes)
* * [misc]simplify:  iters left: 1 (244 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (pow (* PI n) (/ k 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (pow (* PI n) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow 2 (/ 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 (* (* PI n) 2) (/ 1 2))) (* (sqrt k) (pow 2 (/ k 2))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt k) (pow 2 (/ k 2))))
* * * * [misc]progress:  [ 63 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ 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 (250 enodes)
* * [misc]simplify:  iters left: 1 (309 enodes)
* [exit]simplify:  Simplified to (* (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k))) (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (* (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k))) (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 64 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (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:  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 (* (* 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))))) (sqrt (sqrt k)))
* [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))))) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 65 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) 1) (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ 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 (303 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)))))
* [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)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 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))))
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt k)) (cbrt (pow (* (* PI n) 2) (/ k 2))))
* * * * [misc]progress:  [ 66 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (sqrt (pow (* (* n PI) 2) (/ 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 (126 enodes)
* * [misc]simplify:  iters left: 1 (147 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))))
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 67 / 157 ] simplifiying candidate #<alt-delta (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 (sqrt k))) (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (57 enodes)
* * [misc]simplify:  iters left: 2 (65 enodes)
* * [misc]simplify:  iters left: 1 (68 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (pow (* (* PI n) 2) (/ k 2)))))
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (pow (* (* PI n) 2) (/ k 2)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 68 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) 1) (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (sqrt (pow (* (* n PI) 2) (/ 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 (156 enodes)
* * [misc]simplify:  iters left: 1 (273 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (pow (* (* PI n) 2) (/ 1 2))))
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (pow (* (* PI n) 2) (/ 1 2))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ 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))))
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt k)) (sqrt (pow (* (* PI n) 2) (/ k 2))))
* * * * [misc]progress:  [ 69 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 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 (103 enodes)
* * [misc]simplify:  iters left: 2 (244 enodes)
* * [misc]simplify:  iters left: 1 (272 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ 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))) (* (pow (* (* PI n) 2) (/ k 2)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow (* (* PI n) 2) (/ k 2)) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 70 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) 1) (sqrt (sqrt k))) (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 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 (133 enodes)
* * [misc]simplify:  iters left: 1 (136 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ 1 2))))
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ 1 2))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 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 (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow (* (* PI n) 2) (/ k 2)) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow (* (* PI n) 2) (/ k 2)) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 71 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) 1) 1) (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) 1) 1)
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* * [misc]simplify:  iters left: 2 (49 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (* (sqrt k) (pow (* (* PI n) 2) (/ k 2))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt k) (pow (* (* PI n) 2) (/ k 2))))
* * * * [misc]progress:  [ 72 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* n PI) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow 2 (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* n 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 (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (* (pow (* PI n) (/ k 2)) (cbrt (sqrt k))) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (* (pow (* PI n) (/ k 2)) (cbrt (sqrt k))) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow 2 (/ 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))) (* (pow 2 (/ k 2)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow 2 (/ k 2)) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 73 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* n PI) (/ k 2))) (sqrt (sqrt k))) (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow 2 (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* n 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))) (* (pow (* PI n) (/ k 2)) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow (* PI n) (/ k 2)) (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow 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))) (* (pow 2 (/ k 2)) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow 2 (/ k 2)) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 74 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* n PI) (/ k 2))) 1) (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow 2 (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* n 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 (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (pow (* PI n) (/ k 2)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (pow (* PI n) (/ k 2)))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow 2 (/ 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 (* (* PI n) 2) (/ 1 2))) (* (sqrt k) (pow 2 (/ k 2))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt k) (pow 2 (/ k 2))))
* * * * [misc]progress:  [ 75 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 76 / 157 ] simplifiying candidate #<alt-delta (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 PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (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:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* * [misc]simplify:  iters left: 2 (49 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (sqrt k))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (sqrt k))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 77 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) 1) (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (pow (* (* PI n) 2) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (pow (* (* PI n) 2) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 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))))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt k)) (cbrt (pow (* (* PI n) 2) (/ k 2))))
* * * * [misc]progress:  [ 78 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* (* PI n) 2) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* (* PI n) 2) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 79 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k))) (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 80 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) 1) (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (sqrt (pow (* (* PI n) 2) (/ k 2))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (pow (* (* PI n) 2) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ 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))))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt k)) (sqrt (pow (* (* PI n) 2) (/ k 2))))
* * * * [misc]progress:  [ 81 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ 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))) (* (pow (* (* PI n) 2) (/ k 2)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow (* (* PI n) 2) (/ k 2)) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 82 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) 1) (sqrt (sqrt k))) (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 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)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 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))) (* (pow (* (* PI n) 2) (/ k 2)) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow (* (* PI n) 2) (/ k 2)) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 83 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) 1) 1) (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) 1) 1)
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2)))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2))) (* (sqrt k) (pow (* (* PI n) 2) (/ k 2))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt k) (pow (* (* PI n) 2) (/ k 2))))
* * * * [misc]progress:  [ 84 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (pow (* n PI) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow 2 (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (pow (* n PI) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (26 enodes)
* * [misc]simplify:  iters left: 3 (31 enodes)
* * [misc]simplify:  iters left: 2 (32 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (pow (* PI n) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (/ 1 (pow (* PI n) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow 2 (/ 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 n) 2) (/ 1 2)) (* (cbrt (sqrt k)) (pow 2 (/ k 2))))
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (* (cbrt (sqrt k)) (pow 2 (/ k 2))))
* * * * [misc]progress:  [ 85 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (pow (* n PI) (/ k 2))) (sqrt (sqrt k))) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow 2 (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (pow (* n PI) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (pow (* PI n) (/ k 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ 1 (pow (* PI n) (/ k 2))) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow 2 (/ 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 n) 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow 2 (/ k 2))))
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow 2 (/ k 2))))
* * * * [misc]progress:  [ 86 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (pow (* n PI) (/ k 2))) 1) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow 2 (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ 1 (pow (* n PI) (/ k 2))) 1)
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* * [misc]simplify:  iters left: 3 (21 enodes)
* [exit]simplify:  Simplified to (/ 1 (pow (* PI n) (/ k 2)))
* [exit]simplify:  Simplified to (/ 1 (pow (* PI n) (/ k 2)))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow 2 (/ 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)) (* (pow 2 (/ k 2)) (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (* (pow 2 (/ k 2)) (sqrt k)))
* * * * [misc]progress:  [ 87 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ 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 (pow (* PI (* 2 n)) (/ k 2)))) (* (cbrt (pow (* PI (* 2 n)) (/ k 2))) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (/ (/ 1 (cbrt (sqrt k))) (cbrt (pow (* PI (* 2 n)) (/ k 2)))) (* (cbrt (pow (* PI (* 2 n)) (/ k 2))) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ 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))))
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ k 2))))
* * * * [misc]progress:  [ 88 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (46 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (pow (* PI (* 2 n)) (/ k 2)))) (* (cbrt (pow (* PI (* 2 n)) (/ k 2))) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (pow (* PI (* 2 n)) (/ k 2)))) (* (cbrt (pow (* PI (* 2 n)) (/ k 2))) (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (cbrt (pow (* (* n PI) 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 (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ k 2))))
* * * * [misc]progress:  [ 89 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) 1) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ 1 (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) 1)
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* * [misc]simplify:  iters left: 2 (40 enodes)
* [exit]simplify:  Simplified to (/ 1 (* (cbrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))))
* [exit]simplify:  Simplified to (/ 1 (* (cbrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ 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 n) 2) (/ 1 2)) (sqrt k)) (cbrt (pow (* (* PI n) 2) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) (cbrt (pow (* (* PI n) 2) (/ k 2))))
* * * * [misc]progress:  [ 90 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (sqrt (pow (* (* n PI) 2) (/ 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))))
* [exit]simplify:  Simplified to (/ (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ 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))))
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (/ k 2))))
* * * * [misc]progress:  [ 91 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k))) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (sqrt (pow (* (* n PI) 2) (/ 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))))
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (pow (* PI (* 2 n)) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (sqrt (pow (* (* n PI) 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 (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (/ k 2))))
* * * * [misc]progress:  [ 92 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (sqrt (pow (* (* n PI) 2) (/ k 2)))) 1) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ 1 (sqrt (pow (* (* n PI) 2) (/ k 2)))) 1)
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (pow (* (* 2 n) PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ 1 (sqrt (pow (* (* 2 n) PI) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ 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 n) 2) (/ 1 2)) (sqrt k)) (sqrt (pow (* (* PI n) 2) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) (sqrt (pow (* (* PI n) 2) (/ k 2))))
* * * * [misc]progress:  [ 93 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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)))
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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 n) 2) (/ 1 2)) (cbrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (cbrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 94 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 1) (sqrt (sqrt k))) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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)))
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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 n) 2) (/ 1 2)) (sqrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 95 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 1) 1) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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
* [exit]simplify:  Simplified to 1
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))
* * * * [misc]progress:  [ 96 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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 n) 2) (/ 1 2)) (cbrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (cbrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 97 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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 n) 2) (/ 1 2)) (sqrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 98 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 1) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ 1 1)
* * [misc]simplify:  iters left: 2 (2 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to 1
* [exit]simplify:  Simplified to 1
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))
* * * * [misc]progress:  [ 99 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow (* (* n PI) 2) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ 1 (pow (* (* n PI) 2) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* (* n PI) 2) (/ 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 n) 2) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ 1 (pow (* (* n PI) 2) (/ 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 PI) n) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ k 2)))
* * * * [misc]progress:  [ 100 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow (* (* n PI) 2) (/ 1 2)) (sqrt (sqrt k))) (/ (/ 1 (pow (* (* n PI) 2) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ 1 (pow (* (* n PI) 2) (/ 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 PI) n) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ k 2)))
* * * * [misc]progress:  [ 101 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow (* (* n PI) 2) (/ 1 2)) 1) (/ (/ 1 (pow (* (* n PI) 2) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow (* (* n PI) 2) (/ 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 n) 2) (/ 1 2))
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (/ 1 2))
* [enter]simplify:  Simplifying (/ (/ 1 (pow (* (* n PI) 2) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt k)) (pow (* (* 2 n) PI) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt k)) (pow (* (* 2 n) PI) (/ k 2)))
* * * * [misc]progress:  [ 102 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))))>
* * * * [misc]progress:  [ 103 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (/ 1 (sqrt k))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt k))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (6 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt k))
* [exit]simplify:  Simplified to (/ 1 (sqrt k))
* * * * [misc]progress:  [ 104 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))
* * [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 (35 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* PI (* 2 n)) (/ k 2)) (sqrt k)) (pow (* PI (* 2 n)) (/ 1 2)))
* [exit]simplify:  Simplified to (/ (* (pow (* PI (* 2 n)) (/ k 2)) (sqrt k)) (pow (* PI (* 2 n)) (/ 1 2)))
* * * * [misc]progress:  [ 105 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (38 enodes)
* * [misc]simplify:  iters left: 3 (45 enodes)
* * [misc]simplify:  iters left: 2 (46 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 106 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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 n) 2) (/ 1 2)) (sqrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 107 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) 1) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) 1)
* * [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 (35 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 108 / 157 ] simplifiying candidate #<alt-delta (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))))) (/ (sqrt k) (cbrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (cbrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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 k) (cbrt (/ (pow (* (* PI 2) n) (/ 1 2)) (pow (* (* PI 2) n) (/ k 2)))))
* [exit]simplify:  Simplified to (/ (sqrt k) (cbrt (/ (pow (* (* PI 2) n) (/ 1 2)) (pow (* (* PI 2) n) (/ k 2)))))
* * * * [misc]progress:  [ 109 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt k) (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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 k) (sqrt (/ (pow (* (* PI 2) n) (/ 1 2)) (pow (* (* PI 2) n) (/ k 2)))))
* [exit]simplify:  Simplified to (/ (sqrt k) (sqrt (/ (pow (* (* PI 2) n) (/ 1 2)) (pow (* (* PI 2) n) (/ k 2)))))
* * * * [misc]progress:  [ 110 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n PI) (/ 1 2)) (pow (* n PI) (/ k 2))) (/ (sqrt k) (/ (pow 2 (/ 1 2)) (pow 2 (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow 2 (/ 1 2)) (pow 2 (/ k 2))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow 2 (/ 1 2))) (pow 2 (/ k 2)))
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow 2 (/ 1 2))) (pow 2 (/ k 2)))
* * * * [misc]progress:  [ 111 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n PI) (/ 1 2)) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt k) (/ (pow 2 (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow 2 (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ k 2)))))
* * [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 (35 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (/ (sqrt k) (pow 2 (/ 1 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (/ (sqrt k) (pow 2 (/ 1 2))))
* * * * [misc]progress:  [ 112 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n PI) (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt k) (/ (pow 2 (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow 2 (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))))
* * [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 (35 enodes)
* [exit]simplify:  Simplified to (* (sqrt (pow (* n (* PI 2)) (/ k 2))) (/ (sqrt k) (pow 2 (/ 1 2))))
* [exit]simplify:  Simplified to (* (sqrt (pow (* n (* PI 2)) (/ k 2))) (/ (sqrt k) (pow 2 (/ 1 2))))
* * * * [misc]progress:  [ 113 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n PI) (/ 1 2)) 1) (/ (sqrt k) (/ (pow 2 (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow 2 (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))
* * [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 (34 enodes)
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow 2 (/ 1 2))) (pow (* PI (* n 2)) (/ k 2)))
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow 2 (/ 1 2))) (pow (* PI (* n 2)) (/ k 2)))
* * * * [misc]progress:  [ 114 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (pow (* n PI) (/ k 2))) (/ (sqrt k) (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow 2 (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (cbrt (pow (* (* n PI) 2) (/ 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 (32 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (* (pow 2 (/ k 2)) (sqrt k)) (cbrt (pow (* (* PI 2) n) (/ 1 2))))
* [exit]simplify:  Simplified to (/ (* (pow 2 (/ k 2)) (sqrt k)) (cbrt (pow (* (* PI 2) n) (/ 1 2))))
* * * * [misc]progress:  [ 115 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt k) (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ k 2)))))
* * [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 (37 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* PI (* 2 n)) (/ k 2))) (/ (sqrt k) (cbrt (pow (* PI (* 2 n)) (/ 1 2)))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* PI (* 2 n)) (/ k 2))) (/ (sqrt k) (cbrt (pow (* PI (* 2 n)) (/ 1 2)))))
* * * * [misc]progress:  [ 116 / 157 ] simplifiying candidate #<alt-delta (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 PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))))
* * [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 (37 enodes)
* [exit]simplify:  Simplified to (* (sqrt (pow (* PI (* 2 n)) (/ k 2))) (/ (sqrt k) (cbrt (pow (* PI (* 2 n)) (/ 1 2)))))
* [exit]simplify:  Simplified to (* (sqrt (pow (* PI (* 2 n)) (/ k 2))) (/ (sqrt k) (cbrt (pow (* PI (* 2 n)) (/ 1 2)))))
* * * * [misc]progress:  [ 117 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) 1) (/ (sqrt k) (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))))
* * [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 (36 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* (* PI 2) n) (/ k 2)) (sqrt k)) (cbrt (pow (* (* PI 2) n) (/ 1 2))))
* [exit]simplify:  Simplified to (/ (* (pow (* (* PI 2) n) (/ k 2)) (sqrt k)) (cbrt (pow (* (* PI 2) n) (/ 1 2))))
* * * * [misc]progress:  [ 118 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* n PI) (/ k 2))) (/ (sqrt k) (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow 2 (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (sqrt (pow (* (* n PI) 2) (/ 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 (32 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (* (pow 2 (/ k 2)) (sqrt k)) (sqrt (pow (* (* PI 2) n) (/ 1 2))))
* [exit]simplify:  Simplified to (/ (* (pow 2 (/ k 2)) (sqrt k)) (sqrt (pow (* (* PI 2) n) (/ 1 2))))
* * * * [misc]progress:  [ 119 / 157 ] simplifiying candidate #<alt-delta (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 PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ k 2)))))
* * [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 (37 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* PI (* 2 n)) (/ k 2))) (/ (sqrt k) (sqrt (pow (* PI (* 2 n)) (/ 1 2)))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* PI (* 2 n)) (/ k 2))) (/ (sqrt k) (sqrt (pow (* PI (* 2 n)) (/ 1 2)))))
* * * * [misc]progress:  [ 120 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt k) (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))))
* * [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 (37 enodes)
* [exit]simplify:  Simplified to (* (sqrt (pow (* PI (* 2 n)) (/ k 2))) (/ (sqrt k) (sqrt (pow (* PI (* 2 n)) (/ 1 2)))))
* [exit]simplify:  Simplified to (* (sqrt (pow (* PI (* 2 n)) (/ k 2))) (/ (sqrt k) (sqrt (pow (* PI (* 2 n)) (/ 1 2)))))
* * * * [misc]progress:  [ 121 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) 1) (/ (sqrt k) (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))))
* * [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 (36 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* (* PI 2) n) (/ k 2)) (sqrt k)) (sqrt (pow (* (* PI 2) n) (/ 1 2))))
* [exit]simplify:  Simplified to (/ (* (pow (* (* PI 2) n) (/ k 2)) (sqrt k)) (sqrt (pow (* (* PI 2) n) (/ 1 2))))
* * * * [misc]progress:  [ 122 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (pow (* n PI) (/ k 2))) (/ (sqrt k) (/ (pow (* (* n PI) 2) (/ 1 2)) (pow 2 (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* (* n PI) 2) (/ 1 2)) (pow 2 (/ k 2))))
* * [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 (35 enodes)
* [exit]simplify:  Simplified to (/ (* (pow 2 (/ k 2)) (sqrt k)) (pow (* PI (* 2 n)) (/ 1 2)))
* [exit]simplify:  Simplified to (/ (* (pow 2 (/ k 2)) (sqrt k)) (pow (* PI (* 2 n)) (/ 1 2)))
* * * * [misc]progress:  [ 123 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt k) (/ (pow (* (* n PI) 2) (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* (* n PI) 2) (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ k 2)))))
* * [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 (36 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* PI 2) n) (/ k 2))) (/ (sqrt k) (pow (* (* PI 2) n) (/ 1 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* PI 2) n) (/ k 2))) (/ (sqrt k) (pow (* (* PI 2) n) (/ 1 2))))
* * * * [misc]progress:  [ 124 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt k) (/ (pow (* (* n PI) 2) (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* (* n PI) 2) (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))))
* * [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 (36 enodes)
* [exit]simplify:  Simplified to (* (sqrt (pow (* (* PI 2) n) (/ k 2))) (/ (sqrt k) (pow (* (* PI 2) n) (/ 1 2))))
* [exit]simplify:  Simplified to (* (sqrt (pow (* (* PI 2) n) (/ k 2))) (/ (sqrt k) (pow (* (* PI 2) n) (/ 1 2))))
* * * * [misc]progress:  [ 125 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 1) (/ (sqrt k) (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))
* * [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 (35 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* PI (* 2 n)) (/ k 2)) (sqrt k)) (pow (* PI (* 2 n)) (/ 1 2)))
* [exit]simplify:  Simplified to (/ (* (pow (* PI (* 2 n)) (/ k 2)) (sqrt k)) (pow (* PI (* 2 n)) (/ 1 2)))
* * * * [misc]progress:  [ 126 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))
* * [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 (35 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* PI (* 2 n)) (/ k 2)) (sqrt k)) (pow (* PI (* 2 n)) (/ 1 2)))
* [exit]simplify:  Simplified to (/ (* (pow (* PI (* 2 n)) (/ k 2)) (sqrt k)) (pow (* PI (* 2 n)) (/ 1 2)))
* * * * [misc]progress:  [ 127 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n PI) 2) (/ 1 2)) (/ (sqrt k) (/ 1 (pow (* (* n PI) 2) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ 1 (pow (* (* n PI) 2) (/ k 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (42 enodes)
* * [misc]simplify:  iters left: 1 (47 enodes)
* [exit]simplify:  Simplified to (* (sqrt k) (pow (* (* PI n) 2) (/ k 2)))
* [exit]simplify:  Simplified to (* (sqrt k) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 128 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n PI) 2) (/ 1 2)) (* (sqrt k) (pow (* (* n PI) 2) (/ k 2)))))>
* [enter]simplify:  Simplifying (* (sqrt k) (pow (* (* n PI) 2) (/ k 2)))
* * [misc]simplify:  iters left: 6 (10 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 (* (pow (* n (* PI 2)) (/ k 2)) (sqrt k))
* [exit]simplify:  Simplified to (* (pow (* n (* PI 2)) (/ k 2)) (sqrt k))
* * * * [misc]progress:  [ 129 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (log1p (expm1 (pow (* (* n PI) 2) (/ 1 2)))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (pow (* (* n PI) 2) (/ 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 (expm1 (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (expm1 (pow (* (* PI n) 2) (/ 1 2)))
* * * * [misc]progress:  [ 130 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (expm1 (log1p (pow (* (* n PI) 2) (/ 1 2)))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (pow (* (* n PI) 2) (/ 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 (log1p (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (log1p (pow (* (* PI n) 2) (/ 1 2)))
* * * * [misc]progress:  [ 131 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (exp (* (log (* (* n PI) 2)) (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* (* n PI) 2)) (/ 1 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (92 enodes)
* * [misc]simplify:  iters left: 2 (180 enodes)
* * [misc]simplify:  iters left: 1 (390 enodes)
* [exit]simplify:  Simplified to (fma (/ 1 2) (log (* PI n)) (/ (log 2) 2))
* [exit]simplify:  Simplified to (fma (/ 1 2) (log (* PI n)) (/ (log 2) 2))
* * * * [misc]progress:  [ 132 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (exp (* (log (* (* n PI) 2)) (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* (* n PI) 2)) (/ 1 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (92 enodes)
* * [misc]simplify:  iters left: 2 (180 enodes)
* * [misc]simplify:  iters left: 1 (390 enodes)
* [exit]simplify:  Simplified to (fma (/ 1 2) (log (* PI n)) (/ (log 2) 2))
* [exit]simplify:  Simplified to (fma (/ 1 2) (log (* PI n)) (/ (log 2) 2))
* * * * [misc]progress:  [ 133 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n PI) 2) (* 1 (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* 1 (/ 1 2))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* [exit]simplify:  Simplified to (/ 1 2)
* [exit]simplify:  Simplified to (/ 1 2)
* * * * [misc]progress:  [ 134 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* (* n PI) 2) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) (cbrt (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* (* n PI) 2) (* (cbrt (/ 1 2)) (cbrt (/ 1 2))))
* * [misc]simplify:  iters left: 6 (10 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 (pow (* (* PI n) 2) (* (cbrt (/ 1 2)) (cbrt (/ 1 2))))
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (* (cbrt (/ 1 2)) (cbrt (/ 1 2))))
* * * * [misc]progress:  [ 135 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* (* n PI) 2) (sqrt (/ 1 2))) (sqrt (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* (* n PI) 2) (sqrt (/ 1 2)))
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* * [misc]simplify:  iters left: 3 (21 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (sqrt (/ 1 2)))
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (sqrt (/ 1 2)))
* * * * [misc]progress:  [ 136 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* (* n PI) 2) 1) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* (* n PI) 2) 1)
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (21 enodes)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* * * * [misc]progress:  [ 137 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* (* n PI) 2) 1) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* (* n PI) 2) 1)
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (21 enodes)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* * * * [misc]progress:  [ 138 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (pow (* n PI) (/ 1 2)) (pow 2 (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n PI) (/ 1 2))
* * [misc]simplify:  iters left: 3 (7 enodes)
* * [misc]simplify:  iters left: 2 (10 enodes)
* [exit]simplify:  Simplified to (pow (* PI n) (/ 1 2))
* [exit]simplify:  Simplified to (pow (* PI n) (/ 1 2))
* [enter]simplify:  Simplifying (pow 2 (/ 1 2))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (6 enodes)
* [exit]simplify:  Simplified to (pow 2 (/ 1 2))
* [exit]simplify:  Simplified to (pow 2 (/ 1 2))
* * * * [misc]progress:  [ 139 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* (* n PI) 2) (/ 1 2)) 1) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 140 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (exp (log (pow (* (* n PI) 2) (/ 1 2)))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (pow (* (* n PI) 2) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (72 enodes)
* * [misc]simplify:  iters left: 2 (182 enodes)
* * [misc]simplify:  iters left: 1 (442 enodes)
* [exit]simplify:  Simplified to (fma (/ 1 2) (log (* 2 PI)) (/ (log n) 2))
* [exit]simplify:  Simplified to (fma (/ 1 2) (log (* 2 PI)) (/ (log n) 2))
* * * * [misc]progress:  [ 141 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (log (exp (pow (* (* n PI) 2) (/ 1 2)))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (pow (* (* n PI) 2) (/ 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 (exp (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (exp (pow (* (* PI n) 2) (/ 1 2)))
* * * * [misc]progress:  [ 142 / 157 ] simplifiying candidate #<alt-delta (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)))>
* [enter]simplify:  Simplifying (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2))))
* * [misc]simplify:  iters left: 6 (10 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 (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2))))
* [enter]simplify:  Simplifying (cbrt (pow (* (* n PI) 2) (/ 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 (cbrt (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (cbrt (pow (* (* PI n) 2) (/ 1 2)))
* * * * [misc]progress:  [ 143 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (cbrt (* (* (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ 1 2)))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (10 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 (pow (pow (* (* PI n) 2) (/ 1 2)) 3)
* [exit]simplify:  Simplified to (pow (pow (* (* PI n) 2) (/ 1 2)) 3)
* * * * [misc]progress:  [ 144 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ 1 2)))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2)))
* [enter]simplify:  Simplifying (sqrt (pow (* (* n PI) 2) (/ 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 (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2)))
* * * * [misc]progress:  [ 145 / 157 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* 1 (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 146 / 157 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))
* * * * [misc]progress:  [ 147 / 157 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))
* * * * [misc]progress:  [ 148 / 157 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))
* * * * [misc]progress:  [ 149 / 157 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))
* * * * [misc]progress:  [ 150 / 157 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))
* * * * [misc]progress:  [ 151 / 157 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))
* * * * [misc]progress:  [ 152 / 157 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* k (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2)))) (- (+ (* +nan.0 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))) (- (+ (* +nan.0 (* (pow k 2) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))) (- (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))))))))))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* k (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2)))) (- (+ (* +nan.0 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))) (- (+ (* +nan.0 (* (pow k 2) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))) (- (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))))))))))))
* * * * [misc]progress:  [ 153 / 157 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* k (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 3) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n)))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* k (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 3) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))))))))
* * * * [misc]progress:  [ 154 / 157 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* k (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* k (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n))))))))))))))
* * * * [misc]progress:  [ 155 / 157 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (67 enodes)
* * [misc]simplify:  iters left: 3 (118 enodes)
* * [misc]simplify:  iters left: 2 (195 enodes)
* * [misc]simplify:  iters left: 1 (308 enodes)
* [exit]simplify:  Simplified to (/ (* (sqrt (* PI 2)) (/ (sqrt n) (sqrt k))) (pow (* n (* PI 2)) (/ k 2)))
* * * * [misc]progress:  [ 156 / 157 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (65 enodes)
* * [misc]simplify:  iters left: 3 (108 enodes)
* * [misc]simplify:  iters left: 2 (236 enodes)
* [exit]simplify:  Simplified to (/ (* (sqrt (* PI 2)) (/ (sqrt n) (sqrt k))) (pow (* (* PI 2) n) (/ k 2)))
* * * * [misc]progress:  [ 157 / 157 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (21 enodes)
* * [misc]simplify:  iters left: 5 (39 enodes)
* * [misc]simplify:  iters left: 4 (64 enodes)
* * [misc]simplify:  iters left: 3 (114 enodes)
* * [misc]simplify:  iters left: 2 (276 enodes)
* [exit]simplify:  Simplified to (/ (/ (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
"ALT DATA: "{"all-alts":["#<alt-delta (λ (k n) (cbrt (* (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (* (sqrt k) k)) (* (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))))))>","#<alt-delta (λ (k n) (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>","#<alt-delta (λ (k n) (* (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (sqrt k)))) (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))) (cbrt (sqrt k)))))>","#<alt-delta (λ (k n) (/ (* (* (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (sqrt k)))>","#<alt-delta (λ (k n) (* (* (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))) (/ (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt k))))>","#<alt-delta (λ (k n) (* (sqrt (/ (pow (* (* n PI) 2) (/ (- 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(k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))"}* * * * [misc]pick:  Picked  #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 4 ] rewriting at (2 1 1 1 1)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2 1 2 1 1)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2 1 1 1 1 2 1)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2 1 1 1 1 1 1)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 4 ] generating series at (2 1 1 1 1)
* [misc]approximate:  Taking taylor expansion of (* (sqrt (* n PI)) (sqrt (* n PI))) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (* n PI)) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (* (sqrt (* n PI)) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (sqrt (* 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 (* 0 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 (* +nan.0 PI)) (* (* +nan.0 PI) 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 (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
* [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 (* +nan.0 (pow PI 2))) (+ (* (* +nan.0 PI) (* +nan.0 PI)) (* (* +nan.0 (pow PI 2)) 0))) into (- (* +nan.0 (pow PI 2)))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (pow PI 2))) into (- (* +nan.0 (pow PI 2)))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 2)))))) (* 2 0)) into (* +nan.0 (pow PI 3))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 2)))))) (* 2 0)) into (* +nan.0 (pow PI 3))
* [misc]backup-simplify:  Simplify (+ (* 0 (* +nan.0 (pow PI 3))) (+ (* (* +nan.0 PI) (* +nan.0 (pow PI 2))) (+ (* (* +nan.0 (pow PI 2)) (* +nan.0 PI)) (* (* +nan.0 (pow PI 3)) 0)))) into (- (* +nan.0 (pow PI 3)))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (pow PI 3))) into (- (* +nan.0 (pow PI 3)))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow (* +nan.0 (pow PI 2)) 2) (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 3)))))) (* 2 0)) into (* +nan.0 (pow PI 4))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow (* +nan.0 (pow PI 2)) 2) (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 3)))))) (* 2 0)) into (* +nan.0 (pow PI 4))
* [misc]backup-simplify:  Simplify (+ (* 0 (* +nan.0 (pow PI 4))) (+ (* (* +nan.0 PI) (* +nan.0 (pow PI 3))) (+ (* (* +nan.0 (pow PI 2)) (* +nan.0 (pow PI 2))) (+ (* (* +nan.0 (pow PI 3)) (* +nan.0 PI)) (* (* +nan.0 (pow PI 4)) 0))))) into (- (* +nan.0 (pow PI 4)))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (pow PI 4))) into (- (* +nan.0 (pow PI 4)))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (pow PI 4))) (pow n 4)) (+ (* (- (* +nan.0 (pow PI 3))) (pow n 3)) (* (- (* +nan.0 (pow PI 2))) (pow n 2)))) into (- (+ (* +nan.0 (* (pow n 4) (pow PI 4))) (- (+ (* +nan.0 (* (pow n 3) (pow PI 3))) (- (* +nan.0 (* (pow n 2) (pow PI 2))))))))
* [misc]approximate:  Taking taylor expansion of (* (sqrt (* (/ 1 n) PI)) (sqrt (* (/ 1 n) PI))) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (* (/ 1 n) PI)) (sqrt (* (/ 1 n) PI))) 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 (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (sqrt (* (/ 1 n) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (* (sqrt (* (/ 1 n) PI)) (sqrt (* (/ 1 n) PI))) 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 (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (sqrt (* (/ 1 n) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 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 (* 0 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 (* +nan.0 PI)) (* (* +nan.0 PI) 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 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 (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 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 (* +nan.0 (pow PI 2))) (+ (* (* +nan.0 PI) (* +nan.0 PI)) (* (* +nan.0 (pow PI 2)) 0))) into (- (* +nan.0 (pow PI 2)))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (pow PI 2))) into (- (* +nan.0 (pow PI 2)))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 2)))))) (* 2 0)) into (* +nan.0 (pow PI 3))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 2)))))) (* 2 0)) into (* +nan.0 (pow PI 3))
* [misc]backup-simplify:  Simplify (+ (* 0 (* +nan.0 (pow PI 3))) (+ (* (* +nan.0 PI) (* +nan.0 (pow PI 2))) (+ (* (* +nan.0 (pow PI 2)) (* +nan.0 PI)) (* (* +nan.0 (pow PI 3)) 0)))) into (- (* +nan.0 (pow PI 3)))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (pow PI 3))) into (- (* +nan.0 (pow PI 3)))
* [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 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow (* +nan.0 (pow PI 2)) 2) (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 3)))))) (* 2 0)) into (* +nan.0 (pow PI 4))
* [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 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow (* +nan.0 (pow PI 2)) 2) (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 3)))))) (* 2 0)) into (* +nan.0 (pow PI 4))
* [misc]backup-simplify:  Simplify (+ (* 0 (* +nan.0 (pow PI 4))) (+ (* (* +nan.0 PI) (* +nan.0 (pow PI 3))) (+ (* (* +nan.0 (pow PI 2)) (* +nan.0 (pow PI 2))) (+ (* (* +nan.0 (pow PI 3)) (* +nan.0 PI)) (* (* +nan.0 (pow PI 4)) 0))))) into (- (* +nan.0 (pow PI 4)))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (pow PI 4))) into (- (* +nan.0 (pow PI 4)))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (pow PI 4))) (pow (/ 1 n) 2)) (+ (* (- (* +nan.0 (pow PI 3))) (/ 1 n)) (- (* +nan.0 (pow PI 2))))) into (- (+ (* +nan.0 (pow PI 2)) (- (+ (* +nan.0 (/ (pow PI 4) (pow n 2))) (- (* +nan.0 (/ (pow PI 3) n)))))))
* [misc]approximate:  Taking taylor expansion of (* (sqrt (* (/ 1 (- n)) PI)) (sqrt (* (/ 1 (- n)) PI))) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (* (/ 1 (- n)) PI)) (sqrt (* (/ 1 (- n)) PI))) 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 (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 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 (- n)) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify 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 (- n)) PI)) (sqrt (* (/ 1 (- n)) PI))) 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 (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 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 (- n)) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 PI) into (* -1 PI)
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ (* -1 PI) (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]backup-simplify:  Simplify (* 0 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 (* +nan.0 PI)) (* (* +nan.0 PI) 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 (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -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) 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 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 (* +nan.0 (pow PI 2))) (+ (* (* +nan.0 PI) (* +nan.0 PI)) (* (* +nan.0 (pow PI 2)) 0))) into (- (* +nan.0 (pow PI 2)))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (pow PI 2))) into (- (* +nan.0 (pow PI 2)))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [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 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 2)))))) (* 2 0)) into (* +nan.0 (pow PI 3))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [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 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 2)))))) (* 2 0)) into (* +nan.0 (pow PI 3))
* [misc]backup-simplify:  Simplify (+ (* 0 (* +nan.0 (pow PI 3))) (+ (* (* +nan.0 PI) (* +nan.0 (pow PI 2))) (+ (* (* +nan.0 (pow PI 2)) (* +nan.0 PI)) (* (* +nan.0 (pow PI 3)) 0)))) into (- (* +nan.0 (pow PI 3)))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (pow PI 3))) into (- (* +nan.0 (pow PI 3)))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [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 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow (* +nan.0 (pow PI 2)) 2) (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 3)))))) (* 2 0)) into (* +nan.0 (pow PI 4))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [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 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow (* +nan.0 (pow PI 2)) 2) (+ (* 2 (* (* +nan.0 PI) (* +nan.0 (pow PI 3)))))) (* 2 0)) into (* +nan.0 (pow PI 4))
* [misc]backup-simplify:  Simplify (+ (* 0 (* +nan.0 (pow PI 4))) (+ (* (* +nan.0 PI) (* +nan.0 (pow PI 3))) (+ (* (* +nan.0 (pow PI 2)) (* +nan.0 (pow PI 2))) (+ (* (* +nan.0 (pow PI 3)) (* +nan.0 PI)) (* (* +nan.0 (pow PI 4)) 0))))) into (- (* +nan.0 (pow PI 4)))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (pow PI 4))) into (- (* +nan.0 (pow PI 4)))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (pow PI 4))) (pow (/ 1 (- n)) 2)) (+ (* (- (* +nan.0 (pow PI 3))) (/ 1 (- n))) (- (* +nan.0 (pow PI 2))))) into (- (+ (* +nan.0 (pow PI 2)) (- (+ (* +nan.0 (/ (pow PI 4) (pow n 2))) (- (* +nan.0 (/ (pow PI 3) n)))))))
* * * * [misc]progress:  [ 2 / 4 ] generating series at (2 1 2 1 1)
* [misc]approximate:  Taking taylor expansion of (* n PI) in (n) around 0
* [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]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 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 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 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 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 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 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* PI n) into (* n PI)
* [misc]approximate:  Taking taylor expansion of (* (/ 1 n) PI) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 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 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 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 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 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 PI))))))) 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 (* (/ 1 (- n)) PI) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 PI) 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 (+ (* -1 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 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 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 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 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 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI)
* * * * [misc]progress:  [ 3 / 4 ] generating series at (2 1 1 1 1 2 1)
* [misc]approximate:  Taking taylor expansion of (* n PI) in (n) around 0
* [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]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 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 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 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 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 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 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* PI n) into (* n PI)
* [misc]approximate:  Taking taylor expansion of (* (/ 1 n) PI) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 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 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 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 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 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 PI))))))) 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 (* (/ 1 (- n)) PI) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 PI) 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 (+ (* -1 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 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 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 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 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 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI)
* * * * [misc]progress:  [ 4 / 4 ] generating series at (2 1 1 1 1 1 1)
* [misc]approximate:  Taking taylor expansion of (* n PI) in (n) around 0
* [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]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 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 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 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 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 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 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* PI n) into (* n PI)
* [misc]approximate:  Taking taylor expansion of (* (/ 1 n) PI) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 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 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 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 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 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 PI))))))) 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 (* (/ 1 (- n)) PI) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 PI) 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 (+ (* -1 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 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 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 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 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 PI))))))) 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 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (log1p (expm1 (* (sqrt (* n PI)) (sqrt (* n PI))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (* (sqrt (* n PI)) (sqrt (* n PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* [exit]simplify:  Simplified to (expm1 (* PI n))
* [exit]simplify:  Simplified to (expm1 (* PI n))
* * * * [misc]progress:  [ 2 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (expm1 (log1p (* (sqrt (* n PI)) (sqrt (* n PI))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (* (sqrt (* n PI)) (sqrt (* n PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* [exit]simplify:  Simplified to (log1p (* PI n))
* [exit]simplify:  Simplified to (log1p (* PI n))
* * * * [misc]progress:  [ 3 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (pow (* n PI) (+ 1/2 1/2)) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (+ 1/2 1/2)
* * [misc]simplify:  iters left: 2 (2 enodes)
* [exit]simplify:  Simplified to (+ 1/2 1/2)
* [exit]simplify:  Simplified to (+ 1/2 1/2)
* * * * [misc]progress:  [ 4 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (pow (sqrt (* n PI)) (+ 1 1)) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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 1)
* [exit]simplify:  Simplified to (+ 1 1)
* * * * [misc]progress:  [ 5 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (pow (* (* n PI) (* n PI)) 1/2) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n PI) (* n PI))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* * [misc]simplify:  iters left: 2 (16 enodes)
* * [misc]simplify:  iters left: 1 (20 enodes)
* [exit]simplify:  Simplified to (* (* PI n) (* PI n))
* [exit]simplify:  Simplified to (* (* PI n) (* PI n))
* * * * [misc]progress:  [ 6 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (pow (* (sqrt (* n PI)) (sqrt (* n PI))) 1) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (sqrt (* n PI)) (sqrt (* n PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (6 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* [exit]simplify:  Simplified to (* PI n)
* [exit]simplify:  Simplified to (* PI n)
* * * * [misc]progress:  [ 7 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (pow (sqrt (* n PI)) 2) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 8 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (pow (sqrt (* n PI)) (+ 1 1)) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 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 1)
* [exit]simplify:  Simplified to (+ 1 1)
* * * * [misc]progress:  [ 9 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (pow (* (sqrt (* n PI)) (sqrt (* n PI))) 1) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 10 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (exp (+ (log (sqrt (* n PI))) (log (sqrt (* n PI))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (+ (log (sqrt (* n PI))) (log (sqrt (* n PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (7 enodes)
* [exit]simplify:  Simplified to (+ (log (sqrt (* PI n))) (log (sqrt (* PI n))))
* [exit]simplify:  Simplified to (+ (log (sqrt (* PI n))) (log (sqrt (* PI n))))
* * * * [misc]progress:  [ 11 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (exp (log (* (sqrt (* n PI)) (sqrt (* n PI))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (* (sqrt (* n PI)) (sqrt (* n PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* [exit]simplify:  Simplified to (log (* PI n))
* [exit]simplify:  Simplified to (log (* PI n))
* * * * [misc]progress:  [ 12 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (log (exp (* (sqrt (* n PI)) (sqrt (* n PI))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* (sqrt (* n PI)) (sqrt (* n PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* [exit]simplify:  Simplified to (exp (* PI n))
* [exit]simplify:  Simplified to (exp (* PI n))
* * * * [misc]progress:  [ 13 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (cbrt (* (* (* (sqrt (* n PI)) (sqrt (* n PI))) (sqrt (* n PI))) (* (* (sqrt (* n PI)) (sqrt (* n PI))) (sqrt (* n PI))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (* (sqrt (* n PI)) (sqrt (* n PI))) (sqrt (* n PI))) (* (* (sqrt (* n PI)) (sqrt (* n PI))) (sqrt (* n PI))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (69 enodes)
* * [misc]simplify:  iters left: 2 (153 enodes)
* * [misc]simplify:  iters left: 1 (228 enodes)
* [exit]simplify:  Simplified to (pow (* PI n) 3)
* [exit]simplify:  Simplified to (pow (* PI n) 3)
* * * * [misc]progress:  [ 14 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (* (cbrt (* (sqrt (* n PI)) (sqrt (* n PI)))) (cbrt (* (sqrt (* n PI)) (sqrt (* n PI))))) (cbrt (* (sqrt (* n PI)) (sqrt (* n PI))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (* (sqrt (* n PI)) (sqrt (* n PI)))) (cbrt (* (sqrt (* n PI)) (sqrt (* n PI)))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (9 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* PI n)) (cbrt (* PI n)))
* [exit]simplify:  Simplified to (* (cbrt (* PI n)) (cbrt (* PI n)))
* [enter]simplify:  Simplifying (cbrt (* (sqrt (* n PI)) (sqrt (* n PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* [exit]simplify:  Simplified to (cbrt (* PI n))
* [exit]simplify:  Simplified to (cbrt (* PI n))
* * * * [misc]progress:  [ 15 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (cbrt (* (* (* (sqrt (* n PI)) (sqrt (* n PI))) (* (sqrt (* n PI)) (sqrt (* n PI)))) (* (sqrt (* n PI)) (sqrt (* n PI))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (* (sqrt (* n PI)) (sqrt (* n PI))) (* (sqrt (* n PI)) (sqrt (* n PI)))) (* (sqrt (* n PI)) (sqrt (* n PI))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (107 enodes)
* * [misc]simplify:  iters left: 2 (237 enodes)
* * [misc]simplify:  iters left: 1 (336 enodes)
* [exit]simplify:  Simplified to (pow (* PI n) 3)
* [exit]simplify:  Simplified to (pow (* PI n) 3)
* * * * [misc]progress:  [ 16 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (sqrt (* (* n PI) (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n PI) (* n PI))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* * [misc]simplify:  iters left: 2 (16 enodes)
* * [misc]simplify:  iters left: 1 (20 enodes)
* [exit]simplify:  Simplified to (* (* PI n) (* PI n))
* [exit]simplify:  Simplified to (* (* PI n) (* PI n))
* * * * [misc]progress:  [ 17 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* (sqrt (* n PI)) (sqrt (* n PI)))) (sqrt (* (sqrt (* n PI)) (sqrt (* n PI))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (* (sqrt (* n PI)) (sqrt (* n PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (9 enodes)
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [enter]simplify:  Simplifying (sqrt (* (sqrt (* n PI)) (sqrt (* n PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (9 enodes)
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [exit]simplify:  Simplified to (sqrt (* PI n))
* * * * [misc]progress:  [ 18 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 19 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* 1 (* (sqrt (* n PI)) (sqrt (* n PI)))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 20 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (* (sqrt (* n PI)) (* (cbrt (sqrt (* n PI))) (cbrt (sqrt (* n PI))))) (cbrt (sqrt (* n PI)))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (sqrt (* n PI)) (* (cbrt (sqrt (* n PI))) (cbrt (sqrt (* n PI)))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* [exit]simplify:  Simplified to (* (cbrt (sqrt (* PI n))) (* (cbrt (sqrt (* PI n))) (sqrt (* PI n))))
* [exit]simplify:  Simplified to (* (cbrt (sqrt (* PI n))) (* (cbrt (sqrt (* PI n))) (sqrt (* PI n))))
* * * * [misc]progress:  [ 21 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (* (sqrt (* n PI)) (sqrt n)) (sqrt PI)) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (sqrt (* n PI)) (sqrt n))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* [exit]simplify:  Simplified to (* (sqrt n) (sqrt (* PI n)))
* [exit]simplify:  Simplified to (* (sqrt n) (sqrt (* PI n)))
* * * * [misc]progress:  [ 22 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (* (sqrt (* n PI)) (sqrt (sqrt (* n PI)))) (sqrt (sqrt (* n PI)))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (sqrt (* n PI)) (sqrt (sqrt (* n PI))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (8 enodes)
* [exit]simplify:  Simplified to (* (sqrt (sqrt (* PI n))) (sqrt (* PI n)))
* [exit]simplify:  Simplified to (* (sqrt (sqrt (* PI n))) (sqrt (* PI n)))
* * * * [misc]progress:  [ 23 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (* (sqrt (* n PI)) 1) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (sqrt (* n PI)) 1)
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (12 enodes)
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [exit]simplify:  Simplified to (sqrt (* PI n))
* * * * [misc]progress:  [ 24 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (* (cbrt (sqrt (* n PI))) (cbrt (sqrt (* n PI)))) (* (cbrt (sqrt (* n PI))) (sqrt (* n PI)))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (sqrt (* n PI))) (sqrt (* n PI)))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (8 enodes)
* [exit]simplify:  Simplified to (* (cbrt (sqrt (* PI n))) (sqrt (* PI n)))
* [exit]simplify:  Simplified to (* (cbrt (sqrt (* PI n))) (sqrt (* PI n)))
* * * * [misc]progress:  [ 25 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt n) (* (sqrt PI) (sqrt (* n PI)))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (sqrt PI) (sqrt (* n PI)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* [exit]simplify:  Simplified to (* (sqrt (* PI n)) (sqrt PI))
* [exit]simplify:  Simplified to (* (sqrt (* PI n)) (sqrt PI))
* * * * [misc]progress:  [ 26 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (sqrt (* n PI))) (* (sqrt (sqrt (* n PI))) (sqrt (* n PI)))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (sqrt (sqrt (* n PI))) (sqrt (* n PI)))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (8 enodes)
* [exit]simplify:  Simplified to (* (sqrt (sqrt (* PI n))) (sqrt (* PI n)))
* [exit]simplify:  Simplified to (* (sqrt (sqrt (* PI n))) (sqrt (* PI n)))
* * * * [misc]progress:  [ 27 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* 1 (* (sqrt (* n PI)) (sqrt (* n PI)))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (sqrt (* n PI)) (sqrt (* n PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (6 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* [exit]simplify:  Simplified to (* PI n)
* [exit]simplify:  Simplified to (* PI n)
* * * * [misc]progress:  [ 28 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 29 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (log1p (expm1 (* n PI))) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (expm1 (* PI n))
* [exit]simplify:  Simplified to (expm1 (* PI n))
* * * * [misc]progress:  [ 30 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (expm1 (log1p (* n PI))) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (log1p (* PI n))
* [exit]simplify:  Simplified to (log1p (* PI n))
* * * * [misc]progress:  [ 31 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (pow (* n PI) 1) 2) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 32 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (exp (log (* n PI))) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (8 enodes)
* * [misc]simplify:  iters left: 1 (9 enodes)
* [exit]simplify:  Simplified to (log (* PI n))
* [exit]simplify:  Simplified to (log (* PI n))
* * * * [misc]progress:  [ 33 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (log (exp (* n PI))) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (exp (* PI n))
* [exit]simplify:  Simplified to (exp (* PI n))
* * * * [misc]progress:  [ 34 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI))) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (* n PI)) (cbrt (* n PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (6 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* PI n)) (cbrt (* PI n)))
* [exit]simplify:  Simplified to (* (cbrt (* PI n)) (cbrt (* PI n)))
* [enter]simplify:  Simplifying (cbrt (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (cbrt (* PI n))
* [exit]simplify:  Simplified to (cbrt (* PI n))
* * * * [misc]progress:  [ 35 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (cbrt (* (* (* n PI) (* n PI)) (* n PI))) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (* n PI) (* n PI)) (* n PI))
* * [misc]simplify:  iters left: 6 (5 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (55 enodes)
* * [misc]simplify:  iters left: 2 (86 enodes)
* * [misc]simplify:  iters left: 1 (89 enodes)
* [exit]simplify:  Simplified to (pow (* PI n) 3)
* [exit]simplify:  Simplified to (pow (* PI n) 3)
* * * * [misc]progress:  [ 36 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [enter]simplify:  Simplifying (sqrt (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [exit]simplify:  Simplified to (sqrt (* PI n))
* * * * [misc]progress:  [ 37 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* 1 (* n PI)) 2) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 38 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 39 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (log1p (expm1 (* n PI))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (expm1 (* PI n))
* [exit]simplify:  Simplified to (expm1 (* PI n))
* * * * [misc]progress:  [ 40 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (expm1 (log1p (* n PI))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (log1p (* PI n))
* [exit]simplify:  Simplified to (log1p (* PI n))
* * * * [misc]progress:  [ 41 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (pow (* n PI) 1))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 42 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (exp (log (* n PI))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (8 enodes)
* * [misc]simplify:  iters left: 1 (9 enodes)
* [exit]simplify:  Simplified to (log (* PI n))
* [exit]simplify:  Simplified to (log (* PI n))
* * * * [misc]progress:  [ 43 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (log (exp (* n PI))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (exp (* PI n))
* [exit]simplify:  Simplified to (exp (* PI n))
* * * * [misc]progress:  [ 44 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (* n PI)) (cbrt (* n PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (6 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* PI n)) (cbrt (* PI n)))
* [exit]simplify:  Simplified to (* (cbrt (* PI n)) (cbrt (* PI n)))
* [enter]simplify:  Simplifying (cbrt (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (cbrt (* PI n))
* [exit]simplify:  Simplified to (cbrt (* PI n))
* * * * [misc]progress:  [ 45 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (cbrt (* (* (* n PI) (* n PI)) (* n PI))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (* n PI) (* n PI)) (* n PI))
* * [misc]simplify:  iters left: 6 (5 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (55 enodes)
* * [misc]simplify:  iters left: 2 (86 enodes)
* * [misc]simplify:  iters left: 1 (89 enodes)
* [exit]simplify:  Simplified to (pow (* PI n) 3)
* [exit]simplify:  Simplified to (pow (* PI n) 3)
* * * * [misc]progress:  [ 46 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* (sqrt (* n PI)) (sqrt (* n PI))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [enter]simplify:  Simplifying (sqrt (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [exit]simplify:  Simplified to (sqrt (* PI n))
* * * * [misc]progress:  [ 47 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* 1 (* n PI)))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 48 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* PI n))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 49 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (log1p (expm1 (* n PI)))) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (expm1 (* PI n))
* [exit]simplify:  Simplified to (expm1 (* PI n))
* * * * [misc]progress:  [ 50 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (expm1 (log1p (* n PI)))) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (log1p (* PI n))
* [exit]simplify:  Simplified to (log1p (* PI n))
* * * * [misc]progress:  [ 51 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (pow (* n PI) 1)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 52 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (exp (log (* n PI)))) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (8 enodes)
* * [misc]simplify:  iters left: 1 (9 enodes)
* [exit]simplify:  Simplified to (log (* PI n))
* [exit]simplify:  Simplified to (log (* PI n))
* * * * [misc]progress:  [ 53 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (log (exp (* n PI)))) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (exp (* PI n))
* [exit]simplify:  Simplified to (exp (* PI n))
* * * * [misc]progress:  [ 54 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI)))) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (* n PI)) (cbrt (* n PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (6 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* PI n)) (cbrt (* PI n)))
* [exit]simplify:  Simplified to (* (cbrt (* PI n)) (cbrt (* PI n)))
* [enter]simplify:  Simplifying (cbrt (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (cbrt (* PI n))
* [exit]simplify:  Simplified to (cbrt (* PI n))
* * * * [misc]progress:  [ 55 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (cbrt (* (* (* n PI) (* n PI)) (* n PI)))) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (* n PI) (* n PI)) (* n PI))
* * [misc]simplify:  iters left: 6 (5 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (55 enodes)
* * [misc]simplify:  iters left: 2 (86 enodes)
* * [misc]simplify:  iters left: 1 (89 enodes)
* [exit]simplify:  Simplified to (pow (* PI n) 3)
* [exit]simplify:  Simplified to (pow (* PI n) 3)
* * * * [misc]progress:  [ 56 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* (sqrt (* n PI)) (sqrt (* n PI)))) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [enter]simplify:  Simplifying (sqrt (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [exit]simplify:  Simplified to (sqrt (* PI n))
* * * * [misc]progress:  [ 57 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* 1 (* n PI))) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 58 / 70 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* PI n)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 59 / 70 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* (- (+ (* +nan.0 (* (pow n 4) (pow PI 4))) (- (+ (* +nan.0 (* (pow n 3) (pow PI 3))) (- (* +nan.0 (* (pow n 2) (pow PI 2)))))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* (- (+ (* +nan.0 (* (pow n 4) (pow PI 4))) (- (+ (* +nan.0 (* (pow n 3) (pow PI 3))) (- (* +nan.0 (* (pow n 2) (pow PI 2)))))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))
* * * * [misc]progress:  [ 60 / 70 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* (- (+ (* +nan.0 (pow PI 2)) (- (+ (* +nan.0 (/ (pow PI 4) (pow n 2))) (- (* +nan.0 (/ (pow PI 3) n))))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* (- (+ (* +nan.0 (pow PI 2)) (- (+ (* +nan.0 (/ (pow PI 4) (pow n 2))) (- (* +nan.0 (/ (pow PI 3) n))))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))
* * * * [misc]progress:  [ 61 / 70 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* (- (+ (* +nan.0 (pow PI 2)) (- (+ (* +nan.0 (/ (pow PI 4) (pow n 2))) (- (* +nan.0 (/ (pow PI 3) n))))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* (- (+ (* +nan.0 (pow PI 2)) (- (+ (* +nan.0 (/ (pow PI 4) (pow n 2))) (- (* +nan.0 (/ (pow PI 3) n))))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))
* * * * [misc]progress:  [ 62 / 70 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* 2 PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2))))
* * * * [misc]progress:  [ 63 / 70 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* 2 PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2))))
* * * * [misc]progress:  [ 64 / 70 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* 2 PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2))))
* * * * [misc]progress:  [ 65 / 70 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* 2 PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2))))
* * * * [misc]progress:  [ 66 / 70 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* 2 PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2))))
* * * * [misc]progress:  [ 67 / 70 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* 2 PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2))))
* * * * [misc]progress:  [ 68 / 70 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* 2 PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2))))
* * * * [misc]progress:  [ 69 / 70 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* 2 PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2))))
* * * * [misc]progress:  [ 70 / 70 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* 2 PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2))))
* * * [misc]progress:  adding candidates to table
* * [misc]progress:  iteration 4 / 4
* * * [misc]progress:  picking best candidate
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(k n) (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))"}* * * * [misc]pick:  Picked  #<alt-delta (λ (k n) (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 4 ] rewriting at (2 1 1)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2 1)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2 1 1 1)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 4 ] generating series at (2 1 1)
* [misc]approximate:  Taking taylor expansion of (pow (* n PI) (/ (- 1 k) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* n PI) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 k) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n PI)) in k
* [misc]taylor:  Taking taylor expansion of (* n PI) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* n PI) into (* n PI)
* [misc]backup-simplify:  Simplify (log (* n PI)) into (log (* n PI))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* n PI))) into (* 1/2 (log (* n PI)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* n PI)))) into (pow (* n PI) 1/2)
* [misc]taylor:  Taking taylor expansion of (pow (* n PI) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (+ 1 (- k)) into (- 1 k)
* [misc]backup-simplify:  Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k))
* [misc]taylor:  Taking taylor expansion of (log (* n 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 (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log n) (log PI))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log PI))) into (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) into (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k))))
* [misc]taylor:  Taking taylor expansion of (pow (* n PI) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (+ 1 (- k)) into (- 1 k)
* [misc]backup-simplify:  Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k))
* [misc]taylor:  Taking taylor expansion of (log (* n 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 (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log n) (log PI))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log PI))) into (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) into (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ (log n) (log PI)) (- 1 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 PI)) (- 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (+ (log n) (log 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 PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]taylor:  Taking taylor expansion of (- 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 (+ (log n) (log PI)) into (+ (log n) (log PI))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (* (+ (log n) (log PI)) 1) into (+ (log n) (log PI))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log n) (log PI))) into (* 1/2 (+ (log n) (log PI)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log PI)))) into (exp (* 1/2 (+ (log n) (log PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log PI)))) into (exp (* 1/2 (+ (log n) (log PI))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 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 PI)) into (+ (log n) (log PI))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log PI)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log n) (log PI)) -1) (* 0 1)) into (- (+ (log n) (log PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (- (+ (log n) (log PI)))) (* 0 (+ (log n) (log PI)))) into (- (+ (* 1/2 (log n)) (* 1/2 (log PI))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log PI)))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log PI)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log PI))) (exp (* 1/2 (+ (log n) (log PI))))))
* [misc]backup-simplify:  Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log PI))) (exp (* 1/2 (+ (log n) (log PI)))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log PI))) (exp (* 1/2 (+ (log n) (log PI))))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 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 PI)) into (+ (log n) (log PI))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log n) (log PI)) 0) (+ (* 0 -1) (* 0 1))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log n) (log PI)))) (* 0 (+ (log n) (log PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log PI)))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 1/8 (pow (log PI) 2)) (+ (* 1/8 (pow (log n) 2)) (* 1/4 (* (log n) (log PI))))) (exp (* 1/2 (+ (log n) (log PI)))))
* [misc]backup-simplify:  Simplify (* (+ (* 1/8 (pow (log PI) 2)) (+ (* 1/8 (pow (log n) 2)) (* 1/4 (* (log n) (log PI))))) (exp (* 1/2 (+ (log n) (log PI))))) into (* (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log n) (log PI))))) (exp (* 1/2 (+ (log n) (log PI)))))
* [misc]backup-simplify:  Simplify (+ (* (* (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log n) (log PI))))) (exp (* 1/2 (+ (log n) (log PI))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log PI))) (exp (* 1/2 (+ (log n) (log PI)))))) (* k 1)) (exp (* 1/2 (+ (log n) (log PI)))))) into (- (+ (* 1/8 (* (pow k 2) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log PI))))))) (+ (* 1/4 (* (pow k 2) (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (+ (exp (* 1/2 (+ (log n) (log PI)))) (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2))))))) (+ (* 1/2 (* k (* (log n) (exp (* 1/2 (+ (log n) (log PI))))))) (* 1/2 (* k (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))))
* [misc]approximate:  Taking taylor expansion of (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (/ 1 n) into (/ 1 n)
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* (/ 1 n) PI) into (/ PI n)
* [misc]backup-simplify:  Simplify (log (/ PI n)) into (log (/ PI n))
* [misc]backup-simplify:  Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ PI n)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log PI) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log PI) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log 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 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 PI) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]taylor:  Taking taylor expansion of (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 PI) (- (log n))) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (* -1 (- (log PI) (log n))) into (* -1 (- (log PI) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* -1 (- (log PI) (log n)))) into (* -1/2 (- (log PI) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log PI) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 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 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log PI) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 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 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log PI) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 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 PI) (log (/ 1 n)))))) into (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (- 1 k))))
* [misc]approximate:  Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- -1) into 1
* [misc]backup-simplify:  Simplify (+ 0 1) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in k
* [misc]taylor:  Taking taylor expansion of (- n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (/ 1 (- n)) into (/ -1 n)
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* (/ -1 n) PI) into (* -1 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -1 (/ PI n)))) into (* 1/2 (log (* -1 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* -1 (/ PI n))))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ -1 k)) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ (/ 1 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)) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 PI) into (* -1 PI)
* [misc]backup-simplify:  Simplify (log (* -1 PI)) into (log (* -1 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -1 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ -1 k)) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ (/ 1 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)) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 PI) into (* -1 PI)
* [misc]backup-simplify:  Simplify (log (* -1 PI)) into (log (* -1 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -1 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 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 (* -1 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 (* -1 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* -1 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* -1 PI) in k
* [misc]taylor:  Taking taylor expansion of -1 in k
* [misc]backup-simplify:  Simplify -1 into -1
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 PI) into (* -1 PI)
* [misc]backup-simplify:  Simplify (log (* -1 PI)) into (log (* -1 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 (* -1 PI)) (- (log n))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1 (- (log (* -1 PI)) (log n))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -1 PI)) (log n))) into (* 1/2 (- (log (* -1 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 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 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -1 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 (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -1 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 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 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -1 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 (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 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 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -1 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -1 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 (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 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 (* -1 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k))))
* * * * [misc]progress:  [ 2 / 4 ] generating series at (2 1)
* [misc]approximate:  Taking taylor expansion of (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* n PI) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 k) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n PI)) in k
* [misc]taylor:  Taking taylor expansion of (* n PI) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* n PI) into (* n PI)
* [misc]backup-simplify:  Simplify (log (* n PI)) into (log (* n PI))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* n PI))) into (* 1/2 (log (* n PI)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* n PI)))) into (pow (* n PI) 1/2)
* [misc]taylor:  Taking taylor expansion of (pow 2 (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log 2)) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 k) in k
* [misc]taylor:  Taking taylor expansion of 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 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2)
* [misc]taylor:  Taking taylor expansion of (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* n PI) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (+ 1 (- k)) into (- 1 k)
* [misc]backup-simplify:  Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k))
* [misc]taylor:  Taking taylor expansion of (log (* n 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 (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log n) (log PI))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log PI))) into (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) into (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k))))
* [misc]taylor:  Taking taylor expansion of (pow 2 (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 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 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (log 2)) into (* 1/2 (* (log 2) (- 1 k)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (log 2) (- 1 k)))) into (exp (* 1/2 (* (log 2) (- 1 k))))
* [misc]taylor:  Taking taylor expansion of (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* n PI) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (+ 1 (- k)) into (- 1 k)
* [misc]backup-simplify:  Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k))
* [misc]taylor:  Taking taylor expansion of (log (* n 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 (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log n) (log PI))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log PI))) into (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) into (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k))))
* [misc]taylor:  Taking taylor expansion of (pow 2 (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 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 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (log 2)) into (* 1/2 (* (log 2) (- 1 k)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (log 2) (- 1 k)))) into (exp (* 1/2 (* (log 2) (- 1 k))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) into (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k)))))
* [misc]taylor:  Taking taylor expansion of (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ (log n) (log PI)) (- 1 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 PI)) (- 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (+ (log n) (log 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 PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]taylor:  Taking taylor expansion of (- 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 (+ (log n) (log PI)) into (+ (log n) (log PI))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (* (+ (log n) (log PI)) 1) into (+ (log n) (log PI))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log n) (log PI))) into (* 1/2 (+ (log n) (log PI)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log PI)))) into (exp (* 1/2 (+ (log n) (log PI))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (log 2) (- 1 k)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (log 2) (- 1 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) (- 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (log 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]taylor:  Taking taylor expansion of (- 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (* (log 2) 1) into (log 2)
* [misc]backup-simplify:  Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2)
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log PI)))) (pow 2 1/2)) into (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))
* [misc]backup-simplify:  Simplify (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))) into (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (log 2))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (log 2) (- 1 k)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 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 PI)) into (+ (log n) (log PI))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log PI)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) 0) (* 0 (exp (* 1/2 (* (log 2) (- 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 (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (log 2) -1) (* 0 1)) into (- (log 2))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (- (log 2))) (* 0 (log 2))) into (- (* 1/2 (log 2)))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 1) 1)))) into (* -1/2 (* (log 2) (sqrt 2)))
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log n) (log PI)) -1) (* 0 1)) into (- (+ (log n) (log PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (- (+ (log n) (log PI)))) (* 0 (+ (log n) (log PI)))) into (- (+ (* 1/2 (log n)) (* 1/2 (log PI))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log PI)))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log PI)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log PI))) (exp (* 1/2 (+ (log n) (log PI))))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log n) (log PI)))) (* -1/2 (* (log 2) (sqrt 2)))) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log PI))) (exp (* 1/2 (+ (log n) (log PI)))))) (pow 2 1/2))) into (- (+ (* 1/2 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log n)))) (* 1/2 (* (log 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log n)))) (* 1/2 (* (log 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))))))) into (- (+ (* 1/2 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log n)))) (* 1/2 (* (log 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))))))
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 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 (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (log 2)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (log 2) (- 1 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 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 PI)) into (+ (log n) (log PI))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (log 2) (- 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 0) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ (* (log 2) 0) (+ (* 0 -1) (* 0 1))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (- (log 2))) (* 0 (log 2)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log 2) 2) (sqrt 2)))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log n) (log PI)) 0) (+ (* 0 -1) (* 0 1))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log n) (log PI)))) (* 0 (+ (log n) (log PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log PI)))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 1/8 (pow (log PI) 2)) (+ (* 1/8 (pow (log n) 2)) (* 1/4 (* (log n) (log PI))))) (exp (* 1/2 (+ (log n) (log PI)))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log n) (log PI)))) (* 1/8 (* (pow (log 2) 2) (sqrt 2)))) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log PI))) (exp (* 1/2 (+ (log n) (log PI)))))) (* -1/2 (* (log 2) (sqrt 2)))) (* (* (+ (* 1/8 (pow (log PI) 2)) (+ (* 1/8 (pow (log n) 2)) (* 1/4 (* (log n) (log PI))))) (exp (* 1/2 (+ (log n) (log PI))))) (pow 2 1/2)))) into (+ (* 1/4 (* (sqrt 2) (* (log 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (+ (* 1/8 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2)))) (+ (* 1/8 (* (pow (log 2) 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (+ (* 1/8 (* (pow (log n) 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (+ (* 1/4 (* (log n) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (* 1/4 (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (sqrt 2))))))))))
* [misc]backup-simplify:  Simplify (+ (* 1/4 (* (sqrt 2) (* (log 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (+ (* 1/8 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2)))) (+ (* 1/8 (* (pow (log 2) 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (+ (* 1/8 (* (pow (log n) 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (+ (* 1/4 (* (log n) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (* 1/4 (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (sqrt 2)))))))))) into (+ (* 1/8 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2)))) (+ (* 1/4 (* (sqrt 2) (* (log 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (+ (* 1/8 (* (pow (log 2) 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (+ (* 1/8 (* (pow (log n) 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (+ (* 1/4 (* (log n) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (* 1/4 (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (sqrt 2))))))))))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/8 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2)))) (+ (* 1/4 (* (sqrt 2) (* (log 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (+ (* 1/8 (* (pow (log 2) 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (+ (* 1/8 (* (pow (log n) 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (+ (* 1/4 (* (log n) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (* 1/4 (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (sqrt 2)))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* 1/2 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log n)))) (* 1/2 (* (log 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))))))) (* k 1)) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) into (- (+ (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log 2) 2))))) (+ (* 1/4 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log n) (log PI)))))) (+ (* 1/8 (* (pow k 2) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2))))) (+ (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))) (+ (* 1/4 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (* (sqrt 2) (log n)))))) (+ (* 1/4 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log 2) (log PI)))))) (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log n) 2))))))))))) (+ (* 1/2 (* k (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log 2))))) (+ (* 1/2 (* k (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (* 1/2 (* k (* (sqrt 2) (* (log n) (exp (* 1/2 (+ (log n) (log PI)))))))))))
* [misc]approximate:  Taking taylor expansion of (* (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) (pow 2 (/ (- 1 (/ 1 k)) 2))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (* (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) (pow 2 (/ (- 1 (/ 1 k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (/ 1 n) into (/ 1 n)
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* (/ 1 n) PI) into (/ PI n)
* [misc]backup-simplify:  Simplify (log (/ PI n)) into (log (/ PI n))
* [misc]backup-simplify:  Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ PI n)))))
* [misc]taylor:  Taking taylor expansion of (pow 2 (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 2)) 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 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (* -1/2 (log 2)) into (* -1/2 (log 2))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log 2))) into (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (* (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) (pow 2 (/ (- 1 (/ 1 k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log PI) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))
* [misc]taylor:  Taking taylor expansion of (pow 2 (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 2)) 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 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (log 2)) into (* 1/2 (* (log 2) (- 1 (/ 1 k))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) into (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (* (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) (pow 2 (/ (- 1 (/ 1 k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log PI) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))
* [misc]taylor:  Taking taylor expansion of (pow 2 (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 2)) 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 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (log 2)) into (* 1/2 (* (log 2) (- 1 (/ 1 k))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) into (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))) into (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))))
* [misc]taylor:  Taking taylor expansion of (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (log 2) (- 1 (/ 1 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) (- 1 (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (log 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]taylor:  Taking taylor expansion of (- 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]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (* (log 2) -1) into (* -1 (log 2))
* [misc]backup-simplify:  Simplify (* 1/2 (* -1 (log 2))) into (* -1/2 (log 2))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) into (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log 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 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 PI) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]taylor:  Taking taylor expansion of (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 PI) (- (log n))) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (* -1 (- (log PI) (log n))) into (* -1 (- (log PI) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* -1 (- (log PI) (log n)))) into (* -1/2 (- (log PI) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))) into (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))) into (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))))
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (log 2))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log PI) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) 0) (* 0 (exp (* 1/2 (* (log 2) (- 1 (/ 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 (* (log 2) (- 1 (/ 1 k))))) 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 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 (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (log 2)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log PI) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (log 2) (- 1 (/ 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 (+ (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log 2))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log PI) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (log 2) (- 1 (/ 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 (* (log 2) (- 1 (/ 1 (/ 1 k)))))) (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log PI) (log (/ 1 n))))))) into (* (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k)))))
* [misc]approximate:  Taking taylor expansion of (* (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) (pow 2 (/ (- 1 (/ 1 (- k))) 2))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (* (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) (pow 2 (/ (- 1 (/ 1 (- k))) 2))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- -1) into 1
* [misc]backup-simplify:  Simplify (+ 0 1) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in k
* [misc]taylor:  Taking taylor expansion of (- n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (/ 1 (- n)) into (/ -1 n)
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* (/ -1 n) PI) into (* -1 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -1 (/ PI n)))) into (* 1/2 (log (* -1 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* -1 (/ PI n))))))
* [misc]taylor:  Taking taylor expansion of (pow 2 (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 2)) 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 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log 2))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2))))
* [misc]taylor:  Taking taylor expansion of (* (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) (pow 2 (/ (- 1 (/ 1 (- k))) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ -1 k)) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ (/ 1 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)) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 PI) into (* -1 PI)
* [misc]backup-simplify:  Simplify (log (* -1 PI)) into (log (* -1 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -1 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (pow 2 (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 2)) 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 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log 2)) into (* 1/2 (* (+ (/ 1 k) 1) (log 2)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2))))
* [misc]taylor:  Taking taylor expansion of (* (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) (pow 2 (/ (- 1 (/ 1 (- k))) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ -1 k)) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ (/ 1 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)) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 PI) into (* -1 PI)
* [misc]backup-simplify:  Simplify (log (* -1 PI)) into (log (* -1 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -1 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (pow 2 (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 2)) 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 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log 2)) into (* 1/2 (* (+ (/ 1 k) 1) (log 2)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))))
* [misc]taylor:  Taking taylor expansion of (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (log 2))) 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)) 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) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (* 1 (log 2)) into (log 2)
* [misc]backup-simplify:  Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 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 (* -1 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 (* -1 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* -1 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* -1 PI) in k
* [misc]taylor:  Taking taylor expansion of -1 in k
* [misc]backup-simplify:  Simplify -1 into -1
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 PI) into (* -1 PI)
* [misc]backup-simplify:  Simplify (log (* -1 PI)) into (log (* -1 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 (* -1 PI)) (- (log n))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1 (- (log (* -1 PI)) (log n))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -1 PI)) (log n))) into (* 1/2 (- (log (* -1 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (log 2))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 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 (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -1 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 (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -1 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))))) 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 k) 1) (log 2)))) 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 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 (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (log 2)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (+ (* (/ (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 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -1 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 (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2))))))) 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 (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log 2))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (+ (* (/ (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) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [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 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -1 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -1 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 (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))))))) 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)))) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -1 PI)) (log (/ 1 (- n)))))))) into (* (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k)))))
* * * * [misc]progress:  [ 3 / 4 ] generating series at (2 1 1 1)
* [misc]approximate:  Taking taylor expansion of (* n PI) in (n) around 0
* [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]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 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 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 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 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 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 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* PI n) into (* n PI)
* [misc]approximate:  Taking taylor expansion of (* (/ 1 n) PI) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 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 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 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 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 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 PI))))))) 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 (* (/ 1 (- n)) PI) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 PI) 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 (+ (* -1 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 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 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 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 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 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI)
* * * * [misc]progress:  [ 4 / 4 ] generating series at (2)
* [misc]approximate:  Taking taylor expansion of (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* n PI) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 k) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n PI)) in k
* [misc]taylor:  Taking taylor expansion of (* n PI) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* n PI) into (* n PI)
* [misc]backup-simplify:  Simplify (log (* n PI)) into (log (* n PI))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* n PI))) into (* 1/2 (log (* n PI)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* n PI)))) into (pow (* n PI) 1/2)
* [misc]taylor:  Taking taylor expansion of (pow 2 (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log 2)) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 k) in k
* [misc]taylor:  Taking taylor expansion of 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 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log 2))) into (pow 2 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 (* n PI) 1/2) (pow 2 1/2)) into (sqrt (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (/ (sqrt (* 2 (* n PI))) +nan.0) into (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))
* [misc]taylor:  Taking taylor expansion of (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* n PI) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (+ 1 (- k)) into (- 1 k)
* [misc]backup-simplify:  Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k))
* [misc]taylor:  Taking taylor expansion of (log (* n 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 (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log n) (log PI))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log PI))) into (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) into (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k))))
* [misc]taylor:  Taking taylor expansion of (pow 2 (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 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 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (log 2)) into (* 1/2 (* (log 2) (- 1 k)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (log 2) (- 1 k)))) into (exp (* 1/2 (* (log 2) (- 1 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 PI)) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) into (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k)))))
* [misc]backup-simplify:  Simplify (/ (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) (sqrt k)) into (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))))
* [misc]taylor:  Taking taylor expansion of (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* n PI) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (+ 1 (- k)) into (- 1 k)
* [misc]backup-simplify:  Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k))
* [misc]taylor:  Taking taylor expansion of (log (* n 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 (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log n) (log PI))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log PI))) into (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) into (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k))))
* [misc]taylor:  Taking taylor expansion of (pow 2 (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 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 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (log 2)) into (* 1/2 (* (log 2) (- 1 k)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (log 2) (- 1 k)))) into (exp (* 1/2 (* (log 2) (- 1 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 PI)) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) into (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k)))))
* [misc]backup-simplify:  Simplify (/ (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) (sqrt k)) into (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))))
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k)))))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ (log n) (log PI)) (- 1 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 PI)) (- 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (+ (log n) (log 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 PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]taylor:  Taking taylor expansion of (- 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 (+ (log n) (log PI)) into (+ (log n) (log PI))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (* (+ (log n) (log PI)) 1) into (+ (log n) (log PI))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log n) (log PI))) into (* 1/2 (+ (log n) (log PI)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log PI)))) into (exp (* 1/2 (+ (log n) (log PI))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (log 2) (- 1 k)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (log 2) (- 1 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) (- 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (log 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]taylor:  Taking taylor expansion of (- 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (* (log 2) 1) into (log 2)
* [misc]backup-simplify:  Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2)
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log PI)))) (pow 2 1/2)) into (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))
* [misc]backup-simplify:  Simplify (* 0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (log 2))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (log 2) (- 1 k)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 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 PI)) into (+ (log n) (log PI))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log PI)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) 0) (* 0 (exp (* 1/2 (* (log 2) (- 1 k)))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 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) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (log 2) -1) (* 0 1)) into (- (log 2))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (- (log 2))) (* 0 (log 2))) into (- (* 1/2 (log 2)))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 1) 1)))) into (* -1/2 (* (log 2) (sqrt 2)))
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log n) (log PI)) -1) (* 0 1)) into (- (+ (log n) (log PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (- (+ (log n) (log PI)))) (* 0 (+ (log n) (log PI)))) into (- (+ (* 1/2 (log n)) (* 1/2 (log PI))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log PI)))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log PI)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log PI))) (exp (* 1/2 (+ (log n) (log PI))))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log n) (log PI)))) (* -1/2 (* (log 2) (sqrt 2)))) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log PI))) (exp (* 1/2 (+ (log n) (log PI)))))) (pow 2 1/2))) into (- (+ (* 1/2 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log n)))) (* 1/2 (* (log 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))))))
* [misc]backup-simplify:  Simplify (+ (* 0 (- (+ (* 1/2 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log n)))) (* 1/2 (* (log 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))))))) (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) into (- (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) into (- (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))))
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 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 (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (log 2)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (log 2) (- 1 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 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 PI)) into (+ (log n) (log PI))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (log 2) (- 1 k))))))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ (* (log 2) 0) (+ (* 0 -1) (* 0 1))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (- (log 2))) (* 0 (log 2)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log 2) 2) (sqrt 2)))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 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 (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log n) (log PI)) 0) (+ (* 0 -1) (* 0 1))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log n) (log PI)))) (* 0 (+ (log n) (log PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log PI)))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 1/8 (pow (log PI) 2)) (+ (* 1/8 (pow (log n) 2)) (* 1/4 (* (log n) (log PI))))) (exp (* 1/2 (+ (log n) (log PI)))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log n) (log PI)))) (* 1/8 (* (pow (log 2) 2) (sqrt 2)))) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log PI))) (exp (* 1/2 (+ (log n) (log PI)))))) (* -1/2 (* (log 2) (sqrt 2)))) (* (* (+ (* 1/8 (pow (log PI) 2)) (+ (* 1/8 (pow (log n) 2)) (* 1/4 (* (log n) (log PI))))) (exp (* 1/2 (+ (log n) (log PI))))) (pow 2 1/2)))) into (+ (* 1/4 (* (sqrt 2) (* (log 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (+ (* 1/8 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2)))) (+ (* 1/8 (* (pow (log 2) 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (+ (* 1/8 (* (pow (log n) 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (+ (* 1/4 (* (log n) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (* 1/4 (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (sqrt 2))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* 0 (+ (* 1/4 (* (sqrt 2) (* (log 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (+ (* 1/8 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2)))) (+ (* 1/8 (* (pow (log 2) 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (+ (* 1/8 (* (pow (log n) 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (+ (* 1/4 (* (log n) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (* 1/4 (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (sqrt 2))))))))))) (+ (* +nan.0 (- (+ (* 1/2 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log n)))) (* 1/2 (* (log 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))))))) (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (- (+ (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (sqrt 2)))) (- (* +nan.0 (* (log n) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (- (+ (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (sqrt 2)))) (- (* +nan.0 (* (log n) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (- (+ (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log 2)))) (- (* +nan.0 (* (log n) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))))))))))
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 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 (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log 2))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (log 2) (- 1 k)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 PI)) into (+ (log n) (log PI))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (log 2) (- 1 k)))))))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (+ (log n) (log PI)) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ (* (log 2) 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (log 2))) (* 0 (log 2))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 3) 6)) (* (/ (pow (- (* 1/2 (log 2))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log 2) 3) (sqrt 2)))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) 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 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (log n) (log PI)) 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (+ (log n) (log PI)))) (* 0 (+ (log n) (log PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log PI)))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log PI)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log PI)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/16 (* (pow (log n) 2) (log PI))) (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (log n) (pow (log PI) 2))) (* 1/48 (pow (log PI) 3))))) (exp (* 1/2 (+ (log n) (log PI))))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log n) (log PI)))) (* -1/48 (* (pow (log 2) 3) (sqrt 2)))) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log PI))) (exp (* 1/2 (+ (log n) (log PI)))))) (* 1/8 (* (pow (log 2) 2) (sqrt 2)))) (+ (* (* (+ (* 1/8 (pow (log PI) 2)) (+ (* 1/8 (pow (log n) 2)) (* 1/4 (* (log n) (log PI))))) (exp (* 1/2 (+ (log n) (log PI))))) (* -1/2 (* (log 2) (sqrt 2)))) (* (* -1 (* (+ (* 1/16 (* (pow (log n) 2) (log PI))) (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (log n) (pow (log PI) 2))) (* 1/48 (pow (log PI) 3))))) (exp (* 1/2 (+ (log n) (log PI)))))) (pow 2 1/2))))) into (- (+ (* 1/8 (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (* (sqrt 2) (log PI)))))) (+ (* 1/16 (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (pow (log 2) 2) (sqrt 2))))) (+ (* 1/16 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (pow (log n) 2) (log PI))))) (+ (* 1/48 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 3)))) (+ (* 1/16 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log n) (pow (log PI) 2))))) (+ (* 1/48 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log n) 3)))) (+ (* 1/48 (* (pow (log 2) 3) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (+ (* 1/16 (* (pow (log n) 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (sqrt 2))))) (+ (* 1/16 (* (log 2) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2))))) (* 1/16 (* (sqrt 2) (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))))))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* 0 (- (+ (* 1/8 (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (* (sqrt 2) (log PI)))))) (+ (* 1/16 (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (pow (log 2) 2) (sqrt 2))))) (+ (* 1/16 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (pow (log n) 2) (log PI))))) (+ (* 1/48 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 3)))) (+ (* 1/16 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log n) (pow (log PI) 2))))) (+ (* 1/48 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log n) 3)))) (+ (* 1/48 (* (pow (log 2) 3) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (+ (* 1/16 (* (pow (log n) 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (sqrt 2))))) (+ (* 1/16 (* (log 2) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2))))) (* 1/16 (* (sqrt 2) (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))))))))))))))) (+ (* +nan.0 (+ (* 1/4 (* (sqrt 2) (* (log 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (+ (* 1/8 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2)))) (+ (* 1/8 (* (pow (log 2) 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (+ (* 1/8 (* (pow (log n) 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (+ (* 1/4 (* (log n) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (* 1/4 (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (sqrt 2))))))))))) (+ (* +nan.0 (- (+ (* 1/2 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log n)))) (* 1/2 (* (log 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))))))) (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log n) (log PI))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (pow (log 2) 2) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log n))))) (- (+ (* +nan.0 (* (log n) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (- (+ (* +nan.0 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2)))) (- (+ (* +nan.0 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log 2)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log 2) (log PI))))))))))))))))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log n) (log PI))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (pow (log 2) 2) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log n))))) (- (+ (* +nan.0 (* (log n) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (- (+ (* +nan.0 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2)))) (- (+ (* +nan.0 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log 2)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log 2) (log PI)))))))))))))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log 2) 2)))) (- (+ (* +nan.0 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log n) (log PI))))) (- (+ (* +nan.0 (* (log n) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (- (+ (* +nan.0 (* (sqrt 2) (* (log 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log n))))) (- (+ (* +nan.0 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (- (+ (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log 2) (log PI))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (sqrt 2)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log n) 2)))))))))))))))))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log 2) 2)))) (- (+ (* +nan.0 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log n) (log PI))))) (- (+ (* +nan.0 (* (log n) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (- (+ (* +nan.0 (* (sqrt 2) (* (log 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log n))))) (- (+ (* +nan.0 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (- (+ (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log 2) (log PI))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (sqrt 2)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log n) 2))))))))))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (- (+ (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log 2)))) (- (* +nan.0 (* (log n) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))))))))))) (* k 1)) (- (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))))) into (- (+ (* +nan.0 (* (pow k 2) (* (sqrt 2) (* (log n) (exp (* 1/2 (+ (log n) (log PI)))))))) (- (+ (* +nan.0 (* (pow k 2) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (pow (log 2) 2) (sqrt 2))))) (- (+ (* +nan.0 (* k (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (- (+ (* +nan.0 (* (pow k 2) (* (log 2) (* (sqrt 2) (* (log n) (exp (* 1/2 (+ (log n) (log PI))))))))) (- (+ (* +nan.0 (* k (* (log 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))))) (- (+ (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log 2))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (* (sqrt 2) (log PI)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log n) (log PI)))))) (- (+ (* +nan.0 (* k (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (- (+ (* +nan.0 (* (pow k 2) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log n) 2))))) (- (+ (* +nan.0 (* (pow k 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (- (* +nan.0 (* k (* (sqrt 2) (* (log n) (exp (* 1/2 (+ (log n) (log PI)))))))))))))))))))))))))))))))))))))
* [misc]approximate:  Taking taylor expansion of (/ (* (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) (pow 2 (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (* (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) (pow 2 (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (* (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) (pow 2 (/ (- 1 (/ 1 k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (/ 1 n) into (/ 1 n)
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* (/ 1 n) PI) into (/ PI n)
* [misc]backup-simplify:  Simplify (log (/ PI n)) into (log (/ PI n))
* [misc]backup-simplify:  Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ PI n)))))
* [misc]taylor:  Taking taylor expansion of (pow 2 (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 2)) 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 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (* -1/2 (log 2)) into (* -1/2 (log 2))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log 2))) into (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ PI n))))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))) into (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ PI n))))))
* [misc]backup-simplify:  Simplify (/ (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ PI n)))))) +nan.0) into (* +nan.0 (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ PI n)))))))
* [misc]taylor:  Taking taylor expansion of (/ (* (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) (pow 2 (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (* (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) (pow 2 (/ (- 1 (/ 1 k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log PI) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))
* [misc]taylor:  Taking taylor expansion of (pow 2 (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 2)) 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 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (log 2)) into (* 1/2 (* (log 2) (- 1 (/ 1 k))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) into (exp (* 1/2 (* (log 2) (- 1 (/ 1 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 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))) into (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))))
* [misc]backup-simplify:  Simplify (/ (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))) (sqrt (/ 1 k))) into (* (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (/ (* (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) (pow 2 (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (* (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) (pow 2 (/ (- 1 (/ 1 k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 1 PI) into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log PI) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))
* [misc]taylor:  Taking taylor expansion of (pow 2 (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 2)) 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 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (log 2)) into (* 1/2 (* (log 2) (- 1 (/ 1 k))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) into (exp (* 1/2 (* (log 2) (- 1 (/ 1 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 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))) into (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))))
* [misc]backup-simplify:  Simplify (/ (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))) (sqrt (/ 1 k))) into (* (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (* (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (log 2) (- 1 (/ 1 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) (- 1 (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (log 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]taylor:  Taking taylor expansion of (- 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]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (* (log 2) -1) into (* -1 (log 2))
* [misc]backup-simplify:  Simplify (* 1/2 (* -1 (log 2))) into (* -1/2 (log 2))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) into (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log 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 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 PI) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]taylor:  Taking taylor expansion of (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 PI) (- (log n))) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (* -1 (- (log PI) (log n))) into (* -1 (- (log PI) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* -1 (- (log PI) (log n)))) into (* -1/2 (- (log PI) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 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 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))) into (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))))
* [misc]backup-simplify:  Simplify (* (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))) 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (log 2))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log PI) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) 0) (* 0 (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 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 (* (log 2) (- 1 (/ 1 k))))) 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))))))
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (log 2)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log PI) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (log 2) (- 1 (/ 1 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) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 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 (* (log 2) (- 1 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))))))
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log 2))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log PI) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (log 2) (- 1 (/ 1 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) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log 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 (* (log 2) (- 1 (/ 1 k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log PI) (log n))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 (/ 1 k)))))) (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log PI) (log (/ 1 n))))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 (/ 1 k)))))) (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log PI) (log (/ 1 n))))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 (/ 1 k)))))) (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log PI) (log (/ 1 n))))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) k)) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (- 1 k))))) (pow k 3))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) (pow k 2))))))))
* [misc]approximate:  Taking taylor expansion of (/ (* (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) (pow 2 (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k)))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (* (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) (pow 2 (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (* (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) (pow 2 (/ (- 1 (/ 1 (- k))) 2))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- -1) into 1
* [misc]backup-simplify:  Simplify (+ 0 1) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) PI)) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in k
* [misc]taylor:  Taking taylor expansion of (- n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (/ 1 (- n)) into (/ -1 n)
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* (/ -1 n) PI) into (* -1 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -1 (/ PI n)))) into (* 1/2 (log (* -1 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* -1 (/ PI n))))))
* [misc]taylor:  Taking taylor expansion of (pow 2 (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 2)) 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 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log 2))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* -1 (/ PI n)))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* -1 (/ PI n)))))))
* [misc]backup-simplify:  Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* -1 (/ PI n))))))) +nan.0) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* -1 (/ PI n))))))))
* [misc]taylor:  Taking taylor expansion of (/ (* (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) (pow 2 (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (* (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) (pow 2 (/ (- 1 (/ 1 (- k))) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ -1 k)) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ (/ 1 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)) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 PI) into (* -1 PI)
* [misc]backup-simplify:  Simplify (log (* -1 PI)) into (log (* -1 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -1 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (pow 2 (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 2)) 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 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log 2)) into (* 1/2 (* (+ (/ 1 k) 1) (log 2)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2))))
* [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 (* -1 PI)) (log n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) (sqrt (/ -1 k))) into (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) (sqrt (/ -1 k)))
* [misc]taylor:  Taking taylor expansion of (/ (* (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) (pow 2 (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (* (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) (pow 2 (/ (- 1 (/ 1 (- k))) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ -1 k)) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ (/ 1 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)) PI)) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) PI) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 PI) into (* -1 PI)
* [misc]backup-simplify:  Simplify (log (* -1 PI)) into (log (* -1 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -1 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (pow 2 (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 2)) 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 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log 2)) into (* 1/2 (* (+ (/ 1 k) 1) (log 2)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2))))
* [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 (* -1 PI)) (log n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) (sqrt (/ -1 k))) into (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) (sqrt (/ -1 k)))
* [misc]taylor:  Taking taylor expansion of (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) (sqrt (/ -1 k))) in k
* [misc]taylor:  Taking taylor expansion of (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (log 2))) 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)) 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) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (log 2) into (log 2)
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (* 1 (log 2)) into (log 2)
* [misc]backup-simplify:  Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 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 (* -1 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 (* -1 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* -1 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* -1 PI) in k
* [misc]taylor:  Taking taylor expansion of -1 in k
* [misc]backup-simplify:  Simplify -1 into -1
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -1 PI) into (* -1 PI)
* [misc]backup-simplify:  Simplify (log (* -1 PI)) into (log (* -1 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 (* -1 PI)) (- (log n))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1 (- (log (* -1 PI)) (log n))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -1 PI)) (log n))) into (* 1/2 (- (log (* -1 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 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)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) +nan.0) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (log 2))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 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 (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -1 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 (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -1 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 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 (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))))) 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)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))))))
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (log 2)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (+ (* (/ (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 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -1 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 (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log 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 (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)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 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 (+ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))))) 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)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -1 PI)) (log (/ 1 (- n)))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -1 PI)) (log (/ 1 (- n)))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -1 PI)) (log (/ 1 (- n))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k)))))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) k)))))))
* * * [misc]progress:  simplifying candidates
* * * * [misc]progress:  [ 1 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (log1p (expm1 (pow (* n PI) (/ (- 1 k) 2)))) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (pow (* n PI) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* [exit]simplify:  Simplified to (expm1 (pow (* PI n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (expm1 (pow (* PI n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 2 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (expm1 (log1p (pow (* n PI) (/ (- 1 k) 2)))) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (pow (* n PI) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* [exit]simplify:  Simplified to (log1p (pow (* PI n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (log1p (pow (* PI n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 3 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (exp (* (log (* n PI)) (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* n PI)) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (106 enodes)
* * [misc]simplify:  iters left: 2 (396 enodes)
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* PI n)))
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* PI n)))
* * * * [misc]progress:  [ 4 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (exp (* (log (* n PI)) (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* n PI)) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (106 enodes)
* * [misc]simplify:  iters left: 2 (396 enodes)
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* PI n)))
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* PI n)))
* * * * [misc]progress:  [ 5 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow (* n PI) (* 1 (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* 1 (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (51 enodes)
* * [misc]simplify:  iters left: 2 (79 enodes)
* * [misc]simplify:  iters left: 1 (117 enodes)
* [exit]simplify:  Simplified to (/ (- 1 k) 2)
* [exit]simplify:  Simplified to (/ (- 1 k) 2)
* * * * [misc]progress:  [ 6 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (/ (pow (* n PI) (/ 1 2)) (pow (* n PI) (/ k 2))) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n PI) (/ 1 2))
* * [misc]simplify:  iters left: 3 (7 enodes)
* * [misc]simplify:  iters left: 2 (10 enodes)
* [exit]simplify:  Simplified to (pow (* PI n) (/ 1 2))
* [exit]simplify:  Simplified to (pow (* PI n) (/ 1 2))
* [enter]simplify:  Simplifying (pow (* n PI) (/ k 2))
* * [misc]simplify:  iters left: 3 (7 enodes)
* * [misc]simplify:  iters left: 2 (8 enodes)
* [exit]simplify:  Simplified to (pow (* PI n) (/ k 2))
* [exit]simplify:  Simplified to (pow (* PI n) (/ k 2))
* * * * [misc]progress:  [ 7 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow (pow (* n PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 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 (pow (* PI n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (pow (* PI n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 8 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow (pow (* n PI) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n PI) (sqrt (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* [exit]simplify:  Simplified to (pow (* PI n) (sqrt (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (pow (* PI n) (sqrt (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 9 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow (pow (* n PI) 1) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n PI) 1)
* * [misc]simplify:  iters left: 3 (5 enodes)
* * [misc]simplify:  iters left: 2 (8 enodes)
* [exit]simplify:  Simplified to (* PI n)
* [exit]simplify:  Simplified to (* PI n)
* * * * [misc]progress:  [ 10 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow (pow (* n PI) (- 1 k)) (/ 1 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n PI) (- 1 k))
* * [misc]simplify:  iters left: 3 (7 enodes)
* * [misc]simplify:  iters left: 2 (12 enodes)
* * [misc]simplify:  iters left: 1 (13 enodes)
* [exit]simplify:  Simplified to (pow (* PI n) (- 1 k))
* [exit]simplify:  Simplified to (pow (* PI n) (- 1 k))
* * * * [misc]progress:  [ 11 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (* (pow n (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow n (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (17 enodes)
* * [misc]simplify:  iters left: 2 (19 enodes)
* [exit]simplify:  Simplified to (pow n (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow n (/ (- 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))
* [exit]simplify:  Simplified to (pow PI (/ (- 1 k) 2))
* * * * [misc]progress:  [ 12 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow (pow (* n PI) (/ (- 1 k) 2)) 1) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* * * * [misc]progress:  [ 13 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (exp (log (pow (* n PI) (/ (- 1 k) 2)))) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (pow (* n PI) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (58 enodes)
* * [misc]simplify:  iters left: 2 (133 enodes)
* * [misc]simplify:  iters left: 1 (491 enodes)
* [exit]simplify:  Simplified to (* (log (* PI n)) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (* (log (* PI n)) (/ (- 1 k) 2))
* * * * [misc]progress:  [ 14 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (log (exp (pow (* n PI) (/ (- 1 k) 2)))) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (pow (* n PI) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* [exit]simplify:  Simplified to (exp (pow (* PI n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (exp (pow (* PI n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 15 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (* (* (cbrt (pow (* n PI) (/ (- 1 k) 2))) (cbrt (pow (* n PI) (/ (- 1 k) 2)))) (cbrt (pow (* n PI) (/ (- 1 k) 2)))) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (pow (* n PI) (/ (- 1 k) 2))) (cbrt (pow (* n PI) (/ (- 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 (* (cbrt (pow (* PI n) (/ (- 1 k) 2))) (cbrt (pow (* PI n) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* PI n) (/ (- 1 k) 2))) (cbrt (pow (* PI n) (/ (- 1 k) 2))))
* [enter]simplify:  Simplifying (cbrt (pow (* n PI) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* [exit]simplify:  Simplified to (cbrt (pow (* PI n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (cbrt (pow (* PI n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 16 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (cbrt (* (* (pow (* n PI) (/ (- 1 k) 2)) (pow (* n PI) (/ (- 1 k) 2))) (pow (* n PI) (/ (- 1 k) 2)))) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (pow (* n PI) (/ (- 1 k) 2)) (pow (* n PI) (/ (- 1 k) 2))) (pow (* n PI) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (27 enodes)
* [exit]simplify:  Simplified to (pow (pow (* PI n) (/ (- 1 k) 2)) 3)
* [exit]simplify:  Simplified to (pow (pow (* PI n) (/ (- 1 k) 2)) 3)
* * * * [misc]progress:  [ 17 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (* (sqrt (pow (* n PI) (/ (- 1 k) 2))) (sqrt (pow (* n PI) (/ (- 1 k) 2)))) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (pow (* n PI) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* PI n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* PI n) (/ (- 1 k) 2)))
* [enter]simplify:  Simplifying (sqrt (pow (* n PI) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* PI n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* PI n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 18 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (* 1 (pow (* n PI) (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* * * * [misc]progress:  [ 19 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (log1p (expm1 (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (expm1 (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (expm1 (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 20 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (expm1 (log1p (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (log1p (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (log1p (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 21 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* n PI) 2)
* * [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)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* * * * [misc]progress:  [ 22 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) 1) (sqrt k)))>
* * * * [misc]progress:  [ 23 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (exp (+ (* (log (* n PI)) (/ (- 1 k) 2)) (* (log 2) (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (+ (* (log (* n PI)) (/ (- 1 k) 2)) (* (log 2) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (34 enodes)
* * [misc]simplify:  iters left: 4 (73 enodes)
* * [misc]simplify:  iters left: 3 (235 enodes)
* [exit]simplify:  Simplified to (* (+ (log 2) (log (* PI n))) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (* (+ (log 2) (log (* PI n))) (/ (- 1 k) 2))
* * * * [misc]progress:  [ 24 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (exp (+ (* (log (* n PI)) (/ (- 1 k) 2)) (log (pow 2 (/ (- 1 k) 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (+ (* (log (* n PI)) (/ (- 1 k) 2)) (log (pow 2 (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (60 enodes)
* * [misc]simplify:  iters left: 3 (154 enodes)
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (+ (log 2) (log (* PI n))))
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (+ (log 2) (log (* PI n))))
* * * * [misc]progress:  [ 25 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (exp (+ (* (log (* n PI)) (/ (- 1 k) 2)) (* (log 2) (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (+ (* (log (* n PI)) (/ (- 1 k) 2)) (* (log 2) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (34 enodes)
* * [misc]simplify:  iters left: 4 (73 enodes)
* * [misc]simplify:  iters left: 3 (235 enodes)
* [exit]simplify:  Simplified to (* (+ (log 2) (log (* PI n))) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (* (+ (log 2) (log (* PI n))) (/ (- 1 k) 2))
* * * * [misc]progress:  [ 26 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (exp (+ (* (log (* n PI)) (/ (- 1 k) 2)) (log (pow 2 (/ (- 1 k) 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (+ (* (log (* n PI)) (/ (- 1 k) 2)) (log (pow 2 (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (60 enodes)
* * [misc]simplify:  iters left: 3 (154 enodes)
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (+ (log 2) (log (* PI n))))
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (+ (log 2) (log (* PI n))))
* * * * [misc]progress:  [ 27 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (exp (+ (log (pow (* n PI) (/ (- 1 k) 2))) (* (log 2) (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (+ (log (pow (* n PI) (/ (- 1 k) 2))) (* (log 2) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (54 enodes)
* * [misc]simplify:  iters left: 3 (151 enodes)
* * [misc]simplify:  iters left: 2 (423 enodes)
* [exit]simplify:  Simplified to (* (+ (log (* PI n)) (log 2)) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (* (+ (log (* PI n)) (log 2)) (/ (- 1 k) 2))
* * * * [misc]progress:  [ 28 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (exp (+ (log (pow (* n PI) (/ (- 1 k) 2))) (log (pow 2 (/ (- 1 k) 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (+ (log (pow (* n PI) (/ (- 1 k) 2))) (log (pow 2 (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (45 enodes)
* * [misc]simplify:  iters left: 3 (98 enodes)
* * [misc]simplify:  iters left: 2 (274 enodes)
* [exit]simplify:  Simplified to (* (+ (log (* PI n)) (log 2)) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (* (+ (log (* PI n)) (log 2)) (/ (- 1 k) 2))
* * * * [misc]progress:  [ 29 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (exp (log (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (50 enodes)
* * [misc]simplify:  iters left: 2 (105 enodes)
* * [misc]simplify:  iters left: 1 (297 enodes)
* [exit]simplify:  Simplified to (* (+ (log (* PI n)) (log 2)) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (* (+ (log (* PI n)) (log 2)) (/ (- 1 k) 2))
* * * * [misc]progress:  [ 30 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (log (exp (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (26 enodes)
* * [misc]simplify:  iters left: 3 (28 enodes)
* [exit]simplify:  Simplified to (exp (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (exp (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 31 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (cbrt (* (* (* (pow (* n PI) (/ (- 1 k) 2)) (pow (* n PI) (/ (- 1 k) 2))) (pow (* n PI) (/ (- 1 k) 2))) (* (* (pow 2 (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (* (pow (* n PI) (/ (- 1 k) 2)) (pow (* n PI) (/ (- 1 k) 2))) (pow (* n PI) (/ (- 1 k) 2))) (* (* (pow 2 (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (58 enodes)
* * [misc]simplify:  iters left: 3 (94 enodes)
* * [misc]simplify:  iters left: 2 (111 enodes)
* * [misc]simplify:  iters left: 1 (114 enodes)
* [exit]simplify:  Simplified to (pow (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) 3)
* [exit]simplify:  Simplified to (pow (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) 3)
* * * * [misc]progress:  [ 32 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (* (cbrt (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (cbrt (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))))) (cbrt (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (cbrt (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (13 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 (* (cbrt (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))) (cbrt (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))))
* [exit]simplify:  Simplified to (* (cbrt (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))) (cbrt (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))))
* [enter]simplify:  Simplifying (cbrt (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (cbrt (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (cbrt (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 33 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (cbrt (* (* (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (48 enodes)
* * [misc]simplify:  iters left: 3 (76 enodes)
* * [misc]simplify:  iters left: 2 (106 enodes)
* * [misc]simplify:  iters left: 1 (109 enodes)
* [exit]simplify:  Simplified to (pow (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) 3)
* [exit]simplify:  Simplified to (pow (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) 3)
* * * * [misc]progress:  [ 34 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (sqrt (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (sqrt (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (sqrt (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (sqrt (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))))
* [enter]simplify:  Simplifying (sqrt (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (sqrt (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (sqrt (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 35 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (pow (* n PI) (/ 1 2)) (pow 2 (/ 1 2))) (* (pow (* n PI) (/ k 2)) (pow 2 (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (pow (* n PI) (/ 1 2)) (pow 2 (/ 1 2)))
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* [exit]simplify:  Simplified to (* (pow 2 (/ 1 2)) (pow (* PI n) (/ 1 2)))
* [exit]simplify:  Simplified to (* (pow 2 (/ 1 2)) (pow (* PI n) (/ 1 2)))
* [enter]simplify:  Simplifying (* (pow (* n PI) (/ k 2)) (pow 2 (/ k 2)))
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (11 enodes)
* [exit]simplify:  Simplified to (* (pow 2 (/ k 2)) (pow (* PI n) (/ k 2)))
* [exit]simplify:  Simplified to (* (pow 2 (/ k 2)) (pow (* PI n) (/ k 2)))
* * * * [misc]progress:  [ 36 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* 1 (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 37 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (* (pow (* n PI) (/ (- 1 k) 2)) (* (cbrt (pow 2 (/ (- 1 k) 2))) (cbrt (pow 2 (/ (- 1 k) 2))))) (cbrt (pow 2 (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (pow (* n PI) (/ (- 1 k) 2)) (* (cbrt (pow 2 (/ (- 1 k) 2))) (cbrt (pow 2 (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (31 enodes)
* [exit]simplify:  Simplified to (* (* (cbrt (pow 2 (/ (- 1 k) 2))) (cbrt (pow 2 (/ (- 1 k) 2)))) (pow (* PI n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (* (* (cbrt (pow 2 (/ (- 1 k) 2))) (cbrt (pow 2 (/ (- 1 k) 2)))) (pow (* PI n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 38 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (* (pow (* n PI) (/ (- 1 k) 2)) (sqrt (pow 2 (/ (- 1 k) 2)))) (sqrt (pow 2 (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (pow (* n PI) (/ (- 1 k) 2)) (sqrt (pow 2 (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (* (sqrt (pow 2 (/ (- 1 k) 2))) (pow (* PI n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (* (sqrt (pow 2 (/ (- 1 k) 2))) (pow (* PI n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 39 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (* (pow (* n PI) (/ (- 1 k) 2)) 1) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (pow (* n PI) (/ (- 1 k) 2)) 1)
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (pow (* PI n) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow (* PI n) (/ (- 1 k) 2))
* * * * [misc]progress:  [ 40 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow n (/ (- 1 k) 2)) (* (pow PI (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (pow PI (/ (- 1 k) 2)) (pow 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 (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 41 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (* (cbrt (pow (* n PI) (/ (- 1 k) 2))) (cbrt (pow (* n PI) (/ (- 1 k) 2)))) (* (cbrt (pow (* n PI) (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (pow (* n PI) (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* PI n) (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (* (cbrt (pow (* PI n) (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 42 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (sqrt (pow (* n PI) (/ (- 1 k) 2))) (* (sqrt (pow (* n PI) (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (sqrt (pow (* n PI) (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (* (sqrt (pow (* PI n) (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (* (sqrt (pow (* PI n) (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 43 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* 1 (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 44 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ 1 2))) (pow 2 (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ 1 2)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (* (pow 2 (/ 1 2)) (pow (* PI n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (* (pow 2 (/ 1 2)) (pow (* PI n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 45 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (pow (* n PI) (/ 1 2)) (pow 2 (/ (- 1 k) 2))) (pow (* n PI) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (pow (* n PI) (/ 1 2)) (pow 2 (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ 1 2)))
* [exit]simplify:  Simplified to (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ 1 2)))
* * * * [misc]progress:  [ 46 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow 2 (/ (- 1 k) 2)) (pow (* n PI) (/ (- 1 k) 2))) (sqrt k)))>
* * * * [misc]progress:  [ 47 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow (log1p (expm1 (* n PI))) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (expm1 (* PI n))
* [exit]simplify:  Simplified to (expm1 (* PI n))
* * * * [misc]progress:  [ 48 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow (expm1 (log1p (* n PI))) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (log1p (* PI n))
* [exit]simplify:  Simplified to (log1p (* PI n))
* * * * [misc]progress:  [ 49 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow (pow (* n PI) 1) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* * * * [misc]progress:  [ 50 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow (exp (log (* n PI))) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (8 enodes)
* * [misc]simplify:  iters left: 1 (9 enodes)
* [exit]simplify:  Simplified to (log (* PI n))
* [exit]simplify:  Simplified to (log (* PI n))
* * * * [misc]progress:  [ 51 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow (log (exp (* n PI))) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (exp (* PI n))
* [exit]simplify:  Simplified to (exp (* PI n))
* * * * [misc]progress:  [ 52 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow (* (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI))) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (* n PI)) (cbrt (* n PI)))
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (6 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* PI n)) (cbrt (* PI n)))
* [exit]simplify:  Simplified to (* (cbrt (* PI n)) (cbrt (* PI n)))
* [enter]simplify:  Simplifying (cbrt (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (cbrt (* PI n))
* [exit]simplify:  Simplified to (cbrt (* PI n))
* * * * [misc]progress:  [ 53 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow (cbrt (* (* (* n PI) (* n PI)) (* n PI))) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (* n PI) (* n PI)) (* n PI))
* * [misc]simplify:  iters left: 6 (5 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (55 enodes)
* * [misc]simplify:  iters left: 2 (86 enodes)
* * [misc]simplify:  iters left: 1 (89 enodes)
* [exit]simplify:  Simplified to (pow (* PI n) 3)
* [exit]simplify:  Simplified to (pow (* PI n) 3)
* * * * [misc]progress:  [ 54 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow (* (sqrt (* n PI)) (sqrt (* n PI))) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [enter]simplify:  Simplifying (sqrt (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [exit]simplify:  Simplified to (sqrt (* PI n))
* * * * [misc]progress:  [ 55 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow (* 1 (* n PI)) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* * * * [misc]progress:  [ 56 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow (* PI n) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* * * * [misc]progress:  [ 57 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (log1p (expm1 (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (expm1 (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* * [misc]simplify:  iters left: 2 (37 enodes)
* * [misc]simplify:  iters left: 1 (38 enodes)
* [exit]simplify:  Simplified to (expm1 (/ (pow (* PI n) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))))
* [exit]simplify:  Simplified to (expm1 (/ (pow (* PI n) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 58 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (expm1 (log1p (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (log1p (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* * [misc]simplify:  iters left: 2 (37 enodes)
* * [misc]simplify:  iters left: 1 (38 enodes)
* [exit]simplify:  Simplified to (log1p (/ (pow (* PI n) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))))
* [exit]simplify:  Simplified to (log1p (/ (pow (* PI n) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 59 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (pow (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)) 1))>
* * * * [misc]progress:  [ 60 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (+ (* (log (* n PI)) (/ (- 1 k) 2)) (* (log 2) (/ (- 1 k) 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (+ (* (log (* n PI)) (/ (- 1 k) 2)) (* (log 2) (/ (- 1 k) 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (41 enodes)
* * [misc]simplify:  iters left: 4 (93 enodes)
* * [misc]simplify:  iters left: 3 (285 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (+ (log 2) (log (* PI n))) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (+ (log 2) (log (* PI n))) (- (log (sqrt k))))
* * * * [misc]progress:  [ 61 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (+ (* (log (* n PI)) (/ (- 1 k) 2)) (log (pow 2 (/ (- 1 k) 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (+ (* (log (* n PI)) (/ (- 1 k) 2)) (log (pow 2 (/ (- 1 k) 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (38 enodes)
* * [misc]simplify:  iters left: 4 (78 enodes)
* * [misc]simplify:  iters left: 3 (204 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (+ (log (* PI n)) (log 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (+ (log (* PI n)) (log 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 62 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (+ (* (log (* n PI)) (/ (- 1 k) 2)) (* (log 2) (/ (- 1 k) 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (+ (* (log (* n PI)) (/ (- 1 k) 2)) (* (log 2) (/ (- 1 k) 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (41 enodes)
* * [misc]simplify:  iters left: 4 (93 enodes)
* * [misc]simplify:  iters left: 3 (285 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (+ (log 2) (log (* PI n))) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (+ (log 2) (log (* PI n))) (- (log (sqrt k))))
* * * * [misc]progress:  [ 63 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (+ (* (log (* n PI)) (/ (- 1 k) 2)) (log (pow 2 (/ (- 1 k) 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (+ (* (log (* n PI)) (/ (- 1 k) 2)) (log (pow 2 (/ (- 1 k) 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (38 enodes)
* * [misc]simplify:  iters left: 4 (78 enodes)
* * [misc]simplify:  iters left: 3 (204 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (+ (log (* PI n)) (log 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (+ (log (* PI n)) (log 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 64 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (+ (log (pow (* n PI) (/ (- 1 k) 2))) (* (log 2) (/ (- 1 k) 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (+ (log (pow (* n PI) (/ (- 1 k) 2))) (* (log 2) (/ (- 1 k) 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (34 enodes)
* * [misc]simplify:  iters left: 4 (72 enodes)
* * [misc]simplify:  iters left: 3 (185 enodes)
* [exit]simplify:  Simplified to (fma (+ (log 2) (log (* PI n))) (/ (- 1 k) 2) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (+ (log 2) (log (* PI n))) (/ (- 1 k) 2) (- (log (sqrt k))))
* * * * [misc]progress:  [ 65 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (+ (log (pow (* n PI) (/ (- 1 k) 2))) (log (pow 2 (/ (- 1 k) 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (+ (log (pow (* n PI) (/ (- 1 k) 2))) (log (pow 2 (/ (- 1 k) 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (62 enodes)
* * [misc]simplify:  iters left: 3 (132 enodes)
* * [misc]simplify:  iters left: 2 (406 enodes)
* [exit]simplify:  Simplified to (fma (+ (log (* PI n)) (log 2)) (/ (- 1 k) 2) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (+ (log (* PI n)) (log 2)) (/ (- 1 k) 2) (- (log (sqrt k))))
* * * * [misc]progress:  [ 66 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (log (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (log (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (71 enodes)
* * [misc]simplify:  iters left: 2 (140 enodes)
* * [misc]simplify:  iters left: 1 (483 enodes)
* [exit]simplify:  Simplified to (fma (+ (log (* PI n)) (log 2)) (/ (- 1 k) 2) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (+ (log (* PI n)) (log 2)) (/ (- 1 k) 2) (- (log (sqrt k))))
* * * * [misc]progress:  [ 67 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (exp (log (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (log (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (61 enodes)
* * [misc]simplify:  iters left: 2 (96 enodes)
* * [misc]simplify:  iters left: 1 (168 enodes)
* [exit]simplify:  Simplified to (fma (+ (log (* PI n)) (log 2)) (/ (- 1 k) 2) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (+ (log (* PI n)) (log 2)) (/ (- 1 k) 2) (- (log (sqrt k))))
* * * * [misc]progress:  [ 68 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (log (exp (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (exp (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* * [misc]simplify:  iters left: 2 (39 enodes)
* * [misc]simplify:  iters left: 1 (40 enodes)
* [exit]simplify:  Simplified to (exp (/ (pow (* PI n) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))))
* [exit]simplify:  Simplified to (exp (/ (pow (* PI n) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 69 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (/ (* (* (* (pow (* n PI) (/ (- 1 k) 2)) (pow (* n PI) (/ (- 1 k) 2))) (pow (* n PI) (/ (- 1 k) 2))) (* (* (pow 2 (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (* (* (pow (* n PI) (/ (- 1 k) 2)) (pow (* n PI) (/ (- 1 k) 2))) (pow (* n PI) (/ (- 1 k) 2))) (* (* (pow 2 (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (42 enodes)
* * [misc]simplify:  iters left: 4 (126 enodes)
* * [misc]simplify:  iters left: 3 (421 enodes)
* [exit]simplify:  Simplified to (* (/ (* (pow (* PI n) (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) (/ k (pow 2 (/ (- 1 k) 2)))) (* (/ (pow (* PI n) (/ (- 1 k) 2)) (sqrt k)) (* (pow 2 (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))))
* [exit]simplify:  Simplified to (* (/ (* (pow (* PI n) (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) (/ k (pow 2 (/ (- 1 k) 2)))) (* (/ (pow (* PI n) (/ (- 1 k) 2)) (sqrt k)) (* (pow 2 (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 70 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (/ (* (* (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (* (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (41 enodes)
* * [misc]simplify:  iters left: 4 (110 enodes)
* * [misc]simplify:  iters left: 3 (376 enodes)
* [exit]simplify:  Simplified to (* (/ (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) (* k (sqrt k))) (* (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))))
* [exit]simplify:  Simplified to (* (/ (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) (* k (sqrt k))) (* (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 71 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (cbrt (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k))) (cbrt (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))) (cbrt (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (cbrt (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k))) (cbrt (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (38 enodes)
* * [misc]simplify:  iters left: 1 (39 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* (pow 2 (/ (- 1 k) 2)) (/ (pow (* PI n) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (* (pow 2 (/ (- 1 k) 2)) (/ (pow (* PI n) (/ (- 1 k) 2)) (sqrt k)))))
* [exit]simplify:  Simplified to (* (cbrt (* (pow 2 (/ (- 1 k) 2)) (/ (pow (* PI n) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (* (pow 2 (/ (- 1 k) 2)) (/ (pow (* PI n) (/ (- 1 k) 2)) (sqrt k)))))
* [enter]simplify:  Simplifying (cbrt (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* * [misc]simplify:  iters left: 2 (37 enodes)
* * [misc]simplify:  iters left: 1 (38 enodes)
* [exit]simplify:  Simplified to (cbrt (/ (pow (* PI n) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))))
* [exit]simplify:  Simplified to (cbrt (/ (pow (* PI n) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 72 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (* (* (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)) (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k))) (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (* (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)) (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k))) (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (73 enodes)
* * [misc]simplify:  iters left: 3 (208 enodes)
* [exit]simplify:  Simplified to (/ (* (/ (pow (* PI n) (/ (- 1 k) 2)) (sqrt k)) (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))) (/ (/ k (pow 2 (/ (- 1 k) 2))) (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))))
* [exit]simplify:  Simplified to (/ (* (/ (pow (* PI n) (/ (- 1 k) 2)) (sqrt k)) (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))) (/ (/ k (pow 2 (/ (- 1 k) 2))) (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 73 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k))) (sqrt (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* * [misc]simplify:  iters left: 2 (37 enodes)
* * [misc]simplify:  iters left: 1 (38 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* PI n) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* PI n) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))))
* [enter]simplify:  Simplifying (sqrt (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* * [misc]simplify:  iters left: 2 (37 enodes)
* * [misc]simplify:  iters left: 1 (38 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* PI n) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* PI n) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 74 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (- (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (- (sqrt k))))>
* [enter]simplify:  Simplifying (- (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* [exit]simplify:  Simplified to (- (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (- (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))))
* [enter]simplify:  Simplifying (- (sqrt k))
* * [misc]simplify:  iters left: 3 (3 enodes)
* [exit]simplify:  Simplified to (- (sqrt k))
* [exit]simplify:  Simplified to (- (sqrt k))
* * * * [misc]progress:  [ 75 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow (* n PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow 2 (/ (- 1 k) 2)) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* n PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (26 enodes)
* * [misc]simplify:  iters left: 3 (28 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow (* PI n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow 2 (/ (- 1 k) 2)) (cbrt (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 2 (/ (- 1 k) 2)) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 76 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow (* n PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* n PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (* PI n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* * [misc]simplify:  iters left: 3 (21 enodes)
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 77 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow (* n PI) (/ (- 1 k) 2)) 1) (/ (pow 2 (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow (* n PI) (/ (- 1 k) 2)) 1)
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (pow (* PI n) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow (* PI n) (/ (- 1 k) 2))
* [enter]simplify:  Simplifying (/ (pow 2 (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt k))
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 78 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k))))>
* * * * [misc]progress:  [ 79 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (/ 1 (sqrt k))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt k))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (6 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt k))
* [exit]simplify:  Simplified to (/ 1 (sqrt k))
* * * * [misc]progress:  [ 80 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (sqrt k) (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 81 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
* [enter]simplify:  Simplifying (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (46 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 (* (pow 2 (/ (- 1 k) 2)) (/ (pow (* PI n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
* [exit]simplify:  Simplified to (* (pow 2 (/ (- 1 k) 2)) (/ (pow (* PI n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 82 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
* [enter]simplify:  Simplifying (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 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 (30 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* * [misc]simplify:  iters left: 2 (37 enodes)
* * [misc]simplify:  iters left: 1 (38 enodes)
* [exit]simplify:  Simplified to (/ (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 83 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) 1) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) 1)
* * [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 (41 enodes)
* * [misc]simplify:  iters left: 2 (49 enodes)
* * [misc]simplify:  iters left: 1 (60 enodes)
* [exit]simplify:  Simplified to (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 84 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n PI) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 85 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow (* n PI) (/ 1 2)) (pow 2 (/ 1 2))) (* (sqrt k) (* (pow (* n PI) (/ k 2)) (pow 2 (/ k 2))))))>
* [enter]simplify:  Simplifying (* (sqrt k) (* (pow (* n PI) (/ k 2)) (pow 2 (/ k 2))))
* * [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 (* (* (pow (* n PI) (/ k 2)) (sqrt k)) (pow 2 (/ k 2)))
* [exit]simplify:  Simplified to (* (* (pow (* n PI) (/ k 2)) (sqrt k)) (pow 2 (/ k 2)))
* * * * [misc]progress:  [ 86 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ 1 2))) (* (sqrt k) (pow 2 (/ k 2)))))>
* [enter]simplify:  Simplifying (* (sqrt k) (pow 2 (/ k 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (7 enodes)
* [exit]simplify:  Simplified to (* (pow 2 (/ k 2)) (sqrt k))
* [exit]simplify:  Simplified to (* (pow 2 (/ k 2)) (sqrt k))
* * * * [misc]progress:  [ 87 / 99 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow (* n PI) (/ 1 2)) (pow 2 (/ (- 1 k) 2))) (* (sqrt k) (pow (* n PI) (/ k 2)))))>
* [enter]simplify:  Simplifying (* (sqrt k) (pow (* n PI) (/ k 2)))
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (11 enodes)
* [exit]simplify:  Simplified to (* (pow (* n PI) (/ k 2)) (sqrt k))
* [exit]simplify:  Simplified to (* (pow (* n PI) (/ k 2)) (sqrt k))
* * * * [misc]progress:  [ 88 / 99 ] simplifiying candidate #<alt-event (λ (k n) (/ (* (- (+ (* 1/8 (* (pow k 2) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log PI))))))) (+ (* 1/4 (* (pow k 2) (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (+ (exp (* 1/2 (+ (log n) (log PI)))) (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2))))))) (+ (* 1/2 (* k (* (log n) (exp (* 1/2 (+ (log n) (log PI))))))) (* 1/2 (* k (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))))) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (* (- (+ (* 1/8 (* (pow k 2) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log PI))))))) (+ (* 1/4 (* (pow k 2) (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (+ (exp (* 1/2 (+ (log n) (log PI)))) (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2))))))) (+ (* 1/2 (* k (* (log n) (exp (* 1/2 (+ (log n) (log PI))))))) (* 1/2 (* k (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))))) (pow 2 (/ (- 1 k) 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (42 enodes)
* * [misc]simplify:  iters left: 5 (118 enodes)
* * [misc]simplify:  iters left: 4 (374 enodes)
* [exit]simplify:  Simplified to (/ (+ (fma (* (* 1/4 k) k) (* (* (log PI) (log n)) (* (pow PI 1/2) (pow n 1/2))) (* (pow PI 1/2) (pow n 1/2))) (- (* (* (* (pow PI 1/2) (pow n 1/2)) (* (* k 1/8) k)) (+ (* (log PI) (log PI)) (* (log n) (log n)))) (* (* 1/2 k) (* (* (pow PI 1/2) (pow n 1/2)) (+ (log PI) (log n)))))) (/ (sqrt k) (pow 2 (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 89 / 99 ] simplifiying candidate #<alt-event (λ (k n) (/ (* (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (- 1 k)))) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (* (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (- 1 k)))) (pow 2 (/ (- 1 k) 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (41 enodes)
* * [misc]simplify:  iters left: 4 (81 enodes)
* * [misc]simplify:  iters left: 3 (242 enodes)
* [exit]simplify:  Simplified to (* (/ (pow 2 (/ (- 1 k) 2)) (sqrt k)) (exp (* (+ (log n) (log PI)) (* (- 1 k) 1/2))))
* * * * [misc]progress:  [ 90 / 99 ] simplifiying candidate #<alt-event (λ (k n) (/ (* (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k)))) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (* (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k)))) (pow 2 (/ (- 1 k) 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (21 enodes)
* * [misc]simplify:  iters left: 5 (46 enodes)
* * [misc]simplify:  iters left: 4 (91 enodes)
* * [misc]simplify:  iters left: 3 (333 enodes)
* [exit]simplify:  Simplified to (/ (pow (exp (* (- 1 k) 1/2)) (+ (+ (log PI) 0) (log n))) (/ (sqrt k) (pow 2 (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 91 / 99 ] simplifiying candidate #<alt-event (λ (k n) (/ (- (+ (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log 2) 2))))) (+ (* 1/4 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log n) (log PI)))))) (+ (* 1/8 (* (pow k 2) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2))))) (+ (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))) (+ (* 1/4 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (* (sqrt 2) (log n)))))) (+ (* 1/4 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log 2) (log PI)))))) (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log n) 2))))))))))) (+ (* 1/2 (* k (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log 2))))) (+ (* 1/2 (* k (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (* 1/2 (* k (* (sqrt 2) (* (log n) (exp (* 1/2 (+ (log n) (log PI))))))))))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (- (+ (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log 2) 2))))) (+ (* 1/4 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log n) (log PI)))))) (+ (* 1/8 (* (pow k 2) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2))))) (+ (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))) (+ (* 1/4 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (* (sqrt 2) (log n)))))) (+ (* 1/4 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log 2) (log PI)))))) (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log n) 2))))))))))) (+ (* 1/2 (* k (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log 2))))) (+ (* 1/2 (* k (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (* 1/2 (* k (* (sqrt 2) (* (log n) (exp (* 1/2 (+ (log n) (log PI))))))))))) (sqrt k))
* * [misc]simplify:  iters left: 6 (69 enodes)
* * [misc]simplify:  iters left: 5 (200 enodes)
* [exit]simplify:  Simplified to (/ (- (+ (+ (fma 1/8 (* (* (* (sqrt 2) (* (log 2) (log 2))) (pow (exp 1/2) (+ (log PI) (log n)))) (* k k)) (* (* (* (* 1/4 k) k) (pow (exp 1/2) (+ (log PI) (log n)))) (* (sqrt 2) (* (log PI) (log n))))) (fma 1/8 (* (* (* (sqrt 2) (* k k)) (* (log PI) (log PI))) (pow (exp 1/2) (+ (log PI) (log n)))) (* (pow (exp 1/2) (+ (log PI) (log n))) (sqrt 2)))) (fma 1/4 (* (* (log n) (* (log 2) (sqrt 2))) (* (* k k) (pow (exp 1/2) (+ (log PI) (log n))))) (fma 1/8 (* (* (log n) (* (sqrt 2) (log n))) (* (* k k) (pow (exp 1/2) (+ (log PI) (log n))))) (* (* (pow (exp 1/2) (+ (log PI) (log n))) (* (* (log 2) (log PI)) (sqrt 2))) (* (* 1/4 k) k))))) (fma (* 1/2 k) (* (pow (exp 1/2) (+ (log PI) (log n))) (* (log 2) (sqrt 2))) (fma (* 1/2 k) (* (* (sqrt 2) (log PI)) (pow (exp 1/2) (+ (log PI) (log n)))) (* (* (* 1/2 k) (* (sqrt 2) (log n))) (pow (exp 1/2) (+ (log PI) (log n))))))) (sqrt k))
* * * * [misc]progress:  [ 92 / 99 ] simplifiying candidate #<alt-event (λ (k n) (/ (* (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (* (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) (sqrt k))
* * [misc]simplify:  iters left: 6 (21 enodes)
* * [misc]simplify:  iters left: 5 (47 enodes)
* * [misc]simplify:  iters left: 4 (110 enodes)
* * [misc]simplify:  iters left: 3 (373 enodes)
* [exit]simplify:  Simplified to (/ (pow (exp (- 1 k)) (fma (+ (log PI) (log n)) 1/2 (* 1/2 (log 2)))) (sqrt k))
* * * * [misc]progress:  [ 93 / 99 ] simplifiying candidate #<alt-event (λ (k n) (/ (* (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (* (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) (sqrt k))
* * [misc]simplify:  iters left: 6 (23 enodes)
* * [misc]simplify:  iters left: 5 (52 enodes)
* * [misc]simplify:  iters left: 4 (120 enodes)
* * [misc]simplify:  iters left: 3 (466 enodes)
* [exit]simplify:  Simplified to (/ (pow (exp (* (- 1 k) 1/2)) (+ (+ 0 (log PI)) (log n))) (/ (sqrt k) (pow (pow 2 1/2) (- 1 k))))
* * * * [misc]progress:  [ 94 / 99 ] simplifiying candidate #<alt-event (λ (k n) (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* * [misc]simplify:  iters left: 1 (37 enodes)
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) (/ (sqrt k) (pow (* PI n) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 95 / 99 ] simplifiying candidate #<alt-event (λ (k n) (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* * [misc]simplify:  iters left: 1 (37 enodes)
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) (/ (sqrt k) (pow (* PI n) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 96 / 99 ] simplifiying candidate #<alt-event (λ (k n) (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* * [misc]simplify:  iters left: 1 (37 enodes)
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) (/ (sqrt k) (pow (* PI n) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 97 / 99 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (* (pow k 2) (* (sqrt 2) (* (log n) (exp (* 1/2 (+ (log n) (log PI)))))))) (- (+ (* +nan.0 (* (pow k 2) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (pow (log 2) 2) (sqrt 2))))) (- (+ (* +nan.0 (* k (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (- (+ (* +nan.0 (* (pow k 2) (* (log 2) (* (sqrt 2) (* (log n) (exp (* 1/2 (+ (log n) (log PI))))))))) (- (+ (* +nan.0 (* k (* (log 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))))) (- (+ (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log 2))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (* (sqrt 2) (log PI)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log n) (log PI)))))) (- (+ (* +nan.0 (* k (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (- (+ (* +nan.0 (* (pow k 2) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log n) 2))))) (- (+ (* +nan.0 (* (pow k 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (- (* +nan.0 (* k (* (sqrt 2) (* (log n) (exp (* 1/2 (+ (log n) (log PI))))))))))))))))))))))))))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (* (pow k 2) (* (sqrt 2) (* (log n) (exp (* 1/2 (+ (log n) (log PI)))))))) (- (+ (* +nan.0 (* (pow k 2) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (pow (log 2) 2) (sqrt 2))))) (- (+ (* +nan.0 (* k (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (- (+ (* +nan.0 (* (pow k 2) (* (log 2) (* (sqrt 2) (* (log n) (exp (* 1/2 (+ (log n) (log PI))))))))) (- (+ (* +nan.0 (* k (* (log 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))))) (- (+ (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log 2))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (* (sqrt 2) (log PI)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log n) (log PI)))))) (- (+ (* +nan.0 (* k (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (- (+ (* +nan.0 (* (pow k 2) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log n) 2))))) (- (+ (* +nan.0 (* (pow k 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (- (* +nan.0 (* k (* (sqrt 2) (* (log n) (exp (* 1/2 (+ (log n) (log PI)))))))))))))))))))))))))))))))))))))
* * * * [misc]progress:  [ 98 / 99 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) k)) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (- 1 k))))) (pow k 3))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) (pow k 2)))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) k)) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (- 1 k))))) (pow k 3))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) (pow k 2))))))))
* * * * [misc]progress:  [ 99 / 99 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k)))))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) k))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k)))))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) k)))))))
* * * [misc]progress:  adding candidates to table
* [misc]progress:  [Phase 3 of 3] Extracting.
* * [misc]regime-changes:  Finding splitpoints for: (#<alt-delta (λ (k n) (cbrt (* (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (* (sqrt k) k)) (* (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))))))> #<alt-delta (λ (k n) (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))> #<alt-delta (λ (k n) (* (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (sqrt k)))) (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))) (cbrt (sqrt k)))))> #<alt-delta (λ (k n) (/ (* (* (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (sqrt k)))> #<alt-delta (λ (k n) (* (* (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))) (/ (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt k))))> #<alt-delta (λ (k n) (* (sqrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))))> #<alt-event (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt-delta (λ (k n) (* (/ (* (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (sqrt k)))))> #<alt-delta (λ (k n) (* (pow (* PI n) (/ (- 1 k) 2)) (/ (pow 2 (/ (- 1 k) 2)) (sqrt k))))> #<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))> #<alt-delta (λ (k n) (* (/ (pow (* n PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k)))))> #<alt-delta (λ (k n) (* (/ (/ (pow (* n PI) (/ 1 2)) (pow (* n PI) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow 2 (/ 1 2)) (pow 2 (/ k 2))) (cbrt (sqrt k)))))>)
* [misc]regimes:  Found splitpoints: (#s(sp 0 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) +nan.0)) , with alts (#<alt-delta (λ (k n) (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>)
* [enter]simplify:  Simplifying (sqrt (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [enter]simplify:  Simplifying (sqrt (* n PI))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (sqrt (* PI n))
* [exit]simplify:  Simplified to (sqrt (* PI n))
* * * * [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 6497 additional inputs, on iter 1 have 1503 / 8000
* * * * [misc]points:  Computing exacts on every 406 of 6497 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 6497 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 6497 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 6497 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 6497 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 6497 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 6497 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 6497 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 6497 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 5227 additional inputs, on iter 2 have 2773 / 8000
* * * * [misc]points:  Computing exacts on every 326 of 5227 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 163 of 5227 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 81 of 5227 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 40 of 5227 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 5227 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 5227 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 5227 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 5227 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 5227 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 4212 additional inputs, on iter 3 have 3788 / 8000
* * * * [misc]points:  Computing exacts on every 263 of 4212 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 131 of 4212 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 65 of 4212 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 32 of 4212 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 4212 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 4212 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 4212 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 4212 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 4212 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 3382 additional inputs, on iter 4 have 4618 / 8000
* * * * [misc]points:  Computing exacts on every 211 of 3382 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 105 of 3382 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 52 of 3382 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 3382 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 3382 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 3382 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 3382 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 3382 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 2788 additional inputs, on iter 5 have 5212 / 8000
* * * * [misc]points:  Computing exacts on every 174 of 2788 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 87 of 2788 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 43 of 2788 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 2788 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 2788 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 2788 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 2788 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 2788 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 2254 additional inputs, on iter 6 have 5746 / 8000
* * * * [misc]points:  Computing exacts on every 140 of 2254 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 70 of 2254 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 35 of 2254 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 2254 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 2254 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 2254 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 2254 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 2254 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 1833 additional inputs, on iter 7 have 6167 / 8000
* * * * [misc]points:  Computing exacts on every 114 of 1833 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 57 of 1833 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 1833 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 1833 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 1833 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 1833 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1833 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 1492 additional inputs, on iter 8 have 6508 / 8000
* * * * [misc]points:  Computing exacts on every 93 of 1492 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 46 of 1492 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 23 of 1492 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 1492 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 1492 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 1492 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1492 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 1215 additional inputs, on iter 9 have 6785 / 8000
* * * * [misc]points:  Computing exacts on every 75 of 1215 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 37 of 1215 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 1215 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 1215 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 1215 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 1215 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1215 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 1004 additional inputs, on iter 10 have 6996 / 8000
* * * * [misc]points:  Computing exacts on every 62 of 1004 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 1004 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 1004 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 1004 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 1004 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1004 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 822 additional inputs, on iter 11 have 7178 / 8000
* * * * [misc]points:  Computing exacts on every 51 of 822 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 822 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 822 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 822 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 822 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 822 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 667 additional inputs, on iter 12 have 7333 / 8000
* * * * [misc]points:  Computing exacts on every 41 of 667 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 667 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 667 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 667 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 667 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 667 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 544 additional inputs, on iter 13 have 7456 / 8000
* * * * [misc]points:  Computing exacts on every 34 of 544 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 544 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 544 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 544 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 544 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 544 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 421 additional inputs, on iter 14 have 7579 / 8000
* * * * [misc]points:  Computing exacts on every 26 of 421 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 421 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 421 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 421 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 421 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 350 additional inputs, on iter 15 have 7650 / 8000
* * * * [misc]points:  Computing exacts on every 21 of 350 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 350 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 350 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 350 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 350 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 281 additional inputs, on iter 16 have 7719 / 8000
* * * * [misc]points:  Computing exacts on every 17 of 281 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 281 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 281 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 281 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 281 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 221 additional inputs, on iter 17 have 7779 / 8000
* * * * [misc]points:  Computing exacts on every 13 of 221 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 221 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 221 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 221 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 164 additional inputs, on iter 18 have 7836 / 8000
* * * * [misc]points:  Computing exacts on every 10 of 164 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 164 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 164 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 164 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 132 additional inputs, on iter 19 have 7868 / 8000
* * * * [misc]points:  Computing exacts on every 8 of 132 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 132 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 132 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 132 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 103 additional inputs, on iter 20 have 7897 / 8000
* * * * [misc]points:  Computing exacts on every 6 of 103 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 103 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 103 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 76 additional inputs, on iter 21 have 7924 / 8000
* * * * [misc]points:  Computing exacts on every 4 of 76 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 76 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 76 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 65 additional inputs, on iter 22 have 7935 / 8000
* * * * [misc]points:  Computing exacts on every 4 of 65 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 65 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 65 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 55 additional inputs, on iter 23 have 7945 / 8000
* * * * [misc]points:  Computing exacts on every 3 of 55 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 55 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 45 additional inputs, on iter 24 have 7955 / 8000
* * * * [misc]points:  Computing exacts on every 2 of 45 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 45 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 26 additional inputs, on iter 26 have 7974 / 8000
* * * * [misc]points:  Computing exacts for 26 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 21 additional inputs, on iter 27 have 7979 / 8000
* * * * [misc]points:  Computing exacts for 21 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 28 have 7985 / 8000
* * * * [misc]points:  Computing exacts for 15 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 11 additional inputs, on iter 29 have 7989 / 8000
* * * * [misc]points:  Computing exacts for 11 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 10 additional inputs, on iter 30 have 7990 / 8000
* * * * [misc]points:  Computing exacts for 10 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 31 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 8 additional inputs, on iter 32 have 7992 / 8000
* * * * [misc]points:  Computing exacts for 8 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 33 have 7994 / 8000
* * * * [misc]points:  Computing exacts for 6 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 34 have 7996 / 8000
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 35 have 7996 / 8000
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 36 have 7996 / 8000
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 37 have 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 38 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 39 have 7998 / 8000
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 40 have 7999 / 8000
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [exit]points:  Sampled 8000 points with exact outputs