* [misc]progress:  [Phase 1 of 3] Setting up.
* * * [misc]progress:  [1/2] Preparing points
* * * * [misc]points:  Sampling 256 additional inputs, on iter 0 have 0 / 256
* * * * [misc]points:  Computing exacts on every 16 of 256 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 64
* * * * [misc]points:  Setting MPFR precision to 320
* * * * [misc]points:  Setting MPFR precision to 576
* * * * [misc]points:  Computing exacts on every 8 of 256 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 320
* * * * [misc]points:  Setting MPFR precision to 576
* * * * [misc]points:  Setting MPFR precision to 832
* * * * [misc]points:  Computing exacts on every 4 of 256 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 576
* * * * [misc]points:  Setting MPFR precision to 832
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  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 207 additional inputs, on iter 1 have 49 / 256
* * * * [misc]points:  Computing exacts on every 12 of 207 points 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 207 points 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 207 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 207 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 2 have 92 / 256
* * * * [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 137 additional inputs, on iter 3 have 119 / 256
* * * * [misc]points:  Computing exacts on every 8 of 137 points 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 137 points 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 137 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 137 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 114 additional inputs, on iter 4 have 142 / 256
* * * * [misc]points:  Computing exacts on every 7 of 114 points 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 114 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 114 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 89 additional inputs, on iter 5 have 167 / 256
* * * * [misc]points:  Computing exacts on every 5 of 89 points 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 89 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 89 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 75 additional inputs, on iter 6 have 181 / 256
* * * * [misc]points:  Computing exacts on every 4 of 75 points 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 75 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 75 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 64 additional inputs, on iter 7 have 192 / 256
* * * * [misc]points:  Computing exacts on every 4 of 64 points 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 64 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 64 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 8 have 201 / 256
* * * * [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 9 have 211 / 256
* * * * [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 37 additional inputs, on iter 10 have 219 / 256
* * * * [misc]points:  Computing exacts on every 2 of 37 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 37 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 31 additional inputs, on iter 11 have 225 / 256
* * * * [misc]points:  Computing exacts for 31 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 12 have 230 / 256
* * * * [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 22 additional inputs, on iter 13 have 234 / 256
* * * * [misc]points:  Computing exacts for 22 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 15 additional inputs, on iter 14 have 241 / 256
* * * * [misc]points:  Computing exacts for 15 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 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 11 additional inputs, on iter 16 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 11 additional inputs, on iter 17 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 18 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 8 additional inputs, on iter 19 have 248 / 256
* * * * [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 20 have 250 / 256
* * * * [misc]points:  Computing exacts for 6 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 5 additional inputs, on iter 21 have 251 / 256
* * * * [misc]points:  Computing exacts for 5 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 5 additional inputs, on iter 22 have 251 / 256
* * * * [misc]points:  Computing exacts for 5 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 5 additional inputs, on iter 23 have 251 / 256
* * * * [misc]points:  Computing exacts for 5 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 24 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 25 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 26 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 27 have 254 / 256
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 28 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
* * * * [misc]points:  Sampling 4 additional inputs, on iter 29 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 (28 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (54 enodes)
* * [misc]simplify:  iters left: 2 (57 enodes)
* * [misc]simplify:  iters left: 1 (65 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))
* * [misc]progress:  iteration 1 / 4
* * * [misc]progress:  picking best candidate
* * * * [misc]pick:  Picked  #<alt (λ (k n) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 3 ] rewriting at (2 1)
* * * * [misc]progress:  [ 2 / 3 ] rewriting at (2 1 1)
* * * * [misc]progress:  [ 3 / 3 ] rewriting at (2)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 3 ] generating series at (2 1)
* [misc]approximate:  Taking taylor expansion of (pow (* PI (* n 2)) (- 1/2 (/ k 2))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* PI (* n 2)) (- 1/2 (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* PI (* n 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* PI (* n 2)))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 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 (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* PI (* n 2))) in k
* [misc]taylor:  Taking taylor expansion of (* PI (* n 2)) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* n 2) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* n 2) into (* 2 n)
* [misc]backup-simplify:  Simplify (* PI (* 2 n)) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [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 (* PI (* n 2)) (- 1/2 (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* PI (* n 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* PI (* n 2)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* PI (* n 2))) in n
* [misc]taylor:  Taking taylor expansion of (* PI (* n 2)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* PI 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* PI 2) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (- (* 1/2 k)) into (- (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (pow (* PI (* n 2)) (- 1/2 (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* PI (* n 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* PI (* n 2)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* PI (* n 2))) in n
* [misc]taylor:  Taking taylor expansion of (* PI (* n 2)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* PI 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* PI 2) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (- (* 1/2 k)) into (- (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 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 (* 1/2 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 k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 1/2 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [misc]backup-simplify:  Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 2) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 2) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
* [misc]backup-simplify:  Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
* [misc]approximate:  Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 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) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* PI (* (/ 1 n) 2))) in k
* [misc]taylor:  Taking taylor expansion of (* PI (* (/ 1 n) 2)) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (/ 1 n) into (/ 1 n)
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* (/ 1 n) 2) into (/ 2 n)
* [misc]backup-simplify:  Simplify (* PI (/ 2 n)) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
* [misc]taylor:  Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* PI (* (/ 1 n) 2))) in n
* [misc]taylor:  Taking taylor expansion of (* PI (* (/ 1 n) 2)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* PI (* (/ 1 n) 2))) in n
* [misc]taylor:  Taking taylor expansion of (* PI (* (/ 1 n) 2)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 (/ 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 (* 1/2 (/ 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 (/ 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 (* 1/2 1) into 1/2
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [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 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]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 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
* [misc]approximate:  Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 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)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* PI (* (/ 1 (- n)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in k
* [misc]taylor:  Taking taylor expansion of (- n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (/ 1 (- n)) into (/ -1 n)
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* (/ -1 n) 2) into (/ -2 n)
* [misc]backup-simplify:  Simplify (* PI (/ -2 n)) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (- -1/2) into 1/2
* [misc]backup-simplify:  Simplify (+ 0 1/2) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]taylor:  Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* PI (* (/ 1 (- n)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* PI -2) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (- (/ -1/2 k)) into (* 1/2 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* PI (* (/ 1 (- n)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* PI -2) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (- (/ -1/2 k)) into (* 1/2 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 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 (/ 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 1/2 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 (* 1/2 1) into 1/2
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [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 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 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 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 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]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)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
* * * * [misc]progress:  [ 2 / 3 ] generating series at (2 1 1)
* [misc]approximate:  Taking taylor expansion of (* PI (* n 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* PI (* n 2)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* PI (* n 2)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* PI 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* PI 2) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 2) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 2) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) n) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* PI (* (/ 1 n) 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* PI (* (/ 1 n) 2)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* PI (* (/ 1 n) 2)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* PI -2) into (* -2 PI)
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 -2)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 -2))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
* * * * [misc]progress:  [ 3 / 3 ] generating series at (2)
* [misc]approximate:  Taking taylor expansion of (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (pow (* PI (* n 2)) (- 1/2 (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* PI (* n 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* PI (* n 2)))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 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 (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* PI (* n 2))) in k
* [misc]taylor:  Taking taylor expansion of (* PI (* n 2)) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* n 2) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* n 2) into (* 2 n)
* [misc]backup-simplify:  Simplify (* PI (* 2 n)) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [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 (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (pow (* PI (* n 2)) (- 1/2 (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* PI (* n 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* PI (* n 2)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* PI (* n 2))) in n
* [misc]taylor:  Taking taylor expansion of (* PI (* n 2)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* PI 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* PI 2) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (- (* 1/2 k)) into (- (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (pow (* PI (* n 2)) (- 1/2 (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* PI (* n 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* PI (* n 2)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* PI (* n 2))) in n
* [misc]taylor:  Taking taylor expansion of (* PI (* n 2)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* PI 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* PI 2) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (- (* 1/2 k)) into (- (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 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 (* 1/2 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 k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 1/2 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [misc]backup-simplify:  Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (* 0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 2) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (/ 0 (sqrt k))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (+ (* 0 (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 2) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
* [misc]backup-simplify:  Simplify (- (+ (* 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 n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))) (+ (* +nan.0 (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (/ 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 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 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 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (- (+ (* 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 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))) (+ (* +nan.0 (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))))))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
* [misc]approximate:  Taking taylor expansion of (/ (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 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) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* PI (* (/ 1 n) 2))) in k
* [misc]taylor:  Taking taylor expansion of (* PI (* (/ 1 n) 2)) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (/ 1 n) into (/ 1 n)
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* (/ 1 n) 2) into (/ 2 n)
* [misc]backup-simplify:  Simplify (* PI (/ 2 n)) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 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 (/ (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) into (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* PI (* (/ 1 n) 2))) in n
* [misc]taylor:  Taking taylor expansion of (* PI (* (/ 1 n) 2)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 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 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt (/ 1 k))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* PI (* (/ 1 n) 2))) in n
* [misc]taylor:  Taking taylor expansion of (* PI (* (/ 1 n) 2)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 1 2) into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 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 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt (/ 1 k))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 (/ 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 (* 1/2 (/ 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 (/ 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 (* 1/2 1) into 1/2
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [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 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2))))))))
* [misc]approximate:  Taking taylor expansion of (/ (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 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)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* PI (* (/ 1 (- n)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in k
* [misc]taylor:  Taking taylor expansion of (- n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (/ 1 (- n)) into (/ -1 n)
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* (/ -1 n) 2) into (/ -2 n)
* [misc]backup-simplify:  Simplify (* PI (/ -2 n)) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (- -1/2) into 1/2
* [misc]backup-simplify:  Simplify (+ 0 1/2) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
* [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 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* PI (* (/ 1 (- n)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* PI -2) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (- (/ -1/2 k)) into (* 1/2 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (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)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k)))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* PI (* (/ 1 (- n)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* -1 2) into -2
* [misc]backup-simplify:  Simplify (* PI -2) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (- (/ -1/2 k)) into (* 1/2 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (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)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k)))
* [misc]taylor:  Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 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 (/ 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 1/2 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 (* 1/2 1) into 1/2
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [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 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (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)) 1/2) (- (log (* -2 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (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)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 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 (- 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)) 1/2) (- (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)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
* * * [misc]progress:  simplifying candidates
* * * * [misc]progress:  [ 1 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (47 enodes)
* * [misc]simplify:  iters left: 3 (109 enodes)
* * [misc]simplify:  iters left: 2 (300 enodes)
* [exit]simplify:  Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))) (sqrt k)))
* * * * [misc]progress:  [ 2 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* PI (* n 2))) (- 1/2 (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 3 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* PI (* n 2)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* PI (* n 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 (* (* 2 n) PI)
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 4 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* PI (* n 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 (* (* 2 n) PI) (/ k 2))
* [misc]simplify:  Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 5 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (cbrt (- 1/2 (/ k 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* * [misc]simplify:  iters left: 3 (11 enodes)
* [exit]simplify:  Simplified to (cbrt (- 1/2 (/ k 2)))
* [misc]simplify:  Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 6 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (- 1/2 (/ k 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* * [misc]simplify:  iters left: 3 (11 enodes)
* [exit]simplify:  Simplified to (sqrt (- 1/2 (/ k 2)))
* [misc]simplify:  Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 7 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (- 1/2 (/ k 2))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* * [misc]simplify:  iters left: 2 (10 enodes)
* [exit]simplify:  Simplified to (- 1/2 (/ k 2))
* [misc]simplify:  Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 8 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* PI (* n 2)) (- (/ k 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) (- (/ k 2)))
* [misc]simplify:  Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 9 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (- (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* PI (* n 2)) (- (/ k 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) (- (/ k 2)))
* [misc]simplify:  Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 10 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow PI (- 1/2 (/ k 2)))
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (9 enodes)
* * [misc]simplify:  iters left: 3 (12 enodes)
* [exit]simplify:  Simplified to (pow PI (- 1/2 (/ k 2)))
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 11 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1) (sqrt k)))>
* * * * [misc]progress:  [ 12 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 13 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 14 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 15 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 16 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 17 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 18 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 19 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (log (* PI (* n 2)))) (- 1/2 (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 20 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log (exp (* PI (* n 2)))) (- 1/2 (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 21 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt (* PI (* n 2))) (cbrt (* PI (* n 2)))) (cbrt (* PI (* n 2)))) (- 1/2 (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 22 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* PI (* n 2)) (* PI (* n 2))) (* PI (* n 2)))) (- 1/2 (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 23 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt (* PI (* n 2))) (sqrt (* PI (* n 2)))) (- 1/2 (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 24 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* PI (* n 2))) (- 1/2 (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 25 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 26 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 27 / 77 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1))>
* * * * [misc]progress:  [ 28 / 77 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (53 enodes)
* * [misc]simplify:  iters left: 3 (137 enodes)
* * [misc]simplify:  iters left: 2 (487 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k)))))
* * * * [misc]progress:  [ 29 / 77 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (53 enodes)
* * [misc]simplify:  iters left: 3 (137 enodes)
* * [misc]simplify:  iters left: 2 (487 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k)))))
* * * * [misc]progress:  [ 30 / 77 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (log (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (71 enodes)
* * [misc]simplify:  iters left: 2 (208 enodes)
* [exit]simplify:  Simplified to (- (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (log (sqrt k)))))
* * * * [misc]progress:  [ 31 / 77 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))>
* * * * [misc]progress:  [ 32 / 77 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))>
* * * * [misc]progress:  [ 33 / 77 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (* (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (67 enodes)
* * [misc]simplify:  iters left: 3 (124 enodes)
* * [misc]simplify:  iters left: 2 (195 enodes)
* * [misc]simplify:  iters left: 1 (309 enodes)
* [exit]simplify:  Simplified to (* (* (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (* k (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (cbrt (* (* (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (* k (sqrt k))))))
* * * * [misc]progress:  [ 34 / 77 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))>
* * * * [misc]progress:  [ 35 / 77 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))>
* * * * [misc]progress:  [ 36 / 77 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))>
* * * * [misc]progress:  [ 37 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (- (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (- (sqrt k))))>
* * * * [misc]progress:  [ 38 / 77 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (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 (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 39 / 77 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (pow (* PI (* n 2)) (- (/ k 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 (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 40 / 77 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* PI (* n 2)) 1/2) 1) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow (* PI (* n 2)) 1/2) 1)
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (sqrt (* (* PI 2) n))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))))
* * * * [misc]progress:  [ 41 / 77 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (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 (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 42 / 77 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (pow (* PI (* n 2)) (- (/ k 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 (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 43 / 77 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* PI (* n 2)) 1/2) 1) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow (* PI (* n 2)) 1/2) 1)
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (sqrt (* (* PI 2) n))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k))))
* * * * [misc]progress:  [ 44 / 77 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (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 PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 45 / 77 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 46 / 77 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow PI (- 1/2 (/ k 2))) 1) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow PI (- 1/2 (/ k 2))) 1)
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* [exit]simplify:  Simplified to (pow PI (- 1/2 (/ k 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k))))
* * * * [misc]progress:  [ 47 / 77 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ 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 (46 enodes)
* * [misc]simplify:  iters left: 3 (50 enodes)
* * [misc]simplify:  iters left: 2 (53 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 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 (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 48 / 77 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 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 (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 49 / 77 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1) (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1)
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (54 enodes)
* * [misc]simplify:  iters left: 2 (80 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 50 / 77 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (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 (34 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 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 (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 51 / 77 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 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 (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 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 (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 52 / 77 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1)
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 53 / 77 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- 1/2 (/ 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)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 54 / 77 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ 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)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 55 / 77 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ (pow (* PI (* n 2)) (- 1/2 (/ 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
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* 1 (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k))))
* * * * [misc]progress:  [ 56 / 77 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k))))>
* * * * [misc]progress:  [ 57 / 77 ] simplifiying candidate #<alt (λ (k n) (* (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (/ 1 (sqrt k))))>
* * * * [misc]progress:  [ 58 / 77 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))>
* * * * [misc]progress:  [ 59 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
* [enter]simplify:  Simplifying (cbrt (sqrt k))
* * [misc]simplify:  iters left: 2 (3 enodes)
* [exit]simplify:  Simplified to (cbrt (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 60 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
* [enter]simplify:  Simplifying (sqrt (sqrt k))
* * [misc]simplify:  iters left: 2 (3 enodes)
* [exit]simplify:  Simplified to (sqrt (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 61 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt k)
* * [misc]simplify:  iters left: 1 (2 enodes)
* [exit]simplify:  Simplified to (sqrt k)
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1) (sqrt k)))
* * * * [misc]progress:  [ 62 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* PI (* n 2)) 1/2) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2))))))>
* [enter]simplify:  Simplifying (pow (* PI (* n 2)) 1/2)
* * [misc]simplify:  iters left: 5 (7 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 (sqrt (* (* 2 n) PI))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2))))))
* * * * [misc]progress:  [ 63 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* PI (* n 2)) 1/2) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2))))))>
* [enter]simplify:  Simplifying (pow (* PI (* n 2)) 1/2)
* * [misc]simplify:  iters left: 5 (7 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 (sqrt (* (* 2 n) PI))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2))))))
* * * * [misc]progress:  [ 64 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))))>
* [enter]simplify:  Simplifying (pow PI (- 1/2 (/ k 2)))
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (9 enodes)
* * [misc]simplify:  iters left: 3 (12 enodes)
* [exit]simplify:  Simplified to (pow PI (- 1/2 (/ k 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2))))))
* * * * [misc]progress:  [ 65 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))>
* [enter]simplify:  Simplifying (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))
* * * * [misc]progress:  [ 66 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))>
* [enter]simplify:  Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (26 enodes)
* * [misc]simplify:  iters left: 3 (27 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))))))
* * * * [misc]progress:  [ 67 / 77 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))>
* * * * [misc]progress:  [ 68 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* PI (* n 2)) 1/2) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (pow (* PI (* n 2)) 1/2)
* * [misc]simplify:  iters left: 5 (7 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 (sqrt (* (* 2 n) PI))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* * * * [misc]progress:  [ 69 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) (sqrt k)))>
* [enter]simplify:  Simplifying (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
* * [misc]simplify:  iters left: 6 (37 enodes)
* * [misc]simplify:  iters left: 5 (105 enodes)
* * [misc]simplify:  iters left: 4 (339 enodes)
* [exit]simplify:  Simplified to (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) (sqrt k)))
* * * * [misc]progress:  [ 70 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (64 enodes)
* * [misc]simplify:  iters left: 3 (171 enodes)
* [exit]simplify:  Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) (sqrt k)))
* * * * [misc]progress:  [ 71 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (65 enodes)
* * [misc]simplify:  iters left: 3 (200 enodes)
* [exit]simplify:  Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k)))
* * * * [misc]progress:  [ 72 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* 2 (* n PI))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* * [misc]simplify:  iters left: 2 (15 enodes)
* * [misc]simplify:  iters left: 1 (17 enodes)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 73 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* 2 (* n PI))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* * [misc]simplify:  iters left: 2 (15 enodes)
* * [misc]simplify:  iters left: 1 (17 enodes)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 74 / 77 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* 2 (* n PI))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* * [misc]simplify:  iters left: 2 (15 enodes)
* * [misc]simplify:  iters left: 1 (17 enodes)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 75 / 77 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
* [misc]simplify:  Simplified (2) to (λ (k n) +nan.0)
* * * * [misc]progress:  [ 76 / 77 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2))))))))
* [misc]simplify:  Simplified (2) to (λ (k n) +nan.0)
* * * * [misc]progress:  [ 77 / 77 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
* [misc]simplify:  Simplified (2) to (λ (k n) +nan.0)
* * * [misc]progress:  adding candidates to table
* * [misc]progress:  iteration 2 / 4
* * * [misc]progress:  picking best candidate
* * * * [misc]pick:  Picked  #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ 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 2)
* * * * [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 (* 2 (* n PI)) (- 1/2 (/ k 2))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* 2 (* n PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* 2 (* n PI)))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 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 (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* n PI))) in k
* [misc]taylor:  Taking taylor expansion of (* 2 (* n 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 (* 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 (* 2 (* n PI)) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* 2 (* n PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* 2 (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (- (* 1/2 k)) into (- (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* 2 (* n PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* 2 (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (- (* 1/2 k)) into (- (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 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 (* 1/2 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 k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 1/2 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [misc]backup-simplify:  Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
* [misc]backup-simplify:  Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
* [misc]approximate:  Taking taylor expansion of (pow (* 2 (* (/ 1 n) PI)) (- 1/2 (/ (/ 1 k) 2))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* (/ 1 n) PI)) (- 1/2 (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* 2 (* (/ 1 n) PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* 2 (* (/ 1 n) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 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) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* (/ 1 n) PI))) in k
* [misc]taylor:  Taking taylor expansion of (* 2 (* (/ 1 n) 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 (* (/ 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 (* 2 (/ PI n)) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* 2 (* (/ 1 n) PI))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* (/ 1 n) PI)) (- 1/2 (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* 2 (* (/ 1 n) PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* 2 (* (/ 1 n) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* (/ 1 n) PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* (/ 1 n) PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* (/ 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 (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* (/ 1 n) PI)) (- 1/2 (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* 2 (* (/ 1 n) PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* 2 (* (/ 1 n) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* (/ 1 n) PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* (/ 1 n) PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* (/ 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 (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 (/ 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 (* 1/2 (/ 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 (/ 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 (* 1/2 1) into 1/2
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [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 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 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 (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 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 (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 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 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]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 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
* [misc]approximate:  Taking taylor expansion of (pow (* 2 (* (/ 1 (- n)) PI)) (- 1/2 (/ (/ 1 (- k)) 2))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* (/ 1 (- n)) PI)) (- 1/2 (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* 2 (* (/ 1 (- n)) PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* 2 (* (/ 1 (- n)) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 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)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* (/ 1 (- n)) PI))) in k
* [misc]taylor:  Taking taylor expansion of (* 2 (* (/ 1 (- n)) 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 (* (/ 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 (* 2 (* -1 (/ PI n))) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (- -1/2) into 1/2
* [misc]backup-simplify:  Simplify (+ 0 1/2) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* 2 (* (/ 1 (- n)) PI))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* (/ 1 (- n)) PI)) (- 1/2 (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* 2 (* (/ 1 (- n)) PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* 2 (* (/ 1 (- n)) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* (/ 1 (- n)) PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* (/ 1 (- n)) PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* (/ 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 (* 2 (* -1 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (- (/ -1/2 k)) into (* 1/2 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* (/ 1 (- n)) PI)) (- 1/2 (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* 2 (* (/ 1 (- n)) PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* 2 (* (/ 1 (- n)) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* (/ 1 (- n)) PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* (/ 1 (- n)) PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* (/ 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 (* 2 (* -1 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (- (/ -1/2 k)) into (* 1/2 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 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 (/ 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 1/2 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 (* 1/2 1) into 1/2
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [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 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 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 (+ (* 2 0) (* 0 (* -1 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (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 (+ (* 2 0) (+ (* 0 0) (* 0 (* -1 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (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 (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* -1 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 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]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)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
* * * * [misc]progress:  [ 2 / 3 ] generating series at (2 1 1 2)
* [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 (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* 2 (* n PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* 2 (* n PI)))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 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 (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* n PI))) in k
* [misc]taylor:  Taking taylor expansion of (* 2 (* n 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 (* 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 (* 2 (* n PI)) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [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 (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* 2 (* n PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* 2 (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (- (* 1/2 k)) into (- (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* 2 (* n PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* 2 (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (- (* 1/2 k)) into (- (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 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 (* 1/2 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 k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 1/2 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [misc]backup-simplify:  Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (* 0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (/ 0 (sqrt k))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (+ (* 0 (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
* [misc]backup-simplify:  Simplify (- (+ (* 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 n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))) (+ (* +nan.0 (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (/ 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 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 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 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (- (+ (* 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 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))) (+ (* +nan.0 (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))))))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
* [misc]approximate:  Taking taylor expansion of (/ (pow (* 2 (* (/ 1 n) PI)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* 2 (* (/ 1 n) PI)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* (/ 1 n) PI)) (- 1/2 (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* 2 (* (/ 1 n) PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* 2 (* (/ 1 n) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 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) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* (/ 1 n) PI))) in k
* [misc]taylor:  Taking taylor expansion of (* 2 (* (/ 1 n) 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 (* (/ 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 (* 2 (/ PI n)) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* 2 (* (/ 1 n) PI))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 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 (/ (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) into (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* 2 (* (/ 1 n) PI)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* (/ 1 n) PI)) (- 1/2 (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* 2 (* (/ 1 n) PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* 2 (* (/ 1 n) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* (/ 1 n) PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* (/ 1 n) PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* (/ 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 (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 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 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt (/ 1 k))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* 2 (* (/ 1 n) PI)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* (/ 1 n) PI)) (- 1/2 (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* 2 (* (/ 1 n) PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* 2 (* (/ 1 n) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* (/ 1 n) PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* (/ 1 n) PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* (/ 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 (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 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 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt (/ 1 k))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 (/ 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 (* 1/2 (/ 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 (/ 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 (* 1/2 1) into 1/2
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [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 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 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 (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 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 (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2))))))))
* [misc]approximate:  Taking taylor expansion of (/ (pow (* 2 (* (/ 1 (- n)) PI)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* 2 (* (/ 1 (- n)) PI)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* (/ 1 (- n)) PI)) (- 1/2 (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* 2 (* (/ 1 (- n)) PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* 2 (* (/ 1 (- n)) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 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)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* (/ 1 (- n)) PI))) in k
* [misc]taylor:  Taking taylor expansion of (* 2 (* (/ 1 (- n)) 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 (* (/ 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 (* 2 (* -1 (/ PI n))) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (- -1/2) into 1/2
* [misc]backup-simplify:  Simplify (+ 0 1/2) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* 2 (* (/ 1 (- n)) PI))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
* [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 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* 2 (* (/ 1 (- n)) PI)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* (/ 1 (- n)) PI)) (- 1/2 (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* 2 (* (/ 1 (- n)) PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* 2 (* (/ 1 (- n)) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* (/ 1 (- n)) PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* (/ 1 (- n)) PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* (/ 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 (* 2 (* -1 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (- (/ -1/2 k)) into (* 1/2 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (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)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k)))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* 2 (* (/ 1 (- n)) PI)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* 2 (* (/ 1 (- n)) PI)) (- 1/2 (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* 2 (* (/ 1 (- n)) PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* 2 (* (/ 1 (- n)) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* (/ 1 (- n)) PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* (/ 1 (- n)) PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* (/ 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 (* 2 (* -1 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (- (/ -1/2 k)) into (* 1/2 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (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)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k)))
* [misc]taylor:  Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 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 (/ 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 1/2 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 (* 1/2 1) into 1/2
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [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 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (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)) 1/2) (- (log (* -2 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 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 (+ (* 2 0) (* 0 (* -1 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (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)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 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 (- 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 (+ (* 2 0) (+ (* 0 0) (* 0 (* -1 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 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 (- 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)) 1/2) (- (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)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
* * * [misc]progress:  simplifying candidates
* * * * [misc]progress:  [ 1 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* 2 (* n PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* 2 (* n PI))) (- 1/2 (/ k 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (47 enodes)
* * [misc]simplify:  iters left: 3 (109 enodes)
* * [misc]simplify:  iters left: 2 (300 enodes)
* [exit]simplify:  Simplified to (* (- 1/2 (/ k 2)) (log (* (* PI n) 2)))
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (exp (* (- 1/2 (/ k 2)) (log (* (* PI n) 2)))) (sqrt k)))
* * * * [misc]progress:  [ 2 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* 2 (* n PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 3 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* 2 (* n PI))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* * [misc]simplify:  iters left: 2 (15 enodes)
* * [misc]simplify:  iters left: 1 (17 enodes)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 4 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* 2 (* n PI)) 1/2) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* 2 (* n PI)) (/ k 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (18 enodes)
* * [misc]simplify:  iters left: 2 (20 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (/ k 2))
* [misc]simplify:  Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* 2 (* n PI)) 1/2) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 5 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* 2 (* n PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (cbrt (- 1/2 (/ k 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* * [misc]simplify:  iters left: 3 (11 enodes)
* [exit]simplify:  Simplified to (cbrt (- 1/2 (/ k 2)))
* [misc]simplify:  Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* 2 (* n PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 6 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* 2 (* n PI)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (- 1/2 (/ k 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* * [misc]simplify:  iters left: 3 (11 enodes)
* [exit]simplify:  Simplified to (sqrt (- 1/2 (/ k 2)))
* [misc]simplify:  Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* 2 (* n PI)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 7 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* 2 (* n PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (- 1/2 (/ k 2))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* * [misc]simplify:  iters left: 2 (10 enodes)
* [exit]simplify:  Simplified to (- 1/2 (/ k 2))
* [misc]simplify:  Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* 2 (* n PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 8 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* 2 (* n PI)) 1/2) (pow (* 2 (* n PI)) (- (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* 2 (* n PI)) (- (/ k 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 (* (* 2 n) PI) (- (/ k 2)))
* [misc]simplify:  Simplified (2 1 2) to (λ (k n) (/ (* (pow (* 2 (* n PI)) 1/2) (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 9 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* 2 (* n PI)) 1/2) (pow (* 2 (* n PI)) (- (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* 2 (* n PI)) (- (/ k 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 (* (* 2 n) PI) (- (/ k 2)))
* [misc]simplify:  Simplified (2 1 2) to (λ (k n) (/ (* (pow (* 2 (* n PI)) 1/2) (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 10 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow 2 (- 1/2 (/ k 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* * [misc]simplify:  iters left: 3 (11 enodes)
* [exit]simplify:  Simplified to (pow 2 (- 1/2 (/ k 2)))
* [misc]simplify:  Simplified (2 1 1) to (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 11 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) 1) (sqrt k)))>
* * * * [misc]progress:  [ 12 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 13 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 14 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 15 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 16 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
* * * * [misc]progress:  [ 17 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
* * * * [misc]progress:  [ 18 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (pow (* n PI) 1)) (- 1/2 (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 19 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (exp (log (* n PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 20 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (log (exp (* n PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 21 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 22 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (cbrt (* (* (* n PI) (* n PI)) (* n PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 23 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* (sqrt (* n PI)) (sqrt (* n PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 24 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* 1 (* n PI))) (- 1/2 (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 25 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* PI n)) (- 1/2 (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 26 / 76 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)) 1))>
* * * * [misc]progress:  [ 27 / 76 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* 2 (* n PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (* (log (* 2 (* n PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (53 enodes)
* * [misc]simplify:  iters left: 3 (137 enodes)
* * [misc]simplify:  iters left: 2 (487 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* PI n) 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (log (* (* PI n) 2))) (log (sqrt k)))))
* * * * [misc]progress:  [ 28 / 76 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* 2 (* n PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (* (log (* 2 (* n PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (53 enodes)
* * [misc]simplify:  iters left: 3 (137 enodes)
* * [misc]simplify:  iters left: 2 (487 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* PI n) 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (log (* (* PI n) 2))) (log (sqrt k)))))
* * * * [misc]progress:  [ 29 / 76 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (log (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (71 enodes)
* * [misc]simplify:  iters left: 2 (208 enodes)
* [exit]simplify:  Simplified to (- (* (log (* (* PI n) 2)) (- 1/2 (/ k 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (log (* (* PI n) 2)) (- 1/2 (/ k 2))) (log (sqrt k)))))
* * * * [misc]progress:  [ 30 / 76 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
* * * * [misc]progress:  [ 31 / 76 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
* * * * [misc]progress:  [ 32 / 76 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (* (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (67 enodes)
* * [misc]simplify:  iters left: 3 (124 enodes)
* * [misc]simplify:  iters left: 2 (195 enodes)
* * [misc]simplify:  iters left: 1 (309 enodes)
* [exit]simplify:  Simplified to (* (* (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (* k (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (cbrt (* (* (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (* k (sqrt k))))))
* * * * [misc]progress:  [ 33 / 76 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
* * * * [misc]progress:  [ 34 / 76 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
* * * * [misc]progress:  [ 35 / 76 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
* * * * [misc]progress:  [ 36 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (- (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (- (sqrt k))))>
* * * * [misc]progress:  [ 37 / 76 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* 2 (* n PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (* (* PI n) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* PI n) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (pow (* 2 (* n PI)) (- (/ k 2))) (cbrt (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) (- (/ k 2))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* PI n) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI n) 2) (- (/ k 2))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 38 / 76 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* 2 (* n PI)) 1/2) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (pow (* 2 (* n PI)) (- (/ k 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) (- (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 39 / 76 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) 1/2) 1) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow (* 2 (* n PI)) 1/2) 1)
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (sqrt (* (* 2 PI) n))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k))))
* * * * [misc]progress:  [ 40 / 76 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* 2 (* n PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (* (* PI n) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* PI n) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (pow (* 2 (* n PI)) (- (/ k 2))) (cbrt (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) (- (/ k 2))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* PI n) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI n) 2) (- (/ k 2))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 41 / 76 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* 2 (* n PI)) 1/2) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (pow (* 2 (* n PI)) (- (/ k 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) (- (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 42 / 76 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) 1/2) 1) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow (* 2 (* n PI)) 1/2) 1)
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (sqrt (* (* 2 PI) n))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k))))
* * * * [misc]progress:  [ 43 / 76 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (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 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 44 / 76 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* [exit]simplify:  Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 45 / 76 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow 2 (- 1/2 (/ k 2))) 1)
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* [exit]simplify:  Simplified to (pow 2 (- 1/2 (/ k 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
* * * * [misc]progress:  [ 46 / 76 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ 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 (46 enodes)
* * [misc]simplify:  iters left: 3 (50 enodes)
* * [misc]simplify:  iters left: 2 (53 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 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 (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 47 / 76 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 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 (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 48 / 76 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1) (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1)
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (54 enodes)
* * [misc]simplify:  iters left: 2 (80 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 49 / 76 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (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 (34 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 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 (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 50 / 76 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 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 (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 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 (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 51 / 76 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) 1)
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (21 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 (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 52 / 76 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 (* n PI)) (- 1/2 (/ 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)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 53 / 76 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- 1/2 (/ 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)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 54 / 76 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ (pow (* 2 (* n PI)) (- 1/2 (/ 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
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* 1 (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))))
* * * * [misc]progress:  [ 55 / 76 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))))>
* * * * [misc]progress:  [ 56 / 76 ] simplifiying candidate #<alt (λ (k n) (* (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (/ 1 (sqrt k))))>
* * * * [misc]progress:  [ 57 / 76 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))))>
* * * * [misc]progress:  [ 58 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
* [enter]simplify:  Simplifying (cbrt (sqrt k))
* * [misc]simplify:  iters left: 2 (3 enodes)
* [exit]simplify:  Simplified to (cbrt (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 59 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
* [enter]simplify:  Simplifying (sqrt (sqrt k))
* * [misc]simplify:  iters left: 2 (3 enodes)
* [exit]simplify:  Simplified to (sqrt (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 60 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) 1) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt k)
* * [misc]simplify:  iters left: 1 (2 enodes)
* [exit]simplify:  Simplified to (sqrt k)
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) 1) (sqrt k)))
* * * * [misc]progress:  [ 61 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) 1/2) (/ (sqrt k) (pow (* 2 (* n PI)) (- (/ k 2))))))>
* [enter]simplify:  Simplifying (pow (* 2 (* n PI)) 1/2)
* * [misc]simplify:  iters left: 5 (7 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 (sqrt (* (* PI n) 2))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (sqrt (* (* PI n) 2)) (/ (sqrt k) (pow (* 2 (* n PI)) (- (/ k 2))))))
* * * * [misc]progress:  [ 62 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) 1/2) (/ (sqrt k) (pow (* 2 (* n PI)) (- (/ k 2))))))>
* [enter]simplify:  Simplifying (pow (* 2 (* n PI)) 1/2)
* * [misc]simplify:  iters left: 5 (7 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 (sqrt (* (* PI n) 2))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (sqrt (* (* PI n) 2)) (/ (sqrt k) (pow (* 2 (* n PI)) (- (/ k 2))))))
* * * * [misc]progress:  [ 63 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (pow 2 (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n PI) (- 1/2 (/ k 2))))))>
* [enter]simplify:  Simplifying (pow 2 (- 1/2 (/ k 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* * [misc]simplify:  iters left: 3 (11 enodes)
* [exit]simplify:  Simplified to (pow 2 (- 1/2 (/ k 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (pow 2 (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n PI) (- 1/2 (/ k 2))))))
* * * * [misc]progress:  [ 64 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))))>
* [enter]simplify:  Simplifying (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (* (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))))
* * * * [misc]progress:  [ 65 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))))>
* [enter]simplify:  Simplifying (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (26 enodes)
* * [misc]simplify:  iters left: 3 (27 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))))
* * * * [misc]progress:  [ 66 / 76 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))))>
* * * * [misc]progress:  [ 67 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) 1/2) (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2)))))>
* [enter]simplify:  Simplifying (pow (* 2 (* n PI)) 1/2)
* * [misc]simplify:  iters left: 5 (7 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 (sqrt (* (* PI n) 2))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (sqrt (* (* PI n) 2)) (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2)))))
* * * * [misc]progress:  [ 68 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) (sqrt k)))>
* [enter]simplify:  Simplifying (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
* * [misc]simplify:  iters left: 6 (37 enodes)
* * [misc]simplify:  iters left: 5 (105 enodes)
* * [misc]simplify:  iters left: 4 (339 enodes)
* [exit]simplify:  Simplified to (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) (sqrt k)))
* * * * [misc]progress:  [ 69 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (64 enodes)
* * [misc]simplify:  iters left: 3 (171 enodes)
* [exit]simplify:  Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) (sqrt k)))
* * * * [misc]progress:  [ 70 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (65 enodes)
* * [misc]simplify:  iters left: 3 (200 enodes)
* [exit]simplify:  Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k)))
* * * * [misc]progress:  [ 71 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n PI)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n PI)
* [misc]simplify:  Simplified (2 1 1 2) to (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 72 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n PI)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n PI)
* [misc]simplify:  Simplified (2 1 1 2) to (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 73 / 76 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n PI)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n PI)
* [misc]simplify:  Simplified (2 1 1 2) to (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))
* * * * [misc]progress:  [ 74 / 76 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
* [misc]simplify:  Simplified (2) to (λ (k n) +nan.0)
* * * * [misc]progress:  [ 75 / 76 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2))))))))
* [misc]simplify:  Simplified (2) to (λ (k n) +nan.0)
* * * * [misc]progress:  [ 76 / 76 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
* [misc]simplify:  Simplified (2) to (λ (k n) +nan.0)
* * * [misc]progress:  adding candidates to table
* * [misc]progress:  iteration 3 / 4
* * * [misc]progress:  picking best candidate
* * * * [misc]pick:  Picked  #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 4 ] rewriting at (2)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2 2 1)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2 2 1 1)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2 2)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 4 ] generating series at (2)
* [misc]approximate:  Taking taylor expansion of (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) in n
* [misc]taylor:  Taking taylor expansion of (pow 2 (- 1/2 (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log 2)) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log 2) 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 k)) into (- (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 k)) (log 2)) into (* (log 2) (- 1/2 (* 1/2 k)))
* [misc]backup-simplify:  Simplify (exp (* (log 2) (- 1/2 (* 1/2 k)))) into (exp (* (log 2) (- 1/2 (* 1/2 k))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (pow (* n PI) (- 1/2 (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 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)) 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 (- (* 1/2 k)) into (- (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (sqrt k)) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (sqrt (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) in k
* [misc]taylor:  Taking taylor expansion of (pow 2 (- 1/2 (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log 2)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 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 (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log 2) 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 0) into 1/2
* [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) (- 1/2 (/ k 2))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (pow (* n PI) (- 1/2 (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* n PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* n PI))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 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 (/ 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)) 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 0) into 1/2
* [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 (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) +nan.0) into (* +nan.0 (sqrt (* n PI)))
* [misc]taylor:  Taking taylor expansion of (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) in k
* [misc]taylor:  Taking taylor expansion of (pow 2 (- 1/2 (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log 2)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 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 (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log 2) 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 0) into 1/2
* [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) (- 1/2 (/ k 2))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (pow (* n PI) (- 1/2 (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* n PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* n PI))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 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 (/ 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)) 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 0) into 1/2
* [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 (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) +nan.0) into (* +nan.0 (sqrt (* n PI)))
* [misc]backup-simplify:  Simplify (* (pow 2 1/2) (* +nan.0 (sqrt (* n PI)))) into (* +nan.0 (sqrt (* PI (* n 2))))
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (sqrt (* PI (* n 2)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (sqrt (* PI (* n 2))) in n
* [misc]taylor:  Taking taylor expansion of (* PI (* n 2)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* PI 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* PI 2) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ (* 2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* n 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* n PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* -1/2 (log (* n PI)))) into (- (* 1/2 (log (* n PI))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* n PI)))) (+ (* (/ (pow (- (* 1/2 (log (* n PI)))) 1) 1)))) into (* -1/2 (* (log (* n PI)) (sqrt (* n PI))))
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ (* -1/2 (* (log (* n PI)) (sqrt (* n PI)))) +nan.0) (+ (* (* +nan.0 (sqrt (* n PI))) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (log (* n PI)) (sqrt (* n PI)))) (- (* +nan.0 (sqrt (* n PI))))))
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* -1/2 (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 (+ (* (pow 2 1/2) (- (+ (* +nan.0 (* (log (* n PI)) (sqrt (* n PI)))) (- (* +nan.0 (sqrt (* n PI))))))) (* (* -1/2 (* (log 2) (sqrt 2))) (* +nan.0 (sqrt (* n PI))))) into (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))))
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (log 2) (sqrt 2)) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (log 2) (sqrt 2)) in n
* [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]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (log (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (log (* 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]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (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 (* (log 2) (sqrt 2)) into (* (log 2) (sqrt 2))
* [misc]backup-simplify:  Simplify (* (* (log 2) (sqrt 2)) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
* [misc]backup-simplify:  Simplify (* (sqrt 2) (+ (log PI) (log n))) into (* (sqrt 2) (+ (log PI) (log n)))
* [misc]backup-simplify:  Simplify (* (* (sqrt 2) (+ (log PI) (log n))) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (* (sqrt 2) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 PI))
* [misc]backup-simplify:  Simplify (- (* +nan.0 PI)) into (- (* +nan.0 PI))
* [misc]backup-simplify:  Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* n PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* n PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 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) (+ (* -1/2 0) (* 0 (log (* n PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* n PI)))) (+ (* (/ (pow (- (* 1/2 (log (* n PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log (* n PI)) 2) (sqrt (* n PI))))
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ (* 1/8 (* (pow (log (* n PI)) 2) (sqrt (* n PI)))) +nan.0) (+ (* (* +nan.0 (sqrt (* n PI))) (/ +nan.0 +nan.0)) (* (- (+ (* +nan.0 (* (log (* n PI)) (sqrt (* n PI)))) (- (* +nan.0 (sqrt (* n PI)))))) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (log (* n PI)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (pow (log (* n PI)) 2) (sqrt (* n PI)))) (- (* +nan.0 (sqrt (* n 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 2) (+ (* 1/2 (/ 0 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) (+ (* -1/2 0) (* 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 (+ (* (pow 2 1/2) (- (+ (* +nan.0 (* (log (* n PI)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (pow (log (* n PI)) 2) (sqrt (* n PI)))) (- (* +nan.0 (sqrt (* n PI))))))))) (+ (* (* -1/2 (* (log 2) (sqrt 2))) (- (+ (* +nan.0 (* (log (* n PI)) (sqrt (* n PI)))) (- (* +nan.0 (sqrt (* n PI))))))) (* (* 1/8 (* (pow (log 2) 2) (sqrt 2))) (* +nan.0 (sqrt (* n PI)))))) into (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))))))))))
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (log 2) (sqrt 2)) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (log 2) (sqrt 2)) in n
* [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]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (pow (log 2) 2) (sqrt 2)) in n
* [misc]taylor:  Taking taylor expansion of (pow (log 2) 2) in n
* [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]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (log 2) (* (sqrt 2) (log (* n PI)))) in n
* [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]taylor:  Taking taylor expansion of (* (sqrt 2) (log (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (log (* 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]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (pow (log (* n PI)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (pow (log (* n PI)) 2) in n
* [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 PI) (log 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 (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (log (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (log (* 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]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (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 (* (log 2) (sqrt 2)) into (* (log 2) (sqrt 2))
* [misc]backup-simplify:  Simplify (* (* (log 2) (sqrt 2)) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (* (log 2) (log 2)) into (pow (log 2) 2)
* [misc]backup-simplify:  Simplify (* (pow (log 2) 2) (sqrt 2)) into (* (pow (log 2) 2) (sqrt 2))
* [misc]backup-simplify:  Simplify (* (* (pow (log 2) 2) (sqrt 2)) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
* [misc]backup-simplify:  Simplify (* (sqrt 2) (+ (log PI) (log n))) into (* (sqrt 2) (+ (log PI) (log n)))
* [misc]backup-simplify:  Simplify (* (log 2) (* (sqrt 2) (+ (log PI) (log n)))) into (* (log 2) (* (sqrt 2) (+ (log PI) (log n))))
* [misc]backup-simplify:  Simplify (* (* (log 2) (* (sqrt 2) (+ (log PI) (log n)))) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
* [misc]backup-simplify:  Simplify (* (+ (log PI) (log n)) (+ (log PI) (log n))) into (pow (+ (log PI) (log n)) 2)
* [misc]backup-simplify:  Simplify (* (sqrt 2) (pow (+ (log PI) (log n)) 2)) into (* (sqrt 2) (pow (+ (log PI) (log n)) 2))
* [misc]backup-simplify:  Simplify (* (* (sqrt 2) (pow (+ (log PI) (log n)) 2)) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
* [misc]backup-simplify:  Simplify (* (sqrt 2) (+ (log PI) (log n))) into (* (sqrt 2) (+ (log PI) (log n)))
* [misc]backup-simplify:  Simplify (* (* (sqrt 2) (+ (log PI) (log n))) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (* (sqrt 2) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (log 2) 0) (* 0 (sqrt 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (log 2) (sqrt 2)) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))) (* 0 0)) into (- (* +nan.0 (* (log 2) (* (sqrt 2) 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 (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
* [misc]backup-simplify:  Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log PI) (log n)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (sqrt 2) (+ (log PI) (log n))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))))
* [misc]backup-simplify:  Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
* [misc]backup-simplify:  Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
* [misc]backup-simplify:  Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))
* [misc]backup-simplify:  Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))
* [misc]backup-simplify:  Simplify (+ (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))
* [misc]backup-simplify:  Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 2) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (pow PI 2)))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (pow PI 2))) into (- (* +nan.0 (pow PI 2)))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (pow PI 2))) (* (pow n 2) (/ 1 k))) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) (* n 1)) (* (- (* +nan.0 PI)) (* n (/ 1 k))))) into (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) k)) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (log n))))) (- (* +nan.0 (/ (* n PI) k)))))))))))))
* [misc]approximate:  Taking taylor expansion of (* (pow 2 (- 1/2 (/ (/ 1 k) 2))) (/ (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (* (pow 2 (- 1/2 (/ (/ 1 k) 2))) (/ (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow 2 (- 1/2 (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log 2)) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log 2) 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 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))
* [misc]backup-simplify:  Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* (/ 1 n) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* (/ 1 n) PI))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 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)) 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 (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))
* [misc]backup-simplify:  Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 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 (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) into (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (* (pow 2 (- 1/2 (/ (/ 1 k) 2))) (/ (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow 2 (- 1/2 (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log 2)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 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) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log 2) 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) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* -1/2 (log 2)) into (* -1/2 (log 2))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 k) 2)) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* (/ 1 n) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* (/ 1 n) PI))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 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) 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)) 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) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n)))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* (/ 1 n) PI)))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 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 (/ (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) into (* +nan.0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (* (pow 2 (- 1/2 (/ (/ 1 k) 2))) (/ (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow 2 (- 1/2 (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log 2)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 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) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log 2) 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) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* -1/2 (log 2)) into (* -1/2 (log 2))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 k) 2)) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* (/ 1 n) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* (/ 1 n) PI))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 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) 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)) 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) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n)))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* (/ 1 n) PI)))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 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 (/ (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) into (* +nan.0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]backup-simplify:  Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* +nan.0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))) into (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n
* [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]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))
* [misc]backup-simplify:  Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))
* [misc]backup-simplify:  Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]backup-simplify:  Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (- (* +nan.0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) (* 0 (* +nan.0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n
* [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]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))
* [misc]backup-simplify:  Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))
* [misc]backup-simplify:  Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]backup-simplify:  Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log PI) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) 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) 1)) (pow 2 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (log 2) 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* +nan.0 0) (* 0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (- (* +nan.0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) (+ (* 0 (- (* +nan.0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) (* 0 (* +nan.0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n
* [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]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))
* [misc]backup-simplify:  Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))
* [misc]backup-simplify:  Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]backup-simplify:  Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (* 1 (/ 1 k))) (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))))) into (- (+ (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k)))))) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))))))))
* [misc]approximate:  Taking taylor expansion of (* (pow 2 (- 1/2 (/ (/ 1 (- k)) 2))) (/ (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (* (pow 2 (- 1/2 (/ (/ 1 (- k)) 2))) (/ (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) in n
* [misc]taylor:  Taking taylor expansion of (pow 2 (- 1/2 (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log 2)) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log 2) 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 k)) into (* 1/2 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))
* [misc]backup-simplify:  Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* (/ 1 (- n)) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* (/ 1 (- n)) PI))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- 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)) 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 (- (/ -1/2 k)) into (* 1/2 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 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)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k)))
* [misc]taylor:  Taking taylor expansion of (* (pow 2 (- 1/2 (/ (/ 1 (- k)) 2))) (/ (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) in k
* [misc]taylor:  Taking taylor expansion of (pow 2 (- 1/2 (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log 2)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 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)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log 2) 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) into 1/2
* [misc]backup-simplify:  Simplify (+ 0 1/2) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* (/ 1 (- n)) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* (/ 1 (- n)) PI))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 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)) 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)) 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) into 1/2
* [misc]backup-simplify:  Simplify (+ 0 1/2) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -1 (/ PI n)))) into (* 1/2 (log (* -1 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* (/ 1 (- n)) PI)))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
* [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 (/ (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]taylor:  Taking taylor expansion of (* (pow 2 (- 1/2 (/ (/ 1 (- k)) 2))) (/ (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) in k
* [misc]taylor:  Taking taylor expansion of (pow 2 (- 1/2 (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log 2)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 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)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log 2) 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) into 1/2
* [misc]backup-simplify:  Simplify (+ 0 1/2) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* (/ 1 (- n)) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* (/ 1 (- n)) PI))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 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)) 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)) 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) into 1/2
* [misc]backup-simplify:  Simplify (+ 0 1/2) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -1 (/ PI n)))) into (* 1/2 (log (* -1 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* (/ 1 (- n)) PI)))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
* [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 (/ (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]backup-simplify:  Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* +nan.0 (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* -1 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -1 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -1 in n
* [misc]backup-simplify:  Simplify -1 into -1
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) 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 (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n
* [misc]taylor:  Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n
* [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]taylor:  Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))
* [misc]backup-simplify:  Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (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 (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (- (* +nan.0 (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))))) (* 0 (* +nan.0 (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* -1 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -1 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -1 in n
* [misc]backup-simplify:  Simplify -1 into -1
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) 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 (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n
* [misc]taylor:  Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n
* [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]taylor:  Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))
* [misc]backup-simplify:  Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (log 2) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* PI (/ 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 (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) 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)) 1/2) 0) (* 0 (- (log (* -1 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 0) (* 0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* +nan.0 0) (* 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (- (* +nan.0 (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))))) (+ (* 0 (- (* +nan.0 (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))))) (* 0 (* +nan.0 (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* -1 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -1 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -1 in n
* [misc]backup-simplify:  Simplify -1 into -1
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) 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 (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n
* [misc]taylor:  Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n
* [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]taylor:  Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))
* [misc]backup-simplify:  Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (* +nan.0 (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k)))))))))))
* * * * [misc]progress:  [ 2 / 4 ] generating series at (2 2 1)
* [misc]approximate:  Taking taylor expansion of (pow (* n PI) (- 1/2 (/ k 2))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* n PI) (- 1/2 (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* n PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* n PI))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 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 (/ 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)) 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 0) into 1/2
* [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) (- 1/2 (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 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)) 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 (- (* 1/2 k)) into (- (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* n PI) (- 1/2 (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 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)) 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 (- (* 1/2 k)) into (- (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))))
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 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 (* 1/2 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 k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 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 (* 1/2 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [misc]backup-simplify:  Simplify (+ (log PI) (log n)) into (+ (log PI) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log PI) (log n))) into (* 1/2 (+ (log PI) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log PI) (log n)))) into (exp (* 1/2 (+ (log PI) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log PI) (log n)))) into (exp (* 1/2 (+ (log PI) (log n))))
* [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 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log PI) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 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 (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 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 1) (* 0 0)) into 1/2
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* -1/2 (+ (log PI) (log n)))) into (- (+ (* 1/2 (log PI)) (* 1/2 (log n))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n)))))
* [misc]backup-simplify:  Simplify (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n)))))
* [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 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log PI) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 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 (/ (+ (* -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 (/ (* (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 1) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log PI) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n))))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n)))))) into (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n))))))
* [misc]backup-simplify:  Simplify (+ (* (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log PI) (log n)))))) into (- (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (+ (* 1/4 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (exp (* 1/2 (+ (log PI) (log n))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) k)))))
* [misc]approximate:  Taking taylor expansion of (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* (/ 1 n) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* (/ 1 n) PI))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 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) 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)) 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) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n)))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* (/ 1 n) PI)))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* (/ 1 n) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* (/ 1 n) PI))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 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)) 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 (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))
* [misc]backup-simplify:  Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* (/ 1 n) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* (/ 1 n) PI))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 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)) 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 (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))
* [misc]backup-simplify:  Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
* [misc]taylor:  Taking taylor expansion of (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
* [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]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 (/ 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 (* 1/2 (/ 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 (/ 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 (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log PI) (- (log n))) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 1) into 1/2
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* (- (log PI) (log n)) -1/2) into (* -1/2 (- (log PI) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]backup-simplify:  Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
* [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 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log PI) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 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 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 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log PI) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 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 (- (+ (* 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 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log PI) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n)))))
* [misc]approximate:  Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* (/ 1 (- n)) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* (/ 1 (- n)) PI))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 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)) 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)) 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) into 1/2
* [misc]backup-simplify:  Simplify (+ 0 1/2) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -1 (/ PI n)))) into (* 1/2 (log (* -1 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* (/ 1 (- n)) PI)))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* (/ 1 (- n)) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* (/ 1 (- n)) PI))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- 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)) 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 (- (/ -1/2 k)) into (* 1/2 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* (/ 1 (- n)) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* (/ 1 (- n)) PI))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- 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)) 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 (- (/ -1/2 k)) into (* 1/2 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 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 (/ 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 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [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 (* 1/2 1) into 1/2
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [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 (* 1/2 (- (log (* -1 PI)) (log n))) into (* 1/2 (- (log (* -1 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (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 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -1 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (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 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (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 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (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)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n)))))) into (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k))))
* * * * [misc]progress:  [ 3 / 4 ] generating series at (2 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:  [ 4 / 4 ] generating series at (2 2)
* [misc]approximate:  Taking taylor expansion of (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (pow (* n PI) (- 1/2 (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* n PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* n PI))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 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 (/ 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)) 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 0) into 1/2
* [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 (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) +nan.0) into (* +nan.0 (sqrt (* n PI)))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (pow (* n PI) (- 1/2 (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 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)) 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 (- (* 1/2 k)) into (- (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (sqrt k)) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (sqrt (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (pow (* n PI) (- 1/2 (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 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)) 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 (- (* 1/2 k)) into (- (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (sqrt k)) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (sqrt (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 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 (* 1/2 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 k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 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 (* 1/2 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [misc]backup-simplify:  Simplify (+ (log PI) (log n)) into (+ (log PI) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log PI) (log n))) into (* 1/2 (+ (log PI) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log PI) (log n)))) into (exp (* 1/2 (+ (log 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 k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) 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 (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log PI) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (sqrt (/ 1 k))) (/ 0 (sqrt k))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 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 1) (* 0 0)) into 1/2
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* -1/2 (+ (log PI) (log n)))) into (- (+ (* 1/2 (log PI)) (* 1/2 (log n))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n)))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log PI) (log n)))) +nan.0) (* (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (+ (log PI) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))))
* [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 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log PI) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (sqrt (/ 1 k))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 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 1) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log PI) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n))))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log PI) (log n)))) +nan.0) (+ (* (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) +nan.0) (* (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n)))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n))))))))
* [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 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log PI) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 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 (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (sqrt (/ 1 k))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 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 (/ (+ (* 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 1) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log PI) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/48 (pow (log PI) 3)) (+ (* 1/16 (* (pow (log PI) 2) (log n))) (* 1/16 (* (log PI) (pow (log n) 2)))))) (exp (* 1/2 (+ (log PI) (log n))))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log PI) (log n)))) +nan.0) (+ (* (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n)))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/48 (pow (log PI) 3)) (+ (* 1/16 (* (pow (log PI) 2) (log n))) (* 1/16 (* (log PI) (pow (log n) 2)))))) (exp (* 1/2 (+ (log PI) (log n)))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log PI) 2))))))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log PI) 2)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log PI) 2))))))))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log PI) 2)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log PI) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (pow k 2)))))))))))))))))))))))
* [misc]approximate:  Taking taylor expansion of (/ (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* (/ 1 n) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* (/ 1 n) PI))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 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) 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)) 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) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n)))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* (/ 1 n) PI)))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 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 (/ (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) into (* +nan.0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* (/ 1 n) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* (/ 1 n) PI))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 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)) 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 (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))
* [misc]backup-simplify:  Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 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 (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) into (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* (/ 1 n) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* (/ 1 n) PI))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 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)) 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 (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))
* [misc]backup-simplify:  Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 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 (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) into (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
* [misc]taylor:  Taking taylor expansion of (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
* [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]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 (/ 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 (* 1/2 (/ 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 (/ 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 (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log PI) (- (log n))) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 1) into 1/2
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* (- (log PI) (log n)) -1/2) into (* -1/2 (- (log PI) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 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 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log PI) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 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 (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log PI) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 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 (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log PI) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 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 (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (pow k 3))))))))
* [misc]approximate:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* (/ 1 (- n)) PI)))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* (/ 1 (- n)) PI))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 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)) 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)) 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) into 1/2
* [misc]backup-simplify:  Simplify (+ 0 1/2) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -1 (/ PI n)))) into (* 1/2 (log (* -1 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* (/ 1 (- n)) PI)))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
* [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 (/ (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* (/ 1 (- n)) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* (/ 1 (- n)) PI))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- 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)) 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 (- (/ -1/2 k)) into (* 1/2 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 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)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k)))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* (/ 1 (- n)) PI)))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* (/ 1 (- n)) PI))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- 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)) 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 (- (/ -1/2 k)) into (* 1/2 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 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)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k)))
* [misc]taylor:  Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 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 (/ 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 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [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 (* 1/2 1) into 1/2
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [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 (* 1/2 (- (log (* -1 PI)) (log n))) into (* 1/2 (- (log (* -1 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (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)) 1/2) (- (log (* -1 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (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 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -1 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (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 (- (/ 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)) 1/2) (- (log (* -1 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 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 (/ (* (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 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 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)) 1/2) (- (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 (- (/ 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)) 1/2) (- (log (* -1 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) k)) (- (+ (* +nan.0 (/ (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (pow k 2))) (- (* +nan.0 (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k))))))))))
* * * [misc]progress:  simplifying candidates
* * * * [misc]progress:  [ 1 / 127 ] simplifiying candidate #<alt (λ (k n) (pow (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) 1))>
* * * * [misc]progress:  [ 2 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log 2) (- 1/2 (/ k 2))) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
* [enter]simplify:  Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (60 enodes)
* * [misc]simplify:  iters left: 3 (191 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))))
* * * * [misc]progress:  [ 3 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log 2) (- 1/2 (/ k 2))) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
* [enter]simplify:  Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (60 enodes)
* * [misc]simplify:  iters left: 3 (191 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))))
* * * * [misc]progress:  [ 4 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log 2) (- 1/2 (/ k 2))) (- (log (pow (* n PI) (- 1/2 (/ k 2)))) (log (sqrt k))))))>
* [enter]simplify:  Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (- (log (pow (* n PI) (- 1/2 (/ k 2)))) (log (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (50 enodes)
* * [misc]simplify:  iters left: 3 (114 enodes)
* * [misc]simplify:  iters left: 2 (427 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))))
* * * * [misc]progress:  [ 5 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log 2) (- 1/2 (/ k 2))) (log (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
* [enter]simplify:  Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (log (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (82 enodes)
* * [misc]simplify:  iters left: 2 (187 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))))
* * * * [misc]progress:  [ 6 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow 2 (- 1/2 (/ k 2)))) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
* [enter]simplify:  Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (56 enodes)
* * [misc]simplify:  iters left: 3 (161 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))))
* * * * [misc]progress:  [ 7 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow 2 (- 1/2 (/ k 2)))) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
* [enter]simplify:  Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (56 enodes)
* * [misc]simplify:  iters left: 3 (161 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))))
* * * * [misc]progress:  [ 8 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow 2 (- 1/2 (/ k 2)))) (- (log (pow (* n PI) (- 1/2 (/ k 2)))) (log (sqrt k))))))>
* [enter]simplify:  Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (- (log (pow (* n PI) (- 1/2 (/ k 2)))) (log (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (46 enodes)
* * [misc]simplify:  iters left: 3 (83 enodes)
* * [misc]simplify:  iters left: 2 (323 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (+ (log (* n PI)) (log 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (log (* n PI)) (log 2))) (log (sqrt k)))))
* * * * [misc]progress:  [ 9 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow 2 (- 1/2 (/ k 2)))) (log (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
* [enter]simplify:  Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (log (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (60 enodes)
* * [misc]simplify:  iters left: 2 (163 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k)))))
* * * * [misc]progress:  [ 10 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (log (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
* * * * [misc]progress:  [ 11 / 127 ] simplifiying candidate #<alt (λ (k n) (log (exp (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
* * * * [misc]progress:  [ 12 / 127 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (/ (* (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (/ (* (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (114 enodes)
* * [misc]simplify:  iters left: 3 (443 enodes)
* [exit]simplify:  Simplified to (* (* (/ (pow (* PI n) (- 1/2 (/ k 2))) (sqrt k)) (* (pow (* PI n) (- 1/2 (/ k 2))) (pow (* PI n) (- 1/2 (/ k 2))))) (* (/ (pow 2 (- 1/2 (/ k 2))) k) (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2))))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (cbrt (* (* (/ (pow (* PI n) (- 1/2 (/ k 2))) (sqrt k)) (* (pow (* PI n) (- 1/2 (/ k 2))) (pow (* PI n) (- 1/2 (/ k 2))))) (* (/ (pow 2 (- 1/2 (/ k 2))) k) (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2))))))))
* * * * [misc]progress:  [ 13 / 127 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (* (* (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (* (* (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (87 enodes)
* * [misc]simplify:  iters left: 3 (228 enodes)
* [exit]simplify:  Simplified to (* (/ (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* PI n) (- 1/2 (/ k 2))))) (* (/ (pow (* PI n) (- 1/2 (/ k 2))) k) (* (pow 2 (- 1/2 (/ k 2))) (pow (* PI n) (- 1/2 (/ k 2))))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (cbrt (* (/ (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* PI n) (- 1/2 (/ k 2))))) (* (/ (pow (* PI n) (- 1/2 (/ k 2))) k) (* (pow 2 (- 1/2 (/ k 2))) (pow (* PI n) (- 1/2 (/ k 2))))))))
* * * * [misc]progress:  [ 14 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))) (cbrt (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
* * * * [misc]progress:  [ 15 / 127 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
* * * * [misc]progress:  [ 16 / 127 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
* * * * [misc]progress:  [ 17 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 1/2) (pow (* n PI) (- 1/2 (/ k 2)))) (* (pow 2 (/ k 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (* (pow 2 1/2) (pow (* n PI) (- 1/2 (/ k 2))))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (* (sqrt 2) (pow (* n PI) (- 1/2 (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (* (sqrt 2) (pow (* n PI) (- 1/2 (/ k 2)))) (* (pow 2 (/ k 2)) (sqrt k))))
* [enter]simplify:  Simplifying (* (pow 2 (/ k 2)) (sqrt k))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (7 enodes)
* [exit]simplify:  Simplified to (* (pow 2 (/ k 2)) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (* (sqrt 2) (pow (* n PI) (- 1/2 (/ k 2)))) (* (pow 2 (/ k 2)) (sqrt k))))
* * * * [misc]progress:  [ 18 / 127 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
* * * * [misc]progress:  [ 19 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (* (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))) (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* [exit]simplify:  Simplified to (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (* (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))) (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))
* * * * [misc]progress:  [ 20 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))
* * * * [misc]progress:  [ 21 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 22 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) (sqrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) (sqrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 23 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) 1)) (/ (pow (* n PI) (- (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow (* n PI) (- (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n PI) (/ (- k) 2)) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) 1)) (/ (pow (* n PI) (/ (- k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 24 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 25 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) (sqrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) (sqrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 26 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) 1)) (/ (pow (* n PI) (- (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow (* n PI) (- (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n PI) (/ (- k) 2)) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) 1)) (/ (pow (* n PI) (/ (- k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 27 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 28 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 29 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow n (- 1/2 (/ k 2))) 1)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow n (- 1/2 (/ k 2))) 1)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))
* * * * [misc]progress:  [ 30 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 31 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 32 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) 1)) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) 1)) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 33 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 34 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 35 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) 1)) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) 1)) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 36 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 37 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ 1 (sqrt (sqrt k)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ 1 (sqrt (sqrt k)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 38 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ 1 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ 1 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
* * * * [misc]progress:  [ 39 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
* * * * [misc]progress:  [ 40 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ 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))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (/ 1 (sqrt k))))
* * * * [misc]progress:  [ 41 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 1/2) (* (pow 2 (- (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (pow 2 1/2)
* * [misc]simplify:  iters left: 1 (3 enodes)
* [exit]simplify:  Simplified to (sqrt 2)
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt 2) (* (pow 2 (- (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))
* * * * [misc]progress:  [ 42 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 1/2) (* (pow 2 (- (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (pow 2 1/2)
* * [misc]simplify:  iters left: 1 (3 enodes)
* [exit]simplify:  Simplified to (sqrt 2)
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt 2) (* (pow 2 (- (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))
* * * * [misc]progress:  [ 43 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt (pow 2 (- 1/2 (/ k 2))))) (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt (pow 2 (- 1/2 (/ k 2)))))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt (pow 2 (- 1/2 (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt (pow 2 (- 1/2 (/ k 2))))) (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))
* * * * [misc]progress:  [ 44 / 127 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (pow 2 (- 1/2 (/ k 2))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* [exit]simplify:  Simplified to (sqrt (pow 2 (- 1/2 (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))
* * * * [misc]progress:  [ 45 / 127 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
* * * * [misc]progress:  [ 46 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt k)
* * [misc]simplify:  iters left: 1 (2 enodes)
* [exit]simplify:  Simplified to (sqrt k)
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))
* * * * [misc]progress:  [ 47 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 1/2) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (pow 2 (/ k 2))))>
* [enter]simplify:  Simplifying (* (pow 2 1/2) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* * [misc]simplify:  iters left: 2 (31 enodes)
* * [misc]simplify:  iters left: 1 (32 enodes)
* [exit]simplify:  Simplified to (* (/ (sqrt 2) (sqrt k)) (pow (* n PI) (- 1/2 (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (* (/ (sqrt 2) (sqrt k)) (pow (* n PI) (- 1/2 (/ k 2)))) (pow 2 (/ k 2))))
* * * * [misc]progress:  [ 48 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) (pow 2 (- 1/2 (/ k 2)))))>
* * * * [misc]progress:  [ 49 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (exp (* (log (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (* (log (* n PI)) (- 1/2 (/ k 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (69 enodes)
* * [misc]simplify:  iters left: 2 (172 enodes)
* * [misc]simplify:  iters left: 1 (337 enodes)
* [exit]simplify:  Simplified to (* (- 1/2 (/ k 2)) (log (* n PI)))
* [misc]simplify:  Simplified (2 2 1 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (exp (* (- 1/2 (/ k 2)) (log (* n PI)))) (sqrt k))))
* * * * [misc]progress:  [ 50 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (exp (* (log (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 51 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (* n PI)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n PI)
* [misc]simplify:  Simplified (2 2 1 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 52 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (/ (pow (* n PI) 1/2) (pow (* n PI) (/ k 2))) (sqrt k))))>
* [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 (* n PI) (/ k 2))
* [misc]simplify:  Simplified (2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (/ (pow (* n PI) 1/2) (pow (* n PI) (/ k 2))) (sqrt k))))
* * * * [misc]progress:  [ 53 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (pow (* n PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (cbrt (- 1/2 (/ k 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* * [misc]simplify:  iters left: 3 (11 enodes)
* [exit]simplify:  Simplified to (cbrt (- 1/2 (/ k 2)))
* [misc]simplify:  Simplified (2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (pow (* n PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 54 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (pow (* n PI) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (sqrt (- 1/2 (/ k 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* * [misc]simplify:  iters left: 3 (11 enodes)
* [exit]simplify:  Simplified to (sqrt (- 1/2 (/ k 2)))
* [misc]simplify:  Simplified (2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (pow (* n PI) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 55 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (pow (* n PI) 1) (- 1/2 (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (- 1/2 (/ k 2))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* * [misc]simplify:  iters left: 2 (10 enodes)
* [exit]simplify:  Simplified to (- 1/2 (/ k 2))
* [misc]simplify:  Simplified (2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (pow (* n PI) 1) (- 1/2 (/ k 2))) (sqrt k))))
* * * * [misc]progress:  [ 56 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (pow (* n PI) 1/2) (pow (* n PI) (- (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (pow (* n PI) (- (/ k 2)))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (11 enodes)
* [exit]simplify:  Simplified to (pow (* n PI) (/ (- k) 2))
* [misc]simplify:  Simplified (2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (pow (* n PI) 1/2) (pow (* n PI) (/ (- k) 2))) (sqrt k))))
* * * * [misc]progress:  [ 57 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (pow (* n PI) 1/2) (pow (* n PI) (- (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (pow (* n PI) (- (/ k 2)))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (11 enodes)
* [exit]simplify:  Simplified to (pow (* n PI) (/ (- k) 2))
* [misc]simplify:  Simplified (2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (pow (* n PI) 1/2) (pow (* n PI) (/ (- k) 2))) (sqrt k))))
* * * * [misc]progress:  [ 58 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (pow n (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (pow n (- 1/2 (/ k 2)))
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (9 enodes)
* * [misc]simplify:  iters left: 3 (12 enodes)
* [exit]simplify:  Simplified to (pow n (- 1/2 (/ k 2)))
* [misc]simplify:  Simplified (2 2 1 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (pow n (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 59 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (pow (* n PI) (- 1/2 (/ k 2))) 1) (sqrt k))))>
* * * * [misc]progress:  [ 60 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (exp (log (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k))))>
* * * * [misc]progress:  [ 61 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (log (exp (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k))))>
* * * * [misc]progress:  [ 62 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k))))>
* * * * [misc]progress:  [ 63 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (cbrt (* (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k))))>
* * * * [misc]progress:  [ 64 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt k))))>
* * * * [misc]progress:  [ 65 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* 1 (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))))>
* * * * [misc]progress:  [ 66 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (pow (* n PI) 1) (- 1/2 (/ k 2))) (sqrt k))))>
* * * * [misc]progress:  [ 67 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (exp (log (* n PI))) (- 1/2 (/ k 2))) (sqrt k))))>
* * * * [misc]progress:  [ 68 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (log (exp (* n PI))) (- 1/2 (/ k 2))) (sqrt k))))>
* * * * [misc]progress:  [ 69 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI))) (- 1/2 (/ k 2))) (sqrt k))))>
* * * * [misc]progress:  [ 70 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (cbrt (* (* (* n PI) (* n PI)) (* n PI))) (- 1/2 (/ k 2))) (sqrt k))))>
* * * * [misc]progress:  [ 71 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* (sqrt (* n PI)) (sqrt (* n PI))) (- 1/2 (/ k 2))) (sqrt k))))>
* * * * [misc]progress:  [ 72 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* 1 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))))>
* * * * [misc]progress:  [ 73 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* PI n) (- 1/2 (/ k 2))) (sqrt k))))>
* * * * [misc]progress:  [ 74 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (pow (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) 1)))>
* * * * [misc]progress:  [ 75 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
* [enter]simplify:  Simplifying (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (99 enodes)
* * [misc]simplify:  iters left: 2 (328 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (log (* n PI))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (- 1/2 (/ k 2)) (log (* n PI))) (log (sqrt k))))))
* * * * [misc]progress:  [ 76 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))))))>
* [enter]simplify:  Simplifying (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (99 enodes)
* * [misc]simplify:  iters left: 2 (328 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (log (* n PI))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (- 1/2 (/ k 2)) (log (* n PI))) (log (sqrt k))))))
* * * * [misc]progress:  [ 77 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (log (pow (* n PI) (- 1/2 (/ k 2)))) (log (sqrt k))))))>
* [enter]simplify:  Simplifying (- (log (pow (* n PI) (- 1/2 (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (45 enodes)
* * [misc]simplify:  iters left: 2 (125 enodes)
* * [misc]simplify:  iters left: 1 (452 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (log (* n PI))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (- 1/2 (/ k 2)) (log (* n PI))) (log (sqrt k))))))
* * * * [misc]progress:  [ 78 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (log (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
* * * * [misc]progress:  [ 79 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (log (exp (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
* * * * [misc]progress:  [ 80 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (cbrt (/ (* (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (* (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (56 enodes)
* * [misc]simplify:  iters left: 3 (104 enodes)
* * [misc]simplify:  iters left: 2 (175 enodes)
* * [misc]simplify:  iters left: 1 (287 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (/ (* (sqrt k) k) (pow (* n PI) (- 1/2 (/ k 2)))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (cbrt (/ (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (/ (* (sqrt k) k) (pow (* n PI) (- 1/2 (/ k 2))))))))
* * * * [misc]progress:  [ 81 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
* * * * [misc]progress:  [ 82 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (cbrt (* (* (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
* * * * [misc]progress:  [ 83 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))>
* * * * [misc]progress:  [ 84 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (- (pow (* n PI) (- 1/2 (/ k 2)))) (- (sqrt k)))))>
* * * * [misc]progress:  [ 85 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (pow (* n PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow (* n PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (* n PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (* n PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))))))
* [enter]simplify:  Simplifying (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (* n PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))))))
* * * * [misc]progress:  [ 86 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (pow (* n PI) 1/2) (sqrt (sqrt k))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow (* n PI) 1/2) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (11 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (* n PI)) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (* n PI)) (sqrt (sqrt k))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))))))
* [enter]simplify:  Simplifying (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (* n PI)) (sqrt (sqrt k))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))))))
* * * * [misc]progress:  [ 87 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (pow (* n PI) 1/2) 1) (/ (pow (* n PI) (- (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* n PI) 1/2) 1)
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (11 enodes)
* * [misc]simplify:  iters left: 3 (13 enodes)
* [exit]simplify:  Simplified to (sqrt (* n PI))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (* n PI)) (/ (pow (* n PI) (- (/ k 2))) (sqrt k)))))
* [enter]simplify:  Simplifying (/ (pow (* n PI) (- (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n PI) (/ (- k) 2)) (sqrt k))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (* n PI)) (/ (pow (* n PI) (/ (- k) 2)) (sqrt k)))))
* * * * [misc]progress:  [ 88 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (pow (* n PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow (* n PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (* n PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (* n PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))))))
* [enter]simplify:  Simplifying (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (* n PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))))))
* * * * [misc]progress:  [ 89 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (pow (* n PI) 1/2) (sqrt (sqrt k))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow (* n PI) 1/2) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (11 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (* n PI)) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (* n PI)) (sqrt (sqrt k))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))))))
* [enter]simplify:  Simplifying (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (* n PI)) (sqrt (sqrt k))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))))))
* * * * [misc]progress:  [ 90 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (pow (* n PI) 1/2) 1) (/ (pow (* n PI) (- (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* n PI) 1/2) 1)
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (11 enodes)
* * [misc]simplify:  iters left: 3 (13 enodes)
* [exit]simplify:  Simplified to (sqrt (* n PI))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (* n PI)) (/ (pow (* n PI) (- (/ k 2))) (sqrt k)))))
* [enter]simplify:  Simplifying (/ (pow (* n PI) (- (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n PI) (/ (- k) 2)) (sqrt k))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (* n PI)) (/ (pow (* n PI) (/ (- k) 2)) (sqrt k)))))
* * * * [misc]progress:  [ 91 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (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 n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))))))
* [enter]simplify:  Simplifying (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))))))
* * * * [misc]progress:  [ 92 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* [exit]simplify:  Simplified to (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))))))
* [enter]simplify:  Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))))))
* * * * [misc]progress:  [ 93 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (pow n (- 1/2 (/ k 2))) 1) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow n (- 1/2 (/ k 2))) 1)
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* [exit]simplify:  Simplified to (pow n (- 1/2 (/ k 2)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))
* [enter]simplify:  Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))
* * * * [misc]progress:  [ 94 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* * [misc]simplify:  iters left: 2 (42 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))))
* * * * [misc]progress:  [ 95 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (cbrt (pow (* n PI) (- 1/2 (/ k 2)))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))
* * * * [misc]progress:  [ 96 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) 1) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) 1)
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (31 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2)))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 97 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (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 (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))))
* * * * [misc]progress:  [ 98 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))
* * * * [misc]progress:  [ 99 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) 1)
* * [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 (sqrt (pow (* n PI) (- 1/2 (/ k 2))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 100 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- 1/2 (/ 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)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))))))
* [enter]simplify:  Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))))))
* * * * [misc]progress:  [ 101 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ 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)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))
* [enter]simplify:  Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))
* * * * [misc]progress:  [ 102 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ 1 1) (/ (pow (* n PI) (- 1/2 (/ 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
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* 1 (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))
* [enter]simplify:  Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* 1 (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))
* * * * [misc]progress:  [ 103 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* 1 (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))))>
* * * * [misc]progress:  [ 104 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow (* n PI) (- 1/2 (/ k 2))) (/ 1 (sqrt k)))))>
* * * * [misc]progress:  [ 105 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ 1 (/ (sqrt k) (pow (* n PI) (- 1/2 (/ k 2)))))))>
* * * * [misc]progress:  [ 106 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (/ (pow (* n PI) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (cbrt (sqrt k))
* * [misc]simplify:  iters left: 2 (3 enodes)
* [exit]simplify:  Simplified to (cbrt (sqrt k))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (/ (pow (* n PI) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 107 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (sqrt k))
* * [misc]simplify:  iters left: 2 (3 enodes)
* [exit]simplify:  Simplified to (sqrt (sqrt k))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 108 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (/ (pow (* n PI) (- 1/2 (/ k 2))) 1) (sqrt k))))>
* [enter]simplify:  Simplifying (sqrt k)
* * [misc]simplify:  iters left: 1 (2 enodes)
* [exit]simplify:  Simplified to (sqrt k)
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (/ (pow (* n PI) (- 1/2 (/ k 2))) 1) (sqrt k))))
* * * * [misc]progress:  [ 109 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) (/ (sqrt k) (pow (* n PI) (- (/ k 2)))))))>
* [enter]simplify:  Simplifying (pow (* n PI) 1/2)
* * [misc]simplify:  iters left: 3 (5 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (sqrt (* n PI))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (* n PI)) (/ (sqrt k) (pow (* n PI) (- (/ k 2)))))))
* * * * [misc]progress:  [ 110 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) (/ (sqrt k) (pow (* n PI) (- (/ k 2)))))))>
* [enter]simplify:  Simplifying (pow (* n PI) 1/2)
* * [misc]simplify:  iters left: 3 (5 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (sqrt (* n PI))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (* n PI)) (/ (sqrt k) (pow (* n PI) (- (/ k 2)))))))
* * * * [misc]progress:  [ 111 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))))))>
* [enter]simplify:  Simplifying (pow n (- 1/2 (/ k 2)))
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (9 enodes)
* * [misc]simplify:  iters left: 3 (12 enodes)
* [exit]simplify:  Simplified to (pow n (- 1/2 (/ k 2)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))))))
* * * * [misc]progress:  [ 112 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))))))>
* [enter]simplify:  Simplifying (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2)))))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2)))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))))))
* * * * [misc]progress:  [ 113 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n PI) (- 1/2 (/ k 2))))))))>
* [enter]simplify:  Simplifying (sqrt (pow (* n PI) (- 1/2 (/ k 2))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* n PI) (- 1/2 (/ k 2))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n PI) (- 1/2 (/ k 2))))))))
* * * * [misc]progress:  [ 114 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ 1 (/ (sqrt k) (pow (* n PI) (- 1/2 (/ k 2)))))))>
* * * * [misc]progress:  [ 115 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) (* (sqrt k) (pow (* n PI) (/ k 2))))))>
* [enter]simplify:  Simplifying (pow (* n PI) 1/2)
* * [misc]simplify:  iters left: 3 (5 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (sqrt (* n PI))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (* n PI)) (* (sqrt k) (pow (* n PI) (/ k 2))))))
* * * * [misc]progress:  [ 116 / 127 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) k)) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (log n))))) (- (* +nan.0 (/ (* n PI) k))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) k)) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (log n))))) (- (* +nan.0 (/ (* n PI) k)))))))))))))
* [misc]simplify:  Simplified (2) to (λ (k n) +nan.0)
* * * * [misc]progress:  [ 117 / 127 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k)))))) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2)))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k)))))) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))))))))
* [misc]simplify:  Simplified (2) to (λ (k n) +nan.0)
* * * * [misc]progress:  [ 118 / 127 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (* +nan.0 (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (* +nan.0 (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k)))))))))))
* [misc]simplify:  Simplified (2) to (λ (k n) +nan.0)
* * * * [misc]progress:  [ 119 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (- (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (+ (* 1/4 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (exp (* 1/2 (+ (log PI) (log n))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) k))))) (sqrt k))))>
* [enter]simplify:  Simplifying (- (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (+ (* 1/4 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (exp (* 1/2 (+ (log PI) (log n))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) k)))))
* * [misc]simplify:  iters left: 6 (36 enodes)
* * [misc]simplify:  iters left: 5 (100 enodes)
* * [misc]simplify:  iters left: 4 (302 enodes)
* [exit]simplify:  Simplified to (+ (- (* (* k (* k 1/8)) (* (* (pow n 1/2) (pow PI 1/2)) (* (log PI) (log PI)))) (* (* (* (pow n 1/2) (pow PI 1/2)) (* k 1/2)) (+ (log PI) (log n)))) (+ (* (pow n 1/2) (pow PI 1/2)) (* (* (pow n 1/2) (pow PI 1/2)) (+ (* (* (* k k) (log n)) (* (log n) 1/8)) (* (* 1/4 (log PI)) (* (* k k) (log n)))))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (+ (- (* (* k (* k 1/8)) (* (* (pow n 1/2) (pow PI 1/2)) (* (log PI) (log PI)))) (* (* (* (pow n 1/2) (pow PI 1/2)) (* k 1/2)) (+ (log PI) (log n)))) (+ (* (pow n 1/2) (pow PI 1/2)) (* (* (pow n 1/2) (pow PI 1/2)) (+ (* (* (* k k) (log n)) (* (log n) 1/8)) (* (* 1/4 (log PI)) (* (* k k) (log n))))))) (sqrt k))))
* * * * [misc]progress:  [ 120 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (sqrt k))))>
* [enter]simplify:  Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n)))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (53 enodes)
* * [misc]simplify:  iters left: 3 (120 enodes)
* * [misc]simplify:  iters left: 2 (377 enodes)
* [exit]simplify:  Simplified to (pow (* n PI) (- 1/2 (* 1/2 k)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (* 1/2 k))) (sqrt k))))
* * * * [misc]progress:  [ 121 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (sqrt k))))>
* [enter]simplify:  Simplifying (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (64 enodes)
* * [misc]simplify:  iters left: 3 (204 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI 1) n) (- 1/2 (* k 1/2)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* (* PI 1) n) (- 1/2 (* k 1/2))) (sqrt k))))
* * * * [misc]progress:  [ 122 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (* n PI)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n PI)
* [misc]simplify:  Simplified (2 2 1 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
* * * * [misc]progress:  [ 123 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (* n PI)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n PI)
* [misc]simplify:  Simplified (2 2 1 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
* * * * [misc]progress:  [ 124 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (* n PI)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n PI)
* [misc]simplify:  Simplified (2 2 1 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))
* * * * [misc]progress:  [ 125 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (pow k 2)))))))))))))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (pow k 2)))))))))))))))))))))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) +nan.0))
* * * * [misc]progress:  [ 126 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (pow k 3))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (pow k 3))))))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) +nan.0))
* * * * [misc]progress:  [ 127 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (- (+ (* +nan.0 (/ (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) k)) (- (+ (* +nan.0 (/ (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (pow k 2))) (- (* +nan.0 (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) k)) (- (+ (* +nan.0 (/ (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (pow k 2))) (- (* +nan.0 (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k))))))))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) +nan.0))
* * * [misc]progress:  adding candidates to table
* * [misc]progress:  iteration 4 / 4
* * * [misc]progress:  picking best candidate
* * * * [misc]pick:  Picked  #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 4 ] rewriting at (2 2 2 1)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2 2)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2 2 2)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 4 ] generating series at (2 2 2 1)
* [misc]approximate:  Taking taylor expansion of (pow PI (- 1/2 (/ k 2))) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 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 (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2)
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 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 (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2)
* [misc]backup-simplify:  Simplify (pow PI 1/2) into (pow PI 1/2)
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI)))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI)))
* [misc]backup-simplify:  Simplify (* -1/2 (* (log PI) (sqrt PI))) into (* -1/2 (* (log PI) (sqrt PI)))
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 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) (+ (* -1/2 0) (* 0 (log PI)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI)))
* [misc]backup-simplify:  Simplify (* 1/8 (* (pow (log PI) 2) (sqrt PI))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI)))
* [misc]backup-simplify:  Simplify (+ (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (log PI) (sqrt PI))) k) (pow PI 1/2))) into (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI))))
* [misc]approximate:  Taking taylor expansion of (pow PI (- 1/2 (/ (/ 1 k) 2))) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 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) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* -1/2 (log PI)) into (* -1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 k) 2)) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k))))
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 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) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* -1/2 (log PI)) into (* -1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 k) 2)) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k))))
* [misc]backup-simplify:  Simplify (pow PI (- 1/2 (* 1/2 (/ 1 k)))) into (pow PI (- 1/2 (* 1/2 (/ 1 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 0 into 0
* [misc]backup-simplify:  Simplify (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) into (pow PI (- 1/2 (* 1/2 k)))
* [misc]approximate:  Taking taylor expansion of (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 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)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (- -1/2) into 1/2
* [misc]backup-simplify:  Simplify (+ 0 1/2) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2))
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 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)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (- -1/2) into 1/2
* [misc]backup-simplify:  Simplify (+ 0 1/2) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2))
* [misc]backup-simplify:  Simplify (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2))
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) into (pow PI (- 1/2 (* 1/2 k)))
* * * * [misc]progress:  [ 2 / 4 ] generating series at (2)
* [misc]approximate:  Taking taylor expansion of (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow 2 (- 1/2 (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log 2)) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log 2) 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 k)) into (- (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 k)) (log 2)) into (* (log 2) (- 1/2 (* 1/2 k)))
* [misc]backup-simplify:  Simplify (exp (* (log 2) (- 1/2 (* 1/2 k)))) into (exp (* (log 2) (- 1/2 (* 1/2 k))))
* [misc]taylor:  Taking taylor expansion of (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) in n
* [misc]taylor:  Taking taylor expansion of (pow n (- 1/2 (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log n))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log n)) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 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) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (log 1) into 0
* [misc]backup-simplify:  Simplify (- (* 1/2 k)) into (- (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) 0) into (log n)
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k)))
* [misc]taylor:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log PI)) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (- (* 1/2 k)) into (- (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 k)) (log PI)) into (* (- 1/2 (* 1/2 k)) (log PI))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 k)) (log PI))) into (pow PI (- 1/2 (* 1/2 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 (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow PI (- 1/2 (* 1/2 k))))
* [misc]taylor:  Taking taylor expansion of (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow 2 (- 1/2 (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log 2)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 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 (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log 2) 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 0) into 1/2
* [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 (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) in k
* [misc]taylor:  Taking taylor expansion of (pow n (- 1/2 (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 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 (/ 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) 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 (+ 1/2 0) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log n)) into (* 1/2 (log n))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log n))) into (pow n 1/2)
* [misc]taylor:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 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 (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log PI))) into (pow 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 PI 1/2) +nan.0) into (* +nan.0 (sqrt PI))
* [misc]taylor:  Taking taylor expansion of (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow 2 (- 1/2 (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log 2)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 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 (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log 2) 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 0) into 1/2
* [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 (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) in k
* [misc]taylor:  Taking taylor expansion of (pow n (- 1/2 (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 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 (/ 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) 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 (+ 1/2 0) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log n)) into (* 1/2 (log n))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log n))) into (pow n 1/2)
* [misc]taylor:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 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 (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log PI))) into (pow 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 PI 1/2) +nan.0) into (* +nan.0 (sqrt PI))
* [misc]backup-simplify:  Simplify (* (pow n 1/2) (* +nan.0 (sqrt PI))) into (* +nan.0 (sqrt (* n PI)))
* [misc]backup-simplify:  Simplify (* (pow 2 1/2) (* +nan.0 (sqrt (* n PI)))) into (* +nan.0 (sqrt (* PI (* n 2))))
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (sqrt (* PI (* n 2)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (sqrt (* PI (* n 2))) in n
* [misc]taylor:  Taking taylor expansion of (* PI (* n 2)) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (* n 2) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* 0 2) into 0
* [misc]backup-simplify:  Simplify (* PI 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 2)) into 2
* [misc]backup-simplify:  Simplify (+ (* PI 2) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ (* 2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI)))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI)))
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ (* -1/2 (* (log PI) (sqrt PI))) +nan.0) (+ (* (* +nan.0 (sqrt PI)) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI)))))
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* -1/2 (log n))) into (- (* 1/2 (log n)))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n)))
* [misc]backup-simplify:  Simplify (+ (* (pow n 1/2) (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI)))))) (* (* -1/2 (* (sqrt n) (log n))) (* +nan.0 (sqrt PI)))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (+ (* +nan.0 (* (log PI) (sqrt (* PI n)))) (- (* +nan.0 (sqrt (* n PI))))))))
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* -1/2 (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 (+ (* (pow 2 1/2) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (+ (* +nan.0 (* (log PI) (sqrt (* PI n)))) (- (* +nan.0 (sqrt (* n PI))))))))) (* (* -1/2 (* (log 2) (sqrt 2))) (* +nan.0 (sqrt (* n PI))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))))))))
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (sqrt 2) (log PI)) (sqrt (* PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (log PI)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]taylor:  Taking taylor expansion of (sqrt (* PI n)) in n
* [misc]taylor:  Taking taylor expansion of (* PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (* PI 0) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 1) (* 0 0)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (log 2) (sqrt 2)) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (log 2) (sqrt 2)) in n
* [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]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (sqrt 2) (log n)) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (log n)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (log n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (log 1) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]backup-simplify:  Simplify (* (sqrt 2) (log PI)) into (* (sqrt 2) (log PI))
* [misc]backup-simplify:  Simplify (* (* (sqrt 2) (log PI)) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (* (log 2) (sqrt 2)) into (* (log 2) (sqrt 2))
* [misc]backup-simplify:  Simplify (* (* (log 2) (sqrt 2)) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (* (sqrt 2) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) 0) into (log n)
* [misc]backup-simplify:  Simplify (* (sqrt 2) (log n)) into (* (sqrt 2) (log n))
* [misc]backup-simplify:  Simplify (* (* (sqrt 2) (log n)) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 PI))
* [misc]backup-simplify:  Simplify (- (* +nan.0 PI)) into (- (* +nan.0 PI))
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 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) (+ (* -1/2 0) (* 0 (log PI)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI)))
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ (* 1/8 (* (pow (log PI) 2) (sqrt PI))) +nan.0) (+ (* (* +nan.0 (sqrt PI)) (/ +nan.0 +nan.0)) (* (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI))))))))
* [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 2) (+ (* 1/2 (/ 0 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) (+ (* -1/2 0) (* 0 (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2)))
* [misc]backup-simplify:  Simplify (+ (* (pow n 1/2) (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI))))))))) (+ (* (* -1/2 (* (sqrt n) (log n))) (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI)))))) (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (* +nan.0 (sqrt PI))))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log n) 2))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log PI) 2))) (- (+ (* +nan.0 (sqrt (* n PI))) (- (* +nan.0 (* (* (log PI) (log n)) (sqrt (* PI 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 2) (+ (* 1/2 (/ 0 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) (+ (* -1/2 0) (* 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 (+ (* (pow 2 1/2) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log n) 2))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log PI) 2))) (- (+ (* +nan.0 (sqrt (* n PI))) (- (* +nan.0 (* (* (log PI) (log n)) (sqrt (* PI n)))))))))))))))) (+ (* (* -1/2 (* (log 2) (sqrt 2))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (+ (* +nan.0 (* (log PI) (sqrt (* PI n)))) (- (* +nan.0 (sqrt (* n PI))))))))) (* (* 1/8 (* (pow (log 2) 2) (sqrt 2))) (* +nan.0 (sqrt (* n PI)))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))))))))))))))
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))))))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))))))))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (pow (log n) 2)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (pow (log n) 2) in n
* [misc]taylor:  Taking taylor expansion of (log n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (log 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) 0) into (log 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 (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))))))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (pow (log PI) 2)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (pow (log PI) 2) in n
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]taylor:  Taking taylor expansion of (sqrt (* PI n)) in n
* [misc]taylor:  Taking taylor expansion of (* PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (* PI 0) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 1) (* 0 0)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (sqrt 2) (log n)) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (log n)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (log n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (log 1) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (* (log PI) (log n))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (* (log PI) (log n)) in n
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]taylor:  Taking taylor expansion of (log n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (log 1) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (* PI n)) in n
* [misc]taylor:  Taking taylor expansion of (* PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (* PI 0) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 1) (* 0 0)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (sqrt 2) (log PI)) (sqrt (* PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (log PI)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]taylor:  Taking taylor expansion of (sqrt (* PI n)) in n
* [misc]taylor:  Taking taylor expansion of (* PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (* PI 0) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 1) (* 0 0)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (log 2) (* (sqrt 2) (log n))) in n
* [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]taylor:  Taking taylor expansion of (* (sqrt 2) (log n)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (log n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (log 1) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* (log 2) (* (sqrt 2) (log PI))) in n
* [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]taylor:  Taking taylor expansion of (* (sqrt 2) (log PI)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]taylor:  Taking taylor expansion of (sqrt (* PI n)) in n
* [misc]taylor:  Taking taylor expansion of (* PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (* PI 0) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 1) (* 0 0)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (pow (log 2) 2) (sqrt 2)) in n
* [misc]taylor:  Taking taylor expansion of (pow (log 2) 2) in n
* [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]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (* (log 2) (sqrt 2)) (sqrt (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (log 2) (sqrt 2)) in n
* [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]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) 0) into (log n)
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) 0) into (log n)
* [misc]backup-simplify:  Simplify (* (log n) (log n)) into (pow (log n) 2)
* [misc]backup-simplify:  Simplify (* (sqrt 2) (pow (log n) 2)) into (* (sqrt 2) (pow (log n) 2))
* [misc]backup-simplify:  Simplify (* (* (sqrt 2) (pow (log n) 2)) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (* (log PI) (log PI)) into (pow (log PI) 2)
* [misc]backup-simplify:  Simplify (* (sqrt 2) (pow (log PI) 2)) into (* (sqrt 2) (pow (log PI) 2))
* [misc]backup-simplify:  Simplify (* (* (sqrt 2) (pow (log PI) 2)) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (* (sqrt 2) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) 0) into (log n)
* [misc]backup-simplify:  Simplify (* (sqrt 2) (log n)) into (* (sqrt 2) (log n))
* [misc]backup-simplify:  Simplify (* (* (sqrt 2) (log n)) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) 0) into (log n)
* [misc]backup-simplify:  Simplify (* (log PI) (log n)) into (* (log PI) (log n))
* [misc]backup-simplify:  Simplify (* (sqrt 2) (* (log PI) (log n))) into (* (sqrt 2) (* (log PI) (log n)))
* [misc]backup-simplify:  Simplify (* (* (sqrt 2) (* (log PI) (log n))) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (* (sqrt 2) (log PI)) into (* (sqrt 2) (log PI))
* [misc]backup-simplify:  Simplify (* (* (sqrt 2) (log PI)) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) 0) into (log n)
* [misc]backup-simplify:  Simplify (* (sqrt 2) (log n)) into (* (sqrt 2) (log n))
* [misc]backup-simplify:  Simplify (* (log 2) (* (sqrt 2) (log n))) into (* (log 2) (* (sqrt 2) (log n)))
* [misc]backup-simplify:  Simplify (* (* (log 2) (* (sqrt 2) (log n))) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (* (sqrt 2) (log PI)) into (* (sqrt 2) (log PI))
* [misc]backup-simplify:  Simplify (* (log 2) (* (sqrt 2) (log PI))) into (* (log 2) (* (sqrt 2) (log PI)))
* [misc]backup-simplify:  Simplify (* (* (log 2) (* (sqrt 2) (log PI))) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (* (log 2) (log 2)) into (pow (log 2) 2)
* [misc]backup-simplify:  Simplify (* (pow (log 2) 2) (sqrt 2)) into (* (pow (log 2) 2) (sqrt 2))
* [misc]backup-simplify:  Simplify (* (* (pow (log 2) 2) (sqrt 2)) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (* (log 2) (sqrt 2)) into (* (log 2) (sqrt 2))
* [misc]backup-simplify:  Simplify (* (* (log 2) (sqrt 2)) 0) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (sqrt 2) 0) (* 0 (log PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (sqrt 2) (log PI)) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (log 2) 0) (* 0 (sqrt 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (log 2) (sqrt 2)) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))) (* 0 0)) into (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))
* [misc]backup-simplify:  Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) 0) into (log n)
* [misc]backup-simplify:  Simplify (+ (* (sqrt 2) 0) (* 0 (log n))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (sqrt 2) (log n)) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* PI (log n)))))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (* PI (log n)))))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* PI (log n)))))
* [misc]backup-simplify:  Simplify (- (- (* +nan.0 (* (sqrt 2) (* PI (log n)))))) into (- (* +nan.0 (* (sqrt 2) (* PI (log n)))))
* [misc]backup-simplify:  Simplify (+ (- (* +nan.0 (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) (* PI (log n)))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))
* [misc]backup-simplify:  Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))
* [misc]backup-simplify:  Simplify (+ (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))
* [misc]backup-simplify:  Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))
* [misc]backup-simplify:  Simplify (+ (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))
* [misc]backup-simplify:  Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 2) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (pow PI 2)))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (pow PI 2))) into (- (* +nan.0 (pow PI 2)))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (pow PI 2))) (* (pow n 2) (/ 1 k))) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) (* n 1)) (* (- (* +nan.0 PI)) (* n (/ 1 k))))) into (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) k)) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (log n))))) (- (* +nan.0 (/ (* n PI) k)))))))))))))
* [misc]approximate:  Taking taylor expansion of (* (pow 2 (- 1/2 (/ (/ 1 k) 2))) (* (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (* (pow 2 (- 1/2 (/ (/ 1 k) 2))) (* (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (pow 2 (- 1/2 (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log 2)) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log 2) 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 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))
* [misc]backup-simplify:  Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (* (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (/ 1 n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (/ 1 n))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 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)) 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]backup-simplify:  Simplify (log 1) into 0
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))
* [misc]backup-simplify:  Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))
* [misc]taylor:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log PI)) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 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 (/ (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (sqrt (/ 1 k))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (* (pow 2 (- 1/2 (/ (/ 1 k) 2))) (* (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))))) in k
* [misc]taylor:  Taking taylor expansion of (pow 2 (- 1/2 (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log 2)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 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) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log 2) 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) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* -1/2 (log 2)) into (* -1/2 (log 2))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 k) 2)) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (* (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (/ 1 n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (/ 1 n))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 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) 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)) 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]backup-simplify:  Simplify (log (/ 1 n)) into (log (/ 1 n))
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n)))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))
* [misc]taylor:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 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) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* -1/2 (log PI)) into (* -1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 k) 2)) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 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 (/ (pow PI (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) into (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (* (pow 2 (- 1/2 (/ (/ 1 k) 2))) (* (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))))) in k
* [misc]taylor:  Taking taylor expansion of (pow 2 (- 1/2 (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log 2)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 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) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log 2) 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) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* -1/2 (log 2)) into (* -1/2 (log 2))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 k) 2)) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (* (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (/ 1 n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (/ 1 n))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 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) 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)) 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]backup-simplify:  Simplify (log (/ 1 n)) into (log (/ 1 n))
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n)))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))
* [misc]taylor:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 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) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* -1/2 (log PI)) into (* -1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 k) 2)) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 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 (/ (pow PI (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) into (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]backup-simplify:  Simplify (* (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))
* [misc]backup-simplify:  Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n
* [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]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))
* [misc]backup-simplify:  Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k))))
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log (/ 1 n)) 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]backup-simplify:  Simplify (log 1) into 0
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))
* [misc]backup-simplify:  Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))
* [misc]backup-simplify:  Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]backup-simplify:  Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k))))))
* [misc]backup-simplify:  Simplify (+ (* (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) (* 0 (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) (* 0 (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n
* [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]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))
* [misc]backup-simplify:  Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k))))
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log (/ 1 n)) 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]backup-simplify:  Simplify (log 1) into 0
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))
* [misc]backup-simplify:  Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))
* [misc]backup-simplify:  Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]backup-simplify:  Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (log PI))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) 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) 1)) (pow 2 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (log 2) 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* +nan.0 0) (* 0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k))))))
* [misc]backup-simplify:  Simplify (+ (* (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) (+ (* 0 (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) (* 0 (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) (* 0 (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n
* [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]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))
* [misc]backup-simplify:  Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k))))
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log (/ 1 n)) 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]backup-simplify:  Simplify (log 1) into 0
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))
* [misc]backup-simplify:  Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))
* [misc]backup-simplify:  Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]backup-simplify:  Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (* 1 (/ 1 k))) (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))))) into (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) k)) (- (+ (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) (- (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) (pow k 2))))))))
* [misc]approximate:  Taking taylor expansion of (* (pow 2 (- 1/2 (/ (/ 1 (- k)) 2))) (* (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (* (pow 2 (- 1/2 (/ (/ 1 (- k)) 2))) (* (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))))) in n
* [misc]taylor:  Taking taylor expansion of (pow 2 (- 1/2 (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log 2)) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log 2) 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 k)) into (* 1/2 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))
* [misc]backup-simplify:  Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]taylor:  Taking taylor expansion of (* (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) in n
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (/ 1 (- n))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (/ 1 (- n)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- 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))) 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]backup-simplify:  Simplify (log -1) into (log -1)
* [misc]backup-simplify:  Simplify (- (/ -1/2 k)) into (* 1/2 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))
* [misc]taylor:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI)) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (- (/ -1/2 k)) into (* 1/2 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2))
* [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 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) into (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k)))
* [misc]taylor:  Taking taylor expansion of (* (pow 2 (- 1/2 (/ (/ 1 (- k)) 2))) (* (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))))) in k
* [misc]taylor:  Taking taylor expansion of (pow 2 (- 1/2 (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log 2)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 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)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log 2) 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) into 1/2
* [misc]backup-simplify:  Simplify (+ 0 1/2) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]taylor:  Taking taylor expansion of (* (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) in k
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (/ 1 (- n))))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (/ 1 (- n)))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 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)) 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))) 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]backup-simplify:  Simplify (log (/ -1 n)) into (log (/ -1 n))
* [misc]backup-simplify:  Simplify (- -1/2) into 1/2
* [misc]backup-simplify:  Simplify (+ 0 1/2) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n)))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (/ 1 (- n))))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2))
* [misc]taylor:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 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)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (- -1/2) into 1/2
* [misc]backup-simplify:  Simplify (+ 0 1/2) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2))
* [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 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]taylor:  Taking taylor expansion of (* (pow 2 (- 1/2 (/ (/ 1 (- k)) 2))) (* (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))))) in k
* [misc]taylor:  Taking taylor expansion of (pow 2 (- 1/2 (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log 2)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 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)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log 2) 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) into 1/2
* [misc]backup-simplify:  Simplify (+ 0 1/2) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log 2)) into (* 1/2 (log 2))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]taylor:  Taking taylor expansion of (* (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) in k
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (/ 1 (- n))))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (/ 1 (- n)))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 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)) 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))) 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]backup-simplify:  Simplify (log (/ -1 n)) into (log (/ -1 n))
* [misc]backup-simplify:  Simplify (- -1/2) into 1/2
* [misc]backup-simplify:  Simplify (+ 0 1/2) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n)))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (/ 1 (- n))))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2))
* [misc]taylor:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 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)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (- -1/2) into 1/2
* [misc]backup-simplify:  Simplify (+ 0 1/2) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2))
* [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 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]backup-simplify:  Simplify (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))
* [misc]backup-simplify:  Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (log (/ -1 n)) in n
* [misc]taylor:  Taking taylor expansion of (/ -1 n) in n
* [misc]taylor:  Taking taylor expansion of -1 in n
* [misc]backup-simplify:  Simplify -1 into -1
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ -1 1) into -1
* [misc]backup-simplify:  Simplify (log -1) into (log -1)
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))
* [misc]taylor:  Taking taylor expansion of (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n
* [misc]taylor:  Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n
* [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]taylor:  Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))
* [misc]backup-simplify:  Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]taylor:  Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n
* [misc]taylor:  Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2))
* [misc]backup-simplify:  Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))
* [misc]backup-simplify:  Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))
* [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 (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))
* [misc]backup-simplify:  Simplify (+ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (* 0 (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) (* 0 (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (log (/ -1 n)) in n
* [misc]taylor:  Taking taylor expansion of (/ -1 n) in n
* [misc]taylor:  Taking taylor expansion of -1 in n
* [misc]backup-simplify:  Simplify -1 into -1
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ -1 1) into -1
* [misc]backup-simplify:  Simplify (log -1) into (log -1)
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))
* [misc]taylor:  Taking taylor expansion of (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n
* [misc]taylor:  Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n
* [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]taylor:  Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))
* [misc]backup-simplify:  Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]taylor:  Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n
* [misc]taylor:  Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2))
* [misc]backup-simplify:  Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))
* [misc]backup-simplify:  Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))
* [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 (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log PI))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (log 2) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -1) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 0) (* 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* +nan.0 0) (* 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))
* [misc]backup-simplify:  Simplify (+ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (+ (* 0 (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (* 0 (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) (+ (* 0 (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) (* 0 (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (log (/ -1 n)) in n
* [misc]taylor:  Taking taylor expansion of (/ -1 n) in n
* [misc]taylor:  Taking taylor expansion of -1 in n
* [misc]backup-simplify:  Simplify -1 into -1
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ -1 1) into -1
* [misc]backup-simplify:  Simplify (log -1) into (log -1)
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))
* [misc]taylor:  Taking taylor expansion of (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n
* [misc]taylor:  Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n
* [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]taylor:  Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))
* [misc]backup-simplify:  Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]taylor:  Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n
* [misc]taylor:  Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
* [misc]backup-simplify:  Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2))
* [misc]backup-simplify:  Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))
* [misc]backup-simplify:  Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))))) (* 1 (/ 1 (- k)))) (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))))) into (- (+ (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) k)))))))
* * * * [misc]progress:  [ 3 / 4 ] generating series at (2 2)
* [misc]approximate:  Taking taylor expansion of (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) in k
* [misc]taylor:  Taking taylor expansion of (pow n (- 1/2 (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 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 (/ 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) 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 (+ 1/2 0) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log n)) into (* 1/2 (log n))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log n))) into (pow n 1/2)
* [misc]taylor:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 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 (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log PI))) into (pow 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 PI 1/2) +nan.0) into (* +nan.0 (sqrt PI))
* [misc]taylor:  Taking taylor expansion of (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) in n
* [misc]taylor:  Taking taylor expansion of (pow n (- 1/2 (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log n))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log n)) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 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) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (log 1) into 0
* [misc]backup-simplify:  Simplify (- (* 1/2 k)) into (- (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) 0) into (log n)
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k)))
* [misc]taylor:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log PI)) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (- (* 1/2 k)) into (- (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 k)) (log PI)) into (* (- 1/2 (* 1/2 k)) (log PI))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 k)) (log PI))) into (pow PI (- 1/2 (* 1/2 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 (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow PI (- 1/2 (* 1/2 k))))
* [misc]taylor:  Taking taylor expansion of (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) in n
* [misc]taylor:  Taking taylor expansion of (pow n (- 1/2 (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log n))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log n)) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ 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) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (log 1) into 0
* [misc]backup-simplify:  Simplify (- (* 1/2 k)) into (- (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) 0) into (log n)
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k)))
* [misc]taylor:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log PI)) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (- (* 1/2 k)) into (- (* 1/2 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 k)) (log PI)) into (* (- 1/2 (* 1/2 k)) (log PI))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 k)) (log PI))) into (pow PI (- 1/2 (* 1/2 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 (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow PI (- 1/2 (* 1/2 k))))
* [misc]backup-simplify:  Simplify (* (pow n (- 1/2 (* 1/2 k))) (* (sqrt (/ 1 k)) (pow PI (- 1/2 (* 1/2 k))))) into (* (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 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 (* 1/2 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 k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (log n) 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 (* 1/2 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log n)) into (* 1/2 (log n))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log n))) into (pow n 1/2)
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 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 (* 1/2 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 k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (* 1/2 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2)
* [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]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 (* (pow n 1/2) (pow PI 1/2)) into (sqrt (* n PI))
* [misc]backup-simplify:  Simplify (* (sqrt (* n PI)) 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log PI))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (pow PI (- 1/2 (* 1/2 k)))) (/ 0 (sqrt k))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) 0) into (log n)
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log n))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (pow n (- 1/2 (* 1/2 k))) 0) (* 0 (* (sqrt (/ 1 k)) (pow PI (- 1/2 (* 1/2 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI)))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI)))
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* -1/2 (log n))) into (- (* 1/2 (log n)))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n)))
* [misc]backup-simplify:  Simplify (+ (* (pow n 1/2) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1/2 (* (sqrt n) (log n))) (pow PI 1/2))) into (- (+ (* 1/2 (* (sqrt (* n PI)) (log PI))) (* 1/2 (* (sqrt (* n PI)) (log n)))))
* [misc]backup-simplify:  Simplify (+ (* (sqrt (* n PI)) +nan.0) (* (- (+ (* 1/2 (* (sqrt (* n PI)) (log PI))) (* 1/2 (* (sqrt (* n PI)) (log n))))) 0)) into (- (* +nan.0 (sqrt (* n PI))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (sqrt (* n PI)))) into (- (* +nan.0 (sqrt (* n PI))))
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (log PI)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log PI))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (pow PI (- 1/2 (* 1/2 k)))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) 0) into (log n)
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (pow n (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (* (sqrt (/ 1 k)) (pow PI (- 1/2 (* 1/2 k))))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI)))
* [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 (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2)))
* [misc]backup-simplify:  Simplify (+ (* (pow n 1/2) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* -1/2 (* (sqrt n) (log n))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (pow PI 1/2)))) into (+ (* 1/8 (* (sqrt (* n PI)) (pow (log n) 2))) (+ (* 1/4 (* (sqrt (* n PI)) (* (log PI) (log n)))) (* 1/8 (* (sqrt (* n PI)) (pow (log PI) 2)))))
* [misc]backup-simplify:  Simplify (+ (* (sqrt (* n PI)) +nan.0) (+ (* (- (+ (* 1/2 (* (sqrt (* n PI)) (log PI))) (* 1/2 (* (sqrt (* n PI)) (log n))))) +nan.0) (* (+ (* 1/8 (* (sqrt (* n PI)) (pow (log n) 2))) (+ (* 1/4 (* (sqrt (* n PI)) (* (log PI) (log n)))) (* 1/8 (* (sqrt (* n PI)) (pow (log PI) 2))))) 0))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (* +nan.0 (sqrt (* n PI))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (* +nan.0 (sqrt (* n PI)))))))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (* +nan.0 (sqrt (* n PI))))))))
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log PI))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (pow PI (- 1/2 (* 1/2 k)))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) 0) into (log n)
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (pow n (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt (/ 1 k)) (pow PI (- 1/2 (* 1/2 k)))))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 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 (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 3) 6)) (* (/ (pow (- (* 1/2 (log PI))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log PI) 3) (sqrt PI)))
* [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 (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 3) 6)) (* (/ (pow (- (* 1/2 (log n))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt n) (pow (log n) 3)))
* [misc]backup-simplify:  Simplify (+ (* (pow n 1/2) (* -1/48 (* (pow (log PI) 3) (sqrt PI)))) (+ (* (* -1/2 (* (sqrt n) (log n))) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1/48 (* (sqrt n) (pow (log n) 3))) (pow PI 1/2))))) into (- (+ (* 1/48 (* (sqrt (* n PI)) (pow (log PI) 3))) (+ (* 1/16 (* (sqrt (* n PI)) (* (pow (log PI) 2) (log n)))) (+ (* 1/48 (* (sqrt (* n PI)) (pow (log n) 3))) (* 1/16 (* (sqrt (* n PI)) (* (log PI) (pow (log n) 2))))))))
* [misc]backup-simplify:  Simplify (+ (* (sqrt (* n PI)) +nan.0) (+ (* (- (+ (* 1/2 (* (sqrt (* n PI)) (log PI))) (* 1/2 (* (sqrt (* n PI)) (log n))))) +nan.0) (+ (* (+ (* 1/8 (* (sqrt (* n PI)) (pow (log n) 2))) (+ (* 1/4 (* (sqrt (* n PI)) (* (log PI) (log n)))) (* 1/8 (* (sqrt (* n PI)) (pow (log PI) 2))))) +nan.0) (* (- (+ (* 1/48 (* (sqrt (* n PI)) (pow (log PI) 3))) (+ (* 1/16 (* (sqrt (* n PI)) (* (pow (log PI) 2) (log n)))) (+ (* 1/48 (* (sqrt (* n PI)) (pow (log n) 3))) (* 1/16 (* (sqrt (* n PI)) (* (log PI) (pow (log n) 2)))))))) 0)))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log n) 2))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (log n)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log PI) 2))) (- (* +nan.0 (sqrt (* n PI))))))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log n) 2))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (log n)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log PI) 2))) (- (* +nan.0 (sqrt (* n PI)))))))))))))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log n) 2))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (log n)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log PI) 2))) (- (* +nan.0 (sqrt (* n PI))))))))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log n) 2))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (log n)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log PI) 2))) (- (* +nan.0 (sqrt (* n PI)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (* +nan.0 (sqrt (* n PI)))))))) (* k 1)) (- (* +nan.0 (sqrt (* n PI)))))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (pow k 2)))) (- (+ (* +nan.0 (sqrt (* n PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log PI) 2) (pow k 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) k)) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) k))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) k))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log n) 2) (pow k 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (pow k 2))))))))))))))))))))))
* [misc]approximate:  Taking taylor expansion of (* (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (* (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (/ 1 n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (/ 1 n))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 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) 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)) 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]backup-simplify:  Simplify (log (/ 1 n)) into (log (/ 1 n))
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n)))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))
* [misc]taylor:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 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) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* -1/2 (log PI)) into (* -1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 k) 2)) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 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 (/ (pow PI (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) into (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (* (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (/ 1 n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (/ 1 n))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 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)) 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]backup-simplify:  Simplify (log 1) into 0
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))
* [misc]backup-simplify:  Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))
* [misc]taylor:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log PI)) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 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 (/ (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (sqrt (/ 1 k))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (* (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (/ 1 n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (/ 1 n))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 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)) 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]backup-simplify:  Simplify (log 1) into 0
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))
* [misc]backup-simplify:  Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))
* [misc]taylor:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log PI)) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
* [misc]backup-simplify:  Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 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 (/ (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (sqrt (/ 1 k))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k))
* [misc]backup-simplify:  Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k))) into (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) in k
* [misc]taylor:  Taking taylor expansion of -1 in k
* [misc]backup-simplify:  Simplify -1 into -1
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 (/ 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 (* 1/2 (/ 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 (/ 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 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 (* 1/2 1) into 1/2
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* -1/2 (log n)) into (* -1/2 (log n))
* [misc]backup-simplify:  Simplify (* -1 (* -1/2 (log n))) into (* 1/2 (log n))
* [misc]backup-simplify:  Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (* 1/2 (/ 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 (* 1/2 (/ 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 (/ 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) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (* 1/2 1) into 1/2
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* -1/2 (log PI)) into (* -1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]backup-simplify:  Simplify (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (log PI))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (* 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (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 (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (* 0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (log PI)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (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))) (+ (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (+ (* 0 0) (* 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (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 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (+ (* 0 0) (* 0 (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (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))) (+ (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (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 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (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 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2))))))))
* [misc]approximate:  Taking taylor expansion of (* (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (* (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) in k
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (/ 1 (- n))))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (/ 1 (- n)))) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 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)) 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))) 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]backup-simplify:  Simplify (log (/ -1 n)) into (log (/ -1 n))
* [misc]backup-simplify:  Simplify (- -1/2) into 1/2
* [misc]backup-simplify:  Simplify (+ 0 1/2) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n)))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (/ 1 (- n))))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2))
* [misc]taylor:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 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)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (- -1/2) into 1/2
* [misc]backup-simplify:  Simplify (+ 0 1/2) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2))
* [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 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]taylor:  Taking taylor expansion of (* (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) in n
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (/ 1 (- n))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (/ 1 (- n)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- 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))) 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]backup-simplify:  Simplify (log -1) into (log -1)
* [misc]backup-simplify:  Simplify (- (/ -1/2 k)) into (* 1/2 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))
* [misc]taylor:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI)) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (- (/ -1/2 k)) into (* 1/2 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2))
* [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 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) into (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k)))
* [misc]taylor:  Taking taylor expansion of (* (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) in n
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (/ 1 (- n))))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (/ 1 (- n)))) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- 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))) 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]backup-simplify:  Simplify (log -1) into (log -1)
* [misc]backup-simplify:  Simplify (- (/ -1/2 k)) into (* 1/2 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))
* [misc]taylor:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI))) in n
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI)) in n
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log PI) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (- (/ -1/2 k)) into (* 1/2 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2)
* [misc]backup-simplify:  Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2))
* [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 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) into (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k)))
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k)))) into (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k)))
* [misc]taylor:  Taking taylor expansion of (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k
* [misc]taylor:  Taking taylor expansion of (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 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 (/ 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 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (- (log -1) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log -1) in k
* [misc]taylor:  Taking taylor expansion of -1 in k
* [misc]backup-simplify:  Simplify -1 into -1
* [misc]backup-simplify:  Simplify (log -1) into (log -1)
* [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 (* 1/2 1) into 1/2
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n)))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ 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 (/ 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 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (* 1/2 1) into 1/2
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2))
* [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 -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)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]backup-simplify:  Simplify (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))
* [misc]backup-simplify:  Simplify (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log PI))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) 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 (/ (* (pow (* 1 0) 1)) (pow -1 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -1) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 0) (* 0 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (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)) 1/2) (- (log -1) (log n)))) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 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)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (log PI)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) (+ (* (/ (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))) (+ (* (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 0) (+ (* 0 0) (* 0 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (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)) 1/2) (- (log -1) (log n)))) 0) (+ (* 0 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 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)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) (* (/ 1 (- k)) 1)) (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))))) into (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2))) (- (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k))))))))))
* * * * [misc]progress:  [ 4 / 4 ] generating series at (2 2 2)
* [misc]approximate:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 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 (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log PI))) into (pow 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 PI 1/2) +nan.0) into (* +nan.0 (sqrt PI))
* [misc]taylor:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ k 2)) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ k 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 (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (+ 1/2 0) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log PI))) into (pow 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 PI 1/2) +nan.0) into (* +nan.0 (sqrt PI))
* [misc]backup-simplify:  Simplify (* +nan.0 (sqrt PI)) into (* +nan.0 (sqrt PI))
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI)))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI)))
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ (* -1/2 (* (log PI) (sqrt PI))) +nan.0) (+ (* (* +nan.0 (sqrt PI)) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI)))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI)))))
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 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) (+ (* -1/2 0) (* 0 (log PI)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI)))
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ (* 1/8 (* (pow (log PI) 2) (sqrt PI))) +nan.0) (+ (* (* +nan.0 (sqrt PI)) (/ +nan.0 +nan.0)) (* (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) k) (+ (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) (* (* +nan.0 (sqrt PI)) (/ 1 k)))) into (- (+ (* +nan.0 (* (* (log PI) k) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) k)) (- (+ (* +nan.0 (* (sqrt PI) (/ 1 k))) (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) k) (sqrt PI))) (- (* +nan.0 (sqrt PI)))))))))))))
* [misc]approximate:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 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) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* -1/2 (log PI)) into (* -1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 k) 2)) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 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 (/ (pow PI (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) into (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 k) 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) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (- 1/2) into -1/2
* [misc]backup-simplify:  Simplify (+ 0 -1/2) into -1/2
* [misc]backup-simplify:  Simplify (* -1/2 (log PI)) into (* -1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 k) 2)) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 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 (/ (pow PI (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) into (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k))))) into (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))) (pow (/ 1 k) 2)) (+ (* (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))) (/ 1 k)) (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) into (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) k)) (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (pow k 2))) (- (* +nan.0 (pow PI (- 1/2 (* 1/2 k)))))))))
* [misc]approximate:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 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)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (- -1/2) into 1/2
* [misc]backup-simplify:  Simplify (+ 0 1/2) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2))
* [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 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]taylor:  Taking taylor expansion of (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI))) in k
* [misc]taylor:  Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI)) in k
* [misc]taylor:  Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 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)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log PI) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (log PI) into (log PI)
* [misc]backup-simplify:  Simplify (- -1/2) into 1/2
* [misc]backup-simplify:  Simplify (+ 0 1/2) into 1/2
* [misc]backup-simplify:  Simplify (* 1/2 (log PI)) into (* 1/2 (log PI))
* [misc]backup-simplify:  Simplify (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2))
* [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 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))
* [misc]backup-simplify:  Simplify (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))
* [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 (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))
* [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 (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))) (/ 1 (- k))) (* +nan.0 (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) into (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) k)) (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (pow k 2))) (- (* +nan.0 (pow PI (- 1/2 (* 1/2 k)))))))))
* * * [misc]progress:  simplifying candidates
* * * * [misc]progress:  [ 1 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (exp (* (log PI) (- 1/2 (/ k 2)))) (sqrt k)))))>
* * * * [misc]progress:  [ 2 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (/ (pow PI 1/2) (pow PI (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (pow PI (/ k 2))
* * [misc]simplify:  iters left: 3 (5 enodes)
* [exit]simplify:  Simplified to (pow PI (/ k 2))
* [misc]simplify:  Simplified (2 2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (/ (pow PI 1/2) (pow PI (/ k 2))) (sqrt k)))))
* * * * [misc]progress:  [ 3 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow (pow PI (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (cbrt (- 1/2 (/ k 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* * [misc]simplify:  iters left: 3 (11 enodes)
* [exit]simplify:  Simplified to (cbrt (- 1/2 (/ k 2)))
* [misc]simplify:  Simplified (2 2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow (pow PI (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 4 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow (pow PI (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (- 1/2 (/ k 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* * [misc]simplify:  iters left: 3 (11 enodes)
* [exit]simplify:  Simplified to (sqrt (- 1/2 (/ k 2)))
* [misc]simplify:  Simplified (2 2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow (pow PI (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 5 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow (pow PI 1) (- 1/2 (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (- 1/2 (/ k 2))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* * [misc]simplify:  iters left: 2 (10 enodes)
* [exit]simplify:  Simplified to (- 1/2 (/ k 2))
* [misc]simplify:  Simplified (2 2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow (pow PI 1) (- 1/2 (/ k 2))) (sqrt k)))))
* * * * [misc]progress:  [ 6 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (* (pow PI 1/2) (pow PI (- (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (pow PI (- (/ k 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* [exit]simplify:  Simplified to (pow PI (/ (- k) 2))
* [misc]simplify:  Simplified (2 2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (* (pow PI 1/2) (pow PI (/ (- k) 2))) (sqrt k)))))
* * * * [misc]progress:  [ 7 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (* (pow PI 1/2) (pow PI (- (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (pow PI (- (/ k 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* [exit]simplify:  Simplified to (pow PI (/ (- k) 2))
* [misc]simplify:  Simplified (2 2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (* (pow PI 1/2) (pow PI (/ (- k) 2))) (sqrt k)))))
* * * * [misc]progress:  [ 8 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow (pow PI (- 1/2 (/ k 2))) 1) (sqrt k)))))>
* * * * [misc]progress:  [ 9 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (exp (log (pow PI (- 1/2 (/ k 2))))) (sqrt k)))))>
* * * * [misc]progress:  [ 10 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (log (exp (pow PI (- 1/2 (/ k 2))))) (sqrt k)))))>
* * * * [misc]progress:  [ 11 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (* (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (cbrt (pow PI (- 1/2 (/ k 2))))) (sqrt k)))))>
* * * * [misc]progress:  [ 12 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (cbrt (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (pow PI (- 1/2 (/ k 2))))) (sqrt k)))))>
* * * * [misc]progress:  [ 13 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (* (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (pow PI (- 1/2 (/ k 2))))) (sqrt k)))))>
* * * * [misc]progress:  [ 14 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (* 1 (pow PI (- 1/2 (/ k 2)))) (sqrt k)))))>
* * * * [misc]progress:  [ 15 / 144 ] simplifiying candidate #<alt (λ (k n) (pow (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) 1))>
* * * * [misc]progress:  [ 16 / 144 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log 2) (- 1/2 (/ k 2))) (+ (* (log n) (- 1/2 (/ k 2))) (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (+ (* (log n) (- 1/2 (/ k 2))) (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k)))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (76 enodes)
* * [misc]simplify:  iters left: 3 (251 enodes)
* [exit]simplify:  Simplified to (- (* (+ (log 2) (+ (log n) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (+ (log 2) (+ (log n) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))
* * * * [misc]progress:  [ 17 / 144 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log 2) (- 1/2 (/ k 2))) (+ (* (log n) (- 1/2 (/ k 2))) (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (+ (* (log n) (- 1/2 (/ k 2))) (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k)))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (72 enodes)
* * [misc]simplify:  iters left: 3 (217 enodes)
* [exit]simplify:  Simplified to (- (* (+ (log PI) (+ (log 2) (log n))) (- 1/2 (/ k 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (+ (log PI) (+ (log 2) (log n))) (- 1/2 (/ k 2))) (log (sqrt k)))))
* * * * [misc]progress:  [ 18 / 144 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log 2) (- 1/2 (/ k 2))) (+ (* (log n) (- 1/2 (/ k 2))) (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (+ (* (log n) (- 1/2 (/ k 2))) (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (61 enodes)
* * [misc]simplify:  iters left: 3 (170 enodes)
* [exit]simplify:  Simplified to (- (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))
* * * * [misc]progress:  [ 19 / 144 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log 2) (- 1/2 (/ k 2))) (+ (log (pow n (- 1/2 (/ k 2)))) (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (+ (log (pow n (- 1/2 (/ k 2)))) (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k)))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (72 enodes)
* * [misc]simplify:  iters left: 3 (205 enodes)
* [exit]simplify:  Simplified to (- (* (+ (+ (log 2) (log PI)) (log n)) (- 1/2 (/ k 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (+ (+ (log 2) (log PI)) (log n)) (- 1/2 (/ k 2))) (log (sqrt k)))))
* * * * [misc]progress:  [ 20 / 144 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log 2) (- 1/2 (/ k 2))) (+ (log (pow n (- 1/2 (/ k 2)))) (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (+ (log (pow n (- 1/2 (/ k 2)))) (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k)))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (68 enodes)
* * [misc]simplify:  iters left: 3 (171 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (+ (+ (log 2) (log PI)) (log n))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (+ (log 2) (log PI)) (log n))) (log (sqrt k)))))
* * * * [misc]progress:  [ 21 / 144 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log 2) (- 1/2 (/ k 2))) (+ (log (pow n (- 1/2 (/ k 2)))) (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (+ (log (pow n (- 1/2 (/ k 2)))) (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (57 enodes)
* * [misc]simplify:  iters left: 3 (132 enodes)
* * [misc]simplify:  iters left: 2 (457 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (+ (+ (log n) (log PI)) (log 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (+ (log n) (log PI)) (log 2))) (log (sqrt k)))))
* * * * [misc]progress:  [ 22 / 144 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log 2) (- 1/2 (/ k 2))) (log (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (log (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (51 enodes)
* * [misc]simplify:  iters left: 3 (101 enodes)
* * [misc]simplify:  iters left: 2 (236 enodes)
* [exit]simplify:  Simplified to (- (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))
* * * * [misc]progress:  [ 23 / 144 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow 2 (- 1/2 (/ k 2)))) (+ (* (log n) (- 1/2 (/ k 2))) (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (+ (* (log n) (- 1/2 (/ k 2))) (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k)))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (72 enodes)
* * [misc]simplify:  iters left: 3 (213 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (+ (log 2) (+ (log n) (log PI)))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (log 2) (+ (log n) (log PI)))) (log (sqrt k)))))
* * * * [misc]progress:  [ 24 / 144 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow 2 (- 1/2 (/ k 2)))) (+ (* (log n) (- 1/2 (/ k 2))) (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (+ (* (log n) (- 1/2 (/ k 2))) (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k)))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (68 enodes)
* * [misc]simplify:  iters left: 3 (179 enodes)
* [exit]simplify:  Simplified to (- (* (+ (+ (log 2) (log PI)) (log n)) (- 1/2 (/ k 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (+ (+ (log 2) (log PI)) (log n)) (- 1/2 (/ k 2))) (log (sqrt k)))))
* * * * [misc]progress:  [ 25 / 144 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow 2 (- 1/2 (/ k 2)))) (+ (* (log n) (- 1/2 (/ k 2))) (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (+ (* (log n) (- 1/2 (/ k 2))) (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (57 enodes)
* * [misc]simplify:  iters left: 3 (140 enodes)
* * [misc]simplify:  iters left: 2 (467 enodes)
* [exit]simplify:  Simplified to (- (* (+ (log 2) (+ (log n) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (+ (log 2) (+ (log n) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))
* * * * [misc]progress:  [ 26 / 144 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow 2 (- 1/2 (/ k 2)))) (+ (log (pow n (- 1/2 (/ k 2)))) (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (+ (log (pow n (- 1/2 (/ k 2)))) (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k)))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (68 enodes)
* * [misc]simplify:  iters left: 3 (167 enodes)
* [exit]simplify:  Simplified to (- (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))
* * * * [misc]progress:  [ 27 / 144 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow 2 (- 1/2 (/ k 2)))) (+ (log (pow n (- 1/2 (/ k 2)))) (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (+ (log (pow n (- 1/2 (/ k 2)))) (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k)))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (34 enodes)
* * [misc]simplify:  iters left: 4 (64 enodes)
* * [misc]simplify:  iters left: 3 (133 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (+ (log 2) (+ (log PI) (log n)))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (log 2) (+ (log PI) (log n)))) (log (sqrt k)))))
* * * * [misc]progress:  [ 28 / 144 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow 2 (- 1/2 (/ k 2)))) (+ (log (pow n (- 1/2 (/ k 2)))) (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (+ (log (pow n (- 1/2 (/ k 2)))) (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (53 enodes)
* * [misc]simplify:  iters left: 3 (102 enodes)
* * [misc]simplify:  iters left: 2 (376 enodes)
* [exit]simplify:  Simplified to (- (* (+ (+ (log 2) (log PI)) (log n)) (- 1/2 (/ k 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (+ (+ (log 2) (log PI)) (log n)) (- 1/2 (/ k 2))) (log (sqrt k)))))
* * * * [misc]progress:  [ 29 / 144 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow 2 (- 1/2 (/ k 2)))) (log (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (log (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (47 enodes)
* * [misc]simplify:  iters left: 3 (83 enodes)
* * [misc]simplify:  iters left: 2 (218 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (+ (+ (log PI) (log n)) (log 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (+ (log PI) (log n)) (log 2))) (log (sqrt k)))))
* * * * [misc]progress:  [ 30 / 144 ] simplifiying candidate #<alt (λ (k n) (exp (log (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* * * * [misc]progress:  [ 31 / 144 ] simplifiying candidate #<alt (λ (k n) (log (exp (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* * * * [misc]progress:  [ 32 / 144 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (* (* (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (/ (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (pow PI (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (* (* (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (/ (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (pow PI (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (22 enodes)
* * [misc]simplify:  iters left: 5 (45 enodes)
* * [misc]simplify:  iters left: 4 (167 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (pow n (- 1/2 (/ k 2))) 3) (pow (pow 2 (- 1/2 (/ k 2))) 3)) (/ (/ (* k (sqrt k)) (pow PI (- 1/2 (/ k 2)))) (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2))))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (cbrt (/ (* (pow (pow n (- 1/2 (/ k 2))) 3) (pow (pow 2 (- 1/2 (/ k 2))) 3)) (/ (/ (* k (sqrt k)) (pow PI (- 1/2 (/ k 2)))) (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2))))))))
* * * * [misc]progress:  [ 33 / 144 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (* (* (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (* (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* [enter]simplify:  Simplifying (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (* (* (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (* (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (41 enodes)
* * [misc]simplify:  iters left: 4 (140 enodes)
* [exit]simplify:  Simplified to (* (* (pow (pow n (- 1/2 (/ k 2))) 3) (pow (pow 2 (- 1/2 (/ k 2))) 3)) (pow (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 3))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (cbrt (* (* (pow (pow n (- 1/2 (/ k 2))) 3) (pow (pow 2 (- 1/2 (/ k 2))) 3)) (pow (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 3))))
* * * * [misc]progress:  [ 34 / 144 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (* (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* [enter]simplify:  Simplifying (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (* (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (116 enodes)
* * [misc]simplify:  iters left: 3 (465 enodes)
* [exit]simplify:  Simplified to (* (* (pow (pow 2 (- 1/2 (/ k 2))) 3) (pow (pow n (- 1/2 (/ k 2))) 3)) (pow (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 3))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (cbrt (* (* (pow (pow 2 (- 1/2 (/ k 2))) 3) (pow (pow n (- 1/2 (/ k 2))) 3)) (pow (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 3))))
* * * * [misc]progress:  [ 35 / 144 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) (cbrt (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) (cbrt (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* * * * [misc]progress:  [ 36 / 144 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* * * * [misc]progress:  [ 37 / 144 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) (sqrt (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* * * * [misc]progress:  [ 38 / 144 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 1/2) (* (pow n 1/2) (pow PI (- 1/2 (/ k 2))))) (* (pow 2 (/ k 2)) (* (pow n (/ k 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (pow 2 1/2) (* (pow n 1/2) (pow PI (- 1/2 (/ 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 (30 enodes)
* [exit]simplify:  Simplified to (* (* (sqrt n) (sqrt 2)) (pow PI (- 1/2 (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (* (* (sqrt n) (sqrt 2)) (pow PI (- 1/2 (/ k 2)))) (* (pow 2 (/ k 2)) (* (pow n (/ k 2)) (sqrt k)))))
* [enter]simplify:  Simplifying (* (pow 2 (/ k 2)) (* (pow n (/ k 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* * [misc]simplify:  iters left: 3 (21 enodes)
* [exit]simplify:  Simplified to (* (pow 2 (/ k 2)) (* (pow n (/ k 2)) (sqrt k)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (* (* (sqrt n) (sqrt 2)) (pow PI (- 1/2 (/ k 2)))) (* (pow 2 (/ k 2)) (* (pow n (/ k 2)) (sqrt k)))))
* * * * [misc]progress:  [ 39 / 144 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 1/2) (* (pow n (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2))))) (* (pow 2 (/ k 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (* (pow 2 1/2) (* (pow n (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (* (* (sqrt 2) (pow PI (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (* (* (sqrt 2) (pow PI (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (* (pow 2 (/ k 2)) (sqrt k))))
* [enter]simplify:  Simplifying (* (pow 2 (/ k 2)) (sqrt k))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (7 enodes)
* [exit]simplify:  Simplified to (* (pow 2 (/ k 2)) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (* (* (sqrt 2) (pow PI (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (* (pow 2 (/ k 2)) (sqrt k))))
* * * * [misc]progress:  [ 40 / 144 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 1/2) (* (pow n 1/2) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) (* (pow 2 (/ k 2)) (pow n (/ k 2)))))>
* [enter]simplify:  Simplifying (* (pow 2 1/2) (* (pow n 1/2) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (60 enodes)
* * [misc]simplify:  iters left: 2 (74 enodes)
* * [misc]simplify:  iters left: 1 (97 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (* (sqrt n) (sqrt 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (* (sqrt n) (sqrt 2)))) (* (pow 2 (/ k 2)) (pow n (/ k 2)))))
* [enter]simplify:  Simplifying (* (pow 2 (/ k 2)) (pow n (/ k 2)))
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* [exit]simplify:  Simplified to (* (pow 2 (/ k 2)) (pow n (/ k 2)))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (* (sqrt n) (sqrt 2)))) (* (pow 2 (/ k 2)) (pow n (/ k 2)))))
* * * * [misc]progress:  [ 41 / 144 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))>
* * * * [misc]progress:  [ 42 / 144 ] simplifiying candidate #<alt (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))
* * * * [misc]progress:  [ 43 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 1/2) (* (pow 2 (- (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))>
* [enter]simplify:  Simplifying (pow 2 1/2)
* * [misc]simplify:  iters left: 1 (3 enodes)
* [exit]simplify:  Simplified to (sqrt 2)
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt 2) (* (pow 2 (- (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))
* * * * [misc]progress:  [ 44 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 1/2) (* (pow 2 (- (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))>
* [enter]simplify:  Simplifying (pow 2 1/2)
* * [misc]simplify:  iters left: 1 (3 enodes)
* [exit]simplify:  Simplified to (sqrt 2)
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt 2) (* (pow 2 (- (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))
* * * * [misc]progress:  [ 45 / 144 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt (pow 2 (- 1/2 (/ k 2))))) (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt (pow 2 (- 1/2 (/ k 2)))))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt (pow 2 (- 1/2 (/ k 2)))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt (pow 2 (- 1/2 (/ k 2))))) (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))
* * * * [misc]progress:  [ 46 / 144 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))>
* [enter]simplify:  Simplifying (sqrt (pow 2 (- 1/2 (/ k 2))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* [exit]simplify:  Simplified to (sqrt (pow 2 (- 1/2 (/ k 2))))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))
* * * * [misc]progress:  [ 47 / 144 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))>
* * * * [misc]progress:  [ 48 / 144 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (* (pow n 1/2) (pow PI (- 1/2 (/ k 2))))) (* (pow n (/ k 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (* (pow n (/ k 2)) (sqrt k))
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* [exit]simplify:  Simplified to (* (pow n (/ k 2)) (sqrt k))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (* (pow n 1/2) (pow PI (- 1/2 (/ k 2))))) (* (pow n (/ k 2)) (sqrt k))))
* * * * [misc]progress:  [ 49 / 144 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2))))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt k)
* * [misc]simplify:  iters left: 1 (2 enodes)
* [exit]simplify:  Simplified to (sqrt k)
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2))))) (sqrt k)))
* * * * [misc]progress:  [ 50 / 144 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (* (pow n 1/2) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) (pow n (/ k 2))))>
* [enter]simplify:  Simplifying (pow n (/ k 2))
* * [misc]simplify:  iters left: 3 (5 enodes)
* [exit]simplify:  Simplified to (pow n (/ k 2))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (* (pow n 1/2) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) (pow n (/ k 2))))
* * * * [misc]progress:  [ 51 / 144 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow 2 1/2) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) (pow 2 (/ k 2))))>
* [enter]simplify:  Simplifying (* (pow 2 1/2) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (59 enodes)
* * [misc]simplify:  iters left: 2 (73 enodes)
* * [misc]simplify:  iters left: 1 (96 enodes)
* [exit]simplify:  Simplified to (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) (* (pow n (- 1/2 (/ k 2))) (sqrt 2)))
* [misc]simplify:  Simplified (2 1) to (λ (k n) (/ (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) (* (pow n (- 1/2 (/ k 2))) (sqrt 2))) (pow 2 (/ k 2))))
* * * * [misc]progress:  [ 52 / 144 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (pow 2 (- 1/2 (/ k 2)))))>
* * * * [misc]progress:  [ 53 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (pow (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) 1)))>
* * * * [misc]progress:  [ 54 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (+ (* (log n) (- 1/2 (/ k 2))) (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (* (log n) (- 1/2 (/ k 2))) (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (48 enodes)
* * [misc]simplify:  iters left: 3 (126 enodes)
* * [misc]simplify:  iters left: 2 (346 enodes)
* [exit]simplify:  Simplified to (- (* (+ (log PI) (log n)) (- 1/2 (/ k 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (+ (log PI) (log n)) (- 1/2 (/ k 2))) (log (sqrt k))))))
* * * * [misc]progress:  [ 55 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (+ (* (log n) (- 1/2 (/ k 2))) (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (* (log n) (- 1/2 (/ k 2))) (- (log (pow PI (- 1/2 (/ k 2)))) (log (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 (95 enodes)
* * [misc]simplify:  iters left: 2 (273 enodes)
* [exit]simplify:  Simplified to (- (* (+ (log PI) (log n)) (- 1/2 (/ k 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (+ (log PI) (log n)) (- 1/2 (/ k 2))) (log (sqrt k))))))
* * * * [misc]progress:  [ 56 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (+ (* (log n) (- 1/2 (/ k 2))) (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (* (log n) (- 1/2 (/ k 2))) (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (38 enodes)
* * [misc]simplify:  iters left: 3 (76 enodes)
* * [misc]simplify:  iters left: 2 (166 enodes)
* * [misc]simplify:  iters left: 1 (420 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (+ (log n) (log PI))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (- 1/2 (/ k 2)) (+ (log n) (log PI))) (log (sqrt k))))))
* * * * [misc]progress:  [ 57 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (+ (log (pow n (- 1/2 (/ k 2)))) (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (log (pow n (- 1/2 (/ k 2)))) (- (* (log PI) (- 1/2 (/ k 2))) (log (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 (95 enodes)
* * [misc]simplify:  iters left: 2 (271 enodes)
* [exit]simplify:  Simplified to (- (* (+ (log PI) (log n)) (- 1/2 (/ k 2))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (+ (log PI) (log n)) (- 1/2 (/ k 2))) (log (sqrt k))))))
* * * * [misc]progress:  [ 58 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (+ (log (pow n (- 1/2 (/ k 2)))) (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (log (pow n (- 1/2 (/ k 2)))) (- (log (pow PI (- 1/2 (/ k 2)))) (log (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 (66 enodes)
* * [misc]simplify:  iters left: 2 (230 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (+ (log n) (log PI))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (- 1/2 (/ k 2)) (+ (log n) (log PI))) (log (sqrt k))))))
* * * * [misc]progress:  [ 59 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (+ (log (pow n (- 1/2 (/ k 2)))) (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (log (pow n (- 1/2 (/ k 2)))) (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (54 enodes)
* * [misc]simplify:  iters left: 2 (145 enodes)
* * [misc]simplify:  iters left: 1 (442 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (+ (log n) (log PI))) (log (sqrt k)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (- 1/2 (/ k 2)) (+ (log n) (log PI))) (log (sqrt k))))))
* * * * [misc]progress:  [ 60 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (log (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* * * * [misc]progress:  [ 61 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (log (exp (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* * * * [misc]progress:  [ 62 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (cbrt (* (* (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (/ (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (pow PI (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (* (* (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (/ (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (pow PI (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (35 enodes)
* * [misc]simplify:  iters left: 4 (111 enodes)
* * [misc]simplify:  iters left: 3 (435 enodes)
* [exit]simplify:  Simplified to (/ (* (* (pow PI (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2))))) (/ (/ (* k (sqrt k)) (pow PI (- 1/2 (/ k 2)))) (pow PI (- 1/2 (/ k 2)))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (cbrt (/ (* (* (pow PI (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2))))) (/ (/ (* k (sqrt k)) (pow PI (- 1/2 (/ k 2)))) (pow PI (- 1/2 (/ k 2))))))))
* * * * [misc]progress:  [ 63 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (cbrt (* (* (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (* (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* [enter]simplify:  Simplifying (* (* (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (* (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (89 enodes)
* * [misc]simplify:  iters left: 3 (229 enodes)
* [exit]simplify:  Simplified to (/ (* (* (pow PI (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2))))) (* (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))) (/ k (pow PI (- 1/2 (/ k 2))))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (cbrt (/ (* (* (pow PI (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2))))) (* (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))) (/ k (pow PI (- 1/2 (/ k 2)))))))))
* * * * [misc]progress:  [ 64 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (cbrt (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) (cbrt (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* * * * [misc]progress:  [ 65 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (cbrt (* (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* * * * [misc]progress:  [ 66 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* * * * [misc]progress:  [ 67 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (pow n 1/2) (pow PI (- 1/2 (/ k 2)))) (* (pow n (/ k 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (pow n 1/2) (pow PI (- 1/2 (/ k 2))))
* * [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 (* (sqrt n) (pow PI (- 1/2 (/ k 2))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (sqrt n) (pow PI (- 1/2 (/ k 2)))) (* (pow n (/ k 2)) (sqrt k)))))
* [enter]simplify:  Simplifying (* (pow n (/ k 2)) (sqrt k))
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* [exit]simplify:  Simplified to (* (pow n (/ k 2)) (sqrt k))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (sqrt n) (pow PI (- 1/2 (/ k 2)))) (* (pow n (/ k 2)) (sqrt k)))))
* * * * [misc]progress:  [ 68 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* 1 (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))>
* * * * [misc]progress:  [ 69 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (* (cbrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) (cbrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))>
* [enter]simplify:  Simplifying (cbrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* [exit]simplify:  Simplified to (cbrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (* (cbrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) (cbrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))
* * * * [misc]progress:  [ 70 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))>
* [enter]simplify:  Simplifying (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))
* * * * [misc]progress:  [ 71 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow PI (- (/ k 2))) (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow PI (- (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (/ (- k) 2)) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow PI (/ (- k) 2)) (cbrt (sqrt k))))))
* * * * [misc]progress:  [ 72 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) (sqrt (sqrt k)))) (/ (pow PI (- (/ k 2))) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow PI (- (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) (sqrt (sqrt k)))) (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k))))))
* * * * [misc]progress:  [ 73 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) 1)) (/ (pow PI (- (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow PI (- (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (- (/ k 2))) (sqrt k))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) 1)) (/ (pow PI (- (/ k 2))) (sqrt k)))))
* * * * [misc]progress:  [ 74 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow PI (- (/ k 2))) (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow PI (- (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (/ (- k) 2)) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow PI (/ (- k) 2)) (cbrt (sqrt k))))))
* * * * [misc]progress:  [ 75 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) (sqrt (sqrt k)))) (/ (pow PI (- (/ k 2))) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow PI (- (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) (sqrt (sqrt k)))) (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k))))))
* * * * [misc]progress:  [ 76 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) 1)) (/ (pow PI (- (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow PI (- (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (- (/ k 2))) (sqrt k))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) 1)) (/ (pow PI (- (/ k 2))) (sqrt k)))))
* * * * [misc]progress:  [ 77 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))))))
* * * * [misc]progress:  [ 78 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))
* * * * [misc]progress:  [ 79 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) 1)) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt k))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) 1)) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 80 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))))))
* * * * [misc]progress:  [ 81 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))
* * * * [misc]progress:  [ 82 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) 1)) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt k))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) 1)) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)))))
* * * * [misc]progress:  [ 83 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))))))
* * * * [misc]progress:  [ 84 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ 1 (sqrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ 1 (sqrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))))))
* * * * [misc]progress:  [ 85 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ 1 1)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ 1 1)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))
* * * * [misc]progress:  [ 86 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) 1) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) 1) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))
* * * * [misc]progress:  [ 87 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ 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))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (/ 1 (sqrt k)))))
* * * * [misc]progress:  [ 88 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n 1/2) (* (pow n (- (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))>
* [enter]simplify:  Simplifying (pow n 1/2)
* * [misc]simplify:  iters left: 1 (3 enodes)
* [exit]simplify:  Simplified to (sqrt n)
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt n) (* (pow n (- (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))
* * * * [misc]progress:  [ 89 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n 1/2) (* (pow n (- (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))>
* [enter]simplify:  Simplifying (pow n 1/2)
* * [misc]simplify:  iters left: 1 (3 enodes)
* [exit]simplify:  Simplified to (sqrt n)
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt n) (* (pow n (- (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))
* * * * [misc]progress:  [ 90 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (cbrt (pow n (- 1/2 (/ k 2)))) (cbrt (pow n (- 1/2 (/ k 2))))) (* (cbrt (pow n (- 1/2 (/ k 2)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (cbrt (pow n (- 1/2 (/ k 2)))) (cbrt (pow n (- 1/2 (/ k 2)))))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow n (- 1/2 (/ k 2)))) (cbrt (pow n (- 1/2 (/ k 2)))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (cbrt (pow n (- 1/2 (/ k 2)))) (cbrt (pow n (- 1/2 (/ k 2))))) (* (cbrt (pow n (- 1/2 (/ k 2)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))
* * * * [misc]progress:  [ 91 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (pow n (- 1/2 (/ k 2)))) (* (sqrt (pow n (- 1/2 (/ k 2)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))>
* [enter]simplify:  Simplifying (sqrt (pow n (- 1/2 (/ k 2))))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* [exit]simplify:  Simplified to (sqrt (pow n (- 1/2 (/ k 2))))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (pow n (- 1/2 (/ k 2)))) (* (sqrt (pow n (- 1/2 (/ k 2)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))
* * * * [misc]progress:  [ 92 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* 1 (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))>
* * * * [misc]progress:  [ 93 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (pow n (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (sqrt k)
* * [misc]simplify:  iters left: 1 (2 enodes)
* [exit]simplify:  Simplified to (sqrt k)
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (pow n (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt k))))
* * * * [misc]progress:  [ 94 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (pow n 1/2) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (pow n (/ k 2)))))>
* [enter]simplify:  Simplifying (* (pow n 1/2) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (27 enodes)
* * [misc]simplify:  iters left: 2 (29 enodes)
* * [misc]simplify:  iters left: 1 (30 enodes)
* [exit]simplify:  Simplified to (* (pow PI (- 1/2 (/ k 2))) (/ (sqrt n) (sqrt k)))
* [misc]simplify:  Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (pow PI (- 1/2 (/ k 2))) (/ (sqrt n) (sqrt k))) (pow n (/ k 2)))))
* * * * [misc]progress:  [ 95 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) (pow n (- 1/2 (/ k 2))))))>
* * * * [misc]progress:  [ 96 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (pow (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1))))>
* * * * [misc]progress:  [ 97 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (exp (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k)))))))>
* [enter]simplify:  Simplifying (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (26 enodes)
* * [misc]simplify:  iters left: 3 (48 enodes)
* * [misc]simplify:  iters left: 2 (84 enodes)
* * [misc]simplify:  iters left: 1 (110 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (log PI)) (log (sqrt k)))
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (exp (- (* (- 1/2 (/ k 2)) (log PI)) (log (sqrt k)))))))
* * * * [misc]progress:  [ 98 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (exp (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k)))))))>
* [enter]simplify:  Simplifying (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* * [misc]simplify:  iters left: 2 (62 enodes)
* * [misc]simplify:  iters left: 1 (115 enodes)
* [exit]simplify:  Simplified to (- (* (- 1/2 (/ k 2)) (log PI)) (log (sqrt k)))
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (exp (- (* (- 1/2 (/ k 2)) (log PI)) (log (sqrt k)))))))
* * * * [misc]progress:  [ 99 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (exp (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* * * * [misc]progress:  [ 100 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (log (exp (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* * * * [misc]progress:  [ 101 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (cbrt (/ (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (pow PI (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (pow PI (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (55 enodes)
* * [misc]simplify:  iters left: 3 (110 enodes)
* * [misc]simplify:  iters left: 2 (193 enodes)
* * [misc]simplify:  iters left: 1 (324 enodes)
* [exit]simplify:  Simplified to (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (/ (pow PI (- 1/2 (/ k 2))) (* (sqrt k) k)))
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (cbrt (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (/ (pow PI (- 1/2 (/ k 2))) (* (sqrt k) k)))))))
* * * * [misc]progress:  [ 102 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (* (cbrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* * * * [misc]progress:  [ 103 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (cbrt (* (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* * * * [misc]progress:  [ 104 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))))>
* * * * [misc]progress:  [ 105 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (- (pow PI (- 1/2 (/ k 2)))) (- (sqrt k))))))>
* * * * [misc]progress:  [ 106 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (pow PI 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (- (/ k 2))) (cbrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (pow PI 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt PI) (cbrt (sqrt k))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (/ (sqrt PI) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow PI (- (/ k 2))) (cbrt (sqrt k)))))))
* [enter]simplify:  Simplifying (/ (pow PI (- (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (/ (- k) 2)) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (/ (sqrt PI) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow PI (/ (- k) 2)) (cbrt (sqrt k)))))))
* * * * [misc]progress:  [ 107 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (pow PI 1/2) (sqrt (sqrt k))) (/ (pow PI (- (/ k 2))) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (pow PI 1/2) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 4 (7 enodes)
* * [misc]simplify:  iters left: 3 (8 enodes)
* [exit]simplify:  Simplified to (/ (sqrt PI) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt PI) (sqrt (sqrt k))) (/ (pow PI (- (/ k 2))) (sqrt (sqrt k)))))))
* [enter]simplify:  Simplifying (/ (pow PI (- (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt PI) (sqrt (sqrt k))) (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k)))))))
* * * * [misc]progress:  [ 108 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (pow PI 1/2) 1) (/ (pow PI (- (/ k 2))) (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow PI 1/2) 1)
* * [misc]simplify:  iters left: 3 (5 enodes)
* * [misc]simplify:  iters left: 2 (8 enodes)
* * [misc]simplify:  iters left: 1 (10 enodes)
* [exit]simplify:  Simplified to (sqrt PI)
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (sqrt PI) (/ (pow PI (- (/ k 2))) (sqrt k))))))
* [enter]simplify:  Simplifying (/ (pow PI (- (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (- (/ k 2))) (sqrt k))
* [misc]simplify:  Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (sqrt PI) (/ (pow PI (- (/ k 2))) (sqrt k))))))
* * * * [misc]progress:  [ 109 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (pow PI 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (- (/ k 2))) (cbrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (pow PI 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt PI) (cbrt (sqrt k))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (/ (sqrt PI) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow PI (- (/ k 2))) (cbrt (sqrt k)))))))
* [enter]simplify:  Simplifying (/ (pow PI (- (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (/ (- k) 2)) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (/ (sqrt PI) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow PI (/ (- k) 2)) (cbrt (sqrt k)))))))
* * * * [misc]progress:  [ 110 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (pow PI 1/2) (sqrt (sqrt k))) (/ (pow PI (- (/ k 2))) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (pow PI 1/2) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 4 (7 enodes)
* * [misc]simplify:  iters left: 3 (8 enodes)
* [exit]simplify:  Simplified to (/ (sqrt PI) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt PI) (sqrt (sqrt k))) (/ (pow PI (- (/ k 2))) (sqrt (sqrt k)))))))
* [enter]simplify:  Simplifying (/ (pow PI (- (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt PI) (sqrt (sqrt k))) (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k)))))))
* * * * [misc]progress:  [ 111 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (pow PI 1/2) 1) (/ (pow PI (- (/ k 2))) (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow PI 1/2) 1)
* * [misc]simplify:  iters left: 3 (5 enodes)
* * [misc]simplify:  iters left: 2 (8 enodes)
* * [misc]simplify:  iters left: 1 (10 enodes)
* [exit]simplify:  Simplified to (sqrt PI)
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (sqrt PI) (/ (pow PI (- (/ k 2))) (sqrt k))))))
* [enter]simplify:  Simplifying (/ (pow PI (- (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (- (/ k 2))) (sqrt k))
* [misc]simplify:  Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (sqrt PI) (/ (pow PI (- (/ k 2))) (sqrt k))))))
* * * * [misc]progress:  [ 112 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (39 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (* (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))))
* [enter]simplify:  Simplifying (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))))
* * * * [misc]progress:  [ 113 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))
* [enter]simplify:  Simplifying (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))
* * * * [misc]progress:  [ 114 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) 1) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) 1)
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (26 enodes)
* * [misc]simplify:  iters left: 3 (28 enodes)
* * [misc]simplify:  iters left: 2 (33 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2)))))
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt k))))))
* [enter]simplify:  Simplifying (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt k))
* [misc]simplify:  Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt k))))))
* * * * [misc]progress:  [ 115 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))))
* [enter]simplify:  Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))))
* * * * [misc]progress:  [ 116 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))
* [enter]simplify:  Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (13 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))
* * * * [misc]progress:  [ 117 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt (pow PI (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) 1)
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (sqrt (pow PI (- 1/2 (/ k 2))))
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (sqrt (pow PI (- 1/2 (/ k 2)))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt k))))))
* [enter]simplify:  Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt k))
* [misc]simplify:  Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (sqrt (pow PI (- 1/2 (/ k 2)))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt k))))))
* * * * [misc]progress:  [ 118 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (- 1/2 (/ 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)))
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))))))
* [enter]simplify:  Simplifying (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))))))
* * * * [misc]progress:  [ 119 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ 1 (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ 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)))
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ 1 (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))))
* [enter]simplify:  Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
* [misc]simplify:  Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ 1 (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))))
* * * * [misc]progress:  [ 120 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ 1 1) (/ (pow PI (- 1/2 (/ 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
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* 1 (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))
* [enter]simplify:  Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
* [misc]simplify:  Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* 1 (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))
* * * * [misc]progress:  [ 121 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* 1 (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))>
* * * * [misc]progress:  [ 122 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (pow PI (- 1/2 (/ k 2))) (/ 1 (sqrt k))))))>
* * * * [misc]progress:  [ 123 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ 1 (/ (sqrt k) (pow PI (- 1/2 (/ k 2))))))))>
* * * * [misc]progress:  [ 124 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (cbrt (sqrt k))
* * [misc]simplify:  iters left: 2 (3 enodes)
* [exit]simplify:  Simplified to (cbrt (sqrt k))
* [misc]simplify:  Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))))
* * * * [misc]progress:  [ 125 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (sqrt (sqrt k))
* * [misc]simplify:  iters left: 2 (3 enodes)
* [exit]simplify:  Simplified to (sqrt (sqrt k))
* [misc]simplify:  Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))))
* * * * [misc]progress:  [ 126 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (/ (pow PI (- 1/2 (/ k 2))) 1) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt k)
* * [misc]simplify:  iters left: 1 (2 enodes)
* [exit]simplify:  Simplified to (sqrt k)
* [misc]simplify:  Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (/ (pow PI (- 1/2 (/ k 2))) 1) (sqrt k)))))
* * * * [misc]progress:  [ 127 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) (/ (sqrt k) (pow PI (- (/ k 2))))))))>
* [enter]simplify:  Simplifying (pow PI 1/2)
* * [misc]simplify:  iters left: 1 (3 enodes)
* [exit]simplify:  Simplified to (sqrt PI)
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (sqrt PI) (/ (sqrt k) (pow PI (- (/ k 2))))))))
* * * * [misc]progress:  [ 128 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) (/ (sqrt k) (pow PI (- (/ k 2))))))))>
* [enter]simplify:  Simplifying (pow PI 1/2)
* * [misc]simplify:  iters left: 1 (3 enodes)
* [exit]simplify:  Simplified to (sqrt PI)
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (sqrt PI) (/ (sqrt k) (pow PI (- (/ k 2))))))))
* * * * [misc]progress:  [ 129 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow PI (- 1/2 (/ k 2)))))))))>
* [enter]simplify:  Simplifying (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2)))))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2)))))
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow PI (- 1/2 (/ k 2)))))))))
* * * * [misc]progress:  [ 130 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow PI (- 1/2 (/ k 2)))))))))>
* [enter]simplify:  Simplifying (sqrt (pow PI (- 1/2 (/ k 2))))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* [exit]simplify:  Simplified to (sqrt (pow PI (- 1/2 (/ k 2))))
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow PI (- 1/2 (/ k 2)))))))))
* * * * [misc]progress:  [ 131 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ 1 (/ (sqrt k) (pow PI (- 1/2 (/ k 2))))))))>
* * * * [misc]progress:  [ 132 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) (* (sqrt k) (pow PI (/ k 2)))))))>
* [enter]simplify:  Simplifying (pow PI 1/2)
* * [misc]simplify:  iters left: 1 (3 enodes)
* [exit]simplify:  Simplified to (sqrt PI)
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (sqrt PI) (* (sqrt k) (pow PI (/ k 2)))))))
* * * * [misc]progress:  [ 133 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) (sqrt k)))))>
* [enter]simplify:  Simplifying (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (39 enodes)
* * [misc]simplify:  iters left: 4 (104 enodes)
* * [misc]simplify:  iters left: 3 (275 enodes)
* [exit]simplify:  Simplified to (+ (* (* (* k (log PI)) (* k (log PI))) (* (sqrt PI) 1/8)) (+ (* (* k (log PI)) (* (sqrt PI) -1/2)) (sqrt PI)))
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (+ (* (* (* k (log PI)) (* k (log PI))) (* (sqrt PI) 1/8)) (+ (* (* k (log PI)) (* (sqrt PI) -1/2)) (sqrt PI))) (sqrt k)))))
* * * * [misc]progress:  [ 134 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt k)))))>
* [enter]simplify:  Simplifying (pow PI (- 1/2 (* 1/2 k)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (9 enodes)
* * [misc]simplify:  iters left: 3 (17 enodes)
* * [misc]simplify:  iters left: 2 (20 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (pow PI (- 1/2 (* k 1/2)))
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (* k 1/2))) (sqrt k)))))
* * * * [misc]progress:  [ 135 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt k)))))>
* [enter]simplify:  Simplifying (pow PI (- 1/2 (* 1/2 k)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (9 enodes)
* * [misc]simplify:  iters left: 3 (17 enodes)
* * [misc]simplify:  iters left: 2 (20 enodes)
* * [misc]simplify:  iters left: 1 (24 enodes)
* [exit]simplify:  Simplified to (pow PI (- 1/2 (* k 1/2)))
* [misc]simplify:  Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (* k 1/2))) (sqrt k)))))
* * * * [misc]progress:  [ 136 / 144 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) k)) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (log n))))) (- (* +nan.0 (/ (* n PI) k))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) k)) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (log n))))) (- (* +nan.0 (/ (* n PI) k)))))))))))))
* [misc]simplify:  Simplified (2) to (λ (k n) +nan.0)
* * * * [misc]progress:  [ 137 / 144 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) k)) (- (+ (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) (- (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) (pow k 2)))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) k)) (- (+ (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) (- (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) (pow k 2))))))))
* [misc]simplify:  Simplified (2) to (λ (k n) +nan.0)
* * * * [misc]progress:  [ 138 / 144 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) k))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) k)))))))
* [misc]simplify:  Simplified (2) to (λ (k n) +nan.0)
* * * * [misc]progress:  [ 139 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (pow k 2)))) (- (+ (* +nan.0 (sqrt (* n PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log PI) 2) (pow k 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) k)) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) k))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) k))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log n) 2) (pow k 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (pow k 2))))))))))))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (pow k 2)))) (- (+ (* +nan.0 (sqrt (* n PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log PI) 2) (pow k 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) k)) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) k))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) k))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log n) 2) (pow k 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (pow k 2))))))))))))))))))))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) +nan.0))
* * * * [misc]progress:  [ 140 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2))))))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) +nan.0))
* * * * [misc]progress:  [ 141 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2))) (- (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2))) (- (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k))))))))))
* [misc]simplify:  Simplified (2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) +nan.0))
* * * * [misc]progress:  [ 142 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (- (+ (* +nan.0 (* (* (log PI) k) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) k)) (- (+ (* +nan.0 (* (sqrt PI) (/ 1 k))) (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) k) (sqrt PI))) (- (* +nan.0 (sqrt PI))))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (* (* (log PI) k) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) k)) (- (+ (* +nan.0 (* (sqrt PI) (/ 1 k))) (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (* (* (pow (log PI) 2) k) (sqrt PI))) (- (* +nan.0 (sqrt PI)))))))))))))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) +nan.0)))
* * * * [misc]progress:  [ 143 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) k)) (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (pow k 2))) (- (* +nan.0 (pow PI (- 1/2 (* 1/2 k))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) k)) (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (pow k 2))) (- (* +nan.0 (pow PI (- 1/2 (* 1/2 k)))))))))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) +nan.0)))
* * * * [misc]progress:  [ 144 / 144 ] simplifiying candidate #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) k)) (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (pow k 2))) (- (* +nan.0 (pow PI (- 1/2 (* 1/2 k))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) k)) (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (pow k 2))) (- (* +nan.0 (pow PI (- 1/2 (* 1/2 k)))))))))
* [misc]simplify:  Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) +nan.0)))
* * * [misc]progress:  adding candidates to table
* [misc]progress:  [Phase 3 of 3] Extracting.
* * [misc]regime:  Finding splitpoints for: (#<alt (λ (k n) (* (sqrt (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))> #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))> #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))> #<alt (λ (k n) (/ (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) (sqrt k)))> #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))> #<alt (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))))> #<alt (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k))))>)
* * * [misc]regime-changes:  Trying 2 branch expressions: (n k)
* * * * [misc]regimes:  Trying to branch on n from (#<alt (λ (k n) (* (sqrt (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))> #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))> #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))> #<alt (λ (k n) (/ (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) (sqrt k)))> #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))> #<alt (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))))> #<alt (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k))))>)
* * * * [misc]regimes:  Trying to branch on k from (#<alt (λ (k n) (* (sqrt (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))> #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))> #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))> #<alt (λ (k n) (/ (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) (sqrt k)))> #<alt (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))))> #<alt (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k))))> #<alt (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k))))>)
* * * [misc]regime:  Found split indices: #<option (#s(si 2 256))>
* [enter]simplify:  Simplifying (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* [exit]simplify:  Simplified to (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* PI n) (- 1/2 (/ k 2))) (sqrt k)))
* * * * [misc]points:  Sampling 8000 additional inputs, on iter 0 have 0 / 8000
* * * * [misc]points:  Computing exacts on every 500 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 250 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 125 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 62 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 31 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 15 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 7 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 3 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 8000 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 6554 additional inputs, on iter 1 have 1446 / 8000
* * * * [misc]points:  Computing exacts on every 409 of 6554 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 204 of 6554 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 102 of 6554 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 51 of 6554 points 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 6554 points 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 6554 points 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 6554 points 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 6554 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 6554 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 5277 additional inputs, on iter 2 have 2723 / 8000
* * * * [misc]points:  Computing exacts on every 329 of 5277 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 164 of 5277 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 82 of 5277 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 41 of 5277 points 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 5277 points 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 5277 points 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 5277 points 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 5277 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 5277 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 4323 additional inputs, on iter 3 have 3677 / 8000
* * * * [misc]points:  Computing exacts on every 270 of 4323 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 135 of 4323 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 67 of 4323 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 33 of 4323 points 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 4323 points 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 4323 points 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 4323 points 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 4323 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 4323 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 3480 additional inputs, on iter 4 have 4520 / 8000
* * * * [misc]points:  Computing exacts on every 217 of 3480 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 108 of 3480 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 54 of 3480 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 27 of 3480 points 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 3480 points 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 3480 points 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 3480 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 3480 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 2864 additional inputs, on iter 5 have 5136 / 8000
* * * * [misc]points:  Computing exacts on every 179 of 2864 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 89 of 2864 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 44 of 2864 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 22 of 2864 points 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 2864 points 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 2864 points 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 2864 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 2864 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 2288 additional inputs, on iter 6 have 5712 / 8000
* * * * [misc]points:  Computing exacts on every 143 of 2288 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 71 of 2288 points 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 2288 points 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 2288 points 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 2288 points 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 2288 points 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 2288 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 2288 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 1851 additional inputs, on iter 7 have 6149 / 8000
* * * * [misc]points:  Computing exacts on every 115 of 1851 points 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 1851 points 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 1851 points 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 1851 points 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 1851 points 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 1851 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1851 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 1533 additional inputs, on iter 8 have 6467 / 8000
* * * * [misc]points:  Computing exacts on every 95 of 1533 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 47 of 1533 points 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 1533 points 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 1533 points 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 1533 points 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 1533 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1533 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 1245 additional inputs, on iter 9 have 6755 / 8000
* * * * [misc]points:  Computing exacts on every 77 of 1245 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 38 of 1245 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 19 of 1245 points 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 1245 points 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 1245 points 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 1245 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1245 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 1025 additional inputs, on iter 10 have 6975 / 8000
* * * * [misc]points:  Computing exacts on every 64 of 1025 points 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 1025 points 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 1025 points 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 1025 points 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 1025 points 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 1025 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1025 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 847 additional inputs, on iter 11 have 7153 / 8000
* * * * [misc]points:  Computing exacts on every 52 of 847 points 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 847 points 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 847 points 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 847 points 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 847 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 847 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 707 additional inputs, on iter 12 have 7293 / 8000
* * * * [misc]points:  Computing exacts on every 44 of 707 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 22 of 707 points 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 707 points 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 707 points 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 707 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 707 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 584 additional inputs, on iter 13 have 7416 / 8000
* * * * [misc]points:  Computing exacts on every 36 of 584 points 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 584 points 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 584 points 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 584 points 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 584 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 584 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 481 additional inputs, on iter 14 have 7519 / 8000
* * * * [misc]points:  Computing exacts on every 30 of 481 points 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 481 points 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 481 points 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 481 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 481 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 398 additional inputs, on iter 15 have 7602 / 8000
* * * * [misc]points:  Computing exacts on every 24 of 398 points 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 398 points 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 398 points 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 398 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 398 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 320 additional inputs, on iter 16 have 7680 / 8000
* * * * [misc]points:  Computing exacts on every 20 of 320 points 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 320 points 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 320 points 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 320 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 320 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 254 additional inputs, on iter 17 have 7746 / 8000
* * * * [misc]points:  Computing exacts on every 15 of 254 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 7 of 254 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 3 of 254 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 254 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 201 additional inputs, on iter 18 have 7799 / 8000
* * * * [misc]points:  Computing exacts on every 12 of 201 points 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 201 points 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 201 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 201 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 175 additional inputs, on iter 19 have 7825 / 8000
* * * * [misc]points:  Computing exacts on every 10 of 175 points 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 175 points 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 175 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 175 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 144 additional inputs, on iter 20 have 7856 / 8000
* * * * [misc]points:  Computing exacts on every 9 of 144 points 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 144 points 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 144 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 144 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 124 additional inputs, on iter 21 have 7876 / 8000
* * * * [misc]points:  Computing exacts on every 7 of 124 points 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 124 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 124 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 102 additional inputs, on iter 22 have 7898 / 8000
* * * * [misc]points:  Computing exacts on every 6 of 102 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 3 of 102 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 102 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 92 additional inputs, on iter 23 have 7908 / 8000
* * * * [misc]points:  Computing exacts on every 5 of 92 points 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 92 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 92 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 71 additional inputs, on iter 24 have 7929 / 8000
* * * * [misc]points:  Computing exacts on every 4 of 71 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 71 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 71 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 61 additional inputs, on iter 25 have 7939 / 8000
* * * * [misc]points:  Computing exacts on every 3 of 61 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 61 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 49 additional inputs, on iter 26 have 7951 / 8000
* * * * [misc]points:  Computing exacts on every 3 of 49 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 49 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 44 additional inputs, on iter 27 have 7956 / 8000
* * * * [misc]points:  Computing exacts on every 2 of 44 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 44 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 41 additional inputs, on iter 28 have 7959 / 8000
* * * * [misc]points:  Computing exacts on every 2 of 41 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 41 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 32 additional inputs, on iter 29 have 7968 / 8000
* * * * [misc]points:  Computing exacts on every 2 of 32 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 32 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 30 additional inputs, on iter 30 have 7970 / 8000
* * * * [misc]points:  Computing exacts for 30 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 31 have 7975 / 8000
* * * * [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 32 have 7980 / 8000
* * * * [misc]points:  Computing exacts for 20 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 15 additional inputs, on iter 33 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 13 additional inputs, on iter 34 have 7987 / 8000
* * * * [misc]points:  Computing exacts for 13 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 10 additional inputs, on iter 35 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 36 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 37 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 7 additional inputs, on iter 38 have 7993 / 8000
* * * * [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 39 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 5 additional inputs, on iter 40 have 7995 / 8000
* * * * [misc]points:  Computing exacts for 5 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 5 additional inputs, on iter 41 have 7995 / 8000
* * * * [misc]points:  Computing exacts for 5 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 42 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 43 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 44 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 45 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
* * * * [misc]points:  Sampling 4 additional inputs, on iter 46 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
* * * * [misc]points:  Sampling 4 additional inputs, on iter 47 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 8001 points with exact outputs