* [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:  Setting MPFR precision to 832
* * * * [misc]points:  Computing exacts on every 8 of 256 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 576
* * * * [misc]points:  Setting MPFR precision to 832
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Computing exacts on every 4 of 256 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 832
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts 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 203 additional inputs, on iter 1 have 53 / 256
* * * * [misc]points:  Computing exacts on every 12 of 203 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 6 of 203 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 3 of 203 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 203 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 166 additional inputs, on iter 2 have 90 / 256
* * * * [misc]points:  Computing exacts on every 10 of 166 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 5 of 166 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 166 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 166 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 146 additional inputs, on iter 3 have 110 / 256
* * * * [misc]points:  Computing exacts on every 9 of 146 points 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 146 points 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 146 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 146 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 116 additional inputs, on iter 4 have 140 / 256
* * * * [misc]points:  Computing exacts on every 7 of 116 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 3 of 116 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 116 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 95 additional inputs, on iter 5 have 161 / 256
* * * * [misc]points:  Computing exacts on every 5 of 95 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 95 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 95 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 78 additional inputs, on iter 6 have 178 / 256
* * * * [misc]points:  Computing exacts on every 4 of 78 points 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 78 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 78 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 59 additional inputs, on iter 7 have 197 / 256
* * * * [misc]points:  Computing exacts on every 3 of 59 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 59 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 43 additional inputs, on iter 8 have 213 / 256
* * * * [misc]points:  Computing exacts on every 2 of 43 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 43 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 29 additional inputs, on iter 9 have 227 / 256
* * * * [misc]points:  Computing exacts for 29 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 21 additional inputs, on iter 10 have 235 / 256
* * * * [misc]points:  Computing exacts for 21 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 17 additional inputs, on iter 11 have 239 / 256
* * * * [misc]points:  Computing exacts for 17 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 14 additional inputs, on iter 12 have 242 / 256
* * * * [misc]points:  Computing exacts for 14 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 10 additional inputs, on iter 13 have 246 / 256
* * * * [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 7 additional inputs, on iter 14 have 249 / 256
* * * * [misc]points:  Computing exacts for 7 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 15 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 16 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 17 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 18 have 253 / 256
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 19 have 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 20 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 21 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 22 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 257 points with exact outputs
* * * [misc]progress:  [2/2] Setting up program.
* [misc]progress:  [Phase 2 of 3] Improving.
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (52 enodes)
* * [misc]simplify:  iters left: 2 (56 enodes)
* * [misc]simplify:  iters left: 1 (63 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))
* * [misc]progress:  iteration 1 / 4
* * * [misc]progress:  picking best candidate
* [misc]none:  Fresh alts: 2
* [misc]none:  All alts: 2
* [misc]none:  Fresh alt: (λ (k n) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* [misc]none:  Fresh alt: (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* [misc]none:  Fresh alt indexes
* [misc]none:  (λ (k n) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))): 0
* [misc]none:  (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))): 1
* [misc]none:  Best fresh alt per point
* [misc]none:  (1.8808646764197965e+211 2.5246982378469546e+26): 0
* [misc]none:  (1.6056134078957726e-81 2.0654753198801362e+38): 0
* [misc]none:  (7.103138391473298e+203 4.991913674121936): 0
* [misc]none:  (3.4858004269611626e-130 1.2049116045831512e-306): 0
* [misc]none:  (6.950790143696708e-299 5.4754162277199545e+172): 0
* [misc]none:  (5.921232829081192e+298 4.202795939018271e+158): 0
* [misc]none:  (1.0394343208136068e-147 2.549337443302021e+95): 0
* [misc]none:  (8.998561140295877e-118 1.0700413456865293e+105): 0
* [misc]none:  (8.786431465145784e-134 5.784799823772606e-59): 0
* [misc]none:  (7.570282140481074e-146 1.0536210697171442e-75): 0
* [misc]none:  (2.6069457677667484e+227 2.421502054149278e+240): 0
* [misc]none:  (1.223212349341741e+210 6.083797656691426e+124): 0
* [misc]none:  (8.208194827684373e-221 3.697769831340425e-212): 0
* [misc]none:  (8.891699857124086e-248 4.741786767196371e-65): 0
* [misc]none:  (1.3953186618456118e-127 1.557559831312346e-158): 0
* [misc]none:  (2.8281459379799287e-223 5.282538753015419e+290): 0
* [misc]none:  (9.348662801176182e-287 6.983734680943984e+302): 0
* [misc]none:  (5.967105222859026e-287 1.4091628731054108e-252): 1
* [misc]none:  (6.812962331114006e-11 4.706553941824653e-123): 0
* [misc]none:  (8.467946903121652e+268 4.636077183112171e+61): 0
* [misc]none:  (6.29303766495041e-83 4.590548637242576e-128): 0
* [misc]none:  (3.213871973385624e-262 1.2212831165558396e+41): 0
* [misc]none:  (5.169867646134535e-44 1639899171736.8787): 0
* [misc]none:  (4.484657738495896e-296 1.2472467031958124e-111): 0
* [misc]none:  (2.630988489772908e-301 8.677705005606349e-192): 0
* [misc]none:  (1.9488674575590774e-219 1.2069336055576329e+297): 0
* [misc]none:  (1.0241786832856672e+275 6.65470667879038e+211): 0
* [misc]none:  (1.2388376925429903 1.0255532946660354e-189): 0
* [misc]none:  (9.403049449769395e-276 9.165910603949256e-61): 0
* [misc]none:  (1.5863716419697854e-305 2.982344844139708e-56): 0
* [misc]none:  (1.7933154604270656e+266 2.0688677513908958e+152): 0
* [misc]none:  (1.724441305022448e-204 1.0270093728501316e+208): 0
* [misc]none:  (1.6991537131626808e-286 2.269053283659137e+97): 0
* [misc]none:  (9.981425531265531e-234 1.5954750517027446e-306): 0
* [misc]none:  (2.6518292064535327e+113 1.1093632157717332e+299): 0
* [misc]none:  (3.5398920819374162e-22 9.097313058752706e+182): 0
* [misc]none:  (1.5662970496145718e+195 5.702344716829955e+277): 0
* [misc]none:  (7.374934384259559e+247 11809.004489533036): 0
* [misc]none:  (3.6837517387134946e+28 2.050724237210542e+237): 0
* [misc]none:  (8.0762754355927e-102 3.924619293995995e+294): 0
* [misc]none:  (6.272017688866778e+294 1475344134974741.5): 0
* [misc]none:  (8.226540875316075e-282 2.9295012263119104e-210): 0
* [misc]none:  (1.1567434189356451e+31 5.033252764508812e+139): 0
* [misc]none:  (1.2230943992415108e+36 2.3021043888776224e+278): 0
* [misc]none:  (5.69357845447944e-284 4.6895957006840323e-293): 0
* [misc]none:  (2.1402493760044758e-237 7.018010476645137e+19): 0
* [misc]none:  (5.836990398641413e+278 8.69236263846091e+82): 0
* [misc]none:  (3.866067932485071e+134 65634290206.02169): 0
* [misc]none:  (3.353542833099014e-216 4.562538568139802e-253): 0
* [misc]none:  (1.9595331698208332e+267 1.734899565778851e+119): 0
* [misc]none:  (6.162344767386832e-71 7.346570549506355e+179): 0
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* [misc]none:  (1.355389858139596e-211 5.3134050984497146e-45): 0
* [misc]none:  (1.7558002847649968e-150 2.8327022791344117e+186): 0
* [misc]none:  (55126108376913.92 1.4270114976186918e+130): 0
* [misc]none:  (2.1677429926485946e-242 1.7597566772342396e-204): 0
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* [misc]none:  (1.061192968818359e-298 3.4390539626492262e-136): 0
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* [misc]none:  (7.707611608802171e+62 1.152518328416828e+180): 0
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* [misc]none:  (2797.2682494851097 5.51985688247549e+99): 0
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* [misc]none:  (3.271929098149761e-144 7.5398414005163625e+267): 0
* [misc]none:  (6.604350361119279e-291 3.861477555295976e-66): 0
* [misc]none:  (8.124998850854922e-91 2.0152844845402166e-297): 0
* [misc]none:  (8.604490187894414e-112 1.3704041407198253e+228): 0
* [misc]none:  (1.6519797365083582e+195 6.316732900885901e+249): 0
* [misc]none:  (2.0115496002781107e-145 7.084575776306543e+174): 0
* [misc]none:  (2.5502245720775025e+302 3.7105227033705403e+214): 0
* [misc]none:  (6.821311827045434e-30 2.8401584433220846e+96): 1
* [misc]none:  (2.6830861914889714e-191 5.086243151153881e+259): 0
* [misc]none:  (1.4517955555700533e-57 3.278760905350017e+239): 0
* [misc]none:  (9.422179697047065e-164 1.3639040980897921e-39): 0
* [misc]none:  (2.8344220272269968e+166 1.5252878664938466e+85): 0
* [misc]none:  (1.9836536473017196e-256 6.844414014257645e+204): 0
* [misc]none:  Picked alt (λ (k n) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]pick:  Picked  #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 3 ] rewriting at (2 1 1)
* * * * [misc]progress:  [ 2 / 3 ] rewriting at (2)
* * * * [misc]progress:  [ 3 / 3 ] rewriting at (2 1)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 3 ] generating series at (2 1 1)
* [misc]approximate:  Taking taylor expansion of (* n (* PI 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* n (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) n) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 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) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 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) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 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 (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
* * * * [misc]progress:  [ 2 / 3 ] generating series at (2)
* [misc]approximate:  Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (* PI 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 k) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in k
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of (* PI 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 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* n (* 2 PI)) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ (pow (* 2 (* n PI)) 1/2) +nan.0) into (* +nan.0 (sqrt (* n (* 2 PI))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (+ 1 (- k)) into (- 1 k)
* [misc]backup-simplify:  Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k))
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (+ 1 (- k)) into (- 1 k)
* [misc]backup-simplify:  Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k))
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (- 1 k) (+ (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (- 1 k) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1 (+ (log (* 2 PI)) (log n))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (* 0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (/ 0 (sqrt k))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* -1 (+ (log (* 2 PI)) (log n)))) into (- (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))
* [misc]backup-simplify:  Simplify (+ (* 0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* 0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))))) (+ (* +nan.0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2))))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* 0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2))))))))) (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))))) (+ (* +nan.0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))))))))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n))))))))))))))))))))))))
* [misc]approximate:  Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 n) 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 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 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)))))))
* [misc]approximate:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- -1) into 1
* [misc]backup-simplify:  Simplify (+ 0 1) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) 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 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 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ -1 k)) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ -1 k)) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
* [misc]taylor:  Taking taylor expansion of (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (+ 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* -2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* -2 PI) in k
* [misc]taylor:  Taking taylor expansion of -2 in k
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (+ 0 1) into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ -1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ -1 k) in k
* [misc]taylor:  Taking taylor expansion of -1 in k
* [misc]backup-simplify:  Simplify -1 into -1
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ -1 1) into -1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))))))))
* * * * [misc]progress:  [ 3 / 3 ] generating series at (2 1)
* [misc]approximate:  Taking taylor expansion of (pow (* n (* PI 2)) (/ (- 1 k) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (* PI 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 k) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in k
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of (* PI 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 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* n (* 2 PI)) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (+ 1 (- k)) into (- 1 k)
* [misc]backup-simplify:  Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k))
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (+ 1 (- k)) into (- 1 k)
* [misc]backup-simplify:  Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k))
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (- 1 k) (+ (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (- 1 k) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1 (+ (log (* 2 PI)) (log n))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* -1 (+ (log (* 2 PI)) (log n)))) into (- (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))
* [misc]backup-simplify:  Simplify (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))))
* [misc]backup-simplify:  Simplify (+ (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k)))))
* [misc]approximate:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 n) 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 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 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
* [misc]approximate:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- -1) into 1
* [misc]backup-simplify:  Simplify (+ 0 1) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) 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 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 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ -1 k)) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ -1 k)) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (+ 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* -2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* -2 PI) in k
* [misc]taylor:  Taking taylor expansion of -2 in k
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (+ 0 1) into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
* * * [misc]progress:  simplifying candidates
* * * * [misc]progress:  [ 1 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (log1p (expm1 (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (expm1 (* (* n 2) PI))
* [exit]simplify:  Simplified to (expm1 (* (* n 2) PI))
* * * * [misc]progress:  [ 2 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (expm1 (log1p (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (log1p (* (* n 2) PI))
* [exit]simplify:  Simplified to (log1p (* (* n 2) PI))
* * * * [misc]progress:  [ 3 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* n (* PI 2)) 1) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 4 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (exp (log (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (log (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (log (* (* PI n) 2))
* [exit]simplify:  Simplified to (log (* (* PI n) 2))
* * * * [misc]progress:  [ 5 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (log (exp (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* * [misc]simplify:  iters left: 2 (35 enodes)
* * [misc]simplify:  iters left: 1 (47 enodes)
* [exit]simplify:  Simplified to (pow (exp 2) (* PI n))
* [exit]simplify:  Simplified to (pow (exp 2) (* PI n))
* * * * [misc]progress:  [ 6 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (18 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2)))
* [exit]simplify:  Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2)))
* [enter]simplify:  Simplifying (cbrt (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (cbrt (* (* n 2) PI))
* [exit]simplify:  Simplified to (cbrt (* (* n 2) PI))
* * * * [misc]progress:  [ 7 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (cbrt (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (59 enodes)
* * [misc]simplify:  iters left: 3 (203 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) 3)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) 3)
* * * * [misc]progress:  [ 8 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (sqrt (* n (* PI 2))) (sqrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* [enter]simplify:  Simplifying (sqrt (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* * * * [misc]progress:  [ 9 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* 1 (* n (* PI 2))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 10 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (* n PI)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* PI n)
* [exit]simplify:  Simplified to (* PI n)
* * * * [misc]progress:  [ 11 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 12 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (log1p (expm1 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (expm1 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (expm1 (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (expm1 (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 13 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (expm1 (log1p (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (log1p (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (log1p (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (log1p (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 14 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (pow (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) 1))>
* * * * [misc]progress:  [ 15 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (34 enodes)
* * [misc]simplify:  iters left: 4 (66 enodes)
* * [misc]simplify:  iters left: 3 (166 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* n 2) PI)) (/ (- 1 k) 2) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* n 2) PI)) (/ (- 1 k) 2) (- (log (sqrt k))))
* * * * [misc]progress:  [ 16 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (34 enodes)
* * [misc]simplify:  iters left: 4 (66 enodes)
* * [misc]simplify:  iters left: 3 (166 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* n 2) PI)) (/ (- 1 k) 2) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* n 2) PI)) (/ (- 1 k) 2) (- (log (sqrt k))))
* * * * [misc]progress:  [ 17 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (log (pow (* n (* PI 2)) (/ (- 1 k) 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (log (pow (* n (* PI 2)) (/ (- 1 k) 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (50 enodes)
* * [misc]simplify:  iters left: 3 (98 enodes)
* * [misc]simplify:  iters left: 2 (302 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* 2 (* PI n))) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* 2 (* PI n))) (- (log (sqrt k))))
* * * * [misc]progress:  [ 18 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (exp (log (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (log (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (62 enodes)
* * [misc]simplify:  iters left: 2 (131 enodes)
* * [misc]simplify:  iters left: 1 (430 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* 2 (* PI n))) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* 2 (* PI n))) (- (log (sqrt k))))
* * * * [misc]progress:  [ 19 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (log (exp (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (exp (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (exp (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (exp (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 20 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (/ (* (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (73 enodes)
* * [misc]simplify:  iters left: 3 (133 enodes)
* * [misc]simplify:  iters left: 2 (215 enodes)
* * [misc]simplify:  iters left: 1 (353 enodes)
* [exit]simplify:  Simplified to (* (* (pow (* (* PI n) 2) (/ (- 1 k) 2)) (pow (* (* PI n) 2) (/ (- 1 k) 2))) (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (* k (sqrt k))))
* [exit]simplify:  Simplified to (* (* (pow (* (* PI n) 2) (/ (- 1 k) 2)) (pow (* (* PI n) 2) (/ (- 1 k) 2))) (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (* k (sqrt k))))
* * * * [misc]progress:  [ 21 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))))
* [enter]simplify:  Simplifying (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (cbrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (cbrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 22 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (* (* (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (* (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (61 enodes)
* * [misc]simplify:  iters left: 3 (90 enodes)
* * [misc]simplify:  iters left: 2 (125 enodes)
* * [misc]simplify:  iters left: 1 (156 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 23 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))
* [enter]simplify:  Simplifying (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 24 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (- (pow (* n (* PI 2)) (/ (- 1 k) 2))) (- (sqrt k))))>
* [enter]simplify:  Simplifying (- (pow (* n (* PI 2)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (- (pow (* (* n 2) PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (- (pow (* (* n 2) PI) (/ (- 1 k) 2)))
* [enter]simplify:  Simplifying (- (sqrt k))
* * [misc]simplify:  iters left: 3 (3 enodes)
* [exit]simplify:  Simplified to (- (sqrt k))
* [exit]simplify:  Simplified to (- (sqrt k))
* * * * [misc]progress:  [ 25 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 26 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 27 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) 1) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow n (/ (- 1 k) 2)) 1)
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (pow n (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow n (/ (- 1 k) 2))
* [enter]simplify:  Simplifying (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* [exit]simplify:  Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))
* [exit]simplify:  Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 28 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (51 enodes)
* * [misc]simplify:  iters left: 3 (57 enodes)
* * [misc]simplify:  iters left: 2 (60 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 29 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 30 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) 1) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) 1)
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (41 enodes)
* * [misc]simplify:  iters left: 3 (49 enodes)
* * [misc]simplify:  iters left: 2 (59 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt k))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt k))
* * * * [misc]progress:  [ 31 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 32 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 33 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) 1) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) 1)
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2)))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt k))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt k))
* * * * [misc]progress:  [ 34 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* [exit]simplify:  Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 35 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 36 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 1) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (/ 1 1)
* * [misc]simplify:  iters left: 2 (2 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to 1
* [exit]simplify:  Simplified to 1
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))
* [exit]simplify:  Simplified to (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 37 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))>
* * * * [misc]progress:  [ 38 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt k))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (6 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt k))
* [exit]simplify:  Simplified to (/ 1 (sqrt k))
* * * * [misc]progress:  [ 39 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (* PI (* n 2)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (* PI (* n 2)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 40 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 41 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 42 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) 1) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) 1)
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (pow (* (* n 2) PI) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow (* (* n 2) PI) (/ (- 1 k) 2))
* * * * [misc]progress:  [ 43 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 44 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (/ (sqrt k) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (sqrt k) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 45 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (sqrt k) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 46 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (* PI (* n 2)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (sqrt k) (pow (* PI (* n 2)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 47 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))
* [exit]simplify:  Simplified to (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))
* * * * [misc]progress:  [ 48 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (log1p (expm1 (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (pow (* n (* PI 2)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (expm1 (pow (* (* n 2) PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (expm1 (pow (* (* n 2) PI) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 49 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (expm1 (log1p (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (pow (* n (* PI 2)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (log1p (pow (* (* n 2) PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (log1p (pow (* (* n 2) PI) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 50 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (exp (* (log (* n (* PI 2))) (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* n (* PI 2))) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (58 enodes)
* * [misc]simplify:  iters left: 3 (145 enodes)
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2))))
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2))))
* * * * [misc]progress:  [ 51 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (exp (* (log (* n (* PI 2))) (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* n (* PI 2))) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (58 enodes)
* * [misc]simplify:  iters left: 3 (145 enodes)
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2))))
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2))))
* * * * [misc]progress:  [ 52 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (* 1 (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* 1 (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (51 enodes)
* * [misc]simplify:  iters left: 2 (66 enodes)
* * [misc]simplify:  iters left: 1 (81 enodes)
* [exit]simplify:  Simplified to (/ (- 1 k) 2)
* [exit]simplify:  Simplified to (/ (- 1 k) 2)
* * * * [misc]progress:  [ 53 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (* PI 2)) (/ 1 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* [exit]simplify:  Simplified to (pow (* 2 (* PI n)) (/ 1 2))
* [exit]simplify:  Simplified to (pow (* 2 (* PI n)) (/ 1 2))
* [enter]simplify:  Simplifying (pow (* n (* PI 2)) (/ k 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (18 enodes)
* * [misc]simplify:  iters left: 2 (20 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (/ k 2))
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (/ k 2))
* * * * [misc]progress:  [ 54 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* n (* PI 2)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (* PI 2)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (pow (* PI (* n 2)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (pow (* PI (* n 2)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 55 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* n (* PI 2)) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (* PI 2)) (sqrt (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (pow (* (* n 2) PI) (sqrt (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (pow (* (* n 2) PI) (sqrt (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 56 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* n (* PI 2)) 1) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (* PI 2)) 1)
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (20 enodes)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* * * * [misc]progress:  [ 57 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* n (* PI 2)) (- 1 k)) (/ 1 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (* PI 2)) (- 1 k))
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (25 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (- 1 k))
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (- 1 k))
* * * * [misc]progress:  [ 58 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow n (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow n (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (17 enodes)
* * [misc]simplify:  iters left: 2 (19 enodes)
* [exit]simplify:  Simplified to (pow n (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow n (/ (- 1 k) 2))
* [enter]simplify:  Simplifying (pow (* PI 2) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (21 enodes)
* [exit]simplify:  Simplified to (pow (* 2 PI) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow (* 2 PI) (/ (- 1 k) 2))
* * * * [misc]progress:  [ 59 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* n (* PI 2)) (/ (- 1 k) 2)) 1) (sqrt k)))>
* * * * [misc]progress:  [ 60 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (exp (log (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (pow (* n (* PI 2)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (90 enodes)
* * [misc]simplify:  iters left: 2 (246 enodes)
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* (* n 2) PI)))
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* (* n 2) PI)))
* * * * [misc]progress:  [ 61 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (log (exp (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (pow (* n (* PI 2)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (exp (pow (* (* n 2) PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (exp (pow (* (* n 2) PI) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 62 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))))
* [enter]simplify:  Simplifying (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 63 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (cbrt (* (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (pow (* n (* PI 2)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (pow (pow (* (* n 2) PI) (/ (- 1 k) 2)) 3)
* [exit]simplify:  Simplified to (pow (pow (* (* n 2) PI) (/ (- 1 k) 2)) 3)
* * * * [misc]progress:  [ 64 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))
* [enter]simplify:  Simplifying (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 65 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* 1 (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)))>
* * * * [misc]progress:  [ 66 / 74 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 67 / 74 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 68 / 74 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 69 / 74 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n)))))))))))))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n))))))))))))))))))))))))
* * * * [misc]progress:  [ 70 / 74 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)))))))
* * * * [misc]progress:  [ 71 / 74 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))))))))
* * * * [misc]progress:  [ 72 / 74 ] simplifiying candidate #<alt-event (λ (k n) (/ (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))))) (sqrt k))
* * [misc]simplify:  iters left: 6 (39 enodes)
* * [misc]simplify:  iters left: 5 (113 enodes)
* * [misc]simplify:  iters left: 4 (377 enodes)
* [exit]simplify:  Simplified to (/ (+ (* (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (* (* k k) 1/8)) (+ (* (log n) (log n)) (* (log (* PI 2)) (log (* PI 2))))) (- (fma (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4)) (* (log (* PI 2)) (* (* k k) (log n))) (* (pow (* PI 2) 1/2) (pow n 1/2))) (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/2)) (fma k (log (* PI 2)) (* (log n) k))))) (sqrt k))
* * * * [misc]progress:  [ 73 / 74 ] simplifiying candidate #<alt-event (λ (k n) (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (78 enodes)
* * [misc]simplify:  iters left: 3 (267 enodes)
* [exit]simplify:  Simplified to (/ (pow (exp (- 1/2 (* 1/2 k))) (+ (log (* PI 2)) (log n))) (sqrt k))
* * * * [misc]progress:  [ 74 / 74 ] simplifiying candidate #<alt-event (λ (k n) (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (78 enodes)
* * [misc]simplify:  iters left: 3 (277 enodes)
* [exit]simplify:  Simplified to (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* PI -2)) (log (/ -1 n)))) (sqrt k))
* * * [misc]progress:  adding candidates to table
* * [misc]progress:  iteration 2 / 4
* * * [misc]progress:  picking best candidate
* [misc]none:  Fresh alts: 11
* [misc]none:  All alts: 11
* [misc]none:  Fresh alt: (λ (k n) (/ (+ (* (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (* (* k k) 1/8)) (+ (* (log n) (log n)) (* (log (* PI 2)) (log (* PI 2))))) (- (fma (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4)) (* (log (* PI 2)) (* (* k k) (log n))) (* (pow (* PI 2) 1/2) (pow n 1/2))) (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/2)) (fma k (log (* PI 2)) (* (log n) k))))) (sqrt k)))
* [misc]none:  Fresh alt: (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))
* [misc]none:  Fresh alt: (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))
* [misc]none:  Fresh alt: (λ (k n) (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))
* [misc]none:  Fresh alt: (λ (k n) (cbrt (/ (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (* n 2) PI) (/ (- 1 k) 2))))))
* [misc]none:  Fresh alt: (λ (k n) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))))
* [misc]none:  Fresh alt: (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))
* [misc]none:  Fresh alt: (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))
* [misc]none:  Fresh alt: (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))
* [misc]none:  Fresh alt: (λ (k n) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))
* [misc]none:  Fresh alt: (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* [misc]none:  Fresh alt indexes
* [misc]none:  (λ (k n) (/ (+ (* (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (* (* k k) 1/8)) (+ (* (log n) (log n)) (* (log (* PI 2)) (log (* PI 2))))) (- (fma (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4)) (* (log (* PI 2)) (* (* k k) (log n))) (* (pow (* PI 2) 1/2) (pow n 1/2))) (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/2)) (fma k (log (* PI 2)) (* (log n) k))))) (sqrt k))): 0
* [misc]none:  (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))): 1
* [misc]none:  (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))): 2
* [misc]none:  (λ (k n) (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k))): 3
* [misc]none:  (λ (k n) (cbrt (/ (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))): 4
* [misc]none:  (λ (k n) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))))): 5
* [misc]none:  (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))): 6
* [misc]none:  (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))): 7
* [misc]none:  (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k))))): 8
* [misc]none:  (λ (k n) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k))))): 9
* [misc]none:  (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))): 10
* [misc]none:  Best fresh alt per point
* [misc]none:  (1.8808646764197965e+211 2.5246982378469546e+26): 1
* [misc]none:  (1.6056134078957726e-81 2.0654753198801362e+38): 0
* [misc]none:  (7.103138391473298e+203 4.991913674121936): 1
* [misc]none:  (3.4858004269611626e-130 1.2049116045831512e-306): 0
* [misc]none:  (6.950790143696708e-299 5.4754162277199545e+172): 2
* [misc]none:  (5.921232829081192e+298 4.202795939018271e+158): 1
* [misc]none:  (1.0394343208136068e-147 2.549337443302021e+95): 2
* [misc]none:  (8.998561140295877e-118 1.0700413456865293e+105): 2
* [misc]none:  (8.786431465145784e-134 5.784799823772606e-59): 0
* [misc]none:  (7.570282140481074e-146 1.0536210697171442e-75): 2
* [misc]none:  (2.6069457677667484e+227 2.421502054149278e+240): 1
* [misc]none:  (1.223212349341741e+210 6.083797656691426e+124): 1
* [misc]none:  (8.208194827684373e-221 3.697769831340425e-212): 0
* [misc]none:  (8.891699857124086e-248 4.741786767196371e-65): 0
* [misc]none:  (1.3953186618456118e-127 1.557559831312346e-158): 1
* [misc]none:  (2.8281459379799287e-223 5.282538753015419e+290): 5
* [misc]none:  (9.348662801176182e-287 6.983734680943984e+302): 2
* [misc]none:  (5.967105222859026e-287 1.4091628731054108e-252): 5
* [misc]none:  (6.812962331114006e-11 4.706553941824653e-123): 6
* [misc]none:  (8.467946903121652e+268 4.636077183112171e+61): 1
* [misc]none:  (6.29303766495041e-83 4.590548637242576e-128): 2
* [misc]none:  (3.213871973385624e-262 1.2212831165558396e+41): 5
* [misc]none:  (5.169867646134535e-44 1639899171736.8787): 2
* [misc]none:  (4.484657738495896e-296 1.2472467031958124e-111): 0
* [misc]none:  (2.630988489772908e-301 8.677705005606349e-192): 0
* [misc]none:  (1.9488674575590774e-219 1.2069336055576329e+297): 0
* [misc]none:  (1.0241786832856672e+275 6.65470667879038e+211): 1
* [misc]none:  (1.2388376925429903 1.0255532946660354e-189): 1
* [misc]none:  (9.403049449769395e-276 9.165910603949256e-61): 2
* [misc]none:  (1.5863716419697854e-305 2.982344844139708e-56): 2
* [misc]none:  (1.7933154604270656e+266 2.0688677513908958e+152): 1
* [misc]none:  (1.724441305022448e-204 1.0270093728501316e+208): 3
* [misc]none:  (1.6991537131626808e-286 2.269053283659137e+97): 0
* [misc]none:  (9.981425531265531e-234 1.5954750517027446e-306): 2
* [misc]none:  (2.6518292064535327e+113 1.1093632157717332e+299): 1
* [misc]none:  (3.5398920819374162e-22 9.097313058752706e+182): 2
* [misc]none:  (1.5662970496145718e+195 5.702344716829955e+277): 1
* [misc]none:  (7.374934384259559e+247 11809.004489533036): 1
* [misc]none:  (3.6837517387134946e+28 2.050724237210542e+237): 1
* [misc]none:  (8.0762754355927e-102 3.924619293995995e+294): 1
* [misc]none:  (6.272017688866778e+294 1475344134974741.5): 1
* [misc]none:  (8.226540875316075e-282 2.9295012263119104e-210): 3
* [misc]none:  (1.1567434189356451e+31 5.033252764508812e+139): 1
* [misc]none:  (1.2230943992415108e+36 2.3021043888776224e+278): 1
* [misc]none:  (5.69357845447944e-284 4.6895957006840323e-293): 8
* [misc]none:  (2.1402493760044758e-237 7.018010476645137e+19): 2
* [misc]none:  (5.836990398641413e+278 8.69236263846091e+82): 1
* [misc]none:  (3.866067932485071e+134 65634290206.02169): 1
* [misc]none:  (3.353542833099014e-216 4.562538568139802e-253): 2
* [misc]none:  (1.9595331698208332e+267 1.734899565778851e+119): 1
* [misc]none:  (6.162344767386832e-71 7.346570549506355e+179): 0
* [misc]none:  (1.7754717488663857e+121 3.494659494474523e+27): 1
* [misc]none:  (1.355389858139596e-211 5.3134050984497146e-45): 0
* [misc]none:  (1.7558002847649968e-150 2.8327022791344117e+186): 0
* [misc]none:  (55126108376913.92 1.4270114976186918e+130): 1
* [misc]none:  (2.1677429926485946e-242 1.7597566772342396e-204): 7
* [misc]none:  (5.672231019728725e-161 4.978844845564056e+84): 2
* [misc]none:  (1.061192968818359e-298 3.4390539626492262e-136): 2
* [misc]none:  (1.8851052094553197e-277 9.953566511035923e-308): 2
* [misc]none:  (2.984618116231375e+88 2.296813947529187e+143): 1
* [misc]none:  (1.1631529018053348e+89 2.354140414905433e+187): 1
* [misc]none:  (2.216720871752684e-160 3.1263904065616715e+268): 2
* [misc]none:  (5.57997653477477e-111 1.5363278110829953e+73): 0
* [misc]none:  (1.0611909380115695e-87 1.295915517178257e-293): 0
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* [misc]none:  (2.648998082938836e-121 6.334062294691454e-67): 2
* [misc]none:  (4.293605985901814e-150 8.709273807481483e+69): 1
* [misc]none:  (7.932758618838293e-45 1.0062256135654257e-12): 9
* [misc]none:  (1.0135699554608461e-103 1.0001039793852175e+214): 1
* [misc]none:  (3.306163540346375e+188 2.601454323484488e+217): 1
* [misc]none:  (4.4505875876233544e-249 1.1235340410501106e+40): 2
* [misc]none:  (7.344373535448876e-228 2.204405021953709e+104): 0
* [misc]none:  (4.0855428097798646e-150 2.727229900429018e-249): 4
* [misc]none:  (6.298377803380903e-45 4.638301673824566e+198): 0
* [misc]none:  (1.5663895259426407e-227 6.068461153265776e+155): 0
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* [misc]none:  (1.5943160592835199e+304 1.045121272346536e+179): 1
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* [misc]none:  All alt indexes
* [misc]none:  (λ (k n) (/ (+ (* (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (* (* k k) 1/8)) (+ (* (log n) (log n)) (* (log (* PI 2)) (log (* PI 2))))) (- (fma (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4)) (* (log (* PI 2)) (* (* k k) (log n))) (* (pow (* PI 2) 1/2) (pow n 1/2))) (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/2)) (fma k (log (* PI 2)) (* (log n) k))))) (sqrt k))): 0
* [misc]none:  (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))): 1
* [misc]none:  (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))): 2
* [misc]none:  (λ (k n) (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k))): 3
* [misc]none:  (λ (k n) (cbrt (/ (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))): 4
* [misc]none:  (λ (k n) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))))): 5
* [misc]none:  (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))): 6
* [misc]none:  (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))): 7
* [misc]none:  (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k))))): 8
* [misc]none:  (λ (k n) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k))))): 9
* [misc]none:  (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))): 10
* [misc]none:  Best alt per point
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* [misc]none:  (8.518821522570516e-60 1.2001411983497562e+106): 2
* [misc]none:  (9.822572373265172e-201 2.558616615476855e-60): 7
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* [misc]none:  (1.1074692942653551e+18 1.558500650765054e+146): 1
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* [misc]none:  (4.546382622074157e-108 3.8495114831696875e-48): 0
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* [misc]none:  (9.30882910260521e+146 2.4925158551302067e+89): 1
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* [misc]none:  (9.153145296775212e-39 2.077022997927436e-139): 0
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* [misc]none:  (2.9573507267394465e-308 4.1771154955437857e-262): 5
* [misc]none:  (5.532920533179142e-152 7.554314233014913e+168): 0
* [misc]none:  (7.775944736851254e-206 7.437550583183719e+153): 0
* [misc]none:  (3.899173844391897e+120 3.705546267531316e+263): 1
* [misc]none:  (5.5950620368202944e-145 4.107096789321886e+47): 4
* [misc]none:  (2.9754862723359673e-209 2.5416139134760705e-289): 0
* [misc]none:  (3.5927665975113976e-239 4.614798558690456e-297): 0
* [misc]none:  (2.668103807085715e+100 5.401731707229941e+72): 1
* [misc]none:  (3.891498638245715e-204 1.8093455138130522e+133): 10
* [misc]none:  (5.932902354540652e-124 2.9604954362664366e+289): 2
* [misc]none:  (3.0539888630764254e-239 9.953908495433605e+227): 0
* [misc]none:  (2.0980661301565718e-60 1.9558316322795932e+229): 1
* [misc]none:  (1.0024360019170988e-151 7.5175772698725994e+230): 2
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* [misc]none:  (5.3266849932814836e+126 2.901363739745472e+210): 1
* [misc]none:  (1.6992513309501048e-129 2.550558153214631e-264): 2
* [misc]none:  (5.7712783914778174e-266 1.5980511259599325e-21): 0
* [misc]none:  (1.7764137706377376e-220 7.270223756267636e-257): 2
* [misc]none:  (3.4765225248477924e-220 5.73355053644598e+126): 2
* [misc]none:  (9.119412205964577e-203 2.775843815614327e-95): 0
* [misc]none:  (7.329474245282433e-48 2.3322335175982515e-233): 1
* [misc]none:  (3.5836534998638334e-135 5.874263446950659e-136): 2
* [misc]none:  (7.149081725669718e+245 3.1834201935962926e+247): 1
* [misc]none:  (1.109245260628489e+101 5.672826308117571e+293): 1
* [misc]none:  (1.969823050847671e+299 8.395990963453484e+106): 1
* [misc]none:  (1.2407901696126049e+210 2605286283632.6167): 1
* [misc]none:  (2.0256515578089416e+140 8.501791068840968e+197): 1
* [misc]none:  (9.544656038170093e+242 1.6519069419163414e+176): 1
* [misc]none:  (7.304105671735325e-242 7.033032775041187e+285): 0
* [misc]none:  (6.81321242648181e-289 1.45222983614977e-105): 1
* [misc]none:  (1.5262661067350401e-10 7.753245307187778e+31): 0
* [misc]none:  (1.4426514360168247e-145 4.904168640083974e+160): 1
* [misc]none:  (7.646129439560017e+176 3.1611172476808926e+209): 1
* [misc]none:  (5.105992271675965e-91 4.769518420383615e-198): 1
* [misc]none:  (6.798513332593515e-94 1.4806341275368096e-15): 0
* [misc]none:  (3.821526442421431e+297 1.2464063226445322e+209): 1
* [misc]none:  (1.09010428308076e-124 6.739673456854575e+249): 1
* [misc]none:  (0.36218343358512595 1.1084878850555635e+104): 2
* [misc]none:  (4.657146692902141e+280 1.9733854398064837e+215): 1
* [misc]none:  (5.412740199293554e+26 6.234082350070098e+32): 1
* [misc]none:  (6.4866276434875264e+44 3.175834271419552e+52): 1
* [misc]none:  (9.151015091612054e-197 1.6592153710205133e-269): 7
* [misc]none:  (6.922703552766224e-109 7.522858670517918e+259): 5
* [misc]none:  (1.5842409508887248e+187 1.8800714745176597e+114): 1
* [misc]none:  (6.991612783699758e+256 1.4552214481837247e+206): 1
* [misc]none:  (1.5567451015893508e-50 3.408101142682615e-113): 0
* [misc]none:  (1.453412145346343e+291 8.360826537804821e+182): 1
* [misc]none:  (2.376066765979685e-112 1.1698610931102194e-130): 1
* [misc]none:  (4.4868661851147195e-129 4.732835307271031e+241): 0
* [misc]none:  (2.4110148371685504e-195 3.4901782791628877e+267): 10
* [misc]none:  (9.254023538292273e-258 2.617971147092364e-76): 2
* [misc]none:  (2.931668337478436e+126 1.4018724764197611e+160): 1
* [misc]none:  (6.673139894543714e-272 2.389729719307196e-186): 1
* [misc]none:  (3.34193429381633e-274 6.07560242102484e+85): 0
* [misc]none:  (5.316440102938414e-63 24130443289213716.0): 5
* [misc]none:  (1.52221681471073e+30 1.552064650669455e+142): 1
* [misc]none:  (5.946958643597572e-214 9.722495709355246e-119): 1
* [misc]none:  (3.9615177849779133e-143 1.1510307484496886e-51): 4
* [misc]none:  (4.116349531400419e+59 3.7023764599519414e+64): 1
* [misc]none:  (3.19314088639968e-300 7.10649025136688e+263): 3
* [misc]none:  (2.6209483109511002e-99 1.0152763243033748e+142): 2
* [misc]none:  (3.9436987604242746e-188 1.2987545615858837e-229): 0
* [misc]none:  (4.072041399031216e+135 3.886264623793198e+50): 1
* [misc]none:  (5.600091178152213e-210 7.360949206952843e-212): 1
* [misc]none:  (5.235172412726717e+152 3.9088394890922115e+223): 1
* [misc]none:  (1.2265182674709907e+198 3.136601910786915e+46): 1
* [misc]none:  (2.296991649120878e+37 3.5701416837580245e+199): 1
* [misc]none:  (4.984374966308376e+225 1.882765755995834e+18): 1
* [misc]none:  (1.939469755263449e-274 2.0558821145728443e-244): 0
* [misc]none:  (7.118304679887613e-64 2.3966615634258388e-54): 0
* [misc]none:  (5.6334012743355e-180 2.2204044591450003e+49): 0
* [misc]none:  (1.2391428993123195e-53 3.206221419912265e+51): 4
* [misc]none:  (5.976566162781828e-262 4.0522267480412145e+189): 0
* [misc]none:  (1.2926844442603449e-272 6.777020097920311e+216): 8
* [misc]none:  (1.4932339006735016e+157 3.1812804254524387e+233): 1
* [misc]none:  (3.7476721237841876e-281 4.811543151950025e-33): 0
* [misc]none:  (6.525431496731668e-64 1.0982823072397984e+136): 2
* [misc]none:  (2.704077310435608e-253 3.1639399211332326e+205): 0
* [misc]none:  (2.7511202385052856e-18 3.82956155404422e-299): 8
* [misc]none:  (4.296582624822391e-200 1.733700273392293e+77): 2
* [misc]none:  (6.683383915725252e-271 1.830961252259433e-59): 2
* [misc]none:  (4.068667347744151e-179 8.630725328355339e+266): 1
* [misc]none:  (2.5976261349663673e+194 4.713564345937309e+51): 1
* [misc]none:  (4.807691125223642e+307 2.4189569765995642e+235): 1
* [misc]none:  (5.0806815187366375e+166 4.873854048773888e+106): 1
* [misc]none:  (1.2300916721937489e+185 5.9776582784273185e+256): 1
* [misc]none:  (3.003386221248247e-77 7.613990227232114e-101): 1
* [misc]none:  (3.438873899519122e+171 1.8186504690640068e+223): 1
* [misc]none:  (5.515506992492392e-277 2.595646488837273e-219): 0
* [misc]none:  (3.108236652528406e-297 7.181266914182018e-165): 0
* [misc]none:  (7.707611608802171e+62 1.152518328416828e+180): 1
* [misc]none:  (4.5690448860660455e-67 1.2792918576789026e+83): 5
* [misc]none:  (3.934156464498665e-121 1.9851718582837827e+233): 0
* [misc]none:  (2797.2682494851097 5.51985688247549e+99): 1
* [misc]none:  (0.0005921945720183679 2.8115284450926948e-120): 2
* [misc]none:  (2.5144530485773557e+177 3.96896356073862e+48): 1
* [misc]none:  (2.9394468165964015e-257 1.5225460242504859e+106): 0
* [misc]none:  (3.271929098149761e-144 7.5398414005163625e+267): 0
* [misc]none:  (6.604350361119279e-291 3.861477555295976e-66): 0
* [misc]none:  (8.124998850854922e-91 2.0152844845402166e-297): 0
* [misc]none:  (8.604490187894414e-112 1.3704041407198253e+228): 1
* [misc]none:  (1.6519797365083582e+195 6.316732900885901e+249): 1
* [misc]none:  (2.0115496002781107e-145 7.084575776306543e+174): 0
* [misc]none:  (2.5502245720775025e+302 3.7105227033705403e+214): 1
* [misc]none:  (6.821311827045434e-30 2.8401584433220846e+96): 1
* [misc]none:  (2.6830861914889714e-191 5.086243151153881e+259): 1
* [misc]none:  (1.4517955555700533e-57 3.278760905350017e+239): 5
* [misc]none:  (9.422179697047065e-164 1.3639040980897921e-39): 0
* [misc]none:  (2.8344220272269968e+166 1.5252878664938466e+85): 1
* [misc]none:  (1.9836536473017196e-256 6.844414014257645e+204): 1
* [misc]none:  Picked alt (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))
* * * * [misc]pick:  Picked  #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 4 ] rewriting at (2 1 2 1)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2 1 1 1)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2 1 1)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 4 ] generating series at (2 1 2 1)
* [misc]approximate:  Taking taylor expansion of (* n (* PI 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* n (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) n) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 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) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 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) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 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 (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
* * * * [misc]progress:  [ 2 / 4 ] generating series at (2 1 1 1)
* [misc]approximate:  Taking taylor expansion of (* n (* PI 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* n (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) n) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 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) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 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) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 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 (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
* * * * [misc]progress:  [ 3 / 4 ] generating series at (2)
* [misc]approximate:  Taking taylor expansion of (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ 1 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* n (* PI 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* n (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in k
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of (* PI 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 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* n (* 2 PI)) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ k 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* n (* PI 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* n (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in k
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of (* PI 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 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* n (* 2 PI)) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp 0) into 1
* [misc]backup-simplify:  Simplify (/ (pow (* 2 (* n PI)) 1/2) 1) into (sqrt (* n (* 2 PI)))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ (sqrt (* n (* 2 PI))) +nan.0) into (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* n (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* n (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* n (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* n (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 k) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* k (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (/ (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt k)) into (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* n (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* n (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* n (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* n (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 k) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* k (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (/ (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt k)) into (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (+ (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* k (+ (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 0 (+ (log (* 2 PI)) (log n))) into 0
* [misc]backup-simplify:  Simplify (* 1/2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (+ (log (* 2 PI)) (log n)))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (+ (log (* 2 PI)) (log n))) (* 0 0)) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))
* [misc]backup-simplify:  Simplify (exp 0) into 1
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 1) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 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 (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1) 1)))) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) +nan.0) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 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 (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (+ (log (* 2 PI)) (log n))) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) 1)) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) +nan.0) (+ (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) +nan.0) (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) 0))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 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 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (+ (log (* 2 PI)) (log n))) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 3) 6)) (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2))))))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2)))))) 1)) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) (/ (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) 1)) (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (- (+ (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (log n)))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 3))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 3))) (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow (log n) 2))))))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) +nan.0) (+ (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) +nan.0) (+ (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) +nan.0) (* (- (+ (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (log n)))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 3))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 3))) (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow (log n) 2)))))))) 0)))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))))))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))))))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n))))))))))))))))))))))))
* [misc]approximate:  Taking taylor expansion of (/ (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (* PI 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 n) 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 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 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) 1/2)
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 n) 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 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 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))
* [misc]backup-simplify:  Simplify (/ (pow (* 2 (/ PI n)) 1/2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) into (* (sqrt (/ (* 2 PI) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ (* (sqrt (/ (* 2 PI) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) +nan.0) into (* +nan.0 (* (sqrt (/ PI n)) (/ (sqrt 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt (/ 1 k))) into (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt (/ 1 k))) into (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (- (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (- (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k
* [misc]taylor:  Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* k (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 3) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))))))))
* [misc]approximate:  Taking taylor expansion of (/ (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) 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 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 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* -2 (/ PI n))))) into (pow (* -2 (/ PI n)) 1/2)
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) 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 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 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* -2 (/ PI n)))) into (* -1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))
* [misc]backup-simplify:  Simplify (/ (pow (* -2 (/ PI n)) 1/2) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) into (* (sqrt (/ (* PI -2) n)) (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ (* (sqrt (/ (* PI -2) n)) (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) +nan.0) into (* +nan.0 (/ (sqrt (* -2 (/ PI n))) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))
* [misc]taylor:  Taking taylor expansion of (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (- (log (* -2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (- (log (* -2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* -2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* -2 PI) in k
* [misc]taylor:  Taking taylor expansion of -2 in k
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k
* [misc]taylor:  Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k
* [misc]taylor:  Taking taylor expansion of -1/2 in k
* [misc]backup-simplify:  Simplify -1/2 into -1/2
* [misc]taylor:  Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k
* [misc]taylor:  Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* -2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* -2 PI) in k
* [misc]taylor:  Taking taylor expansion of -2 in k
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* -1/2 (- (log (* -2 PI)) (log n))) into (* -1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]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 (/ (- (log (* -2 PI)) (log n)) k))) 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -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 (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))
* [misc]backup-simplify:  Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (+ (* (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (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 (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))
* [misc]backup-simplify:  Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (+ (* (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))))
* * * * [misc]progress:  [ 4 / 4 ] generating series at (2 1 1)
* [misc]approximate:  Taking taylor expansion of (pow (* n (* PI 2)) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* n (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* n (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* n (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* n (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]approximate:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n)))))
* [misc]approximate:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* -2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* -2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* -2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 1)))) 24) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 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) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* -2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* -2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* -2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* -2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* -2 PI) 1)))) 120) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 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 (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* -2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* -2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* -2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* -2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* -2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* -2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* -2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* -2 PI) 1)))) 720) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n)))))
* * * [misc]progress:  simplifying candidates
* * * * [misc]progress:  [ 1 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (log1p (expm1 (* n (* PI 2)))) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (expm1 (* (* n 2) PI))
* [exit]simplify:  Simplified to (expm1 (* (* n 2) PI))
* * * * [misc]progress:  [ 2 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (expm1 (log1p (* n (* PI 2)))) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (log1p (* (* n 2) PI))
* [exit]simplify:  Simplified to (log1p (* (* n 2) PI))
* * * * [misc]progress:  [ 3 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (pow (* n (* PI 2)) 1) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 4 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (exp (log (* n (* PI 2)))) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (log (* (* PI n) 2))
* [exit]simplify:  Simplified to (log (* (* PI n) 2))
* * * * [misc]progress:  [ 5 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (log (exp (* n (* PI 2)))) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* * [misc]simplify:  iters left: 2 (35 enodes)
* * [misc]simplify:  iters left: 1 (47 enodes)
* [exit]simplify:  Simplified to (pow (exp 2) (* PI n))
* [exit]simplify:  Simplified to (pow (exp 2) (* PI n))
* * * * [misc]progress:  [ 6 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (18 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2)))
* [exit]simplify:  Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2)))
* [enter]simplify:  Simplifying (cbrt (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (cbrt (* (* n 2) PI))
* [exit]simplify:  Simplified to (cbrt (* (* n 2) PI))
* * * * [misc]progress:  [ 7 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (cbrt (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (59 enodes)
* * [misc]simplify:  iters left: 3 (203 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) 3)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) 3)
* * * * [misc]progress:  [ 8 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* (sqrt (* n (* PI 2))) (sqrt (* n (* PI 2)))) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* [enter]simplify:  Simplifying (sqrt (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* * * * [misc]progress:  [ 9 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* 1 (* n (* PI 2))) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 10 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* (* n PI) 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 (* PI n)
* [exit]simplify:  Simplified to (* PI n)
* * * * [misc]progress:  [ 11 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* (* PI 2) n) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 12 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (log1p (expm1 (* n (* PI 2)))) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (expm1 (* (* n 2) PI))
* [exit]simplify:  Simplified to (expm1 (* (* n 2) PI))
* * * * [misc]progress:  [ 13 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (expm1 (log1p (* n (* PI 2)))) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (log1p (* (* n 2) PI))
* [exit]simplify:  Simplified to (log1p (* (* n 2) PI))
* * * * [misc]progress:  [ 14 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* n (* PI 2)) 1) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 15 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (exp (log (* n (* PI 2)))) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (log (* (* PI n) 2))
* [exit]simplify:  Simplified to (log (* (* PI n) 2))
* * * * [misc]progress:  [ 16 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (log (exp (* n (* PI 2)))) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* * [misc]simplify:  iters left: 2 (35 enodes)
* * [misc]simplify:  iters left: 1 (47 enodes)
* [exit]simplify:  Simplified to (pow (exp 2) (* PI n))
* [exit]simplify:  Simplified to (pow (exp 2) (* PI n))
* * * * [misc]progress:  [ 17 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (18 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2)))
* [exit]simplify:  Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2)))
* [enter]simplify:  Simplifying (cbrt (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (cbrt (* (* n 2) PI))
* [exit]simplify:  Simplified to (cbrt (* (* n 2) PI))
* * * * [misc]progress:  [ 18 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (cbrt (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (59 enodes)
* * [misc]simplify:  iters left: 3 (203 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) 3)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) 3)
* * * * [misc]progress:  [ 19 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (sqrt (* n (* PI 2))) (sqrt (* n (* PI 2)))) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* [enter]simplify:  Simplifying (sqrt (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* * * * [misc]progress:  [ 20 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* 1 (* n (* PI 2))) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 21 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* n (* PI 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 (* PI n)
* [exit]simplify:  Simplified to (* PI n)
* * * * [misc]progress:  [ 22 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* PI 2) n) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 23 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (log1p (expm1 (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (expm1 (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (expm1 (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* [exit]simplify:  Simplified to (expm1 (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* * * * [misc]progress:  [ 24 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (expm1 (log1p (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (log1p (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (log1p (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* [exit]simplify:  Simplified to (log1p (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* * * * [misc]progress:  [ 25 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (pow (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) 1))>
* * * * [misc]progress:  [ 26 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (* (log (* n (* PI 2))) (/ 1 2)) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* n (* PI 2))) (/ 1 2)) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (97 enodes)
* * [misc]simplify:  iters left: 3 (307 enodes)
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 27 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (* (log (* n (* PI 2))) (/ 1 2)) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* n (* PI 2))) (/ 1 2)) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (97 enodes)
* * [misc]simplify:  iters left: 3 (307 enodes)
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 28 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (* (log (* n (* PI 2))) (/ 1 2)) (log (pow (* n (* PI 2)) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* n (* PI 2))) (/ 1 2)) (log (pow (* n (* PI 2)) (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (87 enodes)
* * [misc]simplify:  iters left: 3 (284 enodes)
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 29 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (* (log (* n (* PI 2))) (/ 1 2)) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* n (* PI 2))) (/ 1 2)) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (97 enodes)
* * [misc]simplify:  iters left: 3 (307 enodes)
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 30 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (* (log (* n (* PI 2))) (/ 1 2)) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* n (* PI 2))) (/ 1 2)) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (97 enodes)
* * [misc]simplify:  iters left: 3 (307 enodes)
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 31 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (* (log (* n (* PI 2))) (/ 1 2)) (log (pow (* n (* PI 2)) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* n (* PI 2))) (/ 1 2)) (log (pow (* n (* PI 2)) (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (87 enodes)
* * [misc]simplify:  iters left: 3 (284 enodes)
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 32 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (log (pow (* n (* PI 2)) (/ 1 2))) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (log (pow (* n (* PI 2)) (/ 1 2))) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (90 enodes)
* * [misc]simplify:  iters left: 3 (263 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 33 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (log (pow (* n (* PI 2)) (/ 1 2))) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (log (pow (* n (* PI 2)) (/ 1 2))) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (90 enodes)
* * [misc]simplify:  iters left: 3 (263 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 34 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (log (pow (* n (* PI 2)) (/ 1 2))) (log (pow (* n (* PI 2)) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (log (pow (* n (* PI 2)) (/ 1 2))) (log (pow (* n (* PI 2)) (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (70 enodes)
* * [misc]simplify:  iters left: 3 (206 enodes)
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* n 2) PI)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* n 2) PI)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 35 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (log (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (log (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (89 enodes)
* * [misc]simplify:  iters left: 2 (283 enodes)
* [exit]simplify:  Simplified to (fma (log (* 2 (* PI n))) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* 2 (* PI n))) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 36 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (exp (log (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (log (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (55 enodes)
* * [misc]simplify:  iters left: 2 (103 enodes)
* * [misc]simplify:  iters left: 1 (295 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* 2 PI) n)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* 2 PI) n)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 37 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (log (exp (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (exp (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (exp (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* [exit]simplify:  Simplified to (exp (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* * * * [misc]progress:  [ 38 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (/ (/ (* (* (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ 1 2))) (* (* (pow (* n (* PI 2)) (/ k 2)) (pow (* n (* PI 2)) (/ k 2))) (pow (* n (* PI 2)) (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (* (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ 1 2))) (* (* (pow (* n (* PI 2)) (/ k 2)) (pow (* n (* PI 2)) (/ k 2))) (pow (* n (* PI 2)) (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (113 enodes)
* * [misc]simplify:  iters left: 3 (390 enodes)
* [exit]simplify:  Simplified to (/ (* (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (* (pow (* (* PI n) 2) (/ k 2)) (/ (* (sqrt k) k) (pow (* (* PI n) 2) (/ 1 2)))))
* [exit]simplify:  Simplified to (/ (* (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (* (pow (* (* PI n) 2) (/ k 2)) (/ (* (sqrt k) k) (pow (* (* PI n) 2) (/ 1 2)))))
* * * * [misc]progress:  [ 39 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (/ (* (* (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (* (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (39 enodes)
* * [misc]simplify:  iters left: 4 (96 enodes)
* * [misc]simplify:  iters left: 3 (266 enodes)
* [exit]simplify:  Simplified to (* (/ (pow (* PI (* n 2)) (/ 1 2)) (* (pow (* PI (* n 2)) (/ k 2)) (* (sqrt k) k))) (* (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))))
* [exit]simplify:  Simplified to (* (/ (pow (* PI (* n 2)) (/ 1 2)) (* (pow (* PI (* n 2)) (/ k 2)) (* (sqrt k) k))) (* (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))))
* * * * [misc]progress:  [ 40 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (cbrt (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))) (cbrt (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))) (cbrt (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (cbrt (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))) (cbrt (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))))
* [exit]simplify:  Simplified to (* (cbrt (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))))
* [enter]simplify:  Simplifying (cbrt (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* [exit]simplify:  Simplified to (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* * * * [misc]progress:  [ 41 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (* (* (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (* (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (69 enodes)
* * [misc]simplify:  iters left: 3 (196 enodes)
* [exit]simplify:  Simplified to (/ (/ (* (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ 1 2))) (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))) (/ (* k (pow (* (* 2 PI) n) (/ k 2))) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)))))
* [exit]simplify:  Simplified to (/ (/ (* (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ 1 2))) (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))) (/ (* k (pow (* (* 2 PI) n) (/ k 2))) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)))))
* * * * [misc]progress:  [ 42 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))) (sqrt (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* [enter]simplify:  Simplifying (sqrt (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* * * * [misc]progress:  [ 43 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (- (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (- (sqrt k))))>
* [enter]simplify:  Simplifying (- (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (- (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))
* [exit]simplify:  Simplified to (- (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))
* [enter]simplify:  Simplifying (- (sqrt k))
* * [misc]simplify:  iters left: 3 (3 enodes)
* [exit]simplify:  Simplified to (- (sqrt k))
* [exit]simplify:  Simplified to (- (sqrt k))
* * * * [misc]progress:  [ 44 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (* (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (45 enodes)
* * [misc]simplify:  iters left: 3 (49 enodes)
* * [misc]simplify:  iters left: 2 (52 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (* (/ (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 45 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (* (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 46 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (* (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))) 1) (/ (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))) 1)
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* * [misc]simplify:  iters left: 2 (52 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))))
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))))
* [enter]simplify:  Simplifying (/ (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k))
* [exit]simplify:  Simplified to (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k))
* * * * [misc]progress:  [ 47 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 48 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 49 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) 1)
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k))
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k))
* * * * [misc]progress:  [ 50 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* * [misc]simplify:  iters left: 2 (31 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (cbrt (sqrt k))) (pow (* 2 PI) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (cbrt (sqrt k))) (pow (* 2 PI) (/ k 2)))
* * * * [misc]progress:  [ 51 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) (sqrt (sqrt k))) (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (pow n (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (pow n (/ k 2)))
* [enter]simplify:  Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt (sqrt k))) (pow (* 2 PI) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt (sqrt k))) (pow (* 2 PI) (/ k 2)))
* * * * [misc]progress:  [ 52 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) 1) (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) 1)
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (21 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* [exit]simplify:  Simplified to (/ (pow n (/ 1 2)) (pow n (/ k 2)))
* [exit]simplify:  Simplified to (/ (pow n (/ 1 2)) (pow n (/ k 2)))
* [enter]simplify:  Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt k)) (pow (* 2 PI) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt k)) (pow (* 2 PI) (/ k 2)))
* * * * [misc]progress:  [ 53 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (46 enodes)
* * [misc]simplify:  iters left: 3 (60 enodes)
* * [misc]simplify:  iters left: 2 (72 enodes)
* * [misc]simplify:  iters left: 1 (75 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (pow (* n (* 2 PI)) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (pow (* n (* 2 PI)) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* (* n 2) PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* (* n 2) PI) (/ k 2))))
* * * * [misc]progress:  [ 54 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (38 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* * [misc]simplify:  iters left: 2 (48 enodes)
* [exit]simplify:  Simplified to (/ (/ (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* (* n 2) PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* (* n 2) PI) (/ k 2))))
* * * * [misc]progress:  [ 55 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) 1) (/ (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) 1)
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* * [misc]simplify:  iters left: 2 (47 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 56 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (45 enodes)
* * [misc]simplify:  iters left: 2 (46 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* n (* 2 PI)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* n (* 2 PI)) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2))))
* * * * [misc]progress:  [ 57 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) (/ (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2))))
* * * * [misc]progress:  [ 58 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) 1) (/ (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) 1)
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (37 enodes)
* [exit]simplify:  Simplified to (/ (pow n (/ 1 2)) (sqrt (pow (* n (* 2 PI)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (pow n (/ 1 2)) (sqrt (pow (* n (* 2 PI)) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 59 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow n (/ 1 2)) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (cbrt (sqrt k))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (cbrt (sqrt k))) (cbrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (cbrt (sqrt k))) (pow (* PI (* n 2)) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (cbrt (sqrt k))) (pow (* PI (* n 2)) (/ k 2)))
* * * * [misc]progress:  [ 60 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) 1) (sqrt (sqrt k))) (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow n (/ 1 2)) 1) (sqrt (sqrt k)))
* * [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 (/ (pow n (/ 1 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow n (/ 1 2)) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt (sqrt k))) (pow (* PI (* n 2)) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt (sqrt k))) (pow (* PI (* n 2)) (/ k 2)))
* * * * [misc]progress:  [ 61 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) 1) 1) (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (pow n (/ 1 2)) 1) 1)
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (11 enodes)
* [exit]simplify:  Simplified to (pow n (/ 1 2))
* [exit]simplify:  Simplified to (pow n (/ 1 2))
* [enter]simplify:  Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt k)) (pow (* (* 2 PI) n) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt k)) (pow (* (* 2 PI) n) (/ k 2)))
* * * * [misc]progress:  [ 62 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (50 enodes)
* * [misc]simplify:  iters left: 3 (86 enodes)
* * [misc]simplify:  iters left: 2 (124 enodes)
* * [misc]simplify:  iters left: 1 (143 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* 2 PI) n) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow n (/ k 2)) (cbrt (pow (* (* 2 PI) n) (/ 1 2)))))
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* 2 PI) n) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow n (/ k 2)) (cbrt (pow (* (* 2 PI) n) (/ 1 2)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* 2 PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* 2 PI) (/ k 2))))
* * * * [misc]progress:  [ 63 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (pow n (/ k 2))) (sqrt (sqrt k))) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (pow n (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (56 enodes)
* * [misc]simplify:  iters left: 2 (64 enodes)
* * [misc]simplify:  iters left: 1 (67 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (pow n (/ k 2))) (/ (sqrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ 1 2)))))
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (pow n (/ k 2))) (/ (sqrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ 1 2)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* 2 PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* 2 PI) (/ k 2))))
* * * * [misc]progress:  [ 64 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (pow n (/ k 2))) 1) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (pow n (/ k 2))) 1)
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (64 enodes)
* * [misc]simplify:  iters left: 2 (152 enodes)
* * [misc]simplify:  iters left: 1 (253 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* PI (* n 2)) (/ 1 2))) (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (pow n (/ k 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* PI (* n 2)) (/ 1 2))) (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (pow n (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (pow (* 2 PI) (/ k 2)) (sqrt k)))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (pow (* 2 PI) (/ k 2)) (sqrt k)))
* * * * [misc]progress:  [ 65 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (73 enodes)
* * [misc]simplify:  iters left: 3 (142 enodes)
* * [misc]simplify:  iters left: 2 (248 enodes)
* * [misc]simplify:  iters left: 1 (309 enodes)
* [exit]simplify:  Simplified to (* (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k))) (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (* (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k))) (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 66 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (59 enodes)
* * [misc]simplify:  iters left: 3 (92 enodes)
* * [misc]simplify:  iters left: 2 (127 enodes)
* * [misc]simplify:  iters left: 1 (145 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 67 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) 1) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) 1)
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (56 enodes)
* * [misc]simplify:  iters left: 3 (95 enodes)
* * [misc]simplify:  iters left: 2 (301 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))))
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 68 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (51 enodes)
* * [misc]simplify:  iters left: 3 (87 enodes)
* * [misc]simplify:  iters left: 2 (127 enodes)
* * [misc]simplify:  iters left: 1 (146 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (pow (* 2 (* PI n)) (/ 1 2)))))
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (pow (* 2 (* PI n)) (/ 1 2)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 69 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (57 enodes)
* * [misc]simplify:  iters left: 2 (65 enodes)
* * [misc]simplify:  iters left: 1 (68 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ 1 2)))))
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ 1 2)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 70 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) 1) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) 1)
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (65 enodes)
* * [misc]simplify:  iters left: 2 (157 enodes)
* * [misc]simplify:  iters left: 1 (277 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* 2 PI) n) (/ 1 2))) (/ (sqrt (pow (* (* 2 PI) n) (/ k 2))) (cbrt (pow (* (* 2 PI) n) (/ 1 2)))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* 2 PI) n) (/ 1 2))) (/ (sqrt (pow (* (* 2 PI) n) (/ k 2))) (cbrt (pow (* (* 2 PI) n) (/ 1 2)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 71 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (56 enodes)
* * [misc]simplify:  iters left: 3 (102 enodes)
* * [misc]simplify:  iters left: 2 (238 enodes)
* * [misc]simplify:  iters left: 1 (272 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* 2 PI) n) (/ 1 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* 2 PI) n) (/ 1 2))) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* 2 PI) n) (/ 1 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* 2 PI) n) (/ 1 2))) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 72 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) 1) (sqrt (sqrt k))) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) 1) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (70 enodes)
* * [misc]simplify:  iters left: 2 (133 enodes)
* * [misc]simplify:  iters left: 1 (138 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* PI (* n 2)) (/ 1 2))) (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* PI (* n 2)) (/ 1 2))) (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 73 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) 1) 1) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) 1) 1)
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* * [misc]simplify:  iters left: 2 (49 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (pow (* PI (* n 2)) (/ k 2)) (sqrt k)))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (pow (* PI (* n 2)) (/ k 2)) (sqrt k)))
* * * * [misc]progress:  [ 74 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (45 enodes)
* * [misc]simplify:  iters left: 2 (46 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* 2 PI) n) (/ 1 2))) (* (pow n (/ k 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* 2 PI) n) (/ 1 2))) (* (pow n (/ k 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* 2 PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* 2 PI) (/ k 2))))
* * * * [misc]progress:  [ 75 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow n (/ k 2))) (sqrt (sqrt k))) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow n (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow n (/ k 2))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow n (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* 2 PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* 2 PI) (/ k 2))))
* * * * [misc]progress:  [ 76 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow n (/ k 2))) 1) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow n (/ k 2))) 1)
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (37 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow n (/ k 2)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow n (/ k 2)))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (pow (* 2 PI) (/ k 2)) (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (pow (* 2 PI) (/ k 2)) (sqrt k)))
* * * * [misc]progress:  [ 77 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (47 enodes)
* * [misc]simplify:  iters left: 3 (61 enodes)
* * [misc]simplify:  iters left: 2 (73 enodes)
* * [misc]simplify:  iters left: 1 (76 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 78 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* * [misc]simplify:  iters left: 2 (49 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 79 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) 1) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) 1)
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* * [misc]simplify:  iters left: 2 (48 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 80 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (46 enodes)
* * [misc]simplify:  iters left: 2 (47 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 81 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 82 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) 1) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) 1)
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* * [misc]simplify:  iters left: 2 (38 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 83 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (50 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 84 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) 1) (sqrt (sqrt k))) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) 1) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 85 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) 1) 1) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) 1) 1)
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2)))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (pow (* PI (* n 2)) (/ k 2)) (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (pow (* PI (* n 2)) (/ k 2)) (sqrt k)))
* * * * [misc]progress:  [ 86 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* PI 2) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (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 (28 enodes)
* * [misc]simplify:  iters left: 2 (29 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (/ 1 (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* PI 2) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI (* n 2)) (/ 1 2)) (* (cbrt (sqrt k)) (pow (* 2 PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (pow (* PI (* n 2)) (/ 1 2)) (* (cbrt (sqrt k)) (pow (* 2 PI) (/ k 2))))
* * * * [misc]progress:  [ 87 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (pow n (/ k 2))) (sqrt (sqrt k))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* PI 2) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (pow n (/ k 2))) (sqrt (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 (/ (/ 1 (sqrt (sqrt k))) (pow n (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt (sqrt k))) (pow n (/ k 2)))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* PI 2) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* 2 PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* 2 PI) (/ k 2))))
* * * * [misc]progress:  [ 88 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (pow n (/ k 2))) 1) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* PI 2) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ 1 (pow n (/ k 2))) 1)
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* * [misc]simplify:  iters left: 3 (18 enodes)
* [exit]simplify:  Simplified to (/ 1 (pow n (/ k 2)))
* [exit]simplify:  Simplified to (/ 1 (pow n (/ k 2)))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* PI 2) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ 1 2)) (* (sqrt k) (pow (* 2 PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ 1 2)) (* (sqrt k) (pow (* 2 PI) (/ k 2))))
* * * * [misc]progress:  [ 89 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (58 enodes)
* * [misc]simplify:  iters left: 2 (70 enodes)
* * [misc]simplify:  iters left: 1 (73 enodes)
* [exit]simplify:  Simplified to (/ (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (* (cbrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))))
* [exit]simplify:  Simplified to (/ (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (* (cbrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 90 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (46 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (* (sqrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (/ k 2)))))
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (* (sqrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (/ k 2)))))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 91 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) 1) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ 1 (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) 1)
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* * [misc]simplify:  iters left: 2 (40 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 92 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* * [misc]simplify:  iters left: 2 (44 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* (* 2 n) PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* (* 2 n) PI) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 93 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (pow (* 2 (* PI n)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (pow (* 2 (* PI n)) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 94 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (sqrt (pow (* n (* PI 2)) (/ k 2)))) 1) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ 1 (sqrt (pow (* n (* PI 2)) (/ k 2)))) 1)
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (pow (* n (* PI 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ 1 (sqrt (pow (* n (* PI 2)) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 95 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 96 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 1) (sqrt (sqrt k))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 1) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 4 (6 enodes)
* * [misc]simplify:  iters left: 3 (8 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 97 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 1) 1) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ 1 1) 1)
* * [misc]simplify:  iters left: 4 (3 enodes)
* * [misc]simplify:  iters left: 3 (5 enodes)
* [exit]simplify:  Simplified to 1
* [exit]simplify:  Simplified to 1
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ 1 2)) (* (sqrt k) (pow (* (* n 2) PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ 1 2)) (* (sqrt k) (pow (* (* n 2) PI) (/ k 2))))
* * * * [misc]progress:  [ 98 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* [exit]simplify:  Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 99 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 100 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 1) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ 1 1)
* * [misc]simplify:  iters left: 2 (2 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to 1
* [exit]simplify:  Simplified to 1
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ 1 2)) (* (sqrt k) (pow (* (* n 2) PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ 1 2)) (* (sqrt k) (pow (* (* n 2) PI) (/ k 2))))
* * * * [misc]progress:  [ 101 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow (* n (* PI 2)) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ 1 (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ 1 (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (31 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (sqrt k))) (pow (* n (* PI 2)) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (sqrt k))) (pow (* n (* PI 2)) (/ k 2)))
* * * * [misc]progress:  [ 102 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (sqrt k))) (/ (/ 1 (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ 1 (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (31 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt (sqrt k))) (pow (* n (* PI 2)) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt (sqrt k))) (pow (* n (* PI 2)) (/ k 2)))
* * * * [misc]progress:  [ 103 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow (* n (* PI 2)) (/ 1 2)) 1) (/ (/ 1 (pow (* n (* PI 2)) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ 1 2)) 1)
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (/ 1 2))
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (/ 1 2))
* [enter]simplify:  Simplifying (/ (/ 1 (pow (* n (* PI 2)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt k)) (pow (* n (* PI 2)) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt k)) (pow (* n (* PI 2)) (/ k 2)))
* * * * [misc]progress:  [ 104 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))))>
* * * * [misc]progress:  [ 105 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (/ 1 (sqrt k))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt k))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (6 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt k))
* [exit]simplify:  Simplified to (/ 1 (sqrt k))
* * * * [misc]progress:  [ 106 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2)))
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2)))
* * * * [misc]progress:  [ 107 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (38 enodes)
* * [misc]simplify:  iters left: 3 (44 enodes)
* * [misc]simplify:  iters left: 2 (45 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 108 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 109 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) 1) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) 1)
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (37 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 110 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt k) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))))
* [exit]simplify:  Simplified to (/ (sqrt k) (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))))
* * * * [misc]progress:  [ 111 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt k) (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (sqrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))))
* [exit]simplify:  Simplified to (/ (sqrt k) (sqrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))))
* * * * [misc]progress:  [ 112 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2))))
* [exit]simplify:  Simplified to (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2))))
* * * * [misc]progress:  [ 113 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* PI 2) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* PI 2) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))
* * * * [misc]progress:  [ 114 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* PI 2) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2))))
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* PI 2) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2))))
* * * * [misc]progress:  [ 115 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow n (/ 1 2)) 1) (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* PI 2) (/ 1 2))) (pow (* 2 (* n PI)) (/ k 2)))
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* PI 2) (/ 1 2))) (pow (* 2 (* n PI)) (/ k 2)))
* * * * [misc]progress:  [ 116 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (pow n (/ k 2))) (/ (sqrt k) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* PI 2) (/ k 2)) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ 1 2))))
* [exit]simplify:  Simplified to (/ (* (pow (* PI 2) (/ k 2)) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ 1 2))))
* * * * [misc]progress:  [ 117 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt k) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ 1 2))))
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ 1 2))))
* * * * [misc]progress:  [ 118 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt k) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* [exit]simplify:  Simplified to (/ (* (sqrt (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ 1 2))))
* [exit]simplify:  Simplified to (/ (* (sqrt (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ 1 2))))
* * * * [misc]progress:  [ 119 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) 1) (/ (sqrt k) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* PI (* n 2)) (/ k 2)) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ 1 2))))
* [exit]simplify:  Simplified to (/ (* (pow (* PI (* n 2)) (/ k 2)) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ 1 2))))
* * * * [misc]progress:  [ 120 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow n (/ k 2))) (/ (sqrt k) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* PI 2) (/ k 2)) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ 1 2))))
* [exit]simplify:  Simplified to (/ (* (pow (* PI 2) (/ k 2)) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ 1 2))))
* * * * [misc]progress:  [ 121 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt k) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ 1 2))))
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ 1 2))))
* * * * [misc]progress:  [ 122 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt k) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* [exit]simplify:  Simplified to (/ (* (sqrt (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ 1 2))))
* [exit]simplify:  Simplified to (/ (* (sqrt (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ 1 2))))
* * * * [misc]progress:  [ 123 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) 1) (/ (sqrt k) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* PI (* n 2)) (/ k 2)) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ 1 2))))
* [exit]simplify:  Simplified to (/ (* (pow (* PI (* n 2)) (/ k 2)) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ 1 2))))
* * * * [misc]progress:  [ 124 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (pow n (/ k 2))) (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* PI 2) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* PI 2) (/ k 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* PI 2) (/ k 2)) (sqrt k)) (pow (* (* n 2) PI) (/ 1 2)))
* [exit]simplify:  Simplified to (/ (* (pow (* PI 2) (/ k 2)) (sqrt k)) (pow (* (* n 2) PI) (/ 1 2)))
* * * * [misc]progress:  [ 125 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* PI (* n 2)) (/ 1 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* PI (* n 2)) (/ 1 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 126 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* PI (* n 2)) (/ 1 2))) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* PI (* n 2)) (/ 1 2))) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 127 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 1) (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2)))
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2)))
* * * * [misc]progress:  [ 128 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2)))
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2)))
* * * * [misc]progress:  [ 129 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (/ (sqrt k) (/ 1 (pow (* n (* PI 2)) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ 1 (pow (* n (* PI 2)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* * [misc]simplify:  iters left: 2 (43 enodes)
* * [misc]simplify:  iters left: 1 (48 enodes)
* [exit]simplify:  Simplified to (* (pow (* 2 (* n PI)) (/ k 2)) (sqrt k))
* [exit]simplify:  Simplified to (* (pow (* 2 (* n PI)) (/ k 2)) (sqrt k))
* * * * [misc]progress:  [ 130 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))
* [exit]simplify:  Simplified to (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))
* * * * [misc]progress:  [ 131 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (log1p (expm1 (pow (* n (* PI 2)) (/ 1 2)))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (expm1 (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (expm1 (pow (* (* PI n) 2) (/ 1 2)))
* * * * [misc]progress:  [ 132 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (expm1 (log1p (pow (* n (* PI 2)) (/ 1 2)))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (log1p (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (log1p (pow (* (* PI n) 2) (/ 1 2)))
* * * * [misc]progress:  [ 133 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (exp (* (log (* n (* PI 2))) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* n (* PI 2))) (/ 1 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (92 enodes)
* * [misc]simplify:  iters left: 2 (180 enodes)
* * [misc]simplify:  iters left: 1 (391 enodes)
* [exit]simplify:  Simplified to (fma (log (* 2 PI)) (/ 1 2) (/ (log n) 2))
* [exit]simplify:  Simplified to (fma (log (* 2 PI)) (/ 1 2) (/ (log n) 2))
* * * * [misc]progress:  [ 134 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (exp (* (log (* n (* PI 2))) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* n (* PI 2))) (/ 1 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (92 enodes)
* * [misc]simplify:  iters left: 2 (180 enodes)
* * [misc]simplify:  iters left: 1 (391 enodes)
* [exit]simplify:  Simplified to (fma (log (* 2 PI)) (/ 1 2) (/ (log n) 2))
* [exit]simplify:  Simplified to (fma (log (* 2 PI)) (/ 1 2) (/ (log n) 2))
* * * * [misc]progress:  [ 135 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (* 1 (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* 1 (/ 1 2))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* [exit]simplify:  Simplified to (/ 1 2)
* [exit]simplify:  Simplified to (/ 1 2)
* * * * [misc]progress:  [ 136 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* n (* PI 2)) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) (cbrt (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (* PI 2)) (* (cbrt (/ 1 2)) (cbrt (/ 1 2))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (pow (* (* n 2) PI) (* (cbrt (/ 1 2)) (cbrt (/ 1 2))))
* [exit]simplify:  Simplified to (pow (* (* n 2) PI) (* (cbrt (/ 1 2)) (cbrt (/ 1 2))))
* * * * [misc]progress:  [ 137 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* n (* PI 2)) (sqrt (/ 1 2))) (sqrt (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (* PI 2)) (sqrt (/ 1 2)))
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* * [misc]simplify:  iters left: 3 (21 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (sqrt (/ 1 2)))
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (sqrt (/ 1 2)))
* * * * [misc]progress:  [ 138 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* n (* PI 2)) 1) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (* PI 2)) 1)
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (20 enodes)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* * * * [misc]progress:  [ 139 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* n (* PI 2)) 1) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (* PI 2)) 1)
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (20 enodes)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* * * * [misc]progress:  [ 140 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (pow n (/ 1 2)) (pow (* PI 2) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow n (/ 1 2))
* * [misc]simplify:  iters left: 3 (5 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (pow n (/ 1 2))
* [exit]simplify:  Simplified to (pow n (/ 1 2))
* [enter]simplify:  Simplifying (pow (* PI 2) (/ 1 2))
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (9 enodes)
* [exit]simplify:  Simplified to (pow (* 2 PI) (/ 1 2))
* [exit]simplify:  Simplified to (pow (* 2 PI) (/ 1 2))
* * * * [misc]progress:  [ 141 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* n (* PI 2)) (/ 1 2)) 1) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 142 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (exp (log (pow (* n (* PI 2)) (/ 1 2)))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (72 enodes)
* * [misc]simplify:  iters left: 2 (182 enodes)
* * [misc]simplify:  iters left: 1 (429 enodes)
* [exit]simplify:  Simplified to (fma (log (* PI n)) (/ 1 2) (/ (log 2) 2))
* [exit]simplify:  Simplified to (fma (log (* PI n)) (/ 1 2) (/ (log 2) 2))
* * * * [misc]progress:  [ 143 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (log (exp (pow (* n (* PI 2)) (/ 1 2)))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (exp (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (exp (pow (* (* PI n) 2) (/ 1 2)))
* * * * [misc]progress:  [ 144 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2))))
* [enter]simplify:  Simplifying (cbrt (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (cbrt (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (cbrt (pow (* (* PI n) 2) (/ 1 2)))
* * * * [misc]progress:  [ 145 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (cbrt (* (* (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ 1 2)))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (pow (pow (* (* n 2) PI) (/ 1 2)) 3)
* [exit]simplify:  Simplified to (pow (pow (* (* n 2) PI) (/ 1 2)) 3)
* * * * [misc]progress:  [ 146 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ 1 2)))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2)))
* [enter]simplify:  Simplifying (sqrt (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2)))
* * * * [misc]progress:  [ 147 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* 1 (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 148 / 159 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 149 / 159 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 150 / 159 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 151 / 159 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 152 / 159 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 153 / 159 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 154 / 159 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n)))))))))))))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n))))))))))))))))))))))))
* * * * [misc]progress:  [ 155 / 159 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* k (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 3) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n)))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* k (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 3) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))))))))
* * * * [misc]progress:  [ 156 / 159 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))))
* * * * [misc]progress:  [ 157 / 159 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (66 enodes)
* * [misc]simplify:  iters left: 3 (119 enodes)
* * [misc]simplify:  iters left: 2 (196 enodes)
* * [misc]simplify:  iters left: 1 (309 enodes)
* [exit]simplify:  Simplified to (/ (* (sqrt (* PI 2)) (/ (sqrt n) (sqrt k))) (pow (* n (* PI 2)) (/ k 2)))
* * * * [misc]progress:  [ 158 / 159 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (39 enodes)
* * [misc]simplify:  iters left: 4 (64 enodes)
* * [misc]simplify:  iters left: 3 (112 enodes)
* * [misc]simplify:  iters left: 2 (241 enodes)
* [exit]simplify:  Simplified to (/ (* (sqrt (* PI 2)) (/ (sqrt n) (sqrt k))) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 159 / 159 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (21 enodes)
* * [misc]simplify:  iters left: 5 (39 enodes)
* * [misc]simplify:  iters left: 4 (64 enodes)
* * [misc]simplify:  iters left: 3 (114 enodes)
* * [misc]simplify:  iters left: 2 (276 enodes)
* [exit]simplify:  Simplified to (/ (/ (/ (sqrt (* PI -2)) (pow (/ -1 n) 1/2)) (sqrt k)) (pow (* 2 (* PI n)) (/ k 2)))
* * * [misc]progress:  adding candidates to table
* * [misc]progress:  iteration 3 / 4
* * * [misc]progress:  picking best candidate
* [misc]none:  Fresh alts: 10
* [misc]none:  All alts: 11
* [misc]none:  Fresh alt: (λ (k n) (/ (+ (* (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (* (* k k) 1/8)) (+ (* (log n) (log n)) (* (log (* PI 2)) (log (* PI 2))))) (- (fma (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4)) (* (log (* PI 2)) (* (* k k) (log n))) (* (pow (* PI 2) 1/2) (pow n 1/2))) (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/2)) (fma k (log (* PI 2)) (* (log n) k))))) (sqrt k)))
* [misc]none:  Fresh alt: (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))
* [misc]none:  Non-fresh alt: (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))
* [misc]none:  Fresh alt: (λ (k n) (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))
* [misc]none:  Fresh alt: (λ (k n) (cbrt (/ (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (* n 2) PI) (/ (- 1 k) 2))))))
* [misc]none:  Fresh alt: (λ (k n) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))))
* [misc]none:  Fresh alt: (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))
* [misc]none:  Fresh alt: (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))
* [misc]none:  Fresh alt: (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))
* [misc]none:  Fresh alt: (λ (k n) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))
* [misc]none:  Fresh alt: (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* [misc]none:  Fresh alt indexes
* [misc]none:  (λ (k n) (/ (+ (* (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (* (* k k) 1/8)) (+ (* (log n) (log n)) (* (log (* PI 2)) (log (* PI 2))))) (- (fma (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4)) (* (log (* PI 2)) (* (* k k) (log n))) (* (pow (* PI 2) 1/2) (pow n 1/2))) (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/2)) (fma k (log (* PI 2)) (* (log n) k))))) (sqrt k))): 0
* [misc]none:  (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))): 1
* [misc]none:  (λ (k n) (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k))): 2
* [misc]none:  (λ (k n) (cbrt (/ (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))): 3
* [misc]none:  (λ (k n) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))))): 4
* [misc]none:  (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))): 5
* [misc]none:  (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))): 6
* [misc]none:  (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k))))): 7
* [misc]none:  (λ (k n) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k))))): 8
* [misc]none:  (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))): 9
* [misc]none:  Best fresh alt per point
* [misc]none:  (1.8808646764197965e+211 2.5246982378469546e+26): 1
* [misc]none:  (1.6056134078957726e-81 2.0654753198801362e+38): 0
* [misc]none:  (7.103138391473298e+203 4.991913674121936): 1
* [misc]none:  (3.4858004269611626e-130 1.2049116045831512e-306): 0
* [misc]none:  (6.950790143696708e-299 5.4754162277199545e+172): 2
* [misc]none:  (5.921232829081192e+298 4.202795939018271e+158): 1
* [misc]none:  (1.0394343208136068e-147 2.549337443302021e+95): 4
* [misc]none:  (8.998561140295877e-118 1.0700413456865293e+105): 2
* [misc]none:  (8.786431465145784e-134 5.784799823772606e-59): 0
* [misc]none:  (7.570282140481074e-146 1.0536210697171442e-75): 2
* [misc]none:  (2.6069457677667484e+227 2.421502054149278e+240): 1
* [misc]none:  (1.223212349341741e+210 6.083797656691426e+124): 1
* [misc]none:  (8.208194827684373e-221 3.697769831340425e-212): 0
* [misc]none:  (8.891699857124086e-248 4.741786767196371e-65): 0
* [misc]none:  (1.3953186618456118e-127 1.557559831312346e-158): 1
* [misc]none:  (2.8281459379799287e-223 5.282538753015419e+290): 4
* [misc]none:  (9.348662801176182e-287 6.983734680943984e+302): 2
* [misc]none:  (5.967105222859026e-287 1.4091628731054108e-252): 4
* [misc]none:  (6.812962331114006e-11 4.706553941824653e-123): 5
* [misc]none:  (8.467946903121652e+268 4.636077183112171e+61): 1
* [misc]none:  (6.29303766495041e-83 4.590548637242576e-128): 4
* [misc]none:  (3.213871973385624e-262 1.2212831165558396e+41): 4
* [misc]none:  (5.169867646134535e-44 1639899171736.8787): 2
* [misc]none:  (4.484657738495896e-296 1.2472467031958124e-111): 0
* [misc]none:  (2.630988489772908e-301 8.677705005606349e-192): 0
* [misc]none:  (1.9488674575590774e-219 1.2069336055576329e+297): 0
* [misc]none:  (1.0241786832856672e+275 6.65470667879038e+211): 1
* [misc]none:  (1.2388376925429903 1.0255532946660354e-189): 1
* [misc]none:  (9.403049449769395e-276 9.165910603949256e-61): 5
* [misc]none:  (1.5863716419697854e-305 2.982344844139708e-56): 4
* [misc]none:  (1.7933154604270656e+266 2.0688677513908958e+152): 1
* [misc]none:  (1.724441305022448e-204 1.0270093728501316e+208): 2
* [misc]none:  (1.6991537131626808e-286 2.269053283659137e+97): 0
* [misc]none:  (9.981425531265531e-234 1.5954750517027446e-306): 4
* [misc]none:  (2.6518292064535327e+113 1.1093632157717332e+299): 1
* [misc]none:  (3.5398920819374162e-22 9.097313058752706e+182): 2
* [misc]none:  (1.5662970496145718e+195 5.702344716829955e+277): 1
* [misc]none:  (7.374934384259559e+247 11809.004489533036): 1
* [misc]none:  (3.6837517387134946e+28 2.050724237210542e+237): 1
* [misc]none:  (8.0762754355927e-102 3.924619293995995e+294): 1
* [misc]none:  (6.272017688866778e+294 1475344134974741.5): 1
* [misc]none:  (8.226540875316075e-282 2.9295012263119104e-210): 2
* [misc]none:  (1.1567434189356451e+31 5.033252764508812e+139): 1
* [misc]none:  (1.2230943992415108e+36 2.3021043888776224e+278): 1
* [misc]none:  (5.69357845447944e-284 4.6895957006840323e-293): 7
* [misc]none:  (2.1402493760044758e-237 7.018010476645137e+19): 5
* [misc]none:  (5.836990398641413e+278 8.69236263846091e+82): 1
* [misc]none:  (3.866067932485071e+134 65634290206.02169): 1
* [misc]none:  (3.353542833099014e-216 4.562538568139802e-253): 4
* [misc]none:  (1.9595331698208332e+267 1.734899565778851e+119): 1
* [misc]none:  (6.162344767386832e-71 7.346570549506355e+179): 0
* [misc]none:  (1.7754717488663857e+121 3.494659494474523e+27): 1
* [misc]none:  (1.355389858139596e-211 5.3134050984497146e-45): 0
* [misc]none:  (1.7558002847649968e-150 2.8327022791344117e+186): 0
* [misc]none:  (55126108376913.92 1.4270114976186918e+130): 1
* [misc]none:  (2.1677429926485946e-242 1.7597566772342396e-204): 6
* [misc]none:  (5.672231019728725e-161 4.978844845564056e+84): 2
* [misc]none:  (1.061192968818359e-298 3.4390539626492262e-136): 4
* [misc]none:  (1.8851052094553197e-277 9.953566511035923e-308): 2
* [misc]none:  (2.984618116231375e+88 2.296813947529187e+143): 1
* [misc]none:  (1.1631529018053348e+89 2.354140414905433e+187): 1
* [misc]none:  (2.216720871752684e-160 3.1263904065616715e+268): 2
* [misc]none:  (5.57997653477477e-111 1.5363278110829953e+73): 0
* [misc]none:  (1.0611909380115695e-87 1.295915517178257e-293): 0
* [misc]none:  (4.355922221873984e-239 9.031875737069326e-50): 1
* [misc]none:  (2.648998082938836e-121 6.334062294691454e-67): 4
* [misc]none:  (4.293605985901814e-150 8.709273807481483e+69): 1
* [misc]none:  (7.932758618838293e-45 1.0062256135654257e-12): 8
* [misc]none:  (1.0135699554608461e-103 1.0001039793852175e+214): 1
* [misc]none:  (3.306163540346375e+188 2.601454323484488e+217): 1
* [misc]none:  (4.4505875876233544e-249 1.1235340410501106e+40): 4
* [misc]none:  (7.344373535448876e-228 2.204405021953709e+104): 0
* [misc]none:  (4.0855428097798646e-150 2.727229900429018e-249): 3
* [misc]none:  (6.298377803380903e-45 4.638301673824566e+198): 0
* [misc]none:  (1.5663895259426407e-227 6.068461153265776e+155): 0
* [misc]none:  (1.9502784809800982e-261 1.23965605071982e+102): 0
* [misc]none:  (5.141713922465631e+255 5.469890187179831e+40): 1
* [misc]none:  (1.8526578386426445e-175 2.8275326066295656e+288): 5
* [misc]none:  (2.3857467758299983e-165 2.359532888074915e-308): 3
* [misc]none:  (7.679851300456857e+192 6.240981309981708e+218): 1
* [misc]none:  (6.9138624756046875e-279 1.0801316959056566e+247): 5
* [misc]none:  (5.335152348688887e+90 6.4886135160508705e+78): 1
* [misc]none:  (1.5943160592835199e+304 1.045121272346536e+179): 1
* [misc]none:  (4.479940531531753e+77 2.569188313217193e+219): 1
* [misc]none:  (7.199360760804118e+153 1.939449439157158e+147): 1
* [misc]none:  (1.9704554468969366e-117 1.9049791632950265e+52): 0
* [misc]none:  (1.1992937437582141e+294 1.3324640280655562e+298): 1
* [misc]none:  (1.2677456751249112e+255 1.0431052541215851e+129): 1
* [misc]none:  (1.2488817056340531e-83 4.423913073109955e+231): 0
* [misc]none:  (7.551810594497609e+137 7.747271752238544e+41): 1
* [misc]none:  (3532359.12009671 2.649701137905713e+290): 1
* [misc]none:  (5.4448976709671744e+17 5.816578520527468): 1
* [misc]none:  (7.890973219793982e-290 5.75019396725634e+90): 9
* [misc]none:  (3.461507194664208e-287 9.464306683916357e-205): 4
* [misc]none:  (6.80008622391683e+66 8.776884557521719e+128): 1
* [misc]none:  (2.4032932153833967e-307 1.0014468698414084e+182): 2
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* [misc]none:  (1.3375485056693512e-111 7.13883396967432e-194): 4
* [misc]none:  (1.8621029182579468e-205 3.4802756915156133e+100): 0
* [misc]none:  (4.242743718877097e-153 6.253830639689608e+48): 3
* [misc]none:  (1.1280342039397313e-68 1.9787651979095224e-233): 0
* [misc]none:  (7.395347580247437e-155 1.057029999564979e+266): 0
* [misc]none:  (3.708681723916961e-166 3.7225891139822097e-149): 1
* [misc]none:  (1.0603280248233059e+259 3.023560588739892e+66): 1
* [misc]none:  (1.2375077238277152e+278 1.0707401671756225e+27): 1
* [misc]none:  (6.821630588440869e-72 1.4176223018107286e+298): 0
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* [misc]none:  (2.0740720677887988e-269 5.879433969539391e+176): 1
* [misc]none:  (3.896120055573036e-95 3.736727437689099e+118): 2
* [misc]none:  (1.9106253173901505e-99 9.727763832869165e-247): 0
* [misc]none:  (3.770567993098138e-237 1.8052434248121697e+137): 9
* [misc]none:  (3.3901294614269435e+288 4.464113006006272e+227): 1
* [misc]none:  (1.783093648240505e+91 1.0537694770045353e+112): 1
* [misc]none:  (1.1370819323594066e-237 3.4501574698600073e+277): 5
* [misc]none:  (5.762919464003385e+81 1.644080282901123e+165): 1
* [misc]none:  (1.4754314640450108e+138 6.420193336082039e+47): 1
* [misc]none:  (4.068001539723228e-123 2.6370190625330334e+154): 2
* [misc]none:  (1.1434045325783696e-222 2.775602789549491e-17): 6
* [misc]none:  (5.358290489185327e-250 4.03836531268848e+246): 5
* [misc]none:  (1.3577803556509862e-104 2.6167414441853318e-297): 0
* [misc]none:  (5.197437093722413e-33 2.0595604121015856e-163): 3
* [misc]none:  (5.2496749459398586e+42 1.9984736776578106e+277): 1
* [misc]none:  (1.608938475476452e+209 1.1400329767261696e+196): 1
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* [misc]none:  (5.111842665639857e-111 1.1720271068664444e+161): 0
* [misc]none:  (2.0595328660748074e-67 3.1294254994459577e-155): 2
* [misc]none:  (3.4456967347035406e-76 1.9814153199736458e-72): 3
* [misc]none:  (8.518821522570516e-60 1.2001411983497562e+106): 5
* [misc]none:  (9.822572373265172e-201 2.558616615476855e-60): 6
* [misc]none:  (9.396150167355826e+262 4.903091423835763e+77): 1
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* [misc]none:  (4.546382622074157e-108 3.8495114831696875e-48): 0
* [misc]none:  (1448560715879084.8 2.8530891400108187e+124): 1
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* [misc]none:  (9.153145296775212e-39 2.077022997927436e-139): 0
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* [misc]none:  (2.9573507267394465e-308 4.1771154955437857e-262): 4
* [misc]none:  (5.532920533179142e-152 7.554314233014913e+168): 0
* [misc]none:  (7.775944736851254e-206 7.437550583183719e+153): 0
* [misc]none:  (3.899173844391897e+120 3.705546267531316e+263): 1
* [misc]none:  (5.5950620368202944e-145 4.107096789321886e+47): 3
* [misc]none:  (2.9754862723359673e-209 2.5416139134760705e-289): 0
* [misc]none:  (3.5927665975113976e-239 4.614798558690456e-297): 0
* [misc]none:  (2.668103807085715e+100 5.401731707229941e+72): 1
* [misc]none:  (3.891498638245715e-204 1.8093455138130522e+133): 9
* [misc]none:  (5.932902354540652e-124 2.9604954362664366e+289): 5
* [misc]none:  (3.0539888630764254e-239 9.953908495433605e+227): 0
* [misc]none:  (2.0980661301565718e-60 1.9558316322795932e+229): 1
* [misc]none:  (1.0024360019170988e-151 7.5175772698725994e+230): 5
* [misc]none:  (1.8900938929376038e+24 1.8609002361575433e+134): 1
* [misc]none:  (5.3266849932814836e+126 2.901363739745472e+210): 1
* [misc]none:  (1.6992513309501048e-129 2.550558153214631e-264): 5
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* [misc]none:  All alt indexes
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* [misc]none:  (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))): 1
* [misc]none:  (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))): 2
* [misc]none:  (λ (k n) (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k))): 3
* [misc]none:  (λ (k n) (cbrt (/ (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))): 4
* [misc]none:  (λ (k n) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))))): 5
* [misc]none:  (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))): 6
* [misc]none:  (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))): 7
* [misc]none:  (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k))))): 8
* [misc]none:  (λ (k n) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k))))): 9
* [misc]none:  (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))): 10
* [misc]none:  Best alt per point
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* [misc]none:  (4.546382622074157e-108 3.8495114831696875e-48): 0
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* [misc]none:  (5.532920533179142e-152 7.554314233014913e+168): 0
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* [misc]none:  (3.5927665975113976e-239 4.614798558690456e-297): 0
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* [misc]none:  (7.149081725669718e+245 3.1834201935962926e+247): 1
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* [misc]none:  (2.0256515578089416e+140 8.501791068840968e+197): 1
* [misc]none:  (9.544656038170093e+242 1.6519069419163414e+176): 1
* [misc]none:  (7.304105671735325e-242 7.033032775041187e+285): 0
* [misc]none:  (6.81321242648181e-289 1.45222983614977e-105): 1
* [misc]none:  (1.5262661067350401e-10 7.753245307187778e+31): 0
* [misc]none:  (1.4426514360168247e-145 4.904168640083974e+160): 1
* [misc]none:  (7.646129439560017e+176 3.1611172476808926e+209): 1
* [misc]none:  (5.105992271675965e-91 4.769518420383615e-198): 1
* [misc]none:  (6.798513332593515e-94 1.4806341275368096e-15): 0
* [misc]none:  (3.821526442421431e+297 1.2464063226445322e+209): 1
* [misc]none:  (1.09010428308076e-124 6.739673456854575e+249): 1
* [misc]none:  (0.36218343358512595 1.1084878850555635e+104): 2
* [misc]none:  (4.657146692902141e+280 1.9733854398064837e+215): 1
* [misc]none:  (5.412740199293554e+26 6.234082350070098e+32): 1
* [misc]none:  (6.4866276434875264e+44 3.175834271419552e+52): 1
* [misc]none:  (9.151015091612054e-197 1.6592153710205133e-269): 7
* [misc]none:  (6.922703552766224e-109 7.522858670517918e+259): 5
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* [misc]none:  (1.5567451015893508e-50 3.408101142682615e-113): 0
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* [misc]none:  (9.254023538292273e-258 2.617971147092364e-76): 2
* [misc]none:  (2.931668337478436e+126 1.4018724764197611e+160): 1
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* [misc]none:  (3.34193429381633e-274 6.07560242102484e+85): 0
* [misc]none:  (5.316440102938414e-63 24130443289213716.0): 5
* [misc]none:  (1.52221681471073e+30 1.552064650669455e+142): 1
* [misc]none:  (5.946958643597572e-214 9.722495709355246e-119): 1
* [misc]none:  (3.9615177849779133e-143 1.1510307484496886e-51): 4
* [misc]none:  (4.116349531400419e+59 3.7023764599519414e+64): 1
* [misc]none:  (3.19314088639968e-300 7.10649025136688e+263): 3
* [misc]none:  (2.6209483109511002e-99 1.0152763243033748e+142): 2
* [misc]none:  (3.9436987604242746e-188 1.2987545615858837e-229): 0
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* [misc]none:  (5.600091178152213e-210 7.360949206952843e-212): 1
* [misc]none:  (5.235172412726717e+152 3.9088394890922115e+223): 1
* [misc]none:  (1.2265182674709907e+198 3.136601910786915e+46): 1
* [misc]none:  (2.296991649120878e+37 3.5701416837580245e+199): 1
* [misc]none:  (4.984374966308376e+225 1.882765755995834e+18): 1
* [misc]none:  (1.939469755263449e-274 2.0558821145728443e-244): 0
* [misc]none:  (7.118304679887613e-64 2.3966615634258388e-54): 0
* [misc]none:  (5.6334012743355e-180 2.2204044591450003e+49): 0
* [misc]none:  (1.2391428993123195e-53 3.206221419912265e+51): 4
* [misc]none:  (5.976566162781828e-262 4.0522267480412145e+189): 0
* [misc]none:  (1.2926844442603449e-272 6.777020097920311e+216): 8
* [misc]none:  (1.4932339006735016e+157 3.1812804254524387e+233): 1
* [misc]none:  (3.7476721237841876e-281 4.811543151950025e-33): 0
* [misc]none:  (6.525431496731668e-64 1.0982823072397984e+136): 2
* [misc]none:  (2.704077310435608e-253 3.1639399211332326e+205): 0
* [misc]none:  (2.7511202385052856e-18 3.82956155404422e-299): 8
* [misc]none:  (4.296582624822391e-200 1.733700273392293e+77): 2
* [misc]none:  (6.683383915725252e-271 1.830961252259433e-59): 2
* [misc]none:  (4.068667347744151e-179 8.630725328355339e+266): 1
* [misc]none:  (2.5976261349663673e+194 4.713564345937309e+51): 1
* [misc]none:  (4.807691125223642e+307 2.4189569765995642e+235): 1
* [misc]none:  (5.0806815187366375e+166 4.873854048773888e+106): 1
* [misc]none:  (1.2300916721937489e+185 5.9776582784273185e+256): 1
* [misc]none:  (3.003386221248247e-77 7.613990227232114e-101): 1
* [misc]none:  (3.438873899519122e+171 1.8186504690640068e+223): 1
* [misc]none:  (5.515506992492392e-277 2.595646488837273e-219): 0
* [misc]none:  (3.108236652528406e-297 7.181266914182018e-165): 0
* [misc]none:  (7.707611608802171e+62 1.152518328416828e+180): 1
* [misc]none:  (4.5690448860660455e-67 1.2792918576789026e+83): 5
* [misc]none:  (3.934156464498665e-121 1.9851718582837827e+233): 0
* [misc]none:  (2797.2682494851097 5.51985688247549e+99): 1
* [misc]none:  (0.0005921945720183679 2.8115284450926948e-120): 2
* [misc]none:  (2.5144530485773557e+177 3.96896356073862e+48): 1
* [misc]none:  (2.9394468165964015e-257 1.5225460242504859e+106): 0
* [misc]none:  (3.271929098149761e-144 7.5398414005163625e+267): 0
* [misc]none:  (6.604350361119279e-291 3.861477555295976e-66): 0
* [misc]none:  (8.124998850854922e-91 2.0152844845402166e-297): 0
* [misc]none:  (8.604490187894414e-112 1.3704041407198253e+228): 1
* [misc]none:  (1.6519797365083582e+195 6.316732900885901e+249): 1
* [misc]none:  (2.0115496002781107e-145 7.084575776306543e+174): 0
* [misc]none:  (2.5502245720775025e+302 3.7105227033705403e+214): 1
* [misc]none:  (6.821311827045434e-30 2.8401584433220846e+96): 1
* [misc]none:  (2.6830861914889714e-191 5.086243151153881e+259): 1
* [misc]none:  (1.4517955555700533e-57 3.278760905350017e+239): 5
* [misc]none:  (9.422179697047065e-164 1.3639040980897921e-39): 0
* [misc]none:  (2.8344220272269968e+166 1.5252878664938466e+85): 1
* [misc]none:  (1.9836536473017196e-256 6.844414014257645e+204): 1
* [misc]none:  Picked alt (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))
* * * * [misc]pick:  Picked  #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 4 ] rewriting at (2 2 2 1)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2 1 1)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2 1)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 4 ] generating series at (2 2 2 1)
* [misc]approximate:  Taking taylor expansion of (* n (* PI 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* n (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) n) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 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) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 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) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 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 (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
* * * * [misc]progress:  [ 2 / 4 ] generating series at (2 1 1)
* [misc]approximate:  Taking taylor expansion of (* n (* PI 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* n (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) n) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 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 (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 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) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 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) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 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 (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
* * * * [misc]progress:  [ 3 / 4 ] generating series at (2)
* [misc]approximate:  Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ 1 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* n (* PI 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* n (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in k
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of (* PI 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 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* n (* 2 PI)) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
* [misc]taylor:  Taking taylor expansion of (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ k 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* n (* PI 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* n (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in k
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of (* PI 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 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* n (* 2 PI)) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp 0) into 1
* [misc]backup-simplify:  Simplify (* 0 1) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log (* 2 (* n PI)))) 1) 1)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (+ (* 0 (* 1/2 (log (* 2 (* n PI))))) (* +nan.0 1)) into (- +nan.0)
* [misc]backup-simplify:  Simplify (/ (pow (* 2 (* n PI)) 1/2) (- +nan.0)) into (* +nan.0 (sqrt (* n (* 2 PI))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* n (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* n (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* n (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* n (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 k) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* k (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (* (sqrt k) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k))) into (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* n (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* n (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* n (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* n (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 k) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* k (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (* (sqrt k) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k))) into (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (+ (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* k (+ (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 0 (+ (log (* 2 PI)) (log n))) into 0
* [misc]backup-simplify:  Simplify (* 1/2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (+ (log (* 2 PI)) (log n)))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (+ (log (* 2 PI)) (log n))) (* 0 0)) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))
* [misc]backup-simplify:  Simplify (exp 0) into 1
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 1) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (sqrt k) 0) (* 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k))) (+ (* (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1) 1)))) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) +nan.0) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k))) (+ (* (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)))) (* 0 (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (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 (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (+ (log (* 2 PI)) (log n))) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) 1)) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) +nan.0) (+ (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) +nan.0) (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) 0))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k))) (+ (* (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)))) (* 0 (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)))) (* 0 (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (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 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (+ (log (* 2 PI)) (log n))) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 3) 6)) (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2))))))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2)))))) 1)) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) (/ (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) 1)) (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (- (+ (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (log n)))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 3))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 3))) (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow (log n) 2))))))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) +nan.0) (+ (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) +nan.0) (+ (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) +nan.0) (* (- (+ (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (log n)))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 3))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 3))) (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow (log n) 2)))))))) 0)))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))))))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))))))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n))))))))))))))))))))))))
* [misc]approximate:  Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (* (sqrt (/ 1 k)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2)))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (* (sqrt (/ 1 k)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (* PI 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 n) 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 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 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) 1/2)
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 n) 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 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 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))
* [misc]backup-simplify:  Simplify (* 0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* +nan.0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) into (- (* +nan.0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))
* [misc]backup-simplify:  Simplify (/ (pow (* 2 (/ PI n)) 1/2) (- (* +nan.0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into (* +nan.0 (* (sqrt (/ (* 2 PI) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (* (sqrt (/ 1 k)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (* (sqrt (/ 1 k)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (- (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (- (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k
* [misc]taylor:  Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 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 (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) (* 0 (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 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 (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) (* 0 (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) (* 0 (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* k (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 3) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))))))))
* [misc]approximate:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (* (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2)))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (* (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2)))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) 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 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 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* -2 (/ PI n))))) into (pow (* -2 (/ PI n)) 1/2)
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) 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 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 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* -2 (/ PI n)))) into (* -1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))
* [misc]backup-simplify:  Simplify (* 0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))
* [misc]backup-simplify:  Simplify (/ (pow (* -2 (/ PI n)) 1/2) (- (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) into (* +nan.0 (* (sqrt (/ (* PI -2) n)) (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (* (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (* (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))
* [misc]taylor:  Taking taylor expansion of (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (- (log (* -2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (- (log (* -2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* -2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* -2 PI) in k
* [misc]taylor:  Taking taylor expansion of -2 in k
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k
* [misc]taylor:  Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k
* [misc]taylor:  Taking taylor expansion of -1/2 in k
* [misc]backup-simplify:  Simplify -1/2 into -1/2
* [misc]taylor:  Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k
* [misc]taylor:  Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* -2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* -2 PI) in k
* [misc]taylor:  Taking taylor expansion of -2 in k
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* -1/2 (- (log (* -2 PI)) (log n))) into (* -1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]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 (/ (- (log (* -2 PI)) (log n)) k))) 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (sqrt (/ -1 k)) 0) (* 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) (/ 0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))
* [misc]backup-simplify:  Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (+ (* (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 (+ (* (sqrt (/ -1 k)) 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) (/ 0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))) (* 0 (/ 0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))
* [misc]backup-simplify:  Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (+ (* (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))))
* * * * [misc]progress:  [ 4 / 4 ] generating series at (2 1)
* [misc]approximate:  Taking taylor expansion of (pow (* n (* PI 2)) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* n (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* n (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* n (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* n (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]approximate:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n)))))
* [misc]approximate:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) 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 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 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* -2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* -2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* -2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 1)))) 24) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 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) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* -2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* -2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* -2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* -2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* -2 PI) 1)))) 120) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 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 (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* -2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* -2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* -2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* -2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* -2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* -2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* -2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* -2 PI) 1)))) 720) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n)))))
* * * [misc]progress:  simplifying candidates
* * * * [misc]progress:  [ 1 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (log1p (expm1 (* n (* PI 2)))) (/ k 2)))))>
* [enter]simplify:  Simplifying (expm1 (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (expm1 (* (* n 2) PI))
* [exit]simplify:  Simplified to (expm1 (* (* n 2) PI))
* * * * [misc]progress:  [ 2 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (expm1 (log1p (* n (* PI 2)))) (/ k 2)))))>
* [enter]simplify:  Simplifying (log1p (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (log1p (* (* n 2) PI))
* [exit]simplify:  Simplified to (log1p (* (* n 2) PI))
* * * * [misc]progress:  [ 3 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (pow (* n (* PI 2)) 1) (/ k 2)))))>
* * * * [misc]progress:  [ 4 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (exp (log (* n (* PI 2)))) (/ k 2)))))>
* [enter]simplify:  Simplifying (log (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (log (* (* PI n) 2))
* [exit]simplify:  Simplified to (log (* (* PI n) 2))
* * * * [misc]progress:  [ 5 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (log (exp (* n (* PI 2)))) (/ k 2)))))>
* [enter]simplify:  Simplifying (exp (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* * [misc]simplify:  iters left: 2 (35 enodes)
* * [misc]simplify:  iters left: 1 (47 enodes)
* [exit]simplify:  Simplified to (pow (exp 2) (* PI n))
* [exit]simplify:  Simplified to (pow (exp 2) (* PI n))
* * * * [misc]progress:  [ 6 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ k 2)))))>
* [enter]simplify:  Simplifying (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (18 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2)))
* [exit]simplify:  Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2)))
* [enter]simplify:  Simplifying (cbrt (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (cbrt (* (* n 2) PI))
* [exit]simplify:  Simplified to (cbrt (* (* n 2) PI))
* * * * [misc]progress:  [ 7 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (cbrt (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))) (/ k 2)))))>
* [enter]simplify:  Simplifying (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (59 enodes)
* * [misc]simplify:  iters left: 3 (203 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) 3)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) 3)
* * * * [misc]progress:  [ 8 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* (sqrt (* n (* PI 2))) (sqrt (* n (* PI 2)))) (/ k 2)))))>
* [enter]simplify:  Simplifying (sqrt (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* [enter]simplify:  Simplifying (sqrt (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* * * * [misc]progress:  [ 9 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* 1 (* n (* PI 2))) (/ k 2)))))>
* * * * [misc]progress:  [ 10 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* (* n PI) 2) (/ k 2)))))>
* [enter]simplify:  Simplifying (* n PI)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* PI n)
* [exit]simplify:  Simplified to (* PI n)
* * * * [misc]progress:  [ 11 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* (* PI 2) n) (/ k 2)))))>
* * * * [misc]progress:  [ 12 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (log1p (expm1 (* n (* PI 2)))) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (expm1 (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (expm1 (* (* n 2) PI))
* [exit]simplify:  Simplified to (expm1 (* (* n 2) PI))
* * * * [misc]progress:  [ 13 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (expm1 (log1p (* n (* PI 2)))) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (log1p (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (log1p (* (* n 2) PI))
* [exit]simplify:  Simplified to (log1p (* (* n 2) PI))
* * * * [misc]progress:  [ 14 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* n (* PI 2)) 1) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* * * * [misc]progress:  [ 15 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (exp (log (* n (* PI 2)))) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (log (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (log (* (* PI n) 2))
* [exit]simplify:  Simplified to (log (* (* PI n) 2))
* * * * [misc]progress:  [ 16 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (log (exp (* n (* PI 2)))) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (exp (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* * [misc]simplify:  iters left: 2 (35 enodes)
* * [misc]simplify:  iters left: 1 (47 enodes)
* [exit]simplify:  Simplified to (pow (exp 2) (* PI n))
* [exit]simplify:  Simplified to (pow (exp 2) (* PI n))
* * * * [misc]progress:  [ 17 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (18 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2)))
* [exit]simplify:  Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2)))
* [enter]simplify:  Simplifying (cbrt (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (cbrt (* (* n 2) PI))
* [exit]simplify:  Simplified to (cbrt (* (* n 2) PI))
* * * * [misc]progress:  [ 18 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (cbrt (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (59 enodes)
* * [misc]simplify:  iters left: 3 (203 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) 3)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) 3)
* * * * [misc]progress:  [ 19 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (sqrt (* n (* PI 2))) (sqrt (* n (* PI 2)))) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (sqrt (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* [enter]simplify:  Simplifying (sqrt (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* * * * [misc]progress:  [ 20 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* 1 (* n (* PI 2))) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* * * * [misc]progress:  [ 21 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* n PI) 2) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (* n PI)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* PI n)
* [exit]simplify:  Simplified to (* PI n)
* * * * [misc]progress:  [ 22 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* PI 2) n) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* * * * [misc]progress:  [ 23 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (log1p (expm1 (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (expm1 (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (31 enodes)
* [exit]simplify:  Simplified to (expm1 (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (expm1 (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 24 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (expm1 (log1p (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (log1p (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (31 enodes)
* [exit]simplify:  Simplified to (log1p (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (log1p (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 25 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (pow (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) 1))>
* * * * [misc]progress:  [ 26 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (* (log (* n (* PI 2))) (/ 1 2)) (+ (log (sqrt k)) (* (log (* n (* PI 2))) (/ k 2))))))>
* [enter]simplify:  Simplifying (- (* (log (* n (* PI 2))) (/ 1 2)) (+ (log (sqrt k)) (* (log (* n (* PI 2))) (/ k 2))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (81 enodes)
* * [misc]simplify:  iters left: 3 (237 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 27 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (* (log (* n (* PI 2))) (/ 1 2)) (+ (log (sqrt k)) (* (log (* n (* PI 2))) (/ k 2))))))>
* [enter]simplify:  Simplifying (- (* (log (* n (* PI 2))) (/ 1 2)) (+ (log (sqrt k)) (* (log (* n (* PI 2))) (/ k 2))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (81 enodes)
* * [misc]simplify:  iters left: 3 (237 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 28 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (* (log (* n (* PI 2))) (/ 1 2)) (+ (log (sqrt k)) (log (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (- (* (log (* n (* PI 2))) (/ 1 2)) (+ (log (sqrt k)) (log (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (78 enodes)
* * [misc]simplify:  iters left: 3 (234 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 29 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (* (log (* n (* PI 2))) (/ 1 2)) (log (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (- (* (log (* n (* PI 2))) (/ 1 2)) (log (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (35 enodes)
* * [misc]simplify:  iters left: 4 (65 enodes)
* * [misc]simplify:  iters left: 3 (161 enodes)
* [exit]simplify:  Simplified to (fma (log (* PI (* n 2))) (/ 1 2) (fma (- (/ k 2)) (log (* PI (* n 2))) (- (log (sqrt k)))))
* [exit]simplify:  Simplified to (fma (log (* PI (* n 2))) (/ 1 2) (fma (- (/ k 2)) (log (* PI (* n 2))) (- (log (sqrt k)))))
* * * * [misc]progress:  [ 30 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (* (log (* n (* PI 2))) (/ 1 2)) (+ (log (sqrt k)) (* (log (* n (* PI 2))) (/ k 2))))))>
* [enter]simplify:  Simplifying (- (* (log (* n (* PI 2))) (/ 1 2)) (+ (log (sqrt k)) (* (log (* n (* PI 2))) (/ k 2))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (81 enodes)
* * [misc]simplify:  iters left: 3 (237 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 31 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (* (log (* n (* PI 2))) (/ 1 2)) (+ (log (sqrt k)) (* (log (* n (* PI 2))) (/ k 2))))))>
* [enter]simplify:  Simplifying (- (* (log (* n (* PI 2))) (/ 1 2)) (+ (log (sqrt k)) (* (log (* n (* PI 2))) (/ k 2))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (81 enodes)
* * [misc]simplify:  iters left: 3 (237 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 32 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (* (log (* n (* PI 2))) (/ 1 2)) (+ (log (sqrt k)) (log (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (- (* (log (* n (* PI 2))) (/ 1 2)) (+ (log (sqrt k)) (log (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (78 enodes)
* * [misc]simplify:  iters left: 3 (234 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 33 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (* (log (* n (* PI 2))) (/ 1 2)) (log (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (- (* (log (* n (* PI 2))) (/ 1 2)) (log (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (35 enodes)
* * [misc]simplify:  iters left: 4 (65 enodes)
* * [misc]simplify:  iters left: 3 (161 enodes)
* [exit]simplify:  Simplified to (fma (log (* PI (* n 2))) (/ 1 2) (fma (- (/ k 2)) (log (* PI (* n 2))) (- (log (sqrt k)))))
* [exit]simplify:  Simplified to (fma (log (* PI (* n 2))) (/ 1 2) (fma (- (/ k 2)) (log (* PI (* n 2))) (- (log (sqrt k)))))
* * * * [misc]progress:  [ 34 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (log (pow (* n (* PI 2)) (/ 1 2))) (+ (log (sqrt k)) (* (log (* n (* PI 2))) (/ k 2))))))>
* [enter]simplify:  Simplifying (- (log (pow (* n (* PI 2)) (/ 1 2))) (+ (log (sqrt k)) (* (log (* n (* PI 2))) (/ k 2))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (35 enodes)
* * [misc]simplify:  iters left: 4 (77 enodes)
* * [misc]simplify:  iters left: 3 (219 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 35 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (log (pow (* n (* PI 2)) (/ 1 2))) (+ (log (sqrt k)) (* (log (* n (* PI 2))) (/ k 2))))))>
* [enter]simplify:  Simplifying (- (log (pow (* n (* PI 2)) (/ 1 2))) (+ (log (sqrt k)) (* (log (* n (* PI 2))) (/ k 2))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (35 enodes)
* * [misc]simplify:  iters left: 4 (77 enodes)
* * [misc]simplify:  iters left: 3 (219 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 36 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (log (pow (* n (* PI 2)) (/ 1 2))) (+ (log (sqrt k)) (log (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (- (log (pow (* n (* PI 2)) (/ 1 2))) (+ (log (sqrt k)) (log (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (61 enodes)
* * [misc]simplify:  iters left: 3 (156 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* n 2) PI)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 37 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (log (pow (* n (* PI 2)) (/ 1 2))) (log (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (- (log (pow (* n (* PI 2)) (/ 1 2))) (log (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (55 enodes)
* * [misc]simplify:  iters left: 3 (128 enodes)
* [exit]simplify:  Simplified to (- (* (log (* PI (* n 2))) (- (/ 1 2) (/ k 2))) (log (sqrt k)))
* [exit]simplify:  Simplified to (- (* (log (* PI (* n 2))) (- (/ 1 2) (/ k 2))) (log (sqrt k)))
* * * * [misc]progress:  [ 38 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (exp (log (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (log (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (41 enodes)
* * [misc]simplify:  iters left: 3 (71 enodes)
* * [misc]simplify:  iters left: 2 (185 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* 2 PI) n)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* 2 PI) n)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 39 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (log (exp (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (exp (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (31 enodes)
* [exit]simplify:  Simplified to (exp (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (exp (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 40 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (/ (* (* (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ 1 2))) (* (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* n (* PI 2)) (/ k 2)) (pow (* n (* PI 2)) (/ k 2))) (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (* (* (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ 1 2))) (* (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* n (* PI 2)) (/ k 2)) (pow (* n (* PI 2)) (/ k 2))) (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (41 enodes)
* * [misc]simplify:  iters left: 4 (134 enodes)
* [exit]simplify:  Simplified to (* (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (* (pow (* (* PI n) 2) (/ k 2)) (pow (* (* PI n) 2) (/ k 2)))) (/ (pow (* (* PI n) 2) (/ 1 2)) (/ (* (sqrt k) k) (pow (* (* PI n) 2) (/ 1 2)))))
* [exit]simplify:  Simplified to (* (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (* (pow (* (* PI n) 2) (/ k 2)) (pow (* (* PI n) 2) (/ k 2)))) (/ (pow (* (* PI n) 2) (/ 1 2)) (/ (* (sqrt k) k) (pow (* (* PI n) 2) (/ 1 2)))))
* * * * [misc]progress:  [ 41 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (/ (* (* (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ 1 2))) (* (* (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (* (* (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ 1 2))) (* (* (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (121 enodes)
* * [misc]simplify:  iters left: 3 (448 enodes)
* [exit]simplify:  Simplified to (* (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (* (pow (* (* PI n) 2) (/ k 2)) k)) (* (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (* (pow (* (* PI n) 2) (/ k 2)) k)) (* (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k))))
* * * * [misc]progress:  [ 42 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (* (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* (* n 2) PI) (/ k 2)) (sqrt k)))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* (* n 2) PI) (/ k 2)) (sqrt k)))))
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* (* n 2) PI) (/ k 2)) (sqrt k)))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* (* n 2) PI) (/ k 2)) (sqrt k)))))
* [enter]simplify:  Simplifying (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (31 enodes)
* [exit]simplify:  Simplified to (cbrt (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (cbrt (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 43 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (* (* (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (* (* (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (81 enodes)
* * [misc]simplify:  iters left: 3 (299 enodes)
* [exit]simplify:  Simplified to (/ (* (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2))) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)))) (* (/ (sqrt k) (pow (* (* 2 PI) n) (/ 1 2))) (* k (pow (* (* 2 PI) n) (/ k 2)))))
* [exit]simplify:  Simplified to (/ (* (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2))) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)))) (* (/ (sqrt k) (pow (* (* 2 PI) n) (/ 1 2))) (* k (pow (* (* 2 PI) n) (/ k 2)))))
* * * * [misc]progress:  [ 44 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (31 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (sqrt (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* [enter]simplify:  Simplifying (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (31 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (sqrt (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 45 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (- (pow (* n (* PI 2)) (/ 1 2))) (- (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))))>
* [enter]simplify:  Simplifying (- (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (- (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (- (pow (* (* PI n) 2) (/ 1 2)))
* [enter]simplify:  Simplifying (- (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (* (pow (* (* n PI) 2) (/ k 2)) (- (sqrt k)))
* [exit]simplify:  Simplified to (* (pow (* (* n PI) 2) (/ k 2)) (- (sqrt k)))
* * * * [misc]progress:  [ 46 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow n (/ 1 2)) (sqrt k)) (/ (pow (* PI 2) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (/ (pow n (/ 1 2)) (sqrt k))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* [exit]simplify:  Simplified to (/ (pow n (/ 1 2)) (sqrt k))
* [exit]simplify:  Simplified to (/ (pow n (/ 1 2)) (sqrt k))
* [enter]simplify:  Simplifying (/ (pow (* PI 2) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (/ (pow (* 2 PI) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)))
* [exit]simplify:  Simplified to (/ (pow (* 2 PI) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)))
* * * * [misc]progress:  [ 47 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt k)) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) (sqrt k))
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) (sqrt k))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (pow (* (* PI n) 2) (/ k 2)))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 48 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt k)) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (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 (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt k))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt k))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (pow (* (* PI n) 2) (/ k 2)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 49 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt k))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (6 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt k))
* [exit]simplify:  Simplified to (/ 1 (sqrt k))
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 50 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))))>
* * * * [misc]progress:  [ 51 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow (* n (* PI 2)) (/ 1 2)) (/ 1 (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ 1 (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))
* * * * [misc]progress:  [ 52 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) (pow (* n (* PI 2)) (/ 1 2)))))>
* [enter]simplify:  Simplifying (/ (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (38 enodes)
* * [misc]simplify:  iters left: 1 (39 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (sqrt k) (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 53 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt k)) (pow (* n (* PI 2)) (/ k 2))))>
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ 1 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) (/ 1 2)) (sqrt k))
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k))
* * * * [misc]progress:  [ 54 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow n (/ 1 2)) (/ (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) (pow (* PI 2) (/ 1 2)))))>
* [enter]simplify:  Simplifying (/ (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) (pow (* PI 2) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (38 enodes)
* * [misc]simplify:  iters left: 1 (39 enodes)
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* PI 2) (/ 1 2))) (pow (* PI (* n 2)) (/ k 2)))
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* PI 2) (/ 1 2))) (pow (* PI (* n 2)) (/ k 2)))
* * * * [misc]progress:  [ 55 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (/ (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2))))))>
* [enter]simplify:  Simplifying (/ (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* * [misc]simplify:  iters left: 2 (39 enodes)
* * [misc]simplify:  iters left: 1 (40 enodes)
* [exit]simplify:  Simplified to (/ (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2))) (cbrt (pow (* 2 (* n PI)) (/ 1 2))))
* [exit]simplify:  Simplified to (/ (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2))) (cbrt (pow (* 2 (* n PI)) (/ 1 2))))
* * * * [misc]progress:  [ 56 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (/ (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) (sqrt (pow (* n (* PI 2)) (/ 1 2))))))>
* [enter]simplify:  Simplifying (/ (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) (sqrt (pow (* n (* PI 2)) (/ 1 2))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* * [misc]simplify:  iters left: 2 (39 enodes)
* * [misc]simplify:  iters left: 1 (40 enodes)
* [exit]simplify:  Simplified to (/ (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2))) (sqrt (pow (* 2 (* n PI)) (/ 1 2))))
* [exit]simplify:  Simplified to (/ (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2))) (sqrt (pow (* 2 (* n PI)) (/ 1 2))))
* * * * [misc]progress:  [ 57 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) (pow (* n (* PI 2)) (/ 1 2)))))>
* [enter]simplify:  Simplifying (/ (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (38 enodes)
* * [misc]simplify:  iters left: 1 (39 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (sqrt k) (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 58 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (log1p (expm1 (pow (* n (* PI 2)) (/ 1 2)))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (expm1 (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (expm1 (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (expm1 (pow (* (* PI n) 2) (/ 1 2)))
* * * * [misc]progress:  [ 59 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (expm1 (log1p (pow (* n (* PI 2)) (/ 1 2)))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (log1p (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (log1p (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (log1p (pow (* (* PI n) 2) (/ 1 2)))
* * * * [misc]progress:  [ 60 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (exp (* (log (* n (* PI 2))) (/ 1 2))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (* (log (* n (* PI 2))) (/ 1 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (92 enodes)
* * [misc]simplify:  iters left: 2 (180 enodes)
* * [misc]simplify:  iters left: 1 (391 enodes)
* [exit]simplify:  Simplified to (fma (log (* 2 PI)) (/ 1 2) (/ (log n) 2))
* [exit]simplify:  Simplified to (fma (log (* 2 PI)) (/ 1 2) (/ (log n) 2))
* * * * [misc]progress:  [ 61 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (exp (* (log (* n (* PI 2))) (/ 1 2))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (* (log (* n (* PI 2))) (/ 1 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (92 enodes)
* * [misc]simplify:  iters left: 2 (180 enodes)
* * [misc]simplify:  iters left: 1 (391 enodes)
* [exit]simplify:  Simplified to (fma (log (* 2 PI)) (/ 1 2) (/ (log n) 2))
* [exit]simplify:  Simplified to (fma (log (* 2 PI)) (/ 1 2) (/ (log n) 2))
* * * * [misc]progress:  [ 62 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (* 1 (/ 1 2))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (* 1 (/ 1 2))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* [exit]simplify:  Simplified to (/ 1 2)
* [exit]simplify:  Simplified to (/ 1 2)
* * * * [misc]progress:  [ 63 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* n (* PI 2)) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) (cbrt (/ 1 2))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (pow (* n (* PI 2)) (* (cbrt (/ 1 2)) (cbrt (/ 1 2))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (pow (* (* n 2) PI) (* (cbrt (/ 1 2)) (cbrt (/ 1 2))))
* [exit]simplify:  Simplified to (pow (* (* n 2) PI) (* (cbrt (/ 1 2)) (cbrt (/ 1 2))))
* * * * [misc]progress:  [ 64 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* n (* PI 2)) (sqrt (/ 1 2))) (sqrt (/ 1 2))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (pow (* n (* PI 2)) (sqrt (/ 1 2)))
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* * [misc]simplify:  iters left: 3 (21 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (sqrt (/ 1 2)))
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (sqrt (/ 1 2)))
* * * * [misc]progress:  [ 65 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* n (* PI 2)) 1) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (pow (* n (* PI 2)) 1)
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (20 enodes)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* * * * [misc]progress:  [ 66 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* n (* PI 2)) 1) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (pow (* n (* PI 2)) 1)
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (20 enodes)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* * * * [misc]progress:  [ 67 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow n (/ 1 2)) (pow (* PI 2) (/ 1 2))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (pow n (/ 1 2))
* * [misc]simplify:  iters left: 3 (5 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (pow n (/ 1 2))
* [exit]simplify:  Simplified to (pow n (/ 1 2))
* [enter]simplify:  Simplifying (pow (* PI 2) (/ 1 2))
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (9 enodes)
* [exit]simplify:  Simplified to (pow (* 2 PI) (/ 1 2))
* [exit]simplify:  Simplified to (pow (* 2 PI) (/ 1 2))
* * * * [misc]progress:  [ 68 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* n (* PI 2)) (/ 1 2)) 1) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* * * * [misc]progress:  [ 69 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (exp (log (pow (* n (* PI 2)) (/ 1 2)))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (log (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (72 enodes)
* * [misc]simplify:  iters left: 2 (182 enodes)
* * [misc]simplify:  iters left: 1 (429 enodes)
* [exit]simplify:  Simplified to (fma (log (* PI n)) (/ 1 2) (/ (log 2) 2))
* [exit]simplify:  Simplified to (fma (log (* PI n)) (/ 1 2) (/ (log 2) 2))
* * * * [misc]progress:  [ 70 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (log (exp (pow (* n (* PI 2)) (/ 1 2)))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (exp (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (exp (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (exp (pow (* (* PI n) 2) (/ 1 2)))
* * * * [misc]progress:  [ 71 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2))))
* [enter]simplify:  Simplifying (cbrt (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (cbrt (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (cbrt (pow (* (* PI n) 2) (/ 1 2)))
* * * * [misc]progress:  [ 72 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (cbrt (* (* (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ 1 2)))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (* (* (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (pow (pow (* (* n 2) PI) (/ 1 2)) 3)
* [exit]simplify:  Simplified to (pow (pow (* (* n 2) PI) (/ 1 2)) 3)
* * * * [misc]progress:  [ 73 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ 1 2)))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (sqrt (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2)))
* [enter]simplify:  Simplifying (sqrt (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2)))
* * * * [misc]progress:  [ 74 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* 1 (pow (* n (* PI 2)) (/ 1 2))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* * * * [misc]progress:  [ 75 / 86 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2)))))>
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 (* PI n)) (/ 1 2)) (sqrt k)) (pow (* 2 (* PI n)) (/ k 2)))
* * * * [misc]progress:  [ 76 / 86 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2)))))>
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 (* PI n)) (/ 1 2)) (sqrt k)) (pow (* 2 (* PI n)) (/ k 2)))
* * * * [misc]progress:  [ 77 / 86 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2)))))>
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 (* PI n)) (/ 1 2)) (sqrt k)) (pow (* 2 (* PI n)) (/ k 2)))
* * * * [misc]progress:  [ 78 / 86 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* 2 (* n PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (/ (pow (* 2 (* n PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* 2 PI) n) (/ 1 2)) (sqrt k)) (pow (* (* 2 PI) n) (/ k 2)))
* * * * [misc]progress:  [ 79 / 86 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* 2 (* n PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (/ (pow (* 2 (* n PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* 2 PI) n) (/ 1 2)) (sqrt k)) (pow (* (* 2 PI) n) (/ k 2)))
* * * * [misc]progress:  [ 80 / 86 ] simplifiying candidate #<alt-event (λ (k n) (/ (pow (* 2 (* n PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (/ (pow (* 2 (* n PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* 2 PI) n) (/ 1 2)) (sqrt k)) (pow (* (* 2 PI) n) (/ k 2)))
* * * * [misc]progress:  [ 81 / 86 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n)))))))))))))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n))))))))))))))))))))))))
* * * * [misc]progress:  [ 82 / 86 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* k (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 3) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n)))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* k (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 3) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))))))))
* * * * [misc]progress:  [ 83 / 86 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))))
* * * * [misc]progress:  [ 84 / 86 ] simplifiying candidate #<alt-event (λ (k n) (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (64 enodes)
* * [misc]simplify:  iters left: 3 (115 enodes)
* * [misc]simplify:  iters left: 2 (194 enodes)
* * [misc]simplify:  iters left: 1 (305 enodes)
* [exit]simplify:  Simplified to (/ (* (sqrt (* n 2)) (/ (sqrt PI) (sqrt k))) (pow (* (* n 2) PI) (/ k 2)))
* * * * [misc]progress:  [ 85 / 86 ] simplifiying candidate #<alt-event (λ (k n) (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (62 enodes)
* * [misc]simplify:  iters left: 3 (109 enodes)
* * [misc]simplify:  iters left: 2 (236 enodes)
* [exit]simplify:  Simplified to (/ (* (sqrt (* PI 2)) (/ (sqrt n) (sqrt k))) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 86 / 86 ] simplifiying candidate #<alt-event (λ (k n) (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (21 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (62 enodes)
* * [misc]simplify:  iters left: 3 (112 enodes)
* * [misc]simplify:  iters left: 2 (271 enodes)
* [exit]simplify:  Simplified to (/ (/ (/ (sqrt (* PI -2)) (pow (/ -1 n) 1/2)) (pow (* PI (* 2 n)) (/ k 2))) (sqrt k))
* * * [misc]progress:  adding candidates to table
* * [misc]progress:  iteration 4 / 4
* * * [misc]progress:  picking best candidate
* [misc]none:  Fresh alts: 9
* [misc]none:  All alts: 11
* [misc]none:  Fresh alt: (λ (k n) (/ (+ (* (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (* (* k k) 1/8)) (+ (* (log n) (log n)) (* (log (* PI 2)) (log (* PI 2))))) (- (fma (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4)) (* (log (* PI 2)) (* (* k k) (log n))) (* (pow (* PI 2) 1/2) (pow n 1/2))) (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/2)) (fma k (log (* PI 2)) (* (log n) k))))) (sqrt k)))
* [misc]none:  Fresh alt: (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))
* [misc]none:  Non-fresh alt: (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))
* [misc]none:  Fresh alt: (λ (k n) (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))
* [misc]none:  Fresh alt: (λ (k n) (cbrt (/ (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (* n 2) PI) (/ (- 1 k) 2))))))
* [misc]none:  Fresh alt: (λ (k n) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))))
* [misc]none:  Non-fresh alt: (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))
* [misc]none:  Fresh alt: (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))
* [misc]none:  Fresh alt: (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))
* [misc]none:  Fresh alt: (λ (k n) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))
* [misc]none:  Fresh alt: (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* [misc]none:  Fresh alt indexes
* [misc]none:  (λ (k n) (/ (+ (* (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (* (* k k) 1/8)) (+ (* (log n) (log n)) (* (log (* PI 2)) (log (* PI 2))))) (- (fma (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4)) (* (log (* PI 2)) (* (* k k) (log n))) (* (pow (* PI 2) 1/2) (pow n 1/2))) (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/2)) (fma k (log (* PI 2)) (* (log n) k))))) (sqrt k))): 0
* [misc]none:  (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))): 1
* [misc]none:  (λ (k n) (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k))): 2
* [misc]none:  (λ (k n) (cbrt (/ (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))): 3
* [misc]none:  (λ (k n) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))))): 4
* [misc]none:  (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))): 5
* [misc]none:  (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k))))): 6
* [misc]none:  (λ (k n) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k))))): 7
* [misc]none:  (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))): 8
* [misc]none:  Best fresh alt per point
* [misc]none:  (1.8808646764197965e+211 2.5246982378469546e+26): 1
* [misc]none:  (1.6056134078957726e-81 2.0654753198801362e+38): 0
* [misc]none:  (7.103138391473298e+203 4.991913674121936): 1
* [misc]none:  (3.4858004269611626e-130 1.2049116045831512e-306): 0
* [misc]none:  (6.950790143696708e-299 5.4754162277199545e+172): 2
* [misc]none:  (5.921232829081192e+298 4.202795939018271e+158): 1
* [misc]none:  (1.0394343208136068e-147 2.549337443302021e+95): 4
* [misc]none:  (8.998561140295877e-118 1.0700413456865293e+105): 2
* [misc]none:  (8.786431465145784e-134 5.784799823772606e-59): 0
* [misc]none:  (7.570282140481074e-146 1.0536210697171442e-75): 2
* [misc]none:  (2.6069457677667484e+227 2.421502054149278e+240): 1
* [misc]none:  (1.223212349341741e+210 6.083797656691426e+124): 1
* [misc]none:  (8.208194827684373e-221 3.697769831340425e-212): 0
* [misc]none:  (8.891699857124086e-248 4.741786767196371e-65): 0
* [misc]none:  (1.3953186618456118e-127 1.557559831312346e-158): 1
* [misc]none:  (2.8281459379799287e-223 5.282538753015419e+290): 4
* [misc]none:  (9.348662801176182e-287 6.983734680943984e+302): 2
* [misc]none:  (5.967105222859026e-287 1.4091628731054108e-252): 4
* [misc]none:  (6.812962331114006e-11 4.706553941824653e-123): 0
* [misc]none:  (8.467946903121652e+268 4.636077183112171e+61): 1
* [misc]none:  (6.29303766495041e-83 4.590548637242576e-128): 4
* [misc]none:  (3.213871973385624e-262 1.2212831165558396e+41): 4
* [misc]none:  (5.169867646134535e-44 1639899171736.8787): 2
* [misc]none:  (4.484657738495896e-296 1.2472467031958124e-111): 0
* [misc]none:  (2.630988489772908e-301 8.677705005606349e-192): 0
* [misc]none:  (1.9488674575590774e-219 1.2069336055576329e+297): 0
* [misc]none:  (1.0241786832856672e+275 6.65470667879038e+211): 1
* [misc]none:  (1.2388376925429903 1.0255532946660354e-189): 1
* [misc]none:  (9.403049449769395e-276 9.165910603949256e-61): 8
* [misc]none:  (1.5863716419697854e-305 2.982344844139708e-56): 4
* [misc]none:  (1.7933154604270656e+266 2.0688677513908958e+152): 1
* [misc]none:  (1.724441305022448e-204 1.0270093728501316e+208): 2
* [misc]none:  (1.6991537131626808e-286 2.269053283659137e+97): 0
* [misc]none:  (9.981425531265531e-234 1.5954750517027446e-306): 4
* [misc]none:  (2.6518292064535327e+113 1.1093632157717332e+299): 1
* [misc]none:  (3.5398920819374162e-22 9.097313058752706e+182): 2
* [misc]none:  (1.5662970496145718e+195 5.702344716829955e+277): 1
* [misc]none:  (7.374934384259559e+247 11809.004489533036): 1
* [misc]none:  (3.6837517387134946e+28 2.050724237210542e+237): 1
* [misc]none:  (8.0762754355927e-102 3.924619293995995e+294): 1
* [misc]none:  (6.272017688866778e+294 1475344134974741.5): 1
* [misc]none:  (8.226540875316075e-282 2.9295012263119104e-210): 2
* [misc]none:  (1.1567434189356451e+31 5.033252764508812e+139): 1
* [misc]none:  (1.2230943992415108e+36 2.3021043888776224e+278): 1
* [misc]none:  (5.69357845447944e-284 4.6895957006840323e-293): 6
* [misc]none:  (2.1402493760044758e-237 7.018010476645137e+19): 5
* [misc]none:  (5.836990398641413e+278 8.69236263846091e+82): 1
* [misc]none:  (3.866067932485071e+134 65634290206.02169): 1
* [misc]none:  (3.353542833099014e-216 4.562538568139802e-253): 4
* [misc]none:  (1.9595331698208332e+267 1.734899565778851e+119): 1
* [misc]none:  (6.162344767386832e-71 7.346570549506355e+179): 0
* [misc]none:  (1.7754717488663857e+121 3.494659494474523e+27): 1
* [misc]none:  (1.355389858139596e-211 5.3134050984497146e-45): 0
* [misc]none:  (1.7558002847649968e-150 2.8327022791344117e+186): 0
* [misc]none:  (55126108376913.92 1.4270114976186918e+130): 1
* [misc]none:  (2.1677429926485946e-242 1.7597566772342396e-204): 5
* [misc]none:  (5.672231019728725e-161 4.978844845564056e+84): 2
* [misc]none:  (1.061192968818359e-298 3.4390539626492262e-136): 4
* [misc]none:  (1.8851052094553197e-277 9.953566511035923e-308): 2
* [misc]none:  (2.984618116231375e+88 2.296813947529187e+143): 1
* [misc]none:  (1.1631529018053348e+89 2.354140414905433e+187): 1
* [misc]none:  (2.216720871752684e-160 3.1263904065616715e+268): 2
* [misc]none:  (5.57997653477477e-111 1.5363278110829953e+73): 0
* [misc]none:  (1.0611909380115695e-87 1.295915517178257e-293): 0
* [misc]none:  (4.355922221873984e-239 9.031875737069326e-50): 1
* [misc]none:  (2.648998082938836e-121 6.334062294691454e-67): 4
* [misc]none:  (4.293605985901814e-150 8.709273807481483e+69): 1
* [misc]none:  (7.932758618838293e-45 1.0062256135654257e-12): 7
* [misc]none:  (1.0135699554608461e-103 1.0001039793852175e+214): 1
* [misc]none:  (3.306163540346375e+188 2.601454323484488e+217): 1
* [misc]none:  (4.4505875876233544e-249 1.1235340410501106e+40): 4
* [misc]none:  (7.344373535448876e-228 2.204405021953709e+104): 0
* [misc]none:  (4.0855428097798646e-150 2.727229900429018e-249): 3
* [misc]none:  (6.298377803380903e-45 4.638301673824566e+198): 0
* [misc]none:  (1.5663895259426407e-227 6.068461153265776e+155): 0
* [misc]none:  (1.9502784809800982e-261 1.23965605071982e+102): 0
* [misc]none:  (5.141713922465631e+255 5.469890187179831e+40): 1
* [misc]none:  (1.8526578386426445e-175 2.8275326066295656e+288): 0
* [misc]none:  (2.3857467758299983e-165 2.359532888074915e-308): 3
* [misc]none:  (7.679851300456857e+192 6.240981309981708e+218): 1
* [misc]none:  (6.9138624756046875e-279 1.0801316959056566e+247): 0
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* [misc]none:  (1.9836536473017196e-256 6.844414014257645e+204): 1
* [misc]none:  All alt indexes
* [misc]none:  (λ (k n) (/ (+ (* (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (* (* k k) 1/8)) (+ (* (log n) (log n)) (* (log (* PI 2)) (log (* PI 2))))) (- (fma (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4)) (* (log (* PI 2)) (* (* k k) (log n))) (* (pow (* PI 2) 1/2) (pow n 1/2))) (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/2)) (fma k (log (* PI 2)) (* (log n) k))))) (sqrt k))): 0
* [misc]none:  (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))): 1
* [misc]none:  (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))): 2
* [misc]none:  (λ (k n) (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k))): 3
* [misc]none:  (λ (k n) (cbrt (/ (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))))): 4
* [misc]none:  (λ (k n) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))))): 5
* [misc]none:  (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))): 6
* [misc]none:  (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))): 7
* [misc]none:  (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k))))): 8
* [misc]none:  (λ (k n) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k))))): 9
* [misc]none:  (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))): 10
* [misc]none:  Best alt per point
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* [misc]none:  (7.570282140481074e-146 1.0536210697171442e-75): 2
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* [misc]none:  (8.208194827684373e-221 3.697769831340425e-212): 0
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* [misc]none:  (6.604350361119279e-291 3.861477555295976e-66): 0
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* [misc]none:  (1.6519797365083582e+195 6.316732900885901e+249): 1
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* [misc]none:  (2.5502245720775025e+302 3.7105227033705403e+214): 1
* [misc]none:  (6.821311827045434e-30 2.8401584433220846e+96): 1
* [misc]none:  (2.6830861914889714e-191 5.086243151153881e+259): 1
* [misc]none:  (1.4517955555700533e-57 3.278760905350017e+239): 5
* [misc]none:  (9.422179697047065e-164 1.3639040980897921e-39): 0
* [misc]none:  (2.8344220272269968e+166 1.5252878664938466e+85): 1
* [misc]none:  (1.9836536473017196e-256 6.844414014257645e+204): 1
* [misc]none:  Picked alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * * * [misc]pick:  Picked  #<alt-event (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 4 ] rewriting at (2 1)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2 2 1)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2 2)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 4 ] generating series at (2 1)
* [misc]approximate:  Taking taylor expansion of (/ 1 (sqrt k)) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (- +nan.0) into (- +nan.0)
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (- +nan.0) into (- +nan.0)
* [misc]backup-simplify:  Simplify (+ (* (- +nan.0) k) (+ (- +nan.0) (* +nan.0 (/ 1 k)))) into (- (+ +nan.0 (- (+ (* +nan.0 k) (- (* +nan.0 (/ 1 k)))))))
* [misc]approximate:  Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]backup-simplify:  Simplify +nan.0 into +nan.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 (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (- +nan.0) into (- +nan.0)
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (- +nan.0) into (- +nan.0)
* [misc]backup-simplify:  Simplify (+ (* (- +nan.0) (pow (/ 1 k) 2)) (+ (* (- +nan.0) (/ 1 k)) +nan.0)) into (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2))))))))
* [misc]approximate:  Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (- +nan.0) into (- +nan.0)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (- +nan.0) into (- +nan.0)
* [misc]backup-simplify:  Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2))))))))
* * * * [misc]progress:  [ 2 / 4 ] generating series at (2)
* [misc]approximate:  Taking taylor expansion of (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k))
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (+ 1 (- k)) into (- 1 k)
* [misc]backup-simplify:  Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k))
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) n)) in n
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) n) in n
* [misc]taylor:  Taking taylor expansion of (* 2 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 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 (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 1) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 k) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) n)) in k
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) n) 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]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) n) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 k) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) n)) in k
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) n) 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]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) n) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
* [misc]backup-simplify:  Simplify (* +nan.0 (pow (* 2 (* n PI)) 1/2)) into (* +nan.0 (sqrt (* n (* 2 PI))))
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (sqrt (* n (* 2 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 (* n (* 2 PI))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* 2 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 (* 2 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) 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 (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (* 0 n)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (- (/ -1 2) (+ (* 1/2 (/ 0 2)))) into -1/2
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI)))))
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI)))))) (* (- +nan.0) (pow (* 2 (* n PI)) 1/2))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))))
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* 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 (* n PI)) (* (sqrt 2) (log (* 2 (* n PI))))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (* n PI)) (sqrt 2)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (sqrt 2) (+ (log (* 2 PI)) (log n))) into (* (+ (log (* 2 PI)) (log n)) (sqrt 2))
* [misc]backup-simplify:  Simplify (* 0 (* (+ (log (* 2 PI)) (log n)) (sqrt 2))) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (* 0 (sqrt 2)) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* +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 (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 n))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* n (* 2 PI))) (pow (log (* 2 (* n PI))) 2)))
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (* 1/8 (* (sqrt (* n (* 2 PI))) (pow (log (* 2 (* n PI))) 2)))) (+ (* (- +nan.0) (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI)))))) (* (- +nan.0) (pow (* 2 (* n PI)) 1/2)))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))))))
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* 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 (* n PI)) (* (sqrt 2) (log (* 2 (* n PI))))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 2 (log (log (* 2 (* n PI)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (log (log (* 2 (* n PI))))) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (log (log (* 2 (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (log (+ (log (* 2 PI)) (log n))) into (log (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 2 (log (+ (log (* 2 PI)) (log n)))) into (* 2 (log (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 2 (log (+ (log (* 2 PI)) (log n))))) into (pow (+ (log (* 2 PI)) (log n)) 2)
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (* n PI)) (sqrt 2)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (sqrt 2) (+ (log (* 2 PI)) (log n))) into (* (+ (log (* 2 PI)) (log n)) (sqrt 2))
* [misc]backup-simplify:  Simplify (* 0 (* (+ (log (* 2 PI)) (log n)) (sqrt 2))) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (* (sqrt 2) (pow (+ (log (* 2 PI)) (log n)) 2)) into (* (pow (+ (log (* 2 PI)) (log n)) 2) (sqrt 2))
* [misc]backup-simplify:  Simplify (* 0 (* (pow (+ (log (* 2 PI)) (log n)) 2) (sqrt 2))) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (* 0 (sqrt 2)) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* (* +nan.0 PI) (* (+ (log (* 2 PI)) (log n)) (sqrt 2)))) into (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))) (* 0 0)) into (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* (* +nan.0 PI) (sqrt 2))) into (- (* +nan.0 (* PI (sqrt 2))))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (- (* +nan.0 (* PI (sqrt 2))))) (* 0 0)) into (- (* +nan.0 (* PI (sqrt 2))))
* [misc]backup-simplify:  Simplify (- (- (* +nan.0 (* PI (sqrt 2))))) into (- (* +nan.0 (* PI (sqrt 2))))
* [misc]backup-simplify:  Simplify (+ (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))) (- (* +nan.0 (* PI (sqrt 2))))) into (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))))
* [misc]backup-simplify:  Simplify (- (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))))) into (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))))) into (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))))
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (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 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))))) (* n 1)) (* (- (* +nan.0 PI)) (* n (/ 1 k))))) into (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) k)) (- (+ (* +nan.0 (* n (* PI (sqrt 2)))) (- (+ (* +nan.0 (/ (* n PI) k)) (- (+ (* +nan.0 (* n (* PI (* (log n) (sqrt 2))))) (- (* +nan.0 (* n (* PI (* (log (* 2 PI)) (sqrt 2))))))))))))))
* [misc]approximate:  Taking taylor expansion of (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k)
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in n
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n
* [misc]taylor:  Taking taylor expansion of (* 2 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) 1) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in k
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 n)) 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]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 (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in k
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 n)) 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]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 (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) into (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 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 (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 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 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (log (* 2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (* (- (log (* 2 PI)) (log n)) (- 1 (/ 1 k))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (+ (* +nan.0 0) (* (- +nan.0) (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 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 (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 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 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (log (* 2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (* (- (log (* 2 PI)) (log n)) (- 1 (/ 1 k))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (- (log (* 2 PI)) (log n)) 0) (* 0 (- 1 (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (+ (* +nan.0 0) (+ (* (- +nan.0) 0) (* (- +nan.0) (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 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 (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 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 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (log (* 2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (* (- (log (* 2 PI)) (log n)) (- 1 (/ 1 k))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))) (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)))))))
* [misc]approximate:  Taking taylor expansion of (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
* [misc]backup-simplify:  Simplify (/ 1 (sqrt (/ -1 k))) into (/ 1 (sqrt (/ -1 k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ -1 k)) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) -1) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- -1) into 1
* [misc]backup-simplify:  Simplify (+ 0 1) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) 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]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 (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ -1 n)) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- -1) into 1
* [misc]backup-simplify:  Simplify (+ 0 1) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) 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]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 (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ -1 n)) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (+ 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log (* -2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -2 in n
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) into (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (+ (* +nan.0 0) (* (- +nan.0) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (+ 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log (* -2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -2 in n
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) into (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (+ 1 (/ 1 k)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (+ (* +nan.0 0) (+ (* (- +nan.0) 0) (* (- +nan.0) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (+ 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log (* -2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -2 in n
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) into (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))))))))
* * * * [misc]progress:  [ 3 / 4 ] generating series at (2 2 1)
* [misc]approximate:  Taking taylor expansion of (* (* 2 PI) n) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) n) in n
* [misc]taylor:  Taking taylor expansion of (* 2 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) n) in n
* [misc]taylor:  Taking taylor expansion of (* 2 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 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 (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 1) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 1) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) n) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n
* [misc]taylor:  Taking taylor expansion of (* 2 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n
* [misc]taylor:  Taking taylor expansion of (* 2 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) 1) 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 (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (* 0 1)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 1))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) -1) 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 (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (* 0 -1)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 -1))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
* * * * [misc]progress:  [ 4 / 4 ] generating series at (2 2)
* [misc]approximate:  Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 k) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) n)) in k
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) n) 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]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) n) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (+ 1 (- k)) into (- 1 k)
* [misc]backup-simplify:  Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k))
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) n)) in n
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) n) in n
* [misc]taylor:  Taking taylor expansion of (* 2 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 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 (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 1) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (+ 1 (- k)) into (- 1 k)
* [misc]backup-simplify:  Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k))
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) n)) in n
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) n) in n
* [misc]taylor:  Taking taylor expansion of (* 2 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 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 (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 1) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (- 1 k) (+ (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (- 1 k) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1 (+ (log (* 2 PI)) (log n))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 1) (* 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) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* -1 (+ (log (* 2 PI)) (log n)))) into (- (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))
* [misc]backup-simplify:  Simplify (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))))
* [misc]backup-simplify:  Simplify (+ (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k)))))
* [misc]approximate:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in k
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 n)) 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]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 (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in n
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n
* [misc]taylor:  Taking taylor expansion of (* 2 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) 1) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in n
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n
* [misc]taylor:  Taking taylor expansion of (* 2 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) 1) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (* 0 1)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 1))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
* [misc]approximate:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- -1) into 1
* [misc]backup-simplify:  Simplify (+ 0 1) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) 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]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 (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ -1 n)) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ -1 k)) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) -1) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ -1 k)) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 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 PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) -1) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (+ 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* -2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* -2 PI) in k
* [misc]taylor:  Taking taylor expansion of -2 in k
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (+ 0 1) into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (* 0 -1)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-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 (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 -1))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-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 (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
* * * [misc]progress:  simplifying candidates
* * * * [misc]progress:  [ 1 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (log1p (expm1 (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (expm1 (/ 1 (sqrt k)))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* [exit]simplify:  Simplified to (expm1 (/ 1 (sqrt k)))
* [exit]simplify:  Simplified to (expm1 (/ 1 (sqrt k)))
* * * * [misc]progress:  [ 2 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (expm1 (log1p (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (log1p (/ 1 (sqrt k)))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* [exit]simplify:  Simplified to (log1p (/ 1 (sqrt k)))
* [exit]simplify:  Simplified to (log1p (/ 1 (sqrt k)))
* * * * [misc]progress:  [ 3 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow (sqrt k) -1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* * * * [misc]progress:  [ 4 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (- 1/2)
* * [misc]simplify:  iters left: 2 (2 enodes)
* [exit]simplify:  Simplified to (- 1/2)
* [exit]simplify:  Simplified to (- 1/2)
* * * * [misc]progress:  [ 5 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow (sqrt k) (- 1)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (- 1)
* * [misc]simplify:  iters left: 2 (2 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (- 1)
* [exit]simplify:  Simplified to (- 1)
* * * * [misc]progress:  [ 6 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow (/ 1 (sqrt k)) 1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* * * * [misc]progress:  [ 7 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (exp (- (log (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (- (log (sqrt k)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* [exit]simplify:  Simplified to (- (log (sqrt k)))
* [exit]simplify:  Simplified to (- (log (sqrt k)))
* * * * [misc]progress:  [ 8 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (exp (log (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (log (/ 1 (sqrt k)))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (11 enodes)
* * [misc]simplify:  iters left: 2 (12 enodes)
* * [misc]simplify:  iters left: 1 (16 enodes)
* [exit]simplify:  Simplified to (- (log (sqrt k)))
* [exit]simplify:  Simplified to (- (log (sqrt k)))
* * * * [misc]progress:  [ 9 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (log (exp (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (exp (/ 1 (sqrt k)))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* [exit]simplify:  Simplified to (exp (/ 1 (sqrt k)))
* [exit]simplify:  Simplified to (exp (/ 1 (sqrt k)))
* * * * [misc]progress:  [ 10 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (cbrt (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (8 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k))))
* [exit]simplify:  Simplified to (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k))))
* [enter]simplify:  Simplifying (cbrt (/ 1 (sqrt k)))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* [exit]simplify:  Simplified to (cbrt (/ 1 (sqrt k)))
* [exit]simplify:  Simplified to (cbrt (/ 1 (sqrt k)))
* * * * [misc]progress:  [ 11 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (cbrt (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (60 enodes)
* * [misc]simplify:  iters left: 1 (79 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 k) (sqrt k))
* [exit]simplify:  Simplified to (/ (/ 1 k) (sqrt k))
* * * * [misc]progress:  [ 12 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (sqrt (/ 1 (sqrt k)))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* [exit]simplify:  Simplified to (sqrt (/ 1 (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ 1 (sqrt k)))
* [enter]simplify:  Simplifying (sqrt (/ 1 (sqrt k)))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* [exit]simplify:  Simplified to (sqrt (/ 1 (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ 1 (sqrt k)))
* * * * [misc]progress:  [ 13 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (- 1) (- (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (- 1)
* * [misc]simplify:  iters left: 2 (2 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (- 1)
* [exit]simplify:  Simplified to (- 1)
* [enter]simplify:  Simplifying (- (sqrt k))
* * [misc]simplify:  iters left: 3 (3 enodes)
* [exit]simplify:  Simplified to (- (sqrt k))
* [exit]simplify:  Simplified to (- (sqrt k))
* * * * [misc]progress:  [ 14 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (* 1 (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* * * * [misc]progress:  [ 15 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (* 1 (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt k))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (6 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt k))
* [exit]simplify:  Simplified to (/ 1 (sqrt k))
* * * * [misc]progress:  [ 16 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (/ (sqrt k) 1)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (/ (sqrt k) 1)
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (6 enodes)
* * [misc]simplify:  iters left: 1 (8 enodes)
* [exit]simplify:  Simplified to (sqrt k)
* [exit]simplify:  Simplified to (sqrt k)
* * * * [misc]progress:  [ 17 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* [exit]simplify:  Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 18 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* * * * [misc]progress:  [ 19 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (/ 1 1)
* * [misc]simplify:  iters left: 2 (2 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to 1
* [exit]simplify:  Simplified to 1
* * * * [misc]progress:  [ 20 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (log1p (expm1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (expm1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (53 enodes)
* * [misc]simplify:  iters left: 2 (57 enodes)
* * [misc]simplify:  iters left: 1 (64 enodes)
* [exit]simplify:  Simplified to (expm1 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (expm1 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 21 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (expm1 (log1p (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (log1p (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (53 enodes)
* * [misc]simplify:  iters left: 2 (57 enodes)
* * [misc]simplify:  iters left: 1 (64 enodes)
* [exit]simplify:  Simplified to (log1p (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (log1p (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 22 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (pow (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1))>
* * * * [misc]progress:  [ 23 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (66 enodes)
* * [misc]simplify:  iters left: 3 (164 enodes)
* [exit]simplify:  Simplified to (fma (log (* n (* PI 2))) (/ (- 1 k) 2) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* n (* PI 2))) (/ (- 1 k) 2) (- (log (sqrt k))))
* * * * [misc]progress:  [ 24 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (66 enodes)
* * [misc]simplify:  iters left: 3 (164 enodes)
* [exit]simplify:  Simplified to (fma (log (* n (* PI 2))) (/ (- 1 k) 2) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* n (* PI 2))) (/ (- 1 k) 2) (- (log (sqrt k))))
* * * * [misc]progress:  [ 25 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (- (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (+ (- (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (50 enodes)
* * [misc]simplify:  iters left: 3 (98 enodes)
* * [misc]simplify:  iters left: 2 (302 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* PI (* n 2))) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* PI (* n 2))) (- (log (sqrt k))))
* * * * [misc]progress:  [ 26 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (75 enodes)
* * [misc]simplify:  iters left: 3 (195 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k))))
* * * * [misc]progress:  [ 27 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (75 enodes)
* * [misc]simplify:  iters left: 3 (195 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k))))
* * * * [misc]progress:  [ 28 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (+ (log (/ 1 (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (59 enodes)
* * [misc]simplify:  iters left: 3 (120 enodes)
* * [misc]simplify:  iters left: 2 (436 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k))))
* * * * [misc]progress:  [ 29 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (exp (log (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (log (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (56 enodes)
* * [misc]simplify:  iters left: 3 (103 enodes)
* * [misc]simplify:  iters left: 2 (193 enodes)
* [exit]simplify:  Simplified to (fma (log (* PI (* n 2))) (/ (- 1 k) 2) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* PI (* n 2))) (/ (- 1 k) 2) (- (log (sqrt k))))
* * * * [misc]progress:  [ 30 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (log (exp (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (exp (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (46 enodes)
* * [misc]simplify:  iters left: 3 (55 enodes)
* * [misc]simplify:  iters left: 2 (59 enodes)
* * [misc]simplify:  iters left: 1 (68 enodes)
* [exit]simplify:  Simplified to (pow (exp (/ 1 (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (pow (exp (/ 1 (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 31 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (41 enodes)
* * [misc]simplify:  iters left: 4 (97 enodes)
* * [misc]simplify:  iters left: 3 (179 enodes)
* * [misc]simplify:  iters left: 2 (347 enodes)
* [exit]simplify:  Simplified to (* (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (* k (sqrt k))))
* [exit]simplify:  Simplified to (* (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (* k (sqrt k))))
* * * * [misc]progress:  [ 32 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (* (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (45 enodes)
* * [misc]simplify:  iters left: 3 (54 enodes)
* * [misc]simplify:  iters left: 2 (58 enodes)
* * [misc]simplify:  iters left: 1 (65 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* [enter]simplify:  Simplifying (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (53 enodes)
* * [misc]simplify:  iters left: 2 (57 enodes)
* * [misc]simplify:  iters left: 1 (64 enodes)
* [exit]simplify:  Simplified to (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 33 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (* (* (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (* (* (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (94 enodes)
* * [misc]simplify:  iters left: 3 (202 enodes)
* * [misc]simplify:  iters left: 2 (465 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 34 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (53 enodes)
* * [misc]simplify:  iters left: 2 (57 enodes)
* * [misc]simplify:  iters left: 1 (64 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* [enter]simplify:  Simplifying (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (53 enodes)
* * [misc]simplify:  iters left: 2 (57 enodes)
* * [misc]simplify:  iters left: 1 (64 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 35 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* 1 (pow (* (* 2 PI) n) (/ 1 2))) (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))))>
* [enter]simplify:  Simplifying (* 1 (pow (* (* 2 PI) n) (/ 1 2)))
* * [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 (25 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (/ 1 2))
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (/ 1 2))
* [enter]simplify:  Simplifying (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (* (sqrt k) (pow (* 2 (* PI n)) (/ k 2)))
* [exit]simplify:  Simplified to (* (sqrt k) (pow (* 2 (* PI n)) (/ k 2)))
* * * * [misc]progress:  [ 36 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
* * * * [misc]progress:  [ 37 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (44 enodes)
* * [misc]simplify:  iters left: 1 (51 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))
* [exit]simplify:  Simplified to (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 38 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt k)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (48 enodes)
* * [misc]simplify:  iters left: 3 (74 enodes)
* * [misc]simplify:  iters left: 2 (102 enodes)
* * [misc]simplify:  iters left: 1 (106 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k))
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k))
* * * * [misc]progress:  [ 39 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (53 enodes)
* * [misc]simplify:  iters left: 2 (57 enodes)
* * [misc]simplify:  iters left: 1 (64 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))
* * * * [misc]progress:  [ 40 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt k)) 1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) 1)
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt k))
* [exit]simplify:  Simplified to (/ 1 (sqrt k))
* * * * [misc]progress:  [ 41 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (* (cbrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* (cbrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ 1 (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (* (cbrt (/ 1 (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 42 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ 1 (sqrt k))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ 1 (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (* (sqrt (/ 1 (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 43 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (52 enodes)
* * [misc]simplify:  iters left: 2 (56 enodes)
* * [misc]simplify:  iters left: 1 (63 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))
* [exit]simplify:  Simplified to (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 44 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (52 enodes)
* * [misc]simplify:  iters left: 2 (56 enodes)
* * [misc]simplify:  iters left: 1 (63 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))
* [exit]simplify:  Simplified to (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 45 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2))) (pow (* (* 2 PI) n) (/ k 2))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* * [misc]simplify:  iters left: 2 (45 enodes)
* * [misc]simplify:  iters left: 1 (52 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k))
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k))
* * * * [misc]progress:  [ 46 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 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 (pow (* (* 2 n) PI) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow (* (* 2 n) PI) (/ (- 1 k) 2))
* * * * [misc]progress:  [ 47 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
* * * * [misc]progress:  [ 48 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (log1p (expm1 (* (* 2 PI) n))) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (expm1 (* (* 2 PI) n))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (expm1 (* 2 (* n PI)))
* [exit]simplify:  Simplified to (expm1 (* 2 (* n PI)))
* * * * [misc]progress:  [ 49 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (expm1 (log1p (* (* 2 PI) n))) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (log1p (* (* 2 PI) n))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (log1p (* 2 (* n PI)))
* [exit]simplify:  Simplified to (log1p (* 2 (* n PI)))
* * * * [misc]progress:  [ 50 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
* * * * [misc]progress:  [ 51 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (log (* (* 2 PI) n))) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (log (* (* 2 PI) n))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (40 enodes)
* [exit]simplify:  Simplified to (log (* (* n PI) 2))
* [exit]simplify:  Simplified to (log (* (* n PI) 2))
* * * * [misc]progress:  [ 52 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (log (exp (* (* 2 PI) n))) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (exp (* (* 2 PI) n))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* * [misc]simplify:  iters left: 2 (29 enodes)
* * [misc]simplify:  iters left: 1 (40 enodes)
* [exit]simplify:  Simplified to (pow (exp PI) (* n 2))
* [exit]simplify:  Simplified to (pow (exp PI) (* n 2))
* * * * [misc]progress:  [ 53 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n))) (cbrt (* (* 2 PI) n))) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n)))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (18 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* (* n PI) 2)) (cbrt (* (* n PI) 2)))
* [exit]simplify:  Simplified to (* (cbrt (* (* n PI) 2)) (cbrt (* (* n PI) 2)))
* [enter]simplify:  Simplifying (cbrt (* (* 2 PI) n))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (cbrt (* 2 (* n PI)))
* [exit]simplify:  Simplified to (cbrt (* 2 (* n PI)))
* * * * [misc]progress:  [ 54 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (53 enodes)
* * [misc]simplify:  iters left: 3 (168 enodes)
* [exit]simplify:  Simplified to (pow (* (* n 2) PI) 3)
* [exit]simplify:  Simplified to (pow (* (* n 2) PI) 3)
* * * * [misc]progress:  [ 55 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (* (sqrt (* (* 2 PI) n)) (sqrt (* (* 2 PI) n))) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (sqrt (* (* 2 PI) n))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (sqrt (* 2 (* n PI)))
* [exit]simplify:  Simplified to (sqrt (* 2 (* n PI)))
* [enter]simplify:  Simplifying (sqrt (* (* 2 PI) n))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (sqrt (* 2 (* n PI)))
* [exit]simplify:  Simplified to (sqrt (* 2 (* n PI)))
* * * * [misc]progress:  [ 56 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (* 1 (* (* 2 PI) n)) (/ (- 1 k) 2))))>
* * * * [misc]progress:  [ 57 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* PI n)) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* PI n)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n PI)
* [exit]simplify:  Simplified to (* n PI)
* * * * [misc]progress:  [ 58 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))>
* * * * [misc]progress:  [ 59 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (log1p (expm1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (expm1 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (expm1 (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (expm1 (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 60 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (expm1 (log1p (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (log1p (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (log1p (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (log1p (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 61 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (58 enodes)
* * [misc]simplify:  iters left: 3 (145 enodes)
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2))))
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2))))
* * * * [misc]progress:  [ 62 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (58 enodes)
* * [misc]simplify:  iters left: 3 (145 enodes)
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2))))
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2))))
* * * * [misc]progress:  [ 63 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* 1 (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (51 enodes)
* * [misc]simplify:  iters left: 2 (66 enodes)
* * [misc]simplify:  iters left: 1 (81 enodes)
* [exit]simplify:  Simplified to (/ (- 1 k) 2)
* [exit]simplify:  Simplified to (/ (- 1 k) 2)
* * * * [misc]progress:  [ 64 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)))))>
* [enter]simplify:  Simplifying (pow (* (* 2 PI) n) (/ 1 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI 2) n) (/ 1 2))
* [exit]simplify:  Simplified to (pow (* (* PI 2) n) (/ 1 2))
* [enter]simplify:  Simplifying (pow (* (* 2 PI) n) (/ 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))
* [exit]simplify:  Simplified to (pow (* 2 (* n PI)) (/ k 2))
* * * * [misc]progress:  [ 65 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 66 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI 2) n) (sqrt (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (pow (* (* PI 2) n) (sqrt (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 67 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (pow (* (* 2 PI) n) 1)
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (20 enodes)
* [exit]simplify:  Simplified to (* (* n PI) 2)
* [exit]simplify:  Simplified to (* (* n PI) 2)
* * * * [misc]progress:  [ 68 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (- 1 k)) (/ 1 2))))>
* [enter]simplify:  Simplifying (pow (* (* 2 PI) n) (- 1 k))
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (25 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI 2) n) (- 1 k))
* [exit]simplify:  Simplified to (pow (* (* PI 2) n) (- 1 k))
* * * * [misc]progress:  [ 69 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (pow (* 2 PI) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (21 enodes)
* [exit]simplify:  Simplified to (pow (* PI 2) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow (* PI 2) (/ (- 1 k) 2))
* [enter]simplify:  Simplifying (pow n (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (17 enodes)
* * [misc]simplify:  iters left: 2 (19 enodes)
* [exit]simplify:  Simplified to (pow n (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow n (/ (- 1 k) 2))
* * * * [misc]progress:  [ 70 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (- 1 k) 2)) 1)))>
* * * * [misc]progress:  [ 71 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (exp (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (90 enodes)
* * [misc]simplify:  iters left: 2 (246 enodes)
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
* * * * [misc]progress:  [ 72 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (log (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (exp (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (exp (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 73 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (* (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
* [enter]simplify:  Simplifying (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 74 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (cbrt (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (pow (pow (* PI (* n 2)) (/ (- 1 k) 2)) 3)
* [exit]simplify:  Simplified to (pow (pow (* PI (* n 2)) (/ (- 1 k) 2)) 3)
* * * * [misc]progress:  [ 75 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (* (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* [enter]simplify:  Simplifying (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 76 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
* * * * [misc]progress:  [ 77 / 88 ] simplifiying candidate #<alt-event (λ (k n) (* (- (+ +nan.0 (- (+ (* +nan.0 k) (- (* +nan.0 (/ 1 k))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* (- (+ +nan.0 (- (+ (* +nan.0 k) (- (* +nan.0 (/ 1 k))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 78 / 88 ] simplifiying candidate #<alt-event (λ (k n) (* (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2)))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2)))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 79 / 88 ] simplifiying candidate #<alt-event (λ (k n) (* (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2)))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2)))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 80 / 88 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) k)) (- (+ (* +nan.0 (* n (* PI (sqrt 2)))) (- (+ (* +nan.0 (/ (* n PI) k)) (- (+ (* +nan.0 (* n (* PI (* (log n) (sqrt 2))))) (- (* +nan.0 (* n (* PI (* (log (* 2 PI)) (sqrt 2)))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) k)) (- (+ (* +nan.0 (* n (* PI (sqrt 2)))) (- (+ (* +nan.0 (/ (* n PI) k)) (- (+ (* +nan.0 (* n (* PI (* (log n) (sqrt 2))))) (- (* +nan.0 (* n (* PI (* (log (* 2 PI)) (sqrt 2))))))))))))))
* * * * [misc]progress:  [ 81 / 88 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)))))))
* * * * [misc]progress:  [ 82 / 88 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))))))))
* * * * [misc]progress:  [ 83 / 88 ] simplifiying candidate #<alt-event (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (52 enodes)
* * [misc]simplify:  iters left: 2 (56 enodes)
* * [misc]simplify:  iters left: 1 (63 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 84 / 88 ] simplifiying candidate #<alt-event (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (52 enodes)
* * [misc]simplify:  iters left: 2 (56 enodes)
* * [misc]simplify:  iters left: 1 (63 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 85 / 88 ] simplifiying candidate #<alt-event (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (52 enodes)
* * [misc]simplify:  iters left: 2 (56 enodes)
* * [misc]simplify:  iters left: 1 (63 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 86 / 88 ] simplifiying candidate #<alt-event (λ (k n) (* (/ 1 (sqrt k)) (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k)))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))))))
* * [misc]simplify:  iters left: 6 (41 enodes)
* * [misc]simplify:  iters left: 5 (117 enodes)
* * [misc]simplify:  iters left: 4 (405 enodes)
* [exit]simplify:  Simplified to (/ (+ (* (* (* k k) (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/8))) (+ (* (log (* PI 2)) (log (* PI 2))) (* (log n) (log n)))) (- (fma (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4)) (* (* (log n) (* k k)) (log (* PI 2))) (* (pow n 1/2) (pow (* PI 2) 1/2))) (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/2)) (fma (log (* PI 2)) k (* (log n) k))))) (sqrt k))
* * * * [misc]progress:  [ 87 / 88 ] simplifiying candidate #<alt-event (λ (k n) (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (41 enodes)
* * [misc]simplify:  iters left: 4 (86 enodes)
* * [misc]simplify:  iters left: 3 (293 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* PI 2) (- 1/2 (* k 1/2))) (pow n (- 1/2 (* k 1/2)))) (sqrt k))
* * * * [misc]progress:  [ 88 / 88 ] simplifiying candidate #<alt-event (λ (k n) (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (41 enodes)
* * [misc]simplify:  iters left: 4 (86 enodes)
* * [misc]simplify:  iters left: 3 (307 enodes)
* [exit]simplify:  Simplified to (/ (pow (pow (exp 1/2) (- 1 k)) (- (log (* PI -2)) (log (/ -1 n)))) (sqrt k))
* * * [misc]progress:  adding candidates to table
* [misc]progress:  [Phase 3 of 3] Extracting.
* * [misc]regime-changes:  Finding splitpoints for: (#<alt-delta (λ (k n) (/ (+ (* (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (* (* k k) 1/8)) (+ (* (log n) (log n)) (* (log (* PI 2)) (log (* PI 2))))) (- (fma (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4)) (* (log (* PI 2)) (* (* k k) (log n))) (* (pow (* PI 2) 1/2) (pow n 1/2))) (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/2)) (fma k (log (* PI 2)) (* (log n) k))))) (sqrt k)))> #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))> #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))> #<alt-delta (λ (k n) (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))> #<alt-delta (λ (k n) (cbrt (/ (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (* n 2) PI) (/ (- 1 k) 2))))))> #<alt-delta (λ (k n) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))))> #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))> #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))> #<alt-delta (λ (k n) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))> #<alt-delta (λ (k n) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))> #<alt-event (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>)
* [misc]regimes:  Found splitpoints: (#s(sp 0 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) +nan.0)) , with alts (#<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>)
* [enter]simplify:  Simplifying (pow (* n (* PI 2)) (/ 1 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* [exit]simplify:  Simplified to (pow (* (* 2 PI) n) (/ 1 2))
* [exit]simplify:  Simplified to (pow (* (* 2 PI) n) (/ 1 2))
* [enter]simplify:  Simplifying (pow (* n (* PI 2)) (/ k 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* [exit]simplify:  Simplified to (pow (* (* 2 PI) n) (/ k 2))
* [exit]simplify:  Simplified to (pow (* (* 2 PI) n) (/ k 2))
* * * * [misc]points:  Sampling 8000 additional inputs, on iter 0 have 0 / 8000
* * * * [misc]points:  Computing exacts on every 500 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 250 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 125 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 62 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 31 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 15 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 7 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 3 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 8000 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 6521 additional inputs, on iter 1 have 1479 / 8000
* * * * [misc]points:  Computing exacts on every 407 of 6521 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 203 of 6521 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 101 of 6521 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 50 of 6521 points 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 6521 points 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 6521 points 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 6521 points 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 6521 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 6521 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 5278 additional inputs, on iter 2 have 2722 / 8000
* * * * [misc]points:  Computing exacts on every 329 of 5278 points 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 5278 points 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 5278 points 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 5278 points 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 5278 points 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 5278 points 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 5278 points 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 5278 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 5278 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4272 additional inputs, on iter 3 have 3728 / 8000
* * * * [misc]points:  Computing exacts on every 267 of 4272 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 133 of 4272 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 66 of 4272 points 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 4272 points 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 4272 points 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 4272 points 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 4272 points 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 4272 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 4272 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 3473 additional inputs, on iter 4 have 4527 / 8000
* * * * [misc]points:  Computing exacts on every 217 of 3473 points 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 3473 points 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 3473 points 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 3473 points 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 3473 points 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 3473 points 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 3473 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 3473 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 2839 additional inputs, on iter 5 have 5161 / 8000
* * * * [misc]points:  Computing exacts on every 177 of 2839 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 88 of 2839 points 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 2839 points 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 2839 points 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 2839 points 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 2839 points 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 2839 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 2839 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 2321 additional inputs, on iter 6 have 5679 / 8000
* * * * [misc]points:  Computing exacts on every 145 of 2321 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 72 of 2321 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 36 of 2321 points 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 2321 points 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 2321 points 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 2321 points 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 2321 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 2321 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 1888 additional inputs, on iter 7 have 6112 / 8000
* * * * [misc]points:  Computing exacts on every 118 of 1888 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 59 of 1888 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 29 of 1888 points 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 1888 points 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 1888 points 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 1888 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1888 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 1536 additional inputs, on iter 8 have 6464 / 8000
* * * * [misc]points:  Computing exacts on every 96 of 1536 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 48 of 1536 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 24 of 1536 points 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 1536 points 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 1536 points 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 1536 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1536 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 1252 additional inputs, on iter 9 have 6748 / 8000
* * * * [misc]points:  Computing exacts on every 78 of 1252 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 39 of 1252 points 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 1252 points 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 1252 points 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 1252 points 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 1252 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1252 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 1020 additional inputs, on iter 10 have 6980 / 8000
* * * * [misc]points:  Computing exacts on every 63 of 1020 points 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 1020 points 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 1020 points 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 1020 points 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 1020 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1020 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 824 additional inputs, on iter 11 have 7176 / 8000
* * * * [misc]points:  Computing exacts on every 51 of 824 points 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 824 points 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 824 points 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 824 points 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 824 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 824 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 655 additional inputs, on iter 12 have 7345 / 8000
* * * * [misc]points:  Computing exacts on every 40 of 655 points 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 655 points 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 655 points 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 655 points 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 655 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 655 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 512 additional inputs, on iter 13 have 7488 / 8000
* * * * [misc]points:  Computing exacts on every 32 of 512 points 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 512 points 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 512 points 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 512 points 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 512 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 512 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 413 additional inputs, on iter 14 have 7587 / 8000
* * * * [misc]points:  Computing exacts on every 25 of 413 points 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 413 points 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 413 points 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 413 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 413 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 340 additional inputs, on iter 15 have 7660 / 8000
* * * * [misc]points:  Computing exacts on every 21 of 340 points 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 340 points 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 340 points 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 340 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 340 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 282 additional inputs, on iter 16 have 7718 / 8000
* * * * [misc]points:  Computing exacts on every 17 of 282 points 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 282 points 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 282 points 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 282 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 282 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 231 additional inputs, on iter 17 have 7769 / 8000
* * * * [misc]points:  Computing exacts on every 14 of 231 points 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 231 points 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 231 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 231 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 192 additional inputs, on iter 18 have 7808 / 8000
* * * * [misc]points:  Computing exacts on every 12 of 192 points 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 192 points 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 192 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 192 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 166 additional inputs, on iter 19 have 7834 / 8000
* * * * [misc]points:  Computing exacts on every 10 of 166 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 5 of 166 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 166 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 166 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 142 additional inputs, on iter 20 have 7858 / 8000
* * * * [misc]points:  Computing exacts on every 8 of 142 points 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 142 points 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 142 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 142 points
* * * * [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 21 have 7886 / 8000
* * * * [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 92 additional inputs, on iter 22 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 68 additional inputs, on iter 23 have 7932 / 8000
* * * * [misc]points:  Computing exacts on every 4 of 68 points 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 68 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 68 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 53 additional inputs, on iter 24 have 7947 / 8000
* * * * [misc]points:  Computing exacts on every 3 of 53 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 53 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 42 additional inputs, on iter 25 have 7958 / 8000
* * * * [misc]points:  Computing exacts on every 2 of 42 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 42 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 34 additional inputs, on iter 26 have 7966 / 8000
* * * * [misc]points:  Computing exacts on every 2 of 34 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 34 points
* * * * [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 27 have 7974 / 8000
* * * * [misc]points:  Computing exacts for 26 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 23 additional inputs, on iter 28 have 7977 / 8000
* * * * [misc]points:  Computing exacts for 23 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 20 additional inputs, on iter 29 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 30 have 7985 / 8000
* * * * [misc]points:  Computing exacts for 15 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 11 additional inputs, on iter 31 have 7989 / 8000
* * * * [misc]points:  Computing exacts for 11 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 8 additional inputs, on iter 32 have 7992 / 8000
* * * * [misc]points:  Computing exacts for 8 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 7 additional inputs, on iter 33 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 34 have 7994 / 8000
* * * * [misc]points:  Computing exacts for 6 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 35 have 7997 / 8000
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 36 have 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 37 have 7998 / 8000
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 38 have 7998 / 8000
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [exit]points:  Sampled 8001 points with exact outputs