* [misc]progress:  [Phase 1 of 3] Setting up.
* * * [misc]progress:  [1/2] Preparing points
* * * * [misc]points:  Sampling 256 additional inputs, on iter 0 have 0 / 256
* * * * [misc]points:  Computing exacts on every 16 of 256 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 64
* * * * [misc]points:  Setting MPFR precision to 320
* * * * [misc]points:  Computing exacts on every 8 of 256 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 64
* * * * [misc]points:  Setting MPFR precision to 320
* * * * [misc]points:  Computing exacts on every 4 of 256 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 64
* * * * [misc]points:  Setting MPFR precision to 320
* * * * [misc]points:  Setting MPFR precision to 576
* * * * [misc]points:  Setting MPFR precision to 832
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 256 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 256 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 207 additional inputs, on iter 1 have 49 / 256
* * * * [misc]points:  Computing exacts on every 12 of 207 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 6 of 207 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 3 of 207 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 207 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 178 additional inputs, on iter 2 have 78 / 256
* * * * [misc]points:  Computing exacts on every 11 of 178 points 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 178 points 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 178 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 178 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 148 additional inputs, on iter 3 have 108 / 256
* * * * [misc]points:  Computing exacts on every 9 of 148 points 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 148 points 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 148 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 148 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 119 additional inputs, on iter 4 have 137 / 256
* * * * [misc]points:  Computing exacts on every 7 of 119 points 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 119 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 119 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 98 additional inputs, on iter 5 have 158 / 256
* * * * [misc]points:  Computing exacts on every 6 of 98 points 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 98 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 98 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 81 additional inputs, on iter 6 have 175 / 256
* * * * [misc]points:  Computing exacts on every 5 of 81 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 81 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 81 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 60 additional inputs, on iter 7 have 196 / 256
* * * * [misc]points:  Computing exacts on every 3 of 60 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 60 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 47 additional inputs, on iter 8 have 209 / 256
* * * * [misc]points:  Computing exacts on every 2 of 47 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 47 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 41 additional inputs, on iter 9 have 215 / 256
* * * * [misc]points:  Computing exacts on every 2 of 41 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 41 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 33 additional inputs, on iter 10 have 223 / 256
* * * * [misc]points:  Computing exacts on every 2 of 33 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 33 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 30 additional inputs, on iter 11 have 226 / 256
* * * * [misc]points:  Computing exacts for 30 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 23 additional inputs, on iter 12 have 233 / 256
* * * * [misc]points:  Computing exacts for 23 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 22 additional inputs, on iter 13 have 234 / 256
* * * * [misc]points:  Computing exacts for 22 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 20 additional inputs, on iter 14 have 236 / 256
* * * * [misc]points:  Computing exacts for 20 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 16 additional inputs, on iter 15 have 240 / 256
* * * * [misc]points:  Computing exacts for 16 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 12 additional inputs, on iter 16 have 244 / 256
* * * * [misc]points:  Computing exacts for 12 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 10 additional inputs, on iter 17 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 8 additional inputs, on iter 18 have 248 / 256
* * * * [misc]points:  Computing exacts for 8 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 8 additional inputs, on iter 19 have 248 / 256
* * * * [misc]points:  Computing exacts for 8 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 8 additional inputs, on iter 20 have 248 / 256
* * * * [misc]points:  Computing exacts for 8 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 6 additional inputs, on iter 21 have 250 / 256
* * * * [misc]points:  Computing exacts for 6 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 22 have 252 / 256
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 23 have 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 24 have 252 / 256
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 25 have 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 26 have 253 / 256
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 27 have 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 28 have 255 / 256
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [exit]points:  Sampled 256 points with exact outputs
* * * [misc]progress:  [2/2] Setting up program.
* [misc]progress:  [Phase 2 of 3] Improving.
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (52 enodes)
* * [misc]simplify:  iters left: 2 (56 enodes)
* * [misc]simplify:  iters left: 1 (63 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))
* * [misc]progress:  iteration 1 / 4
* * * [misc]progress:  picking best candidate
* [misc]none:  Fresh alts: 2
* [misc]none:  All alts: 2
* [misc]none:  Fresh alt: (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* [misc]none:  Fresh alt: (λ (k n) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* [misc]none:  Fresh alt indexes
* [misc]none:  (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))): 0
* [misc]none:  (λ (k n) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))): 1
* [misc]none:  Best fresh alt per point
* [misc]none:  (1.1753256432511238e-228 5.527561153609885e-287): 0
* [misc]none:  (2.624640256823317e-85 2.1533006547486818e+157): 0
* [misc]none:  (3.864150256146345e-97 1.2168501550248481e+60): 0
* [misc]none:  (1.1034521727253742e+17 2.3546907275770535e+149): 0
* [misc]none:  (4.3978295980804844e+144 1.5940531292003016e+119): 0
* [misc]none:  (8.840444084563038e-183 3.964069453939573e+73): 0
* [misc]none:  (1.8837875011322252e+302 1.142354404454184e+266): 0
* [misc]none:  (1.5644360507224123e+19 4.363934278187088e+36): 0
* [misc]none:  (6.602676095404578e+23 6.481090586123572e+252): 0
* [misc]none:  (1.5239258836830995e-62 6.476581985608727e-189): 0
* [misc]none:  (1.3456142459532974e-123 7.606121529176208e-260): 0
* [misc]none:  (3.923033144444403e-103 1.878039942854939e+236): 1
* [misc]none:  (2.3267596557987687e-21 1.2639416915267611e-09): 0
* [misc]none:  (1.4839483695271912e-180 4.236319359533113e+21): 0
* [misc]none:  (2.1399535245004834e+276 3.270611459166715e+34): 0
* [misc]none:  (8.536370391567958e-84 1.891164136132134e+49): 0
* [misc]none:  (4.605809248193487e-97 5.777947225580052e-244): 0
* [misc]none:  (1.0165054836861686e-60 1036775558997374.6): 0
* [misc]none:  (6.352335681656861e-39 6.801961567112795e+279): 0
* [misc]none:  (2.2893883612111785e+80 7.528311916305203e+295): 0
* [misc]none:  (2.7413875160814023e+201 1.9627886189524338e+80): 0
* [misc]none:  (1.460288206470917e-107 1.8754037265125923e+53): 0
* [misc]none:  (2.3582038021458647e-169 4.644032469475324e-293): 1
* [misc]none:  (8.013982873164087e-167 1066969.5668890544): 0
* [misc]none:  (2.9748193650490664e-13 6.657312786881122e+279): 0
* [misc]none:  (7.2184051181595065e-137 6.692885675611668e+43): 0
* [misc]none:  (1.3817340317984848e-70 3.4202164367419544e+286): 1
* [misc]none:  (1.8044196814330305e+68 3808.014138654811): 0
* [misc]none:  (9.8707896780761e+48 2540391067475.896): 0
* [misc]none:  (5.584074513505766e-81 2.134581621197641e-254): 1
* [misc]none:  (1.2790373697624338e+97 4.3076365657194535e+77): 0
* [misc]none:  (3.411814803264884e+189 1.3989843540242142e+234): 0
* [misc]none:  (4.939526601471352e-267 1.2916853433589735e+258): 0
* [misc]none:  (3.7319651198431935e-112 2.6162260071326735e+122): 0
* [misc]none:  (2.1501333373436194e-13 2.3749769913787073e+138): 0
* [misc]none:  (4.213048508546599e-178 9.867184629677251e+277): 0
* [misc]none:  (1.048151880557531e-99 8.951548511660437e+82): 1
* [misc]none:  (3.0143613697172596e-88 5.13242722798329e-86): 0
* [misc]none:  (3.6883120681099563e-37 29787000.29181533): 1
* [misc]none:  (2.4030720834689912e-265 3.871884306060819e+43): 0
* [misc]none:  (8.264072396301485e+225 2.0454004757131322e+253): 0
* [misc]none:  (5.092016746590215e+18 5.258570611990399e+144): 0
* [misc]none:  (8.209474020100443e-75 2.310883431864556e-193): 1
* [misc]none:  (2.557633984455684e-236 1.7871658499983865e+111): 0
* [misc]none:  (1.5798885167282891e+240 9.168081447109565e+225): 0
* [misc]none:  (2.330493073693622e-81 5.988090947952116e+260): 0
* [misc]none:  (3.911253144021059e-37 4.2992902330261985e-14): 0
* [misc]none:  (8.116538701041032e-246 7.045701647143625e+294): 0
* [misc]none:  (7.496050392254423e-292 2.3504027171160204e-302): 0
* [misc]none:  (9.136070273410123e+229 1.1006311214931305e+95): 0
* [misc]none:  (6.90507981640539e+283 7.09998869491861e+138): 0
* [misc]none:  (1.8060877419691232e-65 2.86323673488602e-51): 0
* [misc]none:  (5.827538351320562e+164 3.5086837666926e+285): 0
* [misc]none:  (2.4392121410472106e-273 7.836522530769743e+59): 1
* [misc]none:  (2.78106913943276e-77 1.1548749713964373e-92): 0
* [misc]none:  (1.9839532685168286e-292 7.3223398651315395e-109): 0
* [misc]none:  (8.488844594771612e-127 2.451558198341499e+117): 1
* [misc]none:  (5.66924427203651e-301 2.5461878029353985e-238): 0
* [misc]none:  (9.172918591990658e-289 7.928641158600483e+228): 0
* [misc]none:  (6.519305542840066e-238 1.4209750521719234e+167): 0
* [misc]none:  (1.3456211831302422e+205 1.958667951410614e+85): 0
* [misc]none:  (4.563333642978473e+297 9.749986200278868e+113): 0
* [misc]none:  (1.4648264101470588e+44 6.844241230211939e+198): 0
* [misc]none:  (2.4013812965708594e+221 7.909441760020457e+74): 0
* [misc]none:  (1.2314924435784377e+276 4.478509484643543e+146): 0
* [misc]none:  (2.5583314633633054e-07 1.699201102491909e+300): 1
* [misc]none:  (1.5042239853613876e-302 9.360780180304737e+153): 1
* [misc]none:  (5.106692251999635e+137 3.2350731648968916e+240): 0
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* [misc]none:  (222693309.28876954 2.0187517395999946e+158): 0
* [misc]none:  (2.1626561181515632e-29 6.562952916996993e-49): 0
* [misc]none:  (3.1723784288762247e-174 1.806578923933048e-16): 0
* [misc]none:  (1.5368130424239484e-258 1.0793824307213477e-07): 0
* [misc]none:  (1.4626644606135493e-149 2.3190166729712657e-212): 0
* [misc]none:  (4.3549030909845e-39 9.058284202735603e+73): 0
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* [misc]none:  (5.648741298751521e+200 2.472667741952997e+135): 0
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* [misc]none:  (5.403613002727931e-172 1.6647025455145767e-98): 0
* [misc]none:  (1.6628636236275568e-296 4.757518029573035e+252): 0
* [misc]none:  (8.616872328504591e-169 2.705259708711105e-42): 0
* [misc]none:  (1.6795280764094681e+192 2.6457818831137444e+63): 0
* [misc]none:  (2.295309343983191e-140 5.571074723663966e-15): 0
* [misc]none:  (1.1191451223002718e-275 3.251721996184718e+286): 0
* [misc]none:  (4.1049298747354824e-124 9.30992191853363e-100): 0
* [misc]none:  (1.3462923322550312e-190 2.328447698134118e+189): 0
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* [misc]none:  (1.740072246435861e-207 1.3636559368742825e-149): 0
* [misc]none:  (1.946944651699716e-139 6.333153678225876e-68): 0
* [misc]none:  (8.70336562916574e-216 7.84549397492709e+169): 1
* [misc]none:  (7.762114448443534e+255 1.682179526351612e+60): 0
* [misc]none:  (6.330170018440137e-77 6.04623429007003e-242): 0
* [misc]none:  (2.3080855823624493e-299 4.50326449267665e+246): 1
* [misc]none:  (1.0100264902476595e-152 6.2370208452565505e-251): 0
* [misc]none:  (0.002518103001908201 2.819308104709626e+146): 0
* [misc]none:  (4.19388438569828e-183 3.636662419716013e-100): 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)
* * * * [misc]progress:  [ 2 / 3 ] rewriting at (2 1 1)
* * * * [misc]progress:  [ 3 / 3 ] rewriting at (2 1)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 3 ] generating series at (2)
* [misc]approximate:  Taking taylor expansion of (/ (pow (* n (* 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:  [ 2 / 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:  [ 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) (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:  [ 2 / 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:  [ 3 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (pow (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) 1))>
* * * * [misc]progress:  [ 4 / 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:  [ 5 / 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:  [ 6 / 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:  [ 7 / 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:  [ 8 / 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:  [ 9 / 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:  [ 10 / 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:  [ 11 / 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:  [ 12 / 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:  [ 13 / 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:  [ 14 / 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:  [ 15 / 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:  [ 16 / 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:  [ 17 / 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:  [ 18 / 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:  [ 19 / 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:  [ 20 / 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:  [ 21 / 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:  [ 22 / 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:  [ 23 / 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:  [ 24 / 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:  [ 25 / 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:  [ 26 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))>
* * * * [misc]progress:  [ 27 / 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:  [ 28 / 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:  [ 29 / 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:  [ 30 / 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:  [ 31 / 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:  [ 32 / 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:  [ 33 / 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:  [ 34 / 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:  [ 35 / 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:  [ 36 / 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:  [ 37 / 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:  [ 38 / 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:  [ 39 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* n (* PI 2)) 1) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 40 / 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:  [ 41 / 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:  [ 42 / 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:  [ 43 / 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:  [ 44 / 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:  [ 45 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* 1 (* n (* PI 2))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 46 / 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:  [ 47 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [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) (- (+ (* +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:  [ 67 / 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:  [ 68 / 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:  [ 69 / 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:  [ 70 / 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:  [ 71 / 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:  [ 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: 13
* [misc]none:  All alts: 13
* [misc]none:  Fresh alt: (λ (k n) (* (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (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)))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))
* [misc]none:  Fresh alt: (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* [misc]none:  Fresh alt: (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* [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) (* (/ (* (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) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))
* [misc]none:  Fresh alt: (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (cbrt (sqrt k)))))
* [misc]none:  Fresh alt: (λ (k n) (/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))))
* [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) (/ (+ (* (* (* (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 (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))
* [misc]none:  Fresh alt indexes
* [misc]none:  (λ (k n) (* (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)))): 0
* [misc]none:  (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))))): 1
* [misc]none:  (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))): 2
* [misc]none:  (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k))))): 3
* [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))))): 4
* [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))))): 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) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (cbrt (sqrt k))))): 7
* [misc]none:  (λ (k n) (/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2))))): 8
* [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)))))): 9
* [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))): 10
* [misc]none:  (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))): 11
* [misc]none:  (λ (k n) (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k))): 12
* [misc]none:  Best fresh alt per point
* [misc]none:  (1.1753256432511238e-228 5.527561153609885e-287): 2
* [misc]none:  (2.624640256823317e-85 2.1533006547486818e+157): 1
* [misc]none:  (3.864150256146345e-97 1.2168501550248481e+60): 0
* [misc]none:  (1.1034521727253742e+17 2.3546907275770535e+149): 0
* [misc]none:  (4.3978295980804844e+144 1.5940531292003016e+119): 0
* [misc]none:  (8.840444084563038e-183 3.964069453939573e+73): 1
* [misc]none:  (1.8837875011322252e+302 1.142354404454184e+266): 0
* [misc]none:  (1.5644360507224123e+19 4.363934278187088e+36): 0
* [misc]none:  (6.602676095404578e+23 6.481090586123572e+252): 0
* [misc]none:  (1.5239258836830995e-62 6.476581985608727e-189): 3
* [misc]none:  (1.3456142459532974e-123 7.606121529176208e-260): 5
* [misc]none:  (3.923033144444403e-103 1.878039942854939e+236): 0
* [misc]none:  (2.3267596557987687e-21 1.2639416915267611e-09): 4
* [misc]none:  (1.4839483695271912e-180 4.236319359533113e+21): 3
* [misc]none:  (2.1399535245004834e+276 3.270611459166715e+34): 0
* [misc]none:  (8.536370391567958e-84 1.891164136132134e+49): 2
* [misc]none:  (4.605809248193487e-97 5.777947225580052e-244): 0
* [misc]none:  (1.0165054836861686e-60 1036775558997374.6): 2
* [misc]none:  (6.352335681656861e-39 6.801961567112795e+279): 6
* [misc]none:  (2.2893883612111785e+80 7.528311916305203e+295): 0
* [misc]none:  (2.7413875160814023e+201 1.9627886189524338e+80): 0
* [misc]none:  (1.460288206470917e-107 1.8754037265125923e+53): 0
* [misc]none:  (2.3582038021458647e-169 4.644032469475324e-293): 2
* [misc]none:  (8.013982873164087e-167 1066969.5668890544): 0
* [misc]none:  (2.9748193650490664e-13 6.657312786881122e+279): 10
* [misc]none:  (7.2184051181595065e-137 6.692885675611668e+43): 1
* [misc]none:  (1.3817340317984848e-70 3.4202164367419544e+286): 2
* [misc]none:  (1.8044196814330305e+68 3808.014138654811): 0
* [misc]none:  (9.8707896780761e+48 2540391067475.896): 0
* [misc]none:  (5.584074513505766e-81 2.134581621197641e-254): 1
* [misc]none:  (1.2790373697624338e+97 4.3076365657194535e+77): 0
* [misc]none:  (3.411814803264884e+189 1.3989843540242142e+234): 0
* [misc]none:  (4.939526601471352e-267 1.2916853433589735e+258): 3
* [misc]none:  (3.7319651198431935e-112 2.6162260071326735e+122): 0
* [misc]none:  (2.1501333373436194e-13 2.3749769913787073e+138): 6
* [misc]none:  (4.213048508546599e-178 9.867184629677251e+277): 8
* [misc]none:  (1.048151880557531e-99 8.951548511660437e+82): 6
* [misc]none:  (3.0143613697172596e-88 5.13242722798329e-86): 2
* [misc]none:  (3.6883120681099563e-37 29787000.29181533): 6
* [misc]none:  (2.4030720834689912e-265 3.871884306060819e+43): 2
* [misc]none:  (8.264072396301485e+225 2.0454004757131322e+253): 0
* [misc]none:  (5.092016746590215e+18 5.258570611990399e+144): 0
* [misc]none:  (8.209474020100443e-75 2.310883431864556e-193): 3
* [misc]none:  (2.557633984455684e-236 1.7871658499983865e+111): 0
* [misc]none:  (1.5798885167282891e+240 9.168081447109565e+225): 0
* [misc]none:  (2.330493073693622e-81 5.988090947952116e+260): 4
* [misc]none:  (3.911253144021059e-37 4.2992902330261985e-14): 2
* [misc]none:  (8.116538701041032e-246 7.045701647143625e+294): 0
* [misc]none:  (7.496050392254423e-292 2.3504027171160204e-302): 4
* [misc]none:  (9.136070273410123e+229 1.1006311214931305e+95): 0
* [misc]none:  (6.90507981640539e+283 7.09998869491861e+138): 0
* [misc]none:  (1.8060877419691232e-65 2.86323673488602e-51): 1
* [misc]none:  (5.827538351320562e+164 3.5086837666926e+285): 0
* [misc]none:  (2.4392121410472106e-273 7.836522530769743e+59): 4
* [misc]none:  (2.78106913943276e-77 1.1548749713964373e-92): 9
* [misc]none:  (1.9839532685168286e-292 7.3223398651315395e-109): 2
* [misc]none:  (8.488844594771612e-127 2.451558198341499e+117): 6
* [misc]none:  (5.66924427203651e-301 2.5461878029353985e-238): 2
* [misc]none:  (9.172918591990658e-289 7.928641158600483e+228): 2
* [misc]none:  (6.519305542840066e-238 1.4209750521719234e+167): 2
* [misc]none:  (1.3456211831302422e+205 1.958667951410614e+85): 0
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* [misc]none:  (1.5042239853613876e-302 9.360780180304737e+153): 3
* [misc]none:  (5.106692251999635e+137 3.2350731648968916e+240): 0
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* [misc]none:  (1.5368130424239484e-258 1.0793824307213477e-07): 2
* [misc]none:  (1.4626644606135493e-149 2.3190166729712657e-212): 2
* [misc]none:  (4.3549030909845e-39 9.058284202735603e+73): 1
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* [misc]none:  (5.403613002727931e-172 1.6647025455145767e-98): 7
* [misc]none:  (1.6628636236275568e-296 4.757518029573035e+252): 4
* [misc]none:  (8.616872328504591e-169 2.705259708711105e-42): 0
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* [misc]none:  (1.1191451223002718e-275 3.251721996184718e+286): 4
* [misc]none:  (4.1049298747354824e-124 9.30992191853363e-100): 4
* [misc]none:  (1.3462923322550312e-190 2.328447698134118e+189): 0
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* [misc]none:  (3.0253434819547994e-130 3.6409363071987465e-75): 6
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* [misc]none:  (2.9761497868954784e-39 1.6756011214932844e-91): 2
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* [misc]none:  (1.2420866124564814e-293 6.3461851602547e-177): 2
* [misc]none:  (2.01314860958205e-179 4.1821161712206335e+98): 2
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* [misc]none:  (1.740072246435861e-207 1.3636559368742825e-149): 2
* [misc]none:  (1.946944651699716e-139 6.333153678225876e-68): 2
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* [misc]none:  (7.762114448443534e+255 1.682179526351612e+60): 0
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* [misc]none:  (1.0100264902476595e-152 6.2370208452565505e-251): 0
* [misc]none:  (0.002518103001908201 2.819308104709626e+146): 6
* [misc]none:  (4.19388438569828e-183 3.636662419716013e-100): 4
* [misc]none:  All alt indexes
* [misc]none:  (λ (k n) (* (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)))): 0
* [misc]none:  (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))))): 1
* [misc]none:  (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))): 2
* [misc]none:  (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k))))): 3
* [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))))): 4
* [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))))): 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) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (cbrt (sqrt k))))): 7
* [misc]none:  (λ (k n) (/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2))))): 8
* [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)))))): 9
* [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))): 10
* [misc]none:  (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))): 11
* [misc]none:  (λ (k n) (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k))): 12
* [misc]none:  Best alt per point
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* [misc]none:  (2.624640256823317e-85 2.1533006547486818e+157): 1
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* [misc]none:  (4.3978295980804844e+144 1.5940531292003016e+119): 0
* [misc]none:  (8.840444084563038e-183 3.964069453939573e+73): 1
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* [misc]none:  (1.5644360507224123e+19 4.363934278187088e+36): 0
* [misc]none:  (6.602676095404578e+23 6.481090586123572e+252): 0
* [misc]none:  (1.5239258836830995e-62 6.476581985608727e-189): 3
* [misc]none:  (1.3456142459532974e-123 7.606121529176208e-260): 5
* [misc]none:  (3.923033144444403e-103 1.878039942854939e+236): 0
* [misc]none:  (2.3267596557987687e-21 1.2639416915267611e-09): 4
* [misc]none:  (1.4839483695271912e-180 4.236319359533113e+21): 3
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* [misc]none:  (1.8269212298308998e+214 1789977963981.046): 0
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* [misc]none:  (6.853656747763464e-298 1.5907488733120222e-68): 2
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* [misc]none:  (6.186245288104366e-177 4.0009214940503626e-296): 1
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* [misc]none:  (2.802805856656922e+299 3267744482859.4893): 0
* [misc]none:  (4.3906960513010925e-288 9.735553079850294e-195): 10
* [misc]none:  (2.617385806499904e-208 6.454193966659965e-12): 2
* [misc]none:  (1.2843486366644783e+218 1.6598105327534946e+245): 0
* [misc]none:  (6.352964037059704e-48 2.0675888684205106e-37): 4
* [misc]none:  (1.434478809327731e-162 1.7673263201240207e+200): 2
* [misc]none:  (4.1358060479750856e+163 2.77377213114978e+181): 0
* [misc]none:  (3.851639943546658e-220 7.262940842293714e+141): 3
* [misc]none:  (1175954691713314.2 1.6505576250215693e+254): 0
* [misc]none:  (1.9640202737101926e+158 4.0355590295024944e+30): 0
* [misc]none:  (3.795139234164696e-109 9.806701774277626e-103): 2
* [misc]none:  (2.6870891996869854e+222 1.403842517343178e+239): 0
* [misc]none:  (2.1939039916199917e-151 6.704445560737266e-185): 0
* [misc]none:  (2.0407374713985817e-67 6.798712177335776e+112): 2
* [misc]none:  (1.37725435443438e-133 2.7744697188841963e+109): 4
* [misc]none:  (4.163796059008999e+263 9.568517745632325e+214): 0
* [misc]none:  (2.4645417753990825e-46 1.1531681692158285e+126): 1
* [misc]none:  (2.8621091346925045e-294 1.532108192832722e+128): 7
* [misc]none:  (1.2420866124564814e-293 6.3461851602547e-177): 2
* [misc]none:  (2.01314860958205e-179 4.1821161712206335e+98): 2
* [misc]none:  (2.5937923840174148e+191 2.0634010725481968e+279): 0
* [misc]none:  (1.740072246435861e-207 1.3636559368742825e-149): 2
* [misc]none:  (1.946944651699716e-139 6.333153678225876e-68): 2
* [misc]none:  (8.70336562916574e-216 7.84549397492709e+169): 0
* [misc]none:  (7.762114448443534e+255 1.682179526351612e+60): 0
* [misc]none:  (6.330170018440137e-77 6.04623429007003e-242): 2
* [misc]none:  (2.3080855823624493e-299 4.50326449267665e+246): 4
* [misc]none:  (1.0100264902476595e-152 6.2370208452565505e-251): 0
* [misc]none:  (0.002518103001908201 2.819308104709626e+146): 6
* [misc]none:  (4.19388438569828e-183 3.636662419716013e-100): 4
* [misc]none:  Picked 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]pick:  Picked  #<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)))))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 4 ] rewriting at (2)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2 2 1)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2 1 1)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2 2 1 1 1)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 4 ] generating series at (2)
* [misc]approximate:  Taking taylor expansion of (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) in k
* [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]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ (* +nan.0 (sqrt (* n (* 2 PI)))) (* 2 (sqrt 0))) into (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) in k
* [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]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ (* +nan.0 (sqrt (* n (* 2 PI)))) (* 2 (sqrt 0))) into (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) in 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]backup-simplify:  Simplify (sqrt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) into (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (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]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]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) in 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]backup-simplify:  Simplify (sqrt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) into (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (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]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]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) in 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]backup-simplify:  Simplify (sqrt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) into (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (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]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]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) in 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]backup-simplify:  Simplify (sqrt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) into (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (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]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]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (* (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))))) 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 (+ (* (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) 0) (* 0 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [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 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]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) 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) 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]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) 0) (+ (* 0 0) (* 0 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))))))) 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 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]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) 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) 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]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))))) 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 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 (- 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)) (* 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 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 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 (pow 0 2) (+ (* 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))) (* 0 (/ 0 (sqrt k))))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) 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 (- 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)) (* 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 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 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 (pow 0 2) (+ (* 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))) (* 0 (/ 0 (sqrt k))))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (pow (/ 1 k) 1/4) (sqrt (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))))))))) 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 (* (sqrt (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) (sqrt (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) (sqrt (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) into (* (sqrt +nan.0) (sqrt (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (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))))))) (* 2 (sqrt (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))))) into (* +nan.0 (* (/ 1 (sqrt +nan.0)) (sqrt (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) into (* (sqrt +nan.0) (sqrt (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (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))))))) (* 2 (sqrt (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))))) into (* +nan.0 (* (/ 1 (sqrt +nan.0)) (sqrt (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))))
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) (sqrt (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))) into (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4))
* [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]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))) into (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4))
* [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]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))))) into 0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) (sqrt (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))) into (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4))
* [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]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))) into (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4))
* [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]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))))) into 0
* [misc]backup-simplify:  Simplify (* (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)) (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4))) 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 (+ (* (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)) 0) (* 0 (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)))) 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]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)))) 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]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]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)) 0) (+ (* 0 0) (* 0 (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4))))) 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]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)))) 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]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]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) (pow k 1/4)))))) 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 (* (sqrt (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) (sqrt (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) (sqrt (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) into (* (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) (sqrt +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 (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (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)))))))) (* 2 (sqrt (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))))) into (* +nan.0 (* (/ 1 (sqrt +nan.0)) (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) into (* (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) (sqrt +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 (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (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)))))))) (* 2 (sqrt (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))))) into (* +nan.0 (* (/ 1 (sqrt +nan.0)) (sqrt (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))))
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) (sqrt (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))) into (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 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 (- 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]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))) into (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 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 (- 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]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) (sqrt (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))) into (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 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 (- 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]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of (sqrt (/ (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)) (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]backup-simplify:  Simplify (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))) into (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 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 (- 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]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))))) into 0
* [misc]backup-simplify:  Simplify (* (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))) (sqrt (/ (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 (+ (* (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))) 0) (* 0 (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (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]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))))) 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]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]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))) 0) (+ (* 0 0) (* 0 (sqrt (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (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:  [ 2 / 4 ] generating series at (2 2 1)
* [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 / 4 ] generating series at (2 1 1)
* [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:  [ 4 / 4 ] generating series at (2 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:  simplifying candidates
* * * * [misc]progress:  [ 1 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (log1p (expm1 (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (expm1 (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* [exit]simplify:  Simplified to (expm1 (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (expm1 (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 2 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (expm1 (log1p (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (log1p (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* [exit]simplify:  Simplified to (log1p (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (log1p (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 3 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (pow (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) (+ 1/2 1/2)))>
* [enter]simplify:  Simplifying (+ 1/2 1/2)
* * [misc]simplify:  iters left: 2 (2 enodes)
* [exit]simplify:  Simplified to (+ 1/2 1/2)
* [exit]simplify:  Simplified to (+ 1/2 1/2)
* * * * [misc]progress:  [ 4 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (pow (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (+ 1 1)))>
* [enter]simplify:  Simplifying (+ 1 1)
* * [misc]simplify:  iters left: 2 (2 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (+ 1 1)
* [exit]simplify:  Simplified to (+ 1 1)
* * * * [misc]progress:  [ 5 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (pow (* (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) 1/2))>
* [enter]simplify:  Simplifying (* (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (52 enodes)
* * [misc]simplify:  iters left: 2 (55 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* PI (* n 2)) (/ (- 1 k) 2)) (pow (* PI (* n 2)) (/ (- 1 k) 2))) k)
* [exit]simplify:  Simplified to (/ (* (pow (* PI (* n 2)) (/ (- 1 k) 2)) (pow (* PI (* n 2)) (/ (- 1 k) 2))) k)
* * * * [misc]progress:  [ 6 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (pow (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) 1))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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 (35 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 7 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (pow (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) 2))>
* * * * [misc]progress:  [ 8 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (pow (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (+ 1 1)))>
* [enter]simplify:  Simplifying (+ 1 1)
* * [misc]simplify:  iters left: 2 (2 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (+ 1 1)
* [exit]simplify:  Simplified to (+ 1 1)
* * * * [misc]progress:  [ 9 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (pow (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) 1))>
* * * * [misc]progress:  [ 10 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (log (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (log (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (log (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (log (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (+ (log (sqrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))) (log (sqrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))))
* [exit]simplify:  Simplified to (+ (log (sqrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))) (log (sqrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))))
* * * * [misc]progress:  [ 11 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (exp (log (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (log (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (41 enodes)
* * [misc]simplify:  iters left: 3 (48 enodes)
* * [misc]simplify:  iters left: 2 (65 enodes)
* * [misc]simplify:  iters left: 1 (132 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:  [ 12 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (log (exp (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (exp (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (38 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* [exit]simplify:  Simplified to (exp (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (exp (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 13 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (* (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (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))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (58 enodes)
* * [misc]simplify:  iters left: 3 (107 enodes)
* * [misc]simplify:  iters left: 2 (162 enodes)
* * [misc]simplify:  iters left: 1 (268 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:  [ 14 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (cbrt (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))) (cbrt (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))) (cbrt (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (* (cbrt (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))) (cbrt (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k))))
* [enter]simplify:  Simplifying (cbrt (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* [exit]simplify:  Simplified to (cbrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (cbrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 15 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (* (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))) (* (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))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (34 enodes)
* * [misc]simplify:  iters left: 4 (62 enodes)
* * [misc]simplify:  iters left: 3 (117 enodes)
* * [misc]simplify:  iters left: 2 (178 enodes)
* * [misc]simplify:  iters left: 1 (301 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:  [ 16 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (sqrt (* (/ (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)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (52 enodes)
* * [misc]simplify:  iters left: 2 (55 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* PI (* n 2)) (/ (- 1 k) 2)) (pow (* PI (* n 2)) (/ (- 1 k) 2))) k)
* [exit]simplify:  Simplified to (/ (* (pow (* PI (* n 2)) (/ (- 1 k) 2)) (pow (* PI (* n 2)) (/ (- 1 k) 2))) k)
* * * * [misc]progress:  [ 17 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))) (sqrt (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))))>
* [enter]simplify:  Simplifying (sqrt (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (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 (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k)))
* [enter]simplify:  Simplifying (sqrt (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (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 (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 18 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 19 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (sqrt (sqrt k)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (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 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (pow (* PI (* n 2)) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow (* PI (* n 2)) (/ (- 1 k) 2))
* [enter]simplify:  Simplifying (* (sqrt (sqrt k)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* [exit]simplify:  Simplified to (sqrt k)
* [exit]simplify:  Simplified to (sqrt k)
* * * * [misc]progress:  [ 20 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))))>
* * * * [misc]progress:  [ 21 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (* (cbrt (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))) (cbrt (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (* (cbrt (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (41 enodes)
* * [misc]simplify:  iters left: 3 (44 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) (* (cbrt (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) (* (cbrt (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))))))
* * * * [misc]progress:  [ 22 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))) (sqrt (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* (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 (17 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* [exit]simplify:  Simplified to (* (fabs (cbrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (fabs (cbrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 23 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))) (sqrt (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (15 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 (* (sqrt (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 24 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (45 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 25 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))))) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 26 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1))) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) 1)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* [exit]simplify:  Simplified to (* (sqrt (pow n (/ (- 1 k) 2))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (pow n (/ (- 1 k) 2))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 27 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (* (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 (20 enodes)
* * [misc]simplify:  iters left: 5 (38 enodes)
* * [misc]simplify:  iters left: 4 (57 enodes)
* * [misc]simplify:  iters left: 3 (63 enodes)
* * [misc]simplify:  iters left: 2 (66 enodes)
* [exit]simplify:  Simplified to (* (fabs (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (fabs (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 28 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt k))))) (sqrt (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (48 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (* (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (* (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 29 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) 1))) (sqrt (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) 1)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (48 enodes)
* * [misc]simplify:  iters left: 3 (56 enodes)
* * [misc]simplify:  iters left: 2 (66 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) (fabs (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) (fabs (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 30 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (45 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 31 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))))) (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 32 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) 1))) (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) 1)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* [exit]simplify:  Simplified to (* (sqrt (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 33 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ 1 (* (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)) (sqrt k))) (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (41 enodes)
* * [misc]simplify:  iters left: 3 (44 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 34 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ 1 (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 k))) (sqrt (/ 1 (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (38 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 35 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ 1 1))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ 1 1)))
* * [misc]simplify:  iters left: 6 (16 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 (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k))) (sqrt 1))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k))) (sqrt 1))
* * * * [misc]progress:  [ 36 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt 1)) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt 1))
* * [misc]simplify:  iters left: 6 (15 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 (* (sqrt 1) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt 1) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 37 / 156 ] 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 (/ 1 (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (15 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 (* (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 38 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))) (sqrt (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))
* * [misc]simplify:  iters left: 6 (15 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 (* (sqrt (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 39 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) 1) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) 1)
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (26 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)) (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 40 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (cbrt (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))) (* (cbrt (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (cbrt (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 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 (* (cbrt (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (cbrt (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 41 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))) (* (sqrt (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 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 (cbrt (/ (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (cbrt (/ (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 42 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (* (sqrt (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 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 (* (sqrt (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 43 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 44 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))) (* (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 45 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow n (/ (- 1 k) 2)) 1)) (* (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (38 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 46 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 47 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))) (* (sqrt (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 48 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) 1)) (* (sqrt (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (38 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt k))))
* * * * [misc]progress:  [ 49 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 50 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (* (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 51 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) 1)) (* (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (38 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt k))))
* * * * [misc]progress:  [ 52 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (38 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (cbrt (sqrt k)))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 53 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ 1 (sqrt (sqrt k)))) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (38 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 54 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ 1 1)) (* (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))) (sqrt (/ (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 (35 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 55 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt 1) (* (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))) (sqrt (/ (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 (35 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 56 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (sqrt (/ 1 (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ 1 (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 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)) (sqrt k))) (sqrt (/ 1 (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ 1 (sqrt k))))
* * * * [misc]progress:  [ 57 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (* (sqrt (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 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 (* (sqrt (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 58 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (* (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))) (sqrt (/ (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 (35 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 59 / 156 ] 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 (sqrt k))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (15 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 (* (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 60 / 156 ] 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)))) (sqrt (sqrt k))))>
* [enter]simplify:  Simplifying (* (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 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 (* (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (* (sqrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 61 / 156 ] 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)))))>
* * * * [misc]progress:  [ 62 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (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:  [ 63 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (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:  [ 64 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (pow (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) 1))))>
* * * * [misc]progress:  [ 65 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (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:  [ 66 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (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:  [ 67 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (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:  [ 68 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (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:  [ 69 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (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:  [ 70 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (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:  [ 71 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* (* (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:  [ 72 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (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:  [ 73 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* (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:  [ 74 / 156 ] 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 (- (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:  [ 75 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* (/ (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:  [ 76 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* (/ (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:  [ 77 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* (/ (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:  [ 78 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* (/ (* (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:  [ 79 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* (/ (* (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:  [ 80 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* (/ (* (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:  [ 81 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* (/ (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:  [ 82 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* (/ (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:  [ 83 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* (/ (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:  [ 84 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* (/ 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:  [ 85 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* (/ 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:  [ 86 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* (/ 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:  [ 87 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (* 1 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))))>
* * * * [misc]progress:  [ 88 / 156 ] 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)) (/ 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:  [ 89 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ 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:  [ 90 / 156 ] 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)) (* (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:  [ 91 / 156 ] 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 (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:  [ 92 / 156 ] 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)) 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:  [ 93 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 94 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (* (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:  [ 95 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 96 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ 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:  [ 97 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 98 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (log1p (expm1 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))) (sqrt (/ (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:  [ 99 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (expm1 (log1p (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))) (sqrt (/ (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:  [ 100 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (pow (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) 1)) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 101 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (exp (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (log (sqrt k))))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (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:  [ 102 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (exp (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (log (sqrt k))))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (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:  [ 103 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (exp (- (log (pow (* n (* PI 2)) (/ (- 1 k) 2))) (log (sqrt k))))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (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:  [ 104 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (exp (log (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))) (sqrt (/ (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:  [ 105 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (log (exp (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))) (sqrt (/ (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:  [ 106 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (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))))) (sqrt (/ (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))) (* (* (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:  [ 107 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (* (* (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))))) (sqrt (/ (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:  [ 108 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (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))))) (sqrt (/ (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:  [ 109 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (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:  [ 110 / 156 ] 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 (- (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:  [ 111 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (* (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt k))))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (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:  [ 112 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k))))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (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:  [ 113 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (* (/ (pow n (/ (- 1 k) 2)) 1) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (* 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:  [ 114 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (* (/ (* (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))))) (sqrt (/ (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)))) (* (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:  [ 115 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (* (/ (* (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))))) (sqrt (/ (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)))) (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:  [ 116 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (* (/ (* (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)))) (sqrt (/ (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:  [ 117 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (* (/ (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))))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (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:  [ 118 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (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:  [ 119 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) 1) (/ (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))) 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:  [ 120 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (cbrt (sqrt k))))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (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:  [ 121 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (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:  [ 122 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (* (/ 1 1) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (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:  [ 123 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (* 1 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 124 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (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:  [ 125 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ 1 (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2))))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
* [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:  [ 126 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (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:  [ 127 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (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:  [ 128 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) 1) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (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:  [ 129 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2))))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
* [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:  [ 130 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (* (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)))))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
* [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:  [ 131 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
* [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:  [ 132 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ 1 (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2))))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
* [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:  [ 133 / 156 ] 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 k) 2)) (sqrt k)))))>
* [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:  [ 134 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 135 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 136 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (pow (* n (* PI 2)) 1) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 137 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 138 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 139 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 140 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 141 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (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:  [ 142 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 1 (* n (* PI 2))) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 143 / 156 ] 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 (* 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:  [ 144 / 156 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 145 / 156 ] 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:  [ 146 / 156 ] 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:  [ 147 / 156 ] 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:  [ 148 / 156 ] simplifiying candidate #<alt-event (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (- (+ (* +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 (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (- (+ (* +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:  [ 149 / 156 ] simplifiying candidate #<alt-event (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (- (+ (* +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 (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (- (+ (* +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:  [ 150 / 156 ] simplifiying candidate #<alt-event (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (- (+ (* +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 (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (- (+ (* +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:  [ 151 / 156 ] simplifiying candidate #<alt-event (λ (k n) (* (sqrt (- (+ (* +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))))))))))))))))))))))))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (- (+ (* +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))))))))))))))))))))))))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 152 / 156 ] simplifiying candidate #<alt-event (λ (k n) (* (sqrt (- (+ (* +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)))))))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (- (+ (* +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)))))))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 153 / 156 ] simplifiying candidate #<alt-event (λ (k n) (* (sqrt (- (+ (* +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))))))))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (- (+ (* +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))))))))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 154 / 156 ] simplifiying candidate #<alt-event (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 155 / 156 ] simplifiying candidate #<alt-event (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 156 / 156 ] simplifiying candidate #<alt-event (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))
* * * [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: 10
* [misc]none:  Fresh alt: (λ (k n) (* (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (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)))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))
* [misc]none:  Fresh alt: (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* [misc]none:  Fresh alt: (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* [misc]none:  Non-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)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt k))))))
* [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) (/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))))
* [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) (/ (+ (* (* (* (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 (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))
* [misc]none:  Fresh alt indexes
* [misc]none:  (λ (k n) (* (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)))): 0
* [misc]none:  (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))))): 1
* [misc]none:  (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))): 2
* [misc]none:  (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k))))): 3
* [misc]none:  (λ (k n) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt k)))))): 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) (/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2))))): 6
* [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)))))): 7
* [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))): 8
* [misc]none:  (λ (k n) (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k))): 9
* [misc]none:  Best fresh alt per point
* [misc]none:  (1.1753256432511238e-228 5.527561153609885e-287): 2
* [misc]none:  (2.624640256823317e-85 2.1533006547486818e+157): 1
* [misc]none:  (3.864150256146345e-97 1.2168501550248481e+60): 0
* [misc]none:  (1.1034521727253742e+17 2.3546907275770535e+149): 0
* [misc]none:  (4.3978295980804844e+144 1.5940531292003016e+119): 0
* [misc]none:  (8.840444084563038e-183 3.964069453939573e+73): 1
* [misc]none:  (1.8837875011322252e+302 1.142354404454184e+266): 0
* [misc]none:  (1.5644360507224123e+19 4.363934278187088e+36): 0
* [misc]none:  (6.602676095404578e+23 6.481090586123572e+252): 0
* [misc]none:  (1.5239258836830995e-62 6.476581985608727e-189): 3
* [misc]none:  (1.3456142459532974e-123 7.606121529176208e-260): 4
* [misc]none:  (3.923033144444403e-103 1.878039942854939e+236): 0
* [misc]none:  (2.3267596557987687e-21 1.2639416915267611e-09): 5
* [misc]none:  (1.4839483695271912e-180 4.236319359533113e+21): 3
* [misc]none:  (2.1399535245004834e+276 3.270611459166715e+34): 0
* [misc]none:  (8.536370391567958e-84 1.891164136132134e+49): 2
* [misc]none:  (4.605809248193487e-97 5.777947225580052e-244): 0
* [misc]none:  (1.0165054836861686e-60 1036775558997374.6): 2
* [misc]none:  (6.352335681656861e-39 6.801961567112795e+279): 5
* [misc]none:  (2.2893883612111785e+80 7.528311916305203e+295): 0
* [misc]none:  (2.7413875160814023e+201 1.9627886189524338e+80): 0
* [misc]none:  (1.460288206470917e-107 1.8754037265125923e+53): 0
* [misc]none:  (2.3582038021458647e-169 4.644032469475324e-293): 2
* [misc]none:  (8.013982873164087e-167 1066969.5668890544): 0
* [misc]none:  (2.9748193650490664e-13 6.657312786881122e+279): 8
* [misc]none:  (7.2184051181595065e-137 6.692885675611668e+43): 1
* [misc]none:  (1.3817340317984848e-70 3.4202164367419544e+286): 2
* [misc]none:  (1.8044196814330305e+68 3808.014138654811): 0
* [misc]none:  (9.8707896780761e+48 2540391067475.896): 0
* [misc]none:  (5.584074513505766e-81 2.134581621197641e-254): 1
* [misc]none:  (1.2790373697624338e+97 4.3076365657194535e+77): 0
* [misc]none:  (3.411814803264884e+189 1.3989843540242142e+234): 0
* [misc]none:  (4.939526601471352e-267 1.2916853433589735e+258): 3
* [misc]none:  (3.7319651198431935e-112 2.6162260071326735e+122): 0
* [misc]none:  (2.1501333373436194e-13 2.3749769913787073e+138): 5
* [misc]none:  (4.213048508546599e-178 9.867184629677251e+277): 6
* [misc]none:  (1.048151880557531e-99 8.951548511660437e+82): 5
* [misc]none:  (3.0143613697172596e-88 5.13242722798329e-86): 2
* [misc]none:  (3.6883120681099563e-37 29787000.29181533): 5
* [misc]none:  (2.4030720834689912e-265 3.871884306060819e+43): 2
* [misc]none:  (8.264072396301485e+225 2.0454004757131322e+253): 0
* [misc]none:  (5.092016746590215e+18 5.258570611990399e+144): 0
* [misc]none:  (8.209474020100443e-75 2.310883431864556e-193): 3
* [misc]none:  (2.557633984455684e-236 1.7871658499983865e+111): 0
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* [misc]none:  (3.911253144021059e-37 4.2992902330261985e-14): 2
* [misc]none:  (8.116538701041032e-246 7.045701647143625e+294): 0
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* [misc]none:  (1.8060877419691232e-65 2.86323673488602e-51): 1
* [misc]none:  (5.827538351320562e+164 3.5086837666926e+285): 0
* [misc]none:  (2.4392121410472106e-273 7.836522530769743e+59): 5
* [misc]none:  (2.78106913943276e-77 1.1548749713964373e-92): 7
* [misc]none:  (1.9839532685168286e-292 7.3223398651315395e-109): 2
* [misc]none:  (8.488844594771612e-127 2.451558198341499e+117): 5
* [misc]none:  (5.66924427203651e-301 2.5461878029353985e-238): 2
* [misc]none:  (9.172918591990658e-289 7.928641158600483e+228): 2
* [misc]none:  (6.519305542840066e-238 1.4209750521719234e+167): 2
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* [misc]none:  (3.4661781947574473e-174 1.0749556482282616e+190): 0
* [misc]none:  (9.59713490648927e-79 2.5679653914894944e+44): 0
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* [misc]none:  (1.740072246435861e-207 1.3636559368742825e-149): 2
* [misc]none:  (1.946944651699716e-139 6.333153678225876e-68): 2
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* [misc]none:  (7.762114448443534e+255 1.682179526351612e+60): 0
* [misc]none:  (6.330170018440137e-77 6.04623429007003e-242): 2
* [misc]none:  (2.3080855823624493e-299 4.50326449267665e+246): 5
* [misc]none:  (1.0100264902476595e-152 6.2370208452565505e-251): 0
* [misc]none:  (0.002518103001908201 2.819308104709626e+146): 5
* [misc]none:  (4.19388438569828e-183 3.636662419716013e-100): 7
* [misc]none:  All alt indexes
* [misc]none:  (λ (k n) (* (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)))): 0
* [misc]none:  (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))))): 1
* [misc]none:  (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))): 2
* [misc]none:  (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k))))): 3
* [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))))): 4
* [misc]none:  (λ (k n) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt k)))))): 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) (/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2))))): 7
* [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)))))): 8
* [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))): 9
* [misc]none:  (λ (k n) (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k))): 10
* [misc]none:  Best alt per point
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* [misc]none:  (1.5644360507224123e+19 4.363934278187088e+36): 0
* [misc]none:  (6.602676095404578e+23 6.481090586123572e+252): 0
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* [misc]none:  (2.3267596557987687e-21 1.2639416915267611e-09): 4
* [misc]none:  (1.4839483695271912e-180 4.236319359533113e+21): 3
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* [misc]none:  (1.2420866124564814e-293 6.3461851602547e-177): 2
* [misc]none:  (2.01314860958205e-179 4.1821161712206335e+98): 2
* [misc]none:  (2.5937923840174148e+191 2.0634010725481968e+279): 0
* [misc]none:  (1.740072246435861e-207 1.3636559368742825e-149): 2
* [misc]none:  (1.946944651699716e-139 6.333153678225876e-68): 2
* [misc]none:  (8.70336562916574e-216 7.84549397492709e+169): 0
* [misc]none:  (7.762114448443534e+255 1.682179526351612e+60): 0
* [misc]none:  (6.330170018440137e-77 6.04623429007003e-242): 2
* [misc]none:  (2.3080855823624493e-299 4.50326449267665e+246): 4
* [misc]none:  (1.0100264902476595e-152 6.2370208452565505e-251): 0
* [misc]none:  (0.002518103001908201 2.819308104709626e+146): 6
* [misc]none:  (4.19388438569828e-183 3.636662419716013e-100): 4
* [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 1)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2 2 2 1)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2 1 1)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 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:  [ 2 / 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:  [ 3 / 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:  [ 4 / 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:  simplifying candidates
* * * * [misc]progress:  [ 1 / 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:  [ 2 / 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:  [ 3 / 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:  [ 4 / 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:  [ 5 / 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:  [ 6 / 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:  [ 7 / 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:  [ 8 / 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:  [ 9 / 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:  [ 10 / 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:  [ 11 / 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:  [ 12 / 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:  [ 13 / 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:  [ 14 / 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:  [ 15 / 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:  [ 16 / 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:  [ 17 / 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:  [ 18 / 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:  [ 19 / 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:  [ 20 / 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:  [ 21 / 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:  [ 22 / 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:  [ 23 / 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:  [ 24 / 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:  [ 25 / 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:  [ 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 (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:  [ 28 / 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:  [ 29 / 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:  [ 30 / 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:  [ 31 / 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:  [ 32 / 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:  [ 33 / 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:  [ 34 / 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:  [ 35 / 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:  [ 36 / 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:  [ 37 / 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:  [ 38 / 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:  [ 39 / 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:  [ 40 / 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:  [ 41 / 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:  [ 42 / 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:  [ 43 / 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:  [ 44 / 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:  [ 45 / 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:  [ 46 / 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:  [ 47 / 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:  [ 48 / 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:  [ 49 / 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:  [ 50 / 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:  [ 51 / 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:  [ 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 (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:  [ 54 / 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:  [ 55 / 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:  [ 56 / 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:  [ 57 / 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:  [ 58 / 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:  [ 59 / 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:  [ 60 / 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:  [ 61 / 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:  [ 62 / 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:  [ 63 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* (* PI 2) n) (/ k 2)))))>
* * * * [misc]progress:  [ 64 / 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:  [ 65 / 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:  [ 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)))))>
* * * * [misc]progress:  [ 67 / 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:  [ 68 / 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:  [ 69 / 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:  [ 70 / 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:  [ 71 / 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:  [ 72 / 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:  [ 73 / 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:  [ 74 / 86 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* PI 2) n) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* * * * [misc]progress:  [ 75 / 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:  [ 76 / 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:  [ 77 / 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:  [ 78 / 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:  [ 79 / 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:  [ 80 / 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:  [ 81 / 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:  [ 82 / 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:  [ 83 / 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:  [ 84 / 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:  [ 85 / 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:  [ 86 / 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:  adding candidates to table
* * [misc]progress:  iteration 4 / 4
* * * [misc]progress:  picking best candidate
* [misc]none:  Fresh alts: 10
* [misc]none:  All alts: 10
* [misc]none:  Fresh alt: (λ (k n) (* (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (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)))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))
* [misc]none:  Fresh alt: (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* [misc]none:  Fresh alt: (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* [misc]none:  Fresh alt: (λ (k n) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt k))))))
* [misc]none:  Fresh alt: (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)))))))
* [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) (/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))))
* [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) (/ (+ (* (* (* (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 (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))
* [misc]none:  Fresh alt indexes
* [misc]none:  (λ (k n) (* (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)))): 0
* [misc]none:  (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))))): 1
* [misc]none:  (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))): 2
* [misc]none:  (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k))))): 3
* [misc]none:  (λ (k n) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt k)))))): 4
* [misc]none:  (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))))))): 5
* [misc]none:  (λ (k n) (/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2))))): 6
* [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)))))): 7
* [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))): 8
* [misc]none:  (λ (k n) (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k))): 9
* [misc]none:  Best fresh alt per point
* [misc]none:  (1.1753256432511238e-228 5.527561153609885e-287): 2
* [misc]none:  (2.624640256823317e-85 2.1533006547486818e+157): 1
* [misc]none:  (3.864150256146345e-97 1.2168501550248481e+60): 0
* [misc]none:  (1.1034521727253742e+17 2.3546907275770535e+149): 0
* [misc]none:  (4.3978295980804844e+144 1.5940531292003016e+119): 0
* [misc]none:  (8.840444084563038e-183 3.964069453939573e+73): 1
* [misc]none:  (1.8837875011322252e+302 1.142354404454184e+266): 0
* [misc]none:  (1.5644360507224123e+19 4.363934278187088e+36): 0
* [misc]none:  (6.602676095404578e+23 6.481090586123572e+252): 0
* [misc]none:  (1.5239258836830995e-62 6.476581985608727e-189): 3
* [misc]none:  (1.3456142459532974e-123 7.606121529176208e-260): 4
* [misc]none:  (3.923033144444403e-103 1.878039942854939e+236): 0
* [misc]none:  (2.3267596557987687e-21 1.2639416915267611e-09): 5
* [misc]none:  (1.4839483695271912e-180 4.236319359533113e+21): 3
* [misc]none:  (2.1399535245004834e+276 3.270611459166715e+34): 0
* [misc]none:  (8.536370391567958e-84 1.891164136132134e+49): 2
* [misc]none:  (4.605809248193487e-97 5.777947225580052e-244): 0
* [misc]none:  (1.0165054836861686e-60 1036775558997374.6): 2
* [misc]none:  (6.352335681656861e-39 6.801961567112795e+279): 8
* [misc]none:  (2.2893883612111785e+80 7.528311916305203e+295): 0
* [misc]none:  (2.7413875160814023e+201 1.9627886189524338e+80): 0
* [misc]none:  (1.460288206470917e-107 1.8754037265125923e+53): 0
* [misc]none:  (2.3582038021458647e-169 4.644032469475324e-293): 2
* [misc]none:  (8.013982873164087e-167 1066969.5668890544): 0
* [misc]none:  (2.9748193650490664e-13 6.657312786881122e+279): 5
* [misc]none:  (7.2184051181595065e-137 6.692885675611668e+43): 1
* [misc]none:  (1.3817340317984848e-70 3.4202164367419544e+286): 2
* [misc]none:  (1.8044196814330305e+68 3808.014138654811): 0
* [misc]none:  (9.8707896780761e+48 2540391067475.896): 0
* [misc]none:  (5.584074513505766e-81 2.134581621197641e-254): 1
* [misc]none:  (1.2790373697624338e+97 4.3076365657194535e+77): 0
* [misc]none:  (3.411814803264884e+189 1.3989843540242142e+234): 0
* [misc]none:  (4.939526601471352e-267 1.2916853433589735e+258): 3
* [misc]none:  (3.7319651198431935e-112 2.6162260071326735e+122): 0
* [misc]none:  (2.1501333373436194e-13 2.3749769913787073e+138): 5
* [misc]none:  (4.213048508546599e-178 9.867184629677251e+277): 6
* [misc]none:  (1.048151880557531e-99 8.951548511660437e+82): 8
* [misc]none:  (3.0143613697172596e-88 5.13242722798329e-86): 2
* [misc]none:  (3.6883120681099563e-37 29787000.29181533): 7
* [misc]none:  (2.4030720834689912e-265 3.871884306060819e+43): 2
* [misc]none:  (8.264072396301485e+225 2.0454004757131322e+253): 0
* [misc]none:  (5.092016746590215e+18 5.258570611990399e+144): 0
* [misc]none:  (8.209474020100443e-75 2.310883431864556e-193): 3
* [misc]none:  (2.557633984455684e-236 1.7871658499983865e+111): 0
* [misc]none:  (1.5798885167282891e+240 9.168081447109565e+225): 0
* [misc]none:  (2.330493073693622e-81 5.988090947952116e+260): 5
* [misc]none:  (3.911253144021059e-37 4.2992902330261985e-14): 2
* [misc]none:  (8.116538701041032e-246 7.045701647143625e+294): 0
* [misc]none:  (7.496050392254423e-292 2.3504027171160204e-302): 4
* [misc]none:  (9.136070273410123e+229 1.1006311214931305e+95): 0
* [misc]none:  (6.90507981640539e+283 7.09998869491861e+138): 0
* [misc]none:  (1.8060877419691232e-65 2.86323673488602e-51): 1
* [misc]none:  (5.827538351320562e+164 3.5086837666926e+285): 0
* [misc]none:  (2.4392121410472106e-273 7.836522530769743e+59): 5
* [misc]none:  (2.78106913943276e-77 1.1548749713964373e-92): 7
* [misc]none:  (1.9839532685168286e-292 7.3223398651315395e-109): 2
* [misc]none:  (8.488844594771612e-127 2.451558198341499e+117): 9
* [misc]none:  (5.66924427203651e-301 2.5461878029353985e-238): 2
* [misc]none:  (9.172918591990658e-289 7.928641158600483e+228): 2
* [misc]none:  (6.519305542840066e-238 1.4209750521719234e+167): 2
* [misc]none:  (1.3456211831302422e+205 1.958667951410614e+85): 0
* [misc]none:  (4.563333642978473e+297 9.749986200278868e+113): 0
* [misc]none:  (1.4648264101470588e+44 6.844241230211939e+198): 0
* [misc]none:  (2.4013812965708594e+221 7.909441760020457e+74): 0
* [misc]none:  (1.2314924435784377e+276 4.478509484643543e+146): 0
* [misc]none:  (2.5583314633633054e-07 1.699201102491909e+300): 5
* [misc]none:  (1.5042239853613876e-302 9.360780180304737e+153): 3
* [misc]none:  (5.106692251999635e+137 3.2350731648968916e+240): 0
* [misc]none:  (1.0970228149908303e-276 7.967769961742838e+186): 1
* [misc]none:  (1.2527851748452608e-242 1.0103123302158147e+112): 2
* [misc]none:  (4.548583366996073e+176 2.950117005694129e+203): 0
* [misc]none:  (222693309.28876954 2.0187517395999946e+158): 0
* [misc]none:  (2.1626561181515632e-29 6.562952916996993e-49): 4
* [misc]none:  (3.1723784288762247e-174 1.806578923933048e-16): 1
* [misc]none:  (1.5368130424239484e-258 1.0793824307213477e-07): 2
* [misc]none:  (1.4626644606135493e-149 2.3190166729712657e-212): 2
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* [misc]none:  (3.531223172330985e-199 5.561790722198777e-82): 9
* [misc]none:  (1.5966125201184553e-193 73.24749757442865): 4
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* [misc]none:  (7.7647175154152615e+59 1.2557511573201489e+275): 0
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* [misc]none:  (1.8269212298308998e+214 1789977963981.046): 0
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* [misc]none:  (2.1545947154827896e+229 2.6209188754640728e+107): 0
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* [misc]none:  (1.2309532522175715e-227 5.849070875002102e-168): 5
* [misc]none:  (5.884862647618943e+102 1.3917287586797797e+215): 0
* [misc]none:  (2.802805856656922e+299 3267744482859.4893): 0
* [misc]none:  (4.3906960513010925e-288 9.735553079850294e-195): 8
* [misc]none:  (2.617385806499904e-208 6.454193966659965e-12): 2
* [misc]none:  (1.2843486366644783e+218 1.6598105327534946e+245): 0
* [misc]none:  (6.352964037059704e-48 2.0675888684205106e-37): 5
* [misc]none:  (1.434478809327731e-162 1.7673263201240207e+200): 2
* [misc]none:  (4.1358060479750856e+163 2.77377213114978e+181): 0
* [misc]none:  (3.851639943546658e-220 7.262940842293714e+141): 3
* [misc]none:  (1175954691713314.2 1.6505576250215693e+254): 0
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* [misc]none:  (3.795139234164696e-109 9.806701774277626e-103): 2
* [misc]none:  (2.6870891996869854e+222 1.403842517343178e+239): 0
* [misc]none:  (2.1939039916199917e-151 6.704445560737266e-185): 0
* [misc]none:  (2.0407374713985817e-67 6.798712177335776e+112): 2
* [misc]none:  (1.37725435443438e-133 2.7744697188841963e+109): 5
* [misc]none:  (4.163796059008999e+263 9.568517745632325e+214): 0
* [misc]none:  (2.4645417753990825e-46 1.1531681692158285e+126): 1
* [misc]none:  (2.8621091346925045e-294 1.532108192832722e+128): 4
* [misc]none:  (1.2420866124564814e-293 6.3461851602547e-177): 2
* [misc]none:  (2.01314860958205e-179 4.1821161712206335e+98): 2
* [misc]none:  (2.5937923840174148e+191 2.0634010725481968e+279): 0
* [misc]none:  (1.740072246435861e-207 1.3636559368742825e-149): 2
* [misc]none:  (1.946944651699716e-139 6.333153678225876e-68): 2
* [misc]none:  (8.70336562916574e-216 7.84549397492709e+169): 0
* [misc]none:  (7.762114448443534e+255 1.682179526351612e+60): 0
* [misc]none:  (6.330170018440137e-77 6.04623429007003e-242): 2
* [misc]none:  (2.3080855823624493e-299 4.50326449267665e+246): 5
* [misc]none:  (1.0100264902476595e-152 6.2370208452565505e-251): 0
* [misc]none:  (0.002518103001908201 2.819308104709626e+146): 5
* [misc]none:  (4.19388438569828e-183 3.636662419716013e-100): 5
* [misc]none:  All alt indexes
* [misc]none:  (λ (k n) (* (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)))): 0
* [misc]none:  (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))))): 1
* [misc]none:  (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))): 2
* [misc]none:  (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k))))): 3
* [misc]none:  (λ (k n) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt k)))))): 4
* [misc]none:  (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))))))): 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) (/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2))))): 7
* [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)))))): 8
* [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))): 9
* [misc]none:  (λ (k n) (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k))): 10
* [misc]none:  Best alt per point
* [misc]none:  (1.1753256432511238e-228 5.527561153609885e-287): 2
* [misc]none:  (2.624640256823317e-85 2.1533006547486818e+157): 1
* [misc]none:  (3.864150256146345e-97 1.2168501550248481e+60): 0
* [misc]none:  (1.1034521727253742e+17 2.3546907275770535e+149): 0
* [misc]none:  (4.3978295980804844e+144 1.5940531292003016e+119): 0
* [misc]none:  (8.840444084563038e-183 3.964069453939573e+73): 1
* [misc]none:  (1.8837875011322252e+302 1.142354404454184e+266): 0
* [misc]none:  (1.5644360507224123e+19 4.363934278187088e+36): 0
* [misc]none:  (6.602676095404578e+23 6.481090586123572e+252): 0
* [misc]none:  (1.5239258836830995e-62 6.476581985608727e-189): 3
* [misc]none:  (1.3456142459532974e-123 7.606121529176208e-260): 4
* [misc]none:  (3.923033144444403e-103 1.878039942854939e+236): 0
* [misc]none:  (2.3267596557987687e-21 1.2639416915267611e-09): 5
* [misc]none:  (1.4839483695271912e-180 4.236319359533113e+21): 3
* [misc]none:  (2.1399535245004834e+276 3.270611459166715e+34): 0
* [misc]none:  (8.536370391567958e-84 1.891164136132134e+49): 2
* [misc]none:  (4.605809248193487e-97 5.777947225580052e-244): 0
* [misc]none:  (1.0165054836861686e-60 1036775558997374.6): 2
* [misc]none:  (6.352335681656861e-39 6.801961567112795e+279): 6
* [misc]none:  (2.2893883612111785e+80 7.528311916305203e+295): 0
* [misc]none:  (2.7413875160814023e+201 1.9627886189524338e+80): 0
* [misc]none:  (1.460288206470917e-107 1.8754037265125923e+53): 0
* [misc]none:  (2.3582038021458647e-169 4.644032469475324e-293): 2
* [misc]none:  (8.013982873164087e-167 1066969.5668890544): 0
* [misc]none:  (2.9748193650490664e-13 6.657312786881122e+279): 5
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* [misc]none:  (1.740072246435861e-207 1.3636559368742825e-149): 2
* [misc]none:  (1.946944651699716e-139 6.333153678225876e-68): 2
* [misc]none:  (8.70336562916574e-216 7.84549397492709e+169): 0
* [misc]none:  (7.762114448443534e+255 1.682179526351612e+60): 0
* [misc]none:  (6.330170018440137e-77 6.04623429007003e-242): 2
* [misc]none:  (2.3080855823624493e-299 4.50326449267665e+246): 5
* [misc]none:  (1.0100264902476595e-152 6.2370208452565505e-251): 0
* [misc]none:  (0.002518103001908201 2.819308104709626e+146): 6
* [misc]none:  (4.19388438569828e-183 3.636662419716013e-100): 5
* [misc]none:  Picked alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* * * * [misc]pick:  Picked  #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 4 ] rewriting at (2 1)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2 2)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2 2 1 1)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 4 ] generating series at (2 1)
* [misc]approximate:  Taking taylor expansion of (/ 1 (sqrt (sqrt k))) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (sqrt k))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (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 (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ +nan.0 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (sqrt k))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (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 (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ +nan.0 (* 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 (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 (+ (* 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 (sqrt (/ 1 k)))) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (sqrt (/ 1 k)))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (/ 1 (sqrt +nan.0)) into (/ 1 (sqrt +nan.0))
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (sqrt (/ 1 k)))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (/ 1 (sqrt +nan.0)) into (/ 1 (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (/ 1 (sqrt +nan.0)) into (/ 1 (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 (sqrt +nan.0)) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) into (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))))
* [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 (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 (sqrt +nan.0)) (/ (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (sqrt +nan.0))) (* (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 5))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 5))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) into (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 5))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))))))
* [misc]backup-simplify:  Simplify (+ (* (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 5))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) (pow (/ 1 k) 2)) (+ (* (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) (/ 1 k)) (/ 1 (sqrt +nan.0)))) into (- (/ 1 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 5) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) k))))))))
* [misc]approximate:  Taking taylor expansion of (/ 1 (sqrt (sqrt (/ 1 (- k))))) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (sqrt (/ 1 (- k))))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (/ 1 (sqrt +nan.0)) into (/ 1 (sqrt +nan.0))
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (sqrt (/ 1 (- k))))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (/ 1 (sqrt +nan.0)) into (/ 1 (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (/ 1 (sqrt +nan.0)) into (/ 1 (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 (sqrt +nan.0)) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) into (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (/ (- +nan.0 (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 (sqrt +nan.0)) (/ (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (sqrt +nan.0))) (* (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 5))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 5))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) into (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 5))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))))))
* [misc]backup-simplify:  Simplify (+ (* (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 5))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) (/ 1 (- k))) (/ 1 (sqrt +nan.0)))) into (- (/ 1 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 5) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) k))))))))
* * * * [misc]progress:  [ 2 / 4 ] generating series at (2 2)
* [misc]approximate:  Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (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 (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 (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ +nan.0 (* 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 (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 (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 (sqrt (sqrt k)) into (pow k 1/4)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (sqrt k)))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (pow k 1/4)) into (* (pow (/ 1 k) 1/4) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (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 (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 (sqrt (sqrt k)) into (pow k 1/4)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (sqrt k)))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (pow k 1/4)) into (* (pow (/ 1 k) 1/4) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))
* [misc]taylor:  Taking taylor expansion of (* (pow (/ 1 k) 1/4) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) in k
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 k) 1/4) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of 1/4 in k
* [misc]backup-simplify:  Simplify 1/4 into 1/4
* [misc]taylor:  Taking taylor expansion of (log (/ 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 (log 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
* [misc]backup-simplify:  Simplify (* 1/4 (- (log k))) into (* -1/4 (log k))
* [misc]backup-simplify:  Simplify (exp (* -1/4 (log k))) into (pow k -1/4)
* [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 (+ (* 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 (pow k 1/4)) (+ (* (* (pow (/ 1 k) 1/4) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (/ 0 (pow k 1/4))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (pow k -1/4) (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (/ 1 k) 1/4))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (/ 1 k) 1/4)) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (/ 1 k) 1/4))
* [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 (pow 0 2) (+)) (* 2 (pow k 1/4))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (pow k 1/4)) (+ (* (* (pow (/ 1 k) 1/4) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (/ 0 (pow k 1/4))) (* 0 (/ 0 (pow k 1/4))))) 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 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
* [misc]backup-simplify:  Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (pow k -1/4) (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))) (* 0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))) (pow (/ 1 k) 1/4)))))
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))) (pow (/ 1 k) 1/4))))) into (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))) (pow (/ 1 k) 1/4)))))
* [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 (+ (* 2 (* 0 0)))) (* 2 (pow k 1/4))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (pow k 1/4)) (+ (* (* (pow (/ 1 k) 1/4) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (/ 0 (pow k 1/4))) (* 0 (/ 0 (pow k 1/4))) (* 0 (/ 0 (pow k 1/4))))) 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 (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
* [misc]backup-simplify:  Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (pow k -1/4) (* (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)))))) (+ (* 0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))) (* 0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))) into (+ (* 1/8 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (* 1/4 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))) (pow (/ 1 k) 1/4)))))
* [misc]backup-simplify:  Simplify (+ (* 1/8 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (* 1/4 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))) (pow (/ 1 k) 1/4))))) into (+ (* 1/8 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (* 1/4 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))) (pow (/ 1 k) 1/4)))))
* [misc]backup-simplify:  Simplify (+ (* (+ (* 1/8 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (* 1/4 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))) (pow (/ 1 k) 1/4))))) (pow (* k 1) 2)) (+ (* (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))) (pow (/ 1 k) 1/4))))) (* k 1)) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (/ 1 k) 1/4)))) into (- (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (/ 1 k) 1/4)) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2)) (pow (pow k 7) 1/4))) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)) (pow (pow k 7) 1/4))) (* 1/4 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))) (pow (pow k 7) 1/4)))))) (+ (* 1/2 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)) (pow (pow k 3) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))) (pow (pow k 3) 1/4)))))
* [misc]approximate:  Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k)))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (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 (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (sqrt +nan.0))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (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 (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 (sqrt (sqrt (/ 1 k))) into (pow (/ 1 k) 1/4)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (sqrt (/ 1 k))))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (/ 1 k) 1/4)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow k 1/4))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (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 (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 (sqrt (sqrt (/ 1 k))) into (pow (/ 1 k) 1/4)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (sqrt (/ 1 k))))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (/ 1 k) 1/4)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow k 1/4))
* [misc]taylor:  Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow k 1/4)) 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 (pow k 1/4) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/4 (log k))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/4 (log k)) in k
* [misc]taylor:  Taking taylor expansion of 1/4 in k
* [misc]backup-simplify:  Simplify 1/4 into 1/4
* [misc]taylor:  Taking taylor expansion of (log k) in k
* [misc]taylor:  Taking 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 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log k)) 0) into (log k)
* [misc]backup-simplify:  Simplify (* 1/4 (log k)) into (* 1/4 (log k))
* [misc]backup-simplify:  Simplify (exp (* 1/4 (log k))) into (pow k 1/4)
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow k 1/4)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow k 1/4))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow k 1/4)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow k 1/4))
* [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 (pow (/ 1 k) 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow k 1/4)) (/ 0 (pow (/ 1 k) 1/4))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log k)) 0) into (log k)
* [misc]backup-simplify:  Simplify (+ (* 1/4 0) (* 0 (log k))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (* 0 (pow k 1/4))) 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]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 (pow 0 2) (+)) (* 2 (pow (/ 1 k) 1/4))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (pow (/ 1 k) 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow k 1/4)) (/ 0 (pow (/ 1 k) 1/4))) (* 0 (/ 0 (pow (/ 1 k) 1/4))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log k)) 0) into (log k)
* [misc]backup-simplify:  Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (pow k 1/4)))) 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]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 (+ (* 2 (* 0 0)))) (* 2 (pow (/ 1 k) 1/4))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (pow (/ 1 k) 1/4)) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow k 1/4)) (/ 0 (pow (/ 1 k) 1/4))) (* 0 (/ 0 (pow (/ 1 k) 1/4))) (* 0 (/ 0 (pow (/ 1 k) 1/4))))) 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)))))) (pow (/ 1 k) 1/4)) into (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow (/ 1 k) 1/4))
* [misc]approximate:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k))))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (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 (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (sqrt +nan.0))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (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 (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 (sqrt (sqrt (/ -1 k))) into (sqrt (sqrt (/ -1 k)))
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (sqrt (/ -1 k))))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (sqrt (/ -1 k)))) into (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ 1 (sqrt (/ -1 k)))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (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 (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 (sqrt (sqrt (/ -1 k))) into (sqrt (sqrt (/ -1 k)))
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (sqrt (/ -1 k))))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (sqrt (/ -1 k)))) into (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ 1 (sqrt (/ -1 k)))))
* [misc]taylor:  Taking taylor expansion of (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ 1 (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 (sqrt (/ -1 k)))) 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 -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 (/ 1 +nan.0) into +nan.0
* [misc]backup-simplify:  Simplify (sqrt +nan.0) into (sqrt +nan.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 (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt +nan.0)) into (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt +nan.0)) into (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt +nan.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) 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 (sqrt (/ -1 k)))) (+ (* (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ 1 (sqrt (/ -1 k))))) (/ 0 (sqrt (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 (sqrt +nan.0))) (* 0 (sqrt +nan.0))) into (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt +nan.0))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt +nan.0)))) into (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt +nan.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]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 (pow 0 2) (+)) (* 2 (sqrt (sqrt (/ -1 k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (sqrt (/ -1 k)))) (+ (* (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ 1 (sqrt (/ -1 k))))) (/ 0 (sqrt (sqrt (/ -1 k))))) (* 0 (/ 0 (sqrt (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 (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (/ (- (- +nan.0) (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))) (+ (* 0 (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt +nan.0))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt +nan.0)))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt +nan.0))))))
* [misc]backup-simplify:  Simplify (+ (* (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))) (sqrt +nan.0)))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))) (sqrt +nan.0)))) (* (/ 1 (- k)) 1)) (* (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))) (sqrt +nan.0)))) into (- (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt +nan.0)) (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (* (sqrt +nan.0) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (* (sqrt +nan.0) k))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (* (pow (sqrt +nan.0) 3) (pow k 2)))))))))
* * * * [misc]progress:  [ 3 / 4 ] generating series at (2)
* [misc]approximate:  Taking taylor expansion of (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (sqrt k))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (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 (sqrt (sqrt k)) into (pow k 1/4)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (sqrt k)))) into 0
* [misc]backup-simplify:  Simplify (/ 1 (pow k 1/4)) into (pow (/ 1 k) 1/4)
* [misc]taylor:  Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (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 (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 (sqrt (sqrt k)) into (pow k 1/4)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (sqrt k)))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (pow k 1/4)) into (* (pow (/ 1 k) 1/4) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))))
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (sqrt k))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (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 (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ +nan.0 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (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 (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 (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ +nan.0 (* 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 (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (sqrt k))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (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 (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ +nan.0 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (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 (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 (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ +nan.0 (* 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]backup-simplify:  Simplify (* +nan.0 (* +nan.0 (sqrt (* n (* 2 PI))))) into (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))
* [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 (* 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 (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* n 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (- (/ -1 2) (+ (* 1/2 (/ 0 2)))) into -1/2
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* 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 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI))))) +nan.0) (+ (* (* +nan.0 (sqrt (* n (* 2 PI)))) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))))
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (/ (- +nan.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 (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))))) (* (- +nan.0) (* +nan.0 (sqrt (* n (* 2 PI)))))) 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 (+ (* 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 (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* n 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* 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 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ (* 1/8 (* (sqrt (* n (* 2 PI))) (pow (log (* 2 (* n PI))) 2))) +nan.0) (+ (* (* +nan.0 (sqrt (* n (* 2 PI)))) (/ +nan.0 +nan.0)) (* (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))) (/ +nan.0 +nan.0)))) 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]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (/ (- +nan.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 (- (+ (* +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))))))))) (+ (* (- +nan.0) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))))) (* (- +nan.0) (* +nan.0 (sqrt (* n (* 2 PI))))))) 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 (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* (* +nan.0 PI) 0) (* (* +nan.0 (pow PI 2)) (sqrt 2)))) into (- (* +nan.0 (* (pow PI 2) (sqrt 2))))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (- (* +nan.0 (* (pow PI 2) (sqrt 2))))) (+ (* 0 (- (* +nan.0 (* PI (sqrt 2))))) (* 0 0))) into (- (* +nan.0 (* (pow PI 2) (sqrt 2))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (pow PI 2) (sqrt 2)))) into (- (* +nan.0 (* (pow PI 2) (sqrt 2))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (* (pow PI 2) (sqrt 2)))) (pow (* n (/ 1 k)) 2)) (+ (* (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))))) (* n (/ 1 k))) (* (- (* +nan.0 (* PI (sqrt 2)))) (* n (pow k -2))))) into (- (+ (* +nan.0 (/ (* (pow n 2) (* (pow PI 2) (sqrt 2))) (pow k 2))) (- (+ (* +nan.0 (/ (* n (* PI (* (log (* 2 PI)) (sqrt 2)))) k)) (- (+ (* +nan.0 (/ (* n (* PI (* (log n) (sqrt 2)))) k)) (- (+ (* +nan.0 (/ (* n (* PI (sqrt 2))) k)) (- (* +nan.0 (/ (* n (* PI (sqrt 2))) (pow k 2))))))))))))
* [misc]approximate:  Taking taylor expansion of (* (/ 1 (sqrt (sqrt (/ 1 k)))) (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k))))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt (sqrt (/ 1 k)))) (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (sqrt (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ 1 k))) into (pow (/ 1 k) 1/4)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (sqrt (/ 1 k))))) into 0
* [misc]backup-simplify:  Simplify (/ 1 (pow (/ 1 k) 1/4)) into (pow k 1/4)
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (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 (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 (sqrt (sqrt (/ 1 k))) into (pow (/ 1 k) 1/4)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (sqrt (/ 1 k))))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (/ 1 k) 1/4)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow k 1/4))
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt (sqrt (/ 1 k)))) (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k))))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (sqrt (/ 1 k)))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (/ 1 (sqrt +nan.0)) into (/ 1 (sqrt +nan.0))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (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 (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (sqrt +nan.0))
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt (sqrt (/ 1 k)))) (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (sqrt (/ 1 k))))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (sqrt (/ 1 k)))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (/ 1 (sqrt +nan.0)) into (/ 1 (sqrt +nan.0))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ (- 1 (/ 1 k)) 2)) (sqrt (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 (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (* (/ 1 (sqrt +nan.0)) (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (sqrt +nan.0))) into (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (pow (sqrt +nan.0) 2))
* [misc]taylor:  Taking taylor expansion of (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (pow (sqrt +nan.0) 2)) in n
* [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]taylor:  Taking taylor expansion of (pow (sqrt +nan.0) 2) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 2 (log (sqrt +nan.0)))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (log (sqrt +nan.0))) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (log (sqrt +nan.0)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt +nan.0) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]backup-simplify:  Simplify (sqrt +nan.0) into (sqrt +nan.0)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt +nan.0))) into 0
* [misc]backup-simplify:  Simplify (log (sqrt +nan.0)) into (log (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (* 2 (log (sqrt +nan.0))) into (* 2 (log (sqrt +nan.0)))
* [misc]backup-simplify:  Simplify (exp (* 2 (log (sqrt +nan.0)))) into (pow (sqrt +nan.0) 2)
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 2)) into (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 2))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 2)) into (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 2))
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt +nan.0)) (+ (* (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (sqrt +nan.0)) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (* +nan.0 (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (pow (sqrt +nan.0) 3))))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 (sqrt +nan.0)) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))))
* [misc]backup-simplify:  Simplify (+ (* (/ 1 (sqrt +nan.0)) (- (* +nan.0 (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (pow (sqrt +nan.0) 3))))) (* (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (sqrt +nan.0)))) into (- (* +nan.0 (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (pow (sqrt +nan.0) 4))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (pow (sqrt +nan.0) 4)))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (pow (sqrt +nan.0) 4))) 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))))) (pow (sqrt +nan.0) 4)) in n
* [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]taylor:  Taking taylor expansion of (pow (sqrt +nan.0) 4) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 4 (log (sqrt +nan.0)))) in n
* [misc]taylor:  Taking taylor expansion of (* 4 (log (sqrt +nan.0))) in n
* [misc]taylor:  Taking taylor expansion of 4 in n
* [misc]backup-simplify:  Simplify 4 into 4
* [misc]taylor:  Taking taylor expansion of (log (sqrt +nan.0)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt +nan.0) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]backup-simplify:  Simplify (sqrt +nan.0) into (sqrt +nan.0)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt +nan.0))) into 0
* [misc]backup-simplify:  Simplify (log (sqrt +nan.0)) into (log (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (* 4 (log (sqrt +nan.0))) into (* 4 (log (sqrt +nan.0)))
* [misc]backup-simplify:  Simplify (exp (* 4 (log (sqrt +nan.0)))) into (pow (sqrt +nan.0) 4)
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 4)) into (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 4))
* [misc]backup-simplify:  Simplify (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 4))) into (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 4)))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 4)))) into (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 4))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 4)))) into (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 4))))
* [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 (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (sqrt +nan.0) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 (log (sqrt +nan.0)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 2 (log (sqrt +nan.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (pow (sqrt +nan.0) 2)) (+ (* (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 2)) (/ 0 (pow (sqrt +nan.0) 2))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (/ (- +nan.0 (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt +nan.0)) (+ (* (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (sqrt +nan.0)) (/ (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (sqrt +nan.0))) (* (- (* +nan.0 (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (pow (sqrt +nan.0) 3)))) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (pow (sqrt +nan.0) 5))))))
* [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 (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 (sqrt +nan.0)) (/ (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (sqrt +nan.0))) (* (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 5))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))))))
* [misc]backup-simplify:  Simplify (+ (* (/ 1 (sqrt +nan.0)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (pow (sqrt +nan.0) 5))))))) (+ (* (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) (- (* +nan.0 (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (pow (sqrt +nan.0) 3))))) (* (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 5))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (sqrt +nan.0))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (pow (sqrt +nan.0) 6))) (- (* +nan.0 (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (pow (sqrt +nan.0) 4))))))
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (pow (sqrt +nan.0) 6))) (- (* +nan.0 (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (pow (sqrt +nan.0) 4)))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (pow (sqrt +nan.0) 6))) (- (* +nan.0 (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (pow (sqrt +nan.0) 4))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (pow (sqrt +nan.0) 6))) 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))))) (pow (sqrt +nan.0) 6)) in n
* [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]taylor:  Taking taylor expansion of (pow (sqrt +nan.0) 6) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 6 (log (sqrt +nan.0)))) in n
* [misc]taylor:  Taking taylor expansion of (* 6 (log (sqrt +nan.0))) in n
* [misc]taylor:  Taking taylor expansion of 6 in n
* [misc]backup-simplify:  Simplify 6 into 6
* [misc]taylor:  Taking taylor expansion of (log (sqrt +nan.0)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt +nan.0) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]backup-simplify:  Simplify (sqrt +nan.0) into (sqrt +nan.0)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt +nan.0))) into 0
* [misc]backup-simplify:  Simplify (log (sqrt +nan.0)) into (log (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (* 6 (log (sqrt +nan.0))) into (* 6 (log (sqrt +nan.0)))
* [misc]backup-simplify:  Simplify (exp (* 6 (log (sqrt +nan.0)))) into (pow (sqrt +nan.0) 6)
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 6)) into (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 6))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (pow (sqrt +nan.0) 4)))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) (pow (sqrt +nan.0) 4))) 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))))) (pow (sqrt +nan.0) 4)) in n
* [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]taylor:  Taking taylor expansion of (pow (sqrt +nan.0) 4) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 4 (log (sqrt +nan.0)))) in n
* [misc]taylor:  Taking taylor expansion of (* 4 (log (sqrt +nan.0))) in n
* [misc]taylor:  Taking taylor expansion of 4 in n
* [misc]backup-simplify:  Simplify 4 into 4
* [misc]taylor:  Taking taylor expansion of (log (sqrt +nan.0)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt +nan.0) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]backup-simplify:  Simplify (sqrt +nan.0) into (sqrt +nan.0)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt +nan.0))) into 0
* [misc]backup-simplify:  Simplify (log (sqrt +nan.0)) into (log (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (* 4 (log (sqrt +nan.0))) into (* 4 (log (sqrt +nan.0)))
* [misc]backup-simplify:  Simplify (exp (* 4 (log (sqrt +nan.0)))) into (pow (sqrt +nan.0) 4)
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 4)) into (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 4))
* [misc]backup-simplify:  Simplify (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 6))) into (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 6)))
* [misc]backup-simplify:  Simplify (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 4))) into (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 4)))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 4)))) into (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 4))))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 6))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 4))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 4))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 6))))))
* [misc]backup-simplify:  Simplify (- (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 4))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 6))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 4))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 6))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 4))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 6)))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 4))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (pow (sqrt +nan.0) 6))))))
* [misc]backup-simplify:  Simplify (+ (* (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow (sqrt +nan.0) 4))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow (sqrt +nan.0) 6)))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow (sqrt +nan.0) 4)))) (* 1 (/ 1 k))) (/ (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow (sqrt +nan.0) 2)))) into (- (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow (sqrt +nan.0) 2)) (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (* (pow (sqrt +nan.0) 4) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (* (pow (sqrt +nan.0) 6) (pow k 2)))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (* (pow (sqrt +nan.0) 4) k))))))))
* [misc]approximate:  Taking taylor expansion of (* (/ 1 (sqrt (sqrt (/ 1 (- k))))) (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k)))))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt (sqrt (/ 1 (- k))))) (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k)))))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (sqrt (/ 1 (- k))))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (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 (sqrt (sqrt (/ -1 k))) into (sqrt (sqrt (/ -1 k)))
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (sqrt (/ -1 k))))) into 0
* [misc]backup-simplify:  Simplify (/ 1 (sqrt (sqrt (/ -1 k)))) into (sqrt (/ 1 (sqrt (/ -1 k))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (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 (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 (sqrt (sqrt (/ -1 k))) into (sqrt (sqrt (/ -1 k)))
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (sqrt (/ -1 k))))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (sqrt (/ -1 k)))) into (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ 1 (sqrt (/ -1 k)))))
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt (sqrt (/ 1 (- k))))) (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k)))))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (sqrt (/ 1 (- k))))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (/ 1 (sqrt +nan.0)) into (/ 1 (sqrt +nan.0))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (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 (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (sqrt +nan.0))
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt (sqrt (/ 1 (- k))))) (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (sqrt (/ 1 (- k)))))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (sqrt (/ 1 (- k))))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (/ 1 (sqrt +nan.0)) into (/ 1 (sqrt +nan.0))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (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 (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 (sqrt +nan.0) into (sqrt +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 (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (sqrt +nan.0)) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (* (/ 1 (sqrt +nan.0)) (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (sqrt +nan.0))) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (pow (sqrt +nan.0) 2))
* [misc]taylor:  Taking taylor expansion of (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (pow (sqrt +nan.0) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (+ 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log (* -2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -2 in n
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ 1 (/ 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]taylor:  Taking taylor expansion of (pow (sqrt +nan.0) 2) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 2 (log (sqrt +nan.0)))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (log (sqrt +nan.0))) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (log (sqrt +nan.0)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt +nan.0) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]backup-simplify:  Simplify (sqrt +nan.0) into (sqrt +nan.0)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt +nan.0))) into 0
* [misc]backup-simplify:  Simplify (log (sqrt +nan.0)) into (log (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (* 2 (log (sqrt +nan.0))) into (* 2 (log (sqrt +nan.0)))
* [misc]backup-simplify:  Simplify (exp (* 2 (log (sqrt +nan.0)))) into (pow (sqrt +nan.0) 2)
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 2)) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 2))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 2)) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 2))
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt +nan.0)) (+ (* (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (sqrt +nan.0)) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (pow (sqrt +nan.0) 3))))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 (sqrt +nan.0)) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))))
* [misc]backup-simplify:  Simplify (+ (* (/ 1 (sqrt +nan.0)) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (pow (sqrt +nan.0) 3))))) (* (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (sqrt +nan.0)))) into (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (pow (sqrt +nan.0) 4))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (pow (sqrt +nan.0) 4)))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (pow (sqrt +nan.0) 4))) 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)))))) (pow (sqrt +nan.0) 4)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (+ 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log (* -2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -2 in n
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ 1 (/ 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]taylor:  Taking taylor expansion of (pow (sqrt +nan.0) 4) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 4 (log (sqrt +nan.0)))) in n
* [misc]taylor:  Taking taylor expansion of (* 4 (log (sqrt +nan.0))) in n
* [misc]taylor:  Taking taylor expansion of 4 in n
* [misc]backup-simplify:  Simplify 4 into 4
* [misc]taylor:  Taking taylor expansion of (log (sqrt +nan.0)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt +nan.0) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]backup-simplify:  Simplify (sqrt +nan.0) into (sqrt +nan.0)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt +nan.0))) into 0
* [misc]backup-simplify:  Simplify (log (sqrt +nan.0)) into (log (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (* 4 (log (sqrt +nan.0))) into (* 4 (log (sqrt +nan.0)))
* [misc]backup-simplify:  Simplify (exp (* 4 (log (sqrt +nan.0)))) into (pow (sqrt +nan.0) 4)
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 4)) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 4))
* [misc]backup-simplify:  Simplify (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 4))) into (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 4)))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 4)))) into (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 4))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 4)))) into (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 4))))
* [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 (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (sqrt +nan.0) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 (log (sqrt +nan.0)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 2 (log (sqrt +nan.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (pow (sqrt +nan.0) 2)) (+ (* (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 2)) (/ 0 (pow (sqrt +nan.0) 2))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (/ (- +nan.0 (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt +nan.0)) (+ (* (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (sqrt +nan.0)) (/ (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (sqrt +nan.0))) (* (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (pow (sqrt +nan.0) 3)))) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (pow (sqrt +nan.0) 5))))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-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 (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 (sqrt +nan.0)) (/ (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (sqrt +nan.0))) (* (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) (/ (/ +nan.0 (sqrt +nan.0)) (sqrt +nan.0))))) into (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 5))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))))))
* [misc]backup-simplify:  Simplify (+ (* (/ 1 (sqrt +nan.0)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (pow (sqrt +nan.0) 5))))))) (+ (* (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (pow (sqrt +nan.0) 3))))) (* (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 5))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (sqrt +nan.0))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (pow (sqrt +nan.0) 4))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (pow (sqrt +nan.0) 6))))))
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (pow (sqrt +nan.0) 4))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (pow (sqrt +nan.0) 6)))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (pow (sqrt +nan.0) 4))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (pow (sqrt +nan.0) 6))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (pow (sqrt +nan.0) 4))) 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)))))) (pow (sqrt +nan.0) 4)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (+ 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log (* -2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -2 in n
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ 1 (/ 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]taylor:  Taking taylor expansion of (pow (sqrt +nan.0) 4) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 4 (log (sqrt +nan.0)))) in n
* [misc]taylor:  Taking taylor expansion of (* 4 (log (sqrt +nan.0))) in n
* [misc]taylor:  Taking taylor expansion of 4 in n
* [misc]backup-simplify:  Simplify 4 into 4
* [misc]taylor:  Taking taylor expansion of (log (sqrt +nan.0)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt +nan.0) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]backup-simplify:  Simplify (sqrt +nan.0) into (sqrt +nan.0)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt +nan.0))) into 0
* [misc]backup-simplify:  Simplify (log (sqrt +nan.0)) into (log (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (* 4 (log (sqrt +nan.0))) into (* 4 (log (sqrt +nan.0)))
* [misc]backup-simplify:  Simplify (exp (* 4 (log (sqrt +nan.0)))) into (pow (sqrt +nan.0) 4)
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 4)) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 4))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (pow (sqrt +nan.0) 6)))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) (pow (sqrt +nan.0) 6))) 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)))))) (pow (sqrt +nan.0) 6)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (+ 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log (* -2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -2 in n
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ 1 (/ 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]taylor:  Taking taylor expansion of (pow (sqrt +nan.0) 6) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 6 (log (sqrt +nan.0)))) in n
* [misc]taylor:  Taking taylor expansion of (* 6 (log (sqrt +nan.0))) in n
* [misc]taylor:  Taking taylor expansion of 6 in n
* [misc]backup-simplify:  Simplify 6 into 6
* [misc]taylor:  Taking taylor expansion of (log (sqrt +nan.0)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt +nan.0) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]backup-simplify:  Simplify (sqrt +nan.0) into (sqrt +nan.0)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt +nan.0))) into 0
* [misc]backup-simplify:  Simplify (log (sqrt +nan.0)) into (log (sqrt +nan.0))
* [misc]backup-simplify:  Simplify (* 6 (log (sqrt +nan.0))) into (* 6 (log (sqrt +nan.0)))
* [misc]backup-simplify:  Simplify (exp (* 6 (log (sqrt +nan.0)))) into (pow (sqrt +nan.0) 6)
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 6)) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 6))
* [misc]backup-simplify:  Simplify (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 4))) into (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 4)))
* [misc]backup-simplify:  Simplify (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 6))) into (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 6)))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 6)))) into (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 6))))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 4))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 6))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 6))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 4))))))
* [misc]backup-simplify:  Simplify (- (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 6))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 4))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 6))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 4))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 6))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 4)))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 6))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (pow (sqrt +nan.0) 4))))))
* [misc]backup-simplify:  Simplify (+ (* (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))) (pow (sqrt +nan.0) 6))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))) (pow (sqrt +nan.0) 4)))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))) (pow (sqrt +nan.0) 4)))) (* 1 (/ 1 (- k)))) (/ (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))) (pow (sqrt +nan.0) 2)))) into (- (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow (sqrt +nan.0) 2)) (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (* (pow (sqrt +nan.0) 4) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (* (pow (sqrt +nan.0) 4) k))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (* (pow (sqrt +nan.0) 6) (pow k 2)))))))))
* * * * [misc]progress:  [ 4 / 4 ] generating series at (2 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:  simplifying candidates
* * * * [misc]progress:  [ 1 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (log1p (expm1 (/ 1 (sqrt (sqrt k))))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (expm1 (/ 1 (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* [exit]simplify:  Simplified to (expm1 (/ 1 (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (expm1 (/ 1 (sqrt (sqrt k))))
* * * * [misc]progress:  [ 2 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (expm1 (log1p (/ 1 (sqrt (sqrt k))))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (log1p (/ 1 (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* [exit]simplify:  Simplified to (log1p (/ 1 (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (log1p (/ 1 (sqrt (sqrt k))))
* * * * [misc]progress:  [ 3 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow (sqrt (sqrt k)) -1) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* * * * [misc]progress:  [ 4 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow (sqrt k) (- 1/2)) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [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 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow (sqrt (sqrt k)) (- 1)) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [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 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow (/ 1 (sqrt (sqrt k))) 1) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* * * * [misc]progress:  [ 7 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (exp (- (log (sqrt (sqrt k))))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (- (log (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 5 (5 enodes)
* [exit]simplify:  Simplified to (- (log (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (- (log (sqrt (sqrt k))))
* * * * [misc]progress:  [ 8 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (exp (log (/ 1 (sqrt (sqrt k))))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (log (/ 1 (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (13 enodes)
* * [misc]simplify:  iters left: 2 (17 enodes)
* * [misc]simplify:  iters left: 1 (30 enodes)
* [exit]simplify:  Simplified to (- (log (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (- (log (sqrt (sqrt k))))
* * * * [misc]progress:  [ 9 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (log (exp (/ 1 (sqrt (sqrt k))))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (exp (/ 1 (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* [exit]simplify:  Simplified to (exp (/ 1 (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (exp (/ 1 (sqrt (sqrt k))))
* * * * [misc]progress:  [ 10 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k))))) (cbrt (/ 1 (sqrt (sqrt k))))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (9 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k)))))
* [exit]simplify:  Simplified to (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (cbrt (/ 1 (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* [exit]simplify:  Simplified to (cbrt (/ 1 (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (cbrt (/ 1 (sqrt (sqrt k))))
* * * * [misc]progress:  [ 11 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (cbrt (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt k))))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (26 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* * [misc]simplify:  iters left: 2 (61 enodes)
* * [misc]simplify:  iters left: 1 (85 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt k)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt k)) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 12 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ 1 (sqrt (sqrt k))))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ 1 (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* [exit]simplify:  Simplified to (sqrt (/ 1 (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (sqrt (/ 1 (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (sqrt (/ 1 (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* [exit]simplify:  Simplified to (sqrt (/ 1 (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (sqrt (/ 1 (sqrt (sqrt k))))
* * * * [misc]progress:  [ 13 / 152 ] 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)
* * [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 (sqrt k)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* [exit]simplify:  Simplified to (- (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (- (sqrt (sqrt k)))
* * * * [misc]progress:  [ 14 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* 1 (/ 1 (sqrt (sqrt k)))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* * * * [misc]progress:  [ 15 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* 1 (/ 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)))
* * * * [misc]progress:  [ 16 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (/ (sqrt (sqrt k)) 1)) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) 1)
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* * [misc]simplify:  iters left: 2 (9 enodes)
* [exit]simplify:  Simplified to (sqrt (sqrt k))
* [exit]simplify:  Simplified to (sqrt (sqrt k))
* * * * [misc]progress:  [ 17 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (cbrt (sqrt (sqrt k)))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
* * * * [misc]progress:  [ 18 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (cbrt (sqrt k)))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* [exit]simplify:  Simplified to (/ 1 (fabs (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ 1 (fabs (cbrt (sqrt k))))
* * * * [misc]progress:  [ 19 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt (sqrt k))))
* * * * [misc]progress:  [ 20 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (sqrt 1)) (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt 1))
* * [misc]simplify:  iters left: 3 (3 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt 1))
* [exit]simplify:  Simplified to (/ 1 (sqrt 1))
* * * * [misc]progress:  [ 21 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt (sqrt k))))
* * * * [misc]progress:  [ 22 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 1) (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (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
* * * * [misc]progress:  [ 23 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (log1p (expm1 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (expm1 (/ (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 (expm1 (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (expm1 (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 24 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (expm1 (log1p (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (log1p (/ (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 (log1p (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (log1p (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 25 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (pow (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))) 1)))>
* * * * [misc]progress:  [ 26 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (exp (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (35 enodes)
* * [misc]simplify:  iters left: 4 (67 enodes)
* * [misc]simplify:  iters left: 3 (166 enodes)
* [exit]simplify:  Simplified to (- (* (/ (- 1 k) 2) (log (* (* PI n) 2))) (log (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (- (* (/ (- 1 k) 2) (log (* (* PI n) 2))) (log (sqrt (sqrt k))))
* * * * [misc]progress:  [ 27 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (exp (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (35 enodes)
* * [misc]simplify:  iters left: 4 (67 enodes)
* * [misc]simplify:  iters left: 3 (166 enodes)
* [exit]simplify:  Simplified to (- (* (/ (- 1 k) 2) (log (* (* PI n) 2))) (log (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (- (* (/ (- 1 k) 2) (log (* (* PI n) 2))) (log (sqrt (sqrt k))))
* * * * [misc]progress:  [ 28 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (exp (- (log (pow (* n (* PI 2)) (/ (- 1 k) 2))) (log (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (- (log (pow (* n (* PI 2)) (/ (- 1 k) 2))) (log (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (51 enodes)
* * [misc]simplify:  iters left: 3 (100 enodes)
* * [misc]simplify:  iters left: 2 (304 enodes)
* [exit]simplify:  Simplified to (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt (sqrt k))))
* * * * [misc]progress:  [ 29 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (exp (log (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (log (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (41 enodes)
* * [misc]simplify:  iters left: 3 (62 enodes)
* * [misc]simplify:  iters left: 2 (134 enodes)
* * [misc]simplify:  iters left: 1 (423 enodes)
* [exit]simplify:  Simplified to (- (* (log (* PI (* n 2))) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (- (* (log (* PI (* n 2))) (/ (- 1 k) 2)) (log (sqrt (sqrt k))))
* * * * [misc]progress:  [ 30 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (log (exp (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (exp (/ (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 (exp (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (exp (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 31 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (cbrt (/ (* (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (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 (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (75 enodes)
* * [misc]simplify:  iters left: 3 (128 enodes)
* * [misc]simplify:  iters left: 2 (183 enodes)
* * [misc]simplify:  iters left: 1 (200 enodes)
* [exit]simplify:  Simplified to (* (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (* (sqrt (sqrt k)) (sqrt k))) (* (pow (* (* PI n) 2) (/ (- 1 k) 2)) (pow (* (* PI n) 2) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (* (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (* (sqrt (sqrt k)) (sqrt k))) (* (pow (* (* PI n) 2) (/ (- 1 k) 2)) (pow (* (* PI n) 2) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 32 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (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)) (sqrt (sqrt k)))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (15 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 (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (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)))) (cbrt (/ (pow (* (* n 2) PI) (/ (- 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:  [ 33 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (cbrt (* (* (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (* (* (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (58 enodes)
* * [misc]simplify:  iters left: 3 (87 enodes)
* * [misc]simplify:  iters left: 2 (128 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 (sqrt k)) (sqrt 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 (sqrt k)) (sqrt k)) (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 34 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (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:  [ 35 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (- (pow (* n (* PI 2)) (/ (- 1 k) 2))) (- (sqrt (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 (sqrt k)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* [exit]simplify:  Simplified to (- (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (- (sqrt (sqrt k)))
* * * * [misc]progress:  [ 36 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow n (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (/ (pow n (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k))))
* * * * [misc]progress:  [ 37 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (pow n (/ (- 1 k) 2)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) (fabs (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) (fabs (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k))))
* * * * [misc]progress:  [ 38 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (11 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 n (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))
* * * * [misc]progress:  [ 39 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ (pow n (/ (- 1 k) 2)) (sqrt 1)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow n (/ (- 1 k) 2)) (sqrt 1))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* * [misc]simplify:  iters left: 3 (21 enodes)
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) (sqrt 1))
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) (sqrt 1))
* [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:  [ 40 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (11 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 n (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))
* * * * [misc]progress:  [ 41 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ (pow n (/ (- 1 k) 2)) 1) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (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 (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:  [ 42 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (34 enodes)
* * [misc]simplify:  iters left: 4 (52 enodes)
* * [misc]simplify:  iters left: 3 (59 enodes)
* * [misc]simplify:  iters left: 2 (62 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))))
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 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 (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))
* * * * [misc]progress:  [ 43 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (46 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (fabs (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (fabs (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 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 (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k))))
* * * * [misc]progress:  [ 44 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (44 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (cbrt (pow (* 2 (* PI n)) (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (cbrt (pow (* 2 (* PI n)) (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 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 (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))
* * * * [misc]progress:  [ 45 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt 1)) (/ (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 1))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (38 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (/ (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt 1)))
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (/ (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt 1)))
* [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:  [ 46 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (44 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (cbrt (pow (* 2 (* PI n)) (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (cbrt (pow (* 2 (* PI n)) (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 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 (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))
* * * * [misc]progress:  [ 47 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ (* (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 (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 (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:  [ 48 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (38 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* 2 (* PI n)) (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 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 (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))
* * * * [misc]progress:  [ 49 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (* (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 (37 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (fabs (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (fabs (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 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 (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k))))
* * * * [misc]progress:  [ 50 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 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 (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 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 (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))
* * * * [misc]progress:  [ 51 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt 1)) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt 1))
* * [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 1))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt 1))
* [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:  [ 52 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 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 (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 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 (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))
* * * * [misc]progress:  [ 53 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) 1) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (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 (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:  [ 54 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (cbrt (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 (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k))))
* * * * [misc]progress:  [ 55 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* [exit]simplify:  Simplified to (/ 1 (fabs (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ 1 (fabs (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (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 (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k))))
* * * * [misc]progress:  [ 56 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (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 (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))
* * * * [misc]progress:  [ 57 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt 1)) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt 1))
* * [misc]simplify:  iters left: 3 (3 enodes)
* * [misc]simplify:  iters left: 2 (5 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt 1))
* [exit]simplify:  Simplified to (/ 1 (sqrt 1))
* [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:  [ 58 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (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 (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))
* * * * [misc]progress:  [ 59 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ 1 1) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (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 (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:  [ 60 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* 1 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))))>
* * * * [misc]progress:  [ 61 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (/ 1 (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)))
* * * * [misc]progress:  [ 62 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* PI 2)) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) (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 (36 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) (pow (* (* n 2) PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) (pow (* (* n 2) PI) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 63 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (cbrt (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (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 (/ (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
* * * * [misc]progress:  [ 64 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (15 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)) (fabs (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow (* 2 (* PI n)) (/ (- 1 k) 2)) (fabs (cbrt (sqrt k))))
* * * * [misc]progress:  [ 65 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (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 (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))
* * * * [misc]progress:  [ 66 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt 1)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt 1))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt 1))
* [exit]simplify:  Simplified to (/ (pow (* PI (* n 2)) (/ (- 1 k) 2)) (sqrt 1))
* * * * [misc]progress:  [ 67 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (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 (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))
* * * * [misc]progress:  [ 68 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) 1) (sqrt (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:  [ 69 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow n (/ (- 1 k) 2)) (/ (sqrt (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 70 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 71 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 72 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ 1 (/ (sqrt (sqrt k)) (pow (* n (* PI 2)) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt (sqrt k)) (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 (36 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) (pow (* (* n 2) PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (sqrt (sqrt k)) (pow (* (* n 2) PI) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 73 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* n (* PI 2)) (/ k 2))))))>
* [enter]simplify:  Simplifying (* (sqrt (sqrt k)) (pow (* n (* PI 2)) (/ k 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* [exit]simplify:  Simplified to (* (pow (* (* n 2) PI) (/ k 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (* (pow (* (* n 2) PI) (/ k 2)) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 74 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (log1p (expm1 (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (expm1 (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (52 enodes)
* * [misc]simplify:  iters left: 3 (73 enodes)
* * [misc]simplify:  iters left: 2 (98 enodes)
* * [misc]simplify:  iters left: 1 (115 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:  [ 75 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (expm1 (log1p (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (log1p (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (52 enodes)
* * [misc]simplify:  iters left: 3 (73 enodes)
* * [misc]simplify:  iters left: 2 (98 enodes)
* * [misc]simplify:  iters left: 1 (115 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:  [ 76 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (pow (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))) 1))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (51 enodes)
* * [misc]simplify:  iters left: 3 (72 enodes)
* * [misc]simplify:  iters left: 2 (95 enodes)
* * [misc]simplify:  iters left: 1 (112 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:  [ 77 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (pow (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))) 1))>
* * * * [misc]progress:  [ 78 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (- (log (sqrt (sqrt k)))) (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (- (log (sqrt (sqrt k)))) (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (39 enodes)
* * [misc]simplify:  iters left: 4 (76 enodes)
* * [misc]simplify:  iters left: 3 (196 enodes)
* [exit]simplify:  Simplified to (- (* (/ (- 1 k) 2) (log (* 2 (* PI n)))) (+ (log (sqrt (sqrt k))) (log (sqrt (sqrt k)))))
* [exit]simplify:  Simplified to (- (* (/ (- 1 k) 2) (log (* 2 (* PI n)))) (+ (log (sqrt (sqrt k))) (log (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 79 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (- (log (sqrt (sqrt k)))) (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (- (log (sqrt (sqrt k)))) (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (39 enodes)
* * [misc]simplify:  iters left: 4 (76 enodes)
* * [misc]simplify:  iters left: 3 (196 enodes)
* [exit]simplify:  Simplified to (- (* (/ (- 1 k) 2) (log (* 2 (* PI n)))) (+ (log (sqrt (sqrt k))) (log (sqrt (sqrt k)))))
* [exit]simplify:  Simplified to (- (* (/ (- 1 k) 2) (log (* 2 (* PI n)))) (+ (log (sqrt (sqrt k))) (log (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 80 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (- (log (sqrt (sqrt k)))) (- (log (pow (* n (* PI 2)) (/ (- 1 k) 2))) (log (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (- (log (sqrt (sqrt k)))) (- (log (pow (* n (* PI 2)) (/ (- 1 k) 2))) (log (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (34 enodes)
* * [misc]simplify:  iters left: 4 (60 enodes)
* * [misc]simplify:  iters left: 3 (122 enodes)
* * [misc]simplify:  iters left: 2 (431 enodes)
* [exit]simplify:  Simplified to (- (* (log (* (* n 2) PI)) (/ (- 1 k) 2)) (+ (log (sqrt (sqrt k))) (log (sqrt (sqrt k)))))
* [exit]simplify:  Simplified to (- (* (log (* (* n 2) PI)) (/ (- 1 k) 2)) (+ (log (sqrt (sqrt k))) (log (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 81 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (- (log (sqrt (sqrt k)))) (log (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (- (log (sqrt (sqrt k)))) (log (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (48 enodes)
* * [misc]simplify:  iters left: 3 (80 enodes)
* * [misc]simplify:  iters left: 2 (181 enodes)
* [exit]simplify:  Simplified to (- (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) (+ (log (sqrt (sqrt k))) (log (sqrt (sqrt k)))))
* [exit]simplify:  Simplified to (- (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) (+ (log (sqrt (sqrt k))) (log (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 82 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (log (/ 1 (sqrt (sqrt k)))) (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (log (/ 1 (sqrt (sqrt k)))) (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (43 enodes)
* * [misc]simplify:  iters left: 4 (89 enodes)
* * [misc]simplify:  iters left: 3 (264 enodes)
* [exit]simplify:  Simplified to (- (* (log (* (* PI n) 2)) (/ (- 1 k) 2)) (+ (log (sqrt (sqrt k))) (log (sqrt (sqrt k)))))
* [exit]simplify:  Simplified to (- (* (log (* (* PI n) 2)) (/ (- 1 k) 2)) (+ (log (sqrt (sqrt k))) (log (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 83 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (log (/ 1 (sqrt (sqrt k)))) (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (log (/ 1 (sqrt (sqrt k)))) (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (log (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (43 enodes)
* * [misc]simplify:  iters left: 4 (89 enodes)
* * [misc]simplify:  iters left: 3 (264 enodes)
* [exit]simplify:  Simplified to (- (* (log (* (* PI n) 2)) (/ (- 1 k) 2)) (+ (log (sqrt (sqrt k))) (log (sqrt (sqrt k)))))
* [exit]simplify:  Simplified to (- (* (log (* (* PI n) 2)) (/ (- 1 k) 2)) (+ (log (sqrt (sqrt k))) (log (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 84 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (log (/ 1 (sqrt (sqrt k)))) (- (log (pow (* n (* PI 2)) (/ (- 1 k) 2))) (log (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (log (/ 1 (sqrt (sqrt k)))) (- (log (pow (* n (* PI 2)) (/ (- 1 k) 2))) (log (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (38 enodes)
* * [misc]simplify:  iters left: 4 (73 enodes)
* * [misc]simplify:  iters left: 3 (182 enodes)
* [exit]simplify:  Simplified to (- (* (log (* PI (* 2 n))) (/ (- 1 k) 2)) (+ (log (sqrt (sqrt k))) (log (sqrt (sqrt k)))))
* [exit]simplify:  Simplified to (- (* (log (* PI (* 2 n))) (/ (- 1 k) 2)) (+ (log (sqrt (sqrt k))) (log (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 85 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (log (/ 1 (sqrt (sqrt k)))) (log (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (+ (log (/ 1 (sqrt (sqrt k)))) (log (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (35 enodes)
* * [misc]simplify:  iters left: 4 (57 enodes)
* * [misc]simplify:  iters left: 3 (113 enodes)
* * [misc]simplify:  iters left: 2 (339 enodes)
* [exit]simplify:  Simplified to (- (* (log (* (* 2 n) PI)) (/ (- 1 k) 2)) (+ (log (sqrt (sqrt k))) (log (sqrt (sqrt k)))))
* [exit]simplify:  Simplified to (- (* (log (* (* 2 n) PI)) (/ (- 1 k) 2)) (+ (log (sqrt (sqrt k))) (log (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 86 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (exp (log (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (log (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (35 enodes)
* * [misc]simplify:  iters left: 4 (66 enodes)
* * [misc]simplify:  iters left: 3 (114 enodes)
* * [misc]simplify:  iters left: 2 (211 enodes)
* * [misc]simplify:  iters left: 1 (406 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* 2 PI) n)) (/ (- 1 k) 2) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* 2 PI) n)) (/ (- 1 k) 2) (- (log (sqrt k))))
* * * * [misc]progress:  [ 87 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (log (exp (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (exp (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (34 enodes)
* * [misc]simplify:  iters left: 4 (54 enodes)
* * [misc]simplify:  iters left: 3 (75 enodes)
* * [misc]simplify:  iters left: 2 (99 enodes)
* * [misc]simplify:  iters left: 1 (117 enodes)
* [exit]simplify:  Simplified to (exp (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (exp (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 88 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (* (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt k)))) (/ (* (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (* (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt k)))) (/ (* (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (21 enodes)
* * [misc]simplify:  iters left: 5 (53 enodes)
* * [misc]simplify:  iters left: 4 (160 enodes)
* [exit]simplify:  Simplified to (* (/ (/ (/ 1 (sqrt k)) (sqrt (sqrt k))) (* (sqrt (sqrt k)) (sqrt k))) (pow (pow (* (* PI 2) n) (/ (- 1 k) 2)) 3))
* [exit]simplify:  Simplified to (* (/ (/ (/ 1 (sqrt k)) (sqrt (sqrt k))) (* (sqrt (sqrt k)) (sqrt k))) (pow (pow (* (* PI 2) n) (/ (- 1 k) 2)) 3))
* * * * [misc]progress:  [ 89 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (* (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt k)))) (* (* (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (* (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt k)))) (* (* (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (49 enodes)
* * [misc]simplify:  iters left: 4 (133 enodes)
* * [misc]simplify:  iters left: 3 (350 enodes)
* [exit]simplify:  Simplified to (* (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) (* (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) (* (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 90 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (cbrt (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))) (cbrt (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))) (cbrt (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (* (cbrt (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))) (cbrt (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (53 enodes)
* * [misc]simplify:  iters left: 3 (74 enodes)
* * [misc]simplify:  iters left: 2 (97 enodes)
* * [misc]simplify:  iters left: 1 (113 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k))))
* [enter]simplify:  Simplifying (cbrt (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (52 enodes)
* * [misc]simplify:  iters left: 3 (73 enodes)
* * [misc]simplify:  iters left: 2 (98 enodes)
* * [misc]simplify:  iters left: 1 (115 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:  [ 91 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (* (* (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (* (* (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (113 enodes)
* * [misc]simplify:  iters left: 3 (293 enodes)
* [exit]simplify:  Simplified to (pow (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)) 3)
* [exit]simplify:  Simplified to (pow (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)) 3)
* * * * [misc]progress:  [ 92 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))) (sqrt (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))))>
* [enter]simplify:  Simplifying (sqrt (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (52 enodes)
* * [misc]simplify:  iters left: 3 (73 enodes)
* * [misc]simplify:  iters left: 2 (98 enodes)
* * [misc]simplify:  iters left: 1 (115 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 (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (52 enodes)
* * [misc]simplify:  iters left: 3 (73 enodes)
* * [misc]simplify:  iters left: 2 (98 enodes)
* * [misc]simplify:  iters left: 1 (115 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:  [ 93 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* 1 (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (sqrt (sqrt k)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* 1 (pow (* n (* PI 2)) (/ (- 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 (* PI n)) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow (* 2 (* PI n)) (/ (- 1 k) 2))
* [enter]simplify:  Simplifying (* (sqrt (sqrt k)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* [exit]simplify:  Simplified to (sqrt k)
* [exit]simplify:  Simplified to (sqrt k)
* * * * [misc]progress:  [ 94 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))))>
* * * * [misc]progress:  [ 95 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (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 (* (/ 1 (sqrt (sqrt k))) (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (50 enodes)
* * [misc]simplify:  iters left: 3 (76 enodes)
* * [misc]simplify:  iters left: 2 (103 enodes)
* * [misc]simplify:  iters left: 1 (107 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (cbrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt (sqrt k))))))
* [exit]simplify:  Simplified to (/ (cbrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (cbrt (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt (sqrt k))))))
* * * * [misc]progress:  [ 96 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (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 (* (/ 1 (sqrt (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (16 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 (66 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 97 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (52 enodes)
* * [misc]simplify:  iters left: 3 (121 enodes)
* * [misc]simplify:  iters left: 2 (309 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow n (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (/ (pow n (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 98 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ (pow n (/ (- 1 k) 2)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ (pow n (/ (- 1 k) 2)) (sqrt (* (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 (43 enodes)
* * [misc]simplify:  iters left: 3 (70 enodes)
* * [misc]simplify:  iters left: 2 (104 enodes)
* * [misc]simplify:  iters left: 1 (144 enodes)
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) (* (sqrt (sqrt k)) (fabs (cbrt (sqrt k)))))
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) (* (sqrt (sqrt k)) (fabs (cbrt (sqrt k)))))
* * * * [misc]progress:  [ 99 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (67 enodes)
* * [misc]simplify:  iters left: 2 (101 enodes)
* * [misc]simplify:  iters left: 1 (159 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
* * * * [misc]progress:  [ 100 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ (pow n (/ (- 1 k) 2)) (sqrt 1))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ (pow n (/ (- 1 k) 2)) (sqrt 1)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (67 enodes)
* * [misc]simplify:  iters left: 2 (101 enodes)
* * [misc]simplify:  iters left: 1 (159 enodes)
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) (* (sqrt 1) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) (* (sqrt 1) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 101 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (67 enodes)
* * [misc]simplify:  iters left: 2 (101 enodes)
* * [misc]simplify:  iters left: 1 (159 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
* * * * [misc]progress:  [ 102 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ (pow n (/ (- 1 k) 2)) 1)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ (pow n (/ (- 1 k) 2)) 1))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (71 enodes)
* * [misc]simplify:  iters left: 2 (103 enodes)
* * [misc]simplify:  iters left: 1 (122 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)))
* * * * [misc]progress:  [ 103 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (41 enodes)
* * [misc]simplify:  iters left: 4 (93 enodes)
* * [misc]simplify:  iters left: 3 (272 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) (/ (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (sqrt (sqrt k)))))
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k)))) (/ (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 104 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (39 enodes)
* * [misc]simplify:  iters left: 4 (68 enodes)
* * [misc]simplify:  iters left: 3 (135 enodes)
* * [misc]simplify:  iters left: 2 (297 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (fabs (cbrt (sqrt k)))) (/ (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (fabs (cbrt (sqrt k)))) (/ (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 105 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k))))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (65 enodes)
* * [misc]simplify:  iters left: 3 (132 enodes)
* * [misc]simplify:  iters left: 2 (305 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (sqrt (sqrt (sqrt k))) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (sqrt (sqrt (sqrt k))) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 106 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt 1))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt 1)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (65 enodes)
* * [misc]simplify:  iters left: 3 (132 enodes)
* * [misc]simplify:  iters left: 2 (305 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (sqrt 1) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (sqrt 1) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 107 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k))))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (65 enodes)
* * [misc]simplify:  iters left: 3 (132 enodes)
* * [misc]simplify:  iters left: 2 (305 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (sqrt (sqrt (sqrt k))) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (sqrt (sqrt (sqrt k))) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 108 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ (* (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 (sqrt k)))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) 1))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (35 enodes)
* * [misc]simplify:  iters left: 4 (65 enodes)
* * [misc]simplify:  iters left: 3 (116 enodes)
* * [misc]simplify:  iters left: 2 (189 enodes)
* * [misc]simplify:  iters left: 1 (357 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 109 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (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 (137 enodes)
* * [misc]simplify:  iters left: 2 (325 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 110 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (57 enodes)
* * [misc]simplify:  iters left: 3 (85 enodes)
* * [misc]simplify:  iters left: 2 (119 enodes)
* * [misc]simplify:  iters left: 1 (183 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (* (fabs (cbrt (sqrt k))) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (* (fabs (cbrt (sqrt k))) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 111 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (54 enodes)
* * [misc]simplify:  iters left: 3 (82 enodes)
* * [misc]simplify:  iters left: 2 (116 enodes)
* * [misc]simplify:  iters left: 1 (174 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (sqrt (sqrt k)) (sqrt (sqrt (sqrt k)))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (sqrt (sqrt k)) (sqrt (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 112 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt 1))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt 1)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (54 enodes)
* * [misc]simplify:  iters left: 3 (82 enodes)
* * [misc]simplify:  iters left: 2 (116 enodes)
* * [misc]simplify:  iters left: 1 (174 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (sqrt (sqrt k)) (sqrt 1)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (sqrt (sqrt k)) (sqrt 1)))
* * * * [misc]progress:  [ 113 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (54 enodes)
* * [misc]simplify:  iters left: 3 (82 enodes)
* * [misc]simplify:  iters left: 2 (116 enodes)
* * [misc]simplify:  iters left: 1 (174 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (sqrt (sqrt k)) (sqrt (sqrt (sqrt k)))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (sqrt (sqrt k)) (sqrt (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 114 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) 1)) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) 1))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (57 enodes)
* * [misc]simplify:  iters left: 3 (86 enodes)
* * [misc]simplify:  iters left: 2 (118 enodes)
* * [misc]simplify:  iters left: 1 (137 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 115 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (cbrt (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (41 enodes)
* * [misc]simplify:  iters left: 3 (78 enodes)
* * [misc]simplify:  iters left: 2 (133 enodes)
* * [misc]simplify:  iters left: 1 (256 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 116 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* * [misc]simplify:  iters left: 2 (54 enodes)
* * [misc]simplify:  iters left: 1 (72 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt (sqrt k))) (fabs (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt (sqrt k))) (fabs (cbrt (sqrt k))))
* * * * [misc]progress:  [ 117 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k))))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* * [misc]simplify:  iters left: 2 (53 enodes)
* * [misc]simplify:  iters left: 1 (63 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
* * * * [misc]progress:  [ 118 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt 1))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt 1)))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* * [misc]simplify:  iters left: 2 (53 enodes)
* * [misc]simplify:  iters left: 1 (63 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt 1)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt 1)) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 119 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k))))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* * [misc]simplify:  iters left: 2 (53 enodes)
* * [misc]simplify:  iters left: 1 (63 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
* * * * [misc]progress:  [ 120 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1 1)) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ 1 1))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* * * * [misc]progress:  [ 121 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) 1) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) 1)
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* * * * [misc]progress:  [ 122 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ 1 (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (pow (* n (* PI 2)) (/ (- 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 (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 123 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k))))) (* (cbrt (/ 1 (sqrt (sqrt k)))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (cbrt (/ 1 (sqrt (sqrt k)))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (49 enodes)
* * [misc]simplify:  iters left: 2 (51 enodes)
* * [misc]simplify:  iters left: 1 (52 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ 1 (sqrt (sqrt k)))) (/ (pow (* PI (* 2 n)) (/ (- 1 k) 2)) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (* (cbrt (/ 1 (sqrt (sqrt k)))) (/ (pow (* PI (* 2 n)) (/ (- 1 k) 2)) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 124 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ 1 (sqrt (sqrt k)))) (* (sqrt (/ 1 (sqrt (sqrt k)))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (sqrt (/ 1 (sqrt (sqrt k)))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (49 enodes)
* * [misc]simplify:  iters left: 2 (51 enodes)
* * [misc]simplify:  iters left: 1 (52 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ 1 (sqrt (sqrt k)))) (/ (pow (* PI (* 2 n)) (/ (- 1 k) 2)) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (/ 1 (sqrt (sqrt k)))) (/ (pow (* PI (* 2 n)) (/ (- 1 k) 2)) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 125 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (51 enodes)
* * [misc]simplify:  iters left: 3 (72 enodes)
* * [misc]simplify:  iters left: 2 (95 enodes)
* * [misc]simplify:  iters left: 1 (112 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:  [ 126 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (51 enodes)
* * [misc]simplify:  iters left: 3 (72 enodes)
* * [misc]simplify:  iters left: 2 (95 enodes)
* * [misc]simplify:  iters left: 1 (112 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:  [ 127 / 152 ] 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))) (pow (* n (* PI 2)) (/ (- 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 (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 128 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* 1 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))) (sqrt (sqrt k))))>
* [enter]simplify:  Simplifying (* 1 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))
* * [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 (50 enodes)
* * [misc]simplify:  iters left: 2 (56 enodes)
* * [misc]simplify:  iters left: 1 (69 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (* (* 2 n) PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 129 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))))>
* * * * [misc]progress:  [ 130 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (log1p (expm1 (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt (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:  [ 131 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (expm1 (log1p (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt (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:  [ 132 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (pow (* n (* PI 2)) 1) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* * * * [misc]progress:  [ 133 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (exp (log (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt (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:  [ 134 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (log (exp (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt (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:  [ 135 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt (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:  [ 136 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (cbrt (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt (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:  [ 137 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (sqrt (* n (* PI 2))) (sqrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt (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:  [ 138 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* 1 (* n (* PI 2))) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* * * * [misc]progress:  [ 139 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt (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:  [ 140 / 152 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* * * * [misc]progress:  [ 141 / 152 ] simplifiying candidate #<alt-event (λ (k n) (* (- (+ +nan.0 (- (+ (* +nan.0 k) (- (* +nan.0 (/ 1 k))))))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (- (+ +nan.0 (- (+ (* +nan.0 k) (- (* +nan.0 (/ 1 k))))))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 142 / 152 ] simplifiying candidate #<alt-event (λ (k n) (* (- (/ 1 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 5) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) k)))))))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (- (/ 1 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 5) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) k)))))))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 143 / 152 ] simplifiying candidate #<alt-event (λ (k n) (* (- (/ 1 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 5) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) k)))))))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (- (/ 1 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 5) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) k)))))))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 144 / 152 ] simplifiying candidate #<alt-event (λ (k n) (* (/ 1 (sqrt (sqrt k))) (- (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (/ 1 k) 1/4)) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2)) (pow (pow k 7) 1/4))) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)) (pow (pow k 7) 1/4))) (* 1/4 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))) (pow (pow k 7) 1/4)))))) (+ (* 1/2 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)) (pow (pow k 3) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))) (pow (pow k 3) 1/4)))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (- (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (/ 1 k) 1/4)) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2)) (pow (pow k 7) 1/4))) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)) (pow (pow k 7) 1/4))) (* 1/4 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))) (pow (pow k 7) 1/4)))))) (+ (* 1/2 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)) (pow (pow k 3) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))) (pow (pow k 3) 1/4))))))
* * [misc]simplify:  iters left: 6 (50 enodes)
* * [misc]simplify:  iters left: 5 (132 enodes)
* * [misc]simplify:  iters left: 4 (397 enodes)
* [exit]simplify:  Simplified to (fma (/ 1 (sqrt (sqrt k))) (fma (pow (pow k 7) 1/4) (* (* (* (pow (* PI 2) 1/2) (pow n 1/2)) 1/8) (+ (* (log n) (log n)) (* (log (* PI 2)) (log (* PI 2))))) (fma (* (* (pow (pow k 7) 1/4) (log (* PI 2))) (* (pow (* PI 2) 1/2) (* (pow n 1/2) (log n)))) 1/4 (* (* (pow (/ 1 k) 1/4) (pow (* PI 2) 1/2)) (pow n 1/2)))) (/ (* (* (- 1/2) (* (pow (* PI 2) 1/2) (pow n 1/2))) (* (pow (pow k 3) 1/4) (+ (log n) (log (* PI 2))))) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 145 / 152 ] simplifiying candidate #<alt-event (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow (/ 1 k) 1/4))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow (/ 1 k) 1/4)))
* * [misc]simplify:  iters left: 6 (23 enodes)
* * [misc]simplify:  iters left: 5 (49 enodes)
* * [misc]simplify:  iters left: 4 (105 enodes)
* * [misc]simplify:  iters left: 3 (331 enodes)
* [exit]simplify:  Simplified to (* (/ (pow (/ 1 k) 1/4) (sqrt (sqrt k))) (* (pow n (- 1/2 (* 1/2 k))) (pow (* PI 2) (- 1/2 (* 1/2 k)))))
* * * * [misc]progress:  [ 146 / 152 ] simplifiying candidate #<alt-event (λ (k n) (* (/ 1 (sqrt (sqrt k))) (- (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt +nan.0)) (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (* (sqrt +nan.0) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (* (sqrt +nan.0) k))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (* (pow (sqrt +nan.0) 3) (pow k 2)))))))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (- (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt +nan.0)) (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (* (sqrt +nan.0) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (* (sqrt +nan.0) k))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (* (pow (sqrt +nan.0) 3) (pow k 2))))))))))
* * * * [misc]progress:  [ 147 / 152 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (* (pow n 2) (* (pow PI 2) (sqrt 2))) (pow k 2))) (- (+ (* +nan.0 (/ (* n (* PI (* (log (* 2 PI)) (sqrt 2)))) k)) (- (+ (* +nan.0 (/ (* n (* PI (* (log n) (sqrt 2)))) k)) (- (+ (* +nan.0 (/ (* n (* PI (sqrt 2))) k)) (- (* +nan.0 (/ (* n (* PI (sqrt 2))) (pow k 2)))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (* (pow n 2) (* (pow PI 2) (sqrt 2))) (pow k 2))) (- (+ (* +nan.0 (/ (* n (* PI (* (log (* 2 PI)) (sqrt 2)))) k)) (- (+ (* +nan.0 (/ (* n (* PI (* (log n) (sqrt 2)))) k)) (- (+ (* +nan.0 (/ (* n (* PI (sqrt 2))) k)) (- (* +nan.0 (/ (* n (* PI (sqrt 2))) (pow k 2))))))))))))
* * * * [misc]progress:  [ 148 / 152 ] simplifiying candidate #<alt-event (λ (k n) (- (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow (sqrt +nan.0) 2)) (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (* (pow (sqrt +nan.0) 4) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (* (pow (sqrt +nan.0) 6) (pow k 2)))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (* (pow (sqrt +nan.0) 4) k)))))))))>
* [enter]simplify:  Simplifying (- (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow (sqrt +nan.0) 2)) (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (* (pow (sqrt +nan.0) 4) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (* (pow (sqrt +nan.0) 6) (pow k 2)))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (* (pow (sqrt +nan.0) 4) k))))))))
* * * * [misc]progress:  [ 149 / 152 ] simplifiying candidate #<alt-event (λ (k n) (- (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow (sqrt +nan.0) 2)) (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (* (pow (sqrt +nan.0) 4) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (* (pow (sqrt +nan.0) 4) k))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (* (pow (sqrt +nan.0) 6) (pow k 2))))))))))>
* [enter]simplify:  Simplifying (- (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow (sqrt +nan.0) 2)) (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (* (pow (sqrt +nan.0) 4) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (* (pow (sqrt +nan.0) 4) k))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (* (pow (sqrt +nan.0) 6) (pow k 2)))))))))
* * * * [misc]progress:  [ 150 / 152 ] simplifiying candidate #<alt-event (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (51 enodes)
* * [misc]simplify:  iters left: 3 (72 enodes)
* * [misc]simplify:  iters left: 2 (95 enodes)
* * [misc]simplify:  iters left: 1 (112 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 151 / 152 ] simplifiying candidate #<alt-event (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (51 enodes)
* * [misc]simplify:  iters left: 3 (72 enodes)
* * [misc]simplify:  iters left: 2 (95 enodes)
* * [misc]simplify:  iters left: 1 (112 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 152 / 152 ] simplifiying candidate #<alt-event (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (51 enodes)
* * [misc]simplify:  iters left: 3 (72 enodes)
* * [misc]simplify:  iters left: 2 (95 enodes)
* * [misc]simplify:  iters left: 1 (112 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (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) (* (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))))> #<alt-delta (λ (k n) (* (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))> #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))> #<alt-delta (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))))> #<alt-delta (λ (k n) (* (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt k))))))> #<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)))))))> #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))> #<alt-delta (λ (k n) (/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))))> #<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) (/ (+ (* (* (* (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 (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))>)
* [misc]regimes:  Found splitpoints: (#s(sp 0 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) +nan.0)) , with alts (#<alt-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 (13 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]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 6486 additional inputs, on iter 1 have 1514 / 8000
* * * * [misc]points:  Computing exacts on every 405 of 6486 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 202 of 6486 points 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 6486 points 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 6486 points 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 6486 points 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 6486 points 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 6486 points 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 6486 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 6486 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 5250 additional inputs, on iter 2 have 2750 / 8000
* * * * [misc]points:  Computing exacts on every 328 of 5250 points 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 5250 points 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 5250 points 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 5250 points 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 5250 points 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 5250 points 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 5250 points 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 5250 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 5250 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4310 additional inputs, on iter 3 have 3690 / 8000
* * * * [misc]points:  Computing exacts on every 269 of 4310 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 134 of 4310 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 67 of 4310 points 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 4310 points 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 4310 points 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 4310 points 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 4310 points 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 4310 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 4310 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 3505 additional inputs, on iter 4 have 4495 / 8000
* * * * [misc]points:  Computing exacts on every 219 of 3505 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 109 of 3505 points 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 3505 points 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 3505 points 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 3505 points 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 3505 points 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 3505 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 3505 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 2854 additional inputs, on iter 5 have 5146 / 8000
* * * * [misc]points:  Computing exacts on every 178 of 2854 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 89 of 2854 points 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 2854 points 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 2854 points 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 2854 points 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 2854 points 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 2854 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 2854 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 2304 additional inputs, on iter 6 have 5696 / 8000
* * * * [misc]points:  Computing exacts on every 144 of 2304 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 72 of 2304 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 36 of 2304 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 18 of 2304 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 9 of 2304 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 4 of 2304 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 2304 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 2304 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 1854 additional inputs, on iter 7 have 6146 / 8000
* * * * [misc]points:  Computing exacts on every 115 of 1854 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 57 of 1854 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 28 of 1854 points 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 1854 points 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 1854 points 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 1854 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1854 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 1507 additional inputs, on iter 8 have 6493 / 8000
* * * * [misc]points:  Computing exacts on every 94 of 1507 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 47 of 1507 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 23 of 1507 points 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 1507 points 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 1507 points 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 1507 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1507 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 1230 additional inputs, on iter 9 have 6770 / 8000
* * * * [misc]points:  Computing exacts on every 76 of 1230 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 38 of 1230 points 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 1230 points 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 1230 points 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 1230 points 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 1230 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1230 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 986 additional inputs, on iter 10 have 7014 / 8000
* * * * [misc]points:  Computing exacts on every 61 of 986 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 30 of 986 points 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 986 points 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 986 points 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 986 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 986 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 801 additional inputs, on iter 11 have 7199 / 8000
* * * * [misc]points:  Computing exacts on every 50 of 801 points 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 801 points 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 801 points 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 801 points 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 801 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 801 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 652 additional inputs, on iter 12 have 7348 / 8000
* * * * [misc]points:  Computing exacts on every 40 of 652 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 20 of 652 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 10 of 652 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 5 of 652 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 652 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 652 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 536 additional inputs, on iter 13 have 7464 / 8000
* * * * [misc]points:  Computing exacts on every 33 of 536 points 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 536 points 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 536 points 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 536 points 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 536 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 536 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 429 additional inputs, on iter 14 have 7571 / 8000
* * * * [misc]points:  Computing exacts on every 26 of 429 points 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 429 points 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 429 points 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 429 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 429 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 336 additional inputs, on iter 15 have 7664 / 8000
* * * * [misc]points:  Computing exacts on every 21 of 336 points 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 336 points 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 336 points 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 336 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 336 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 268 additional inputs, on iter 16 have 7732 / 8000
* * * * [misc]points:  Computing exacts on every 16 of 268 points 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 268 points 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 268 points 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 268 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 268 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 210 additional inputs, on iter 17 have 7790 / 8000
* * * * [misc]points:  Computing exacts on every 13 of 210 points 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 210 points 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 210 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 210 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 172 additional inputs, on iter 18 have 7828 / 8000
* * * * [misc]points:  Computing exacts on every 10 of 172 points 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 172 points 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 172 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 172 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 138 additional inputs, on iter 19 have 7862 / 8000
* * * * [misc]points:  Computing exacts on every 8 of 138 points 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 138 points 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 138 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 138 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 105 additional inputs, on iter 20 have 7895 / 8000
* * * * [misc]points:  Computing exacts on every 6 of 105 points 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 105 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 105 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 90 additional inputs, on iter 21 have 7910 / 8000
* * * * [misc]points:  Computing exacts on every 5 of 90 points 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 90 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 90 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 69 additional inputs, on iter 22 have 7931 / 8000
* * * * [misc]points:  Computing exacts on every 4 of 69 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 69 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 69 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 59 additional inputs, on iter 23 have 7941 / 8000
* * * * [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 51 additional inputs, on iter 24 have 7949 / 8000
* * * * [misc]points:  Computing exacts on every 3 of 51 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 51 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 44 additional inputs, on iter 25 have 7956 / 8000
* * * * [misc]points:  Computing exacts on every 2 of 44 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 44 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 35 additional inputs, on iter 26 have 7965 / 8000
* * * * [misc]points:  Computing exacts on every 2 of 35 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 35 points
* * * * [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 18 additional inputs, on iter 29 have 7982 / 8000
* * * * [misc]points:  Computing exacts for 18 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 16 additional inputs, on iter 30 have 7984 / 8000
* * * * [misc]points:  Computing exacts for 16 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 13 additional inputs, on iter 31 have 7987 / 8000
* * * * [misc]points:  Computing exacts for 13 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 11 additional inputs, on iter 32 have 7989 / 8000
* * * * [misc]points:  Computing exacts for 11 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 9 additional inputs, on iter 33 have 7991 / 8000
* * * * [misc]points:  Computing exacts for 9 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 5 additional inputs, on iter 34 have 7995 / 8000
* * * * [misc]points:  Computing exacts for 5 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 5 additional inputs, on iter 35 have 7995 / 8000
* * * * [misc]points:  Computing exacts for 5 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 36 have 7996 / 8000
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 37 have 7996 / 8000
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 38 have 7999 / 8000
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [exit]points:  Sampled 8001 points with exact outputs