* [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:  Setting MPFR precision to 576
* * * * [misc]points:  Computing exacts on every 4 of 256 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 320
* * * * [misc]points:  Setting MPFR precision to 576
* * * * [misc]points:  Setting MPFR precision to 832
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 256 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 256 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 212 additional inputs, on iter 1 have 44 / 256
* * * * [misc]points:  Computing exacts on every 13 of 212 points 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 212 points 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 212 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 212 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 169 additional inputs, on iter 2 have 87 / 256
* * * * [misc]points:  Computing exacts on every 10 of 169 points 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 169 points 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 169 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 169 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 133 additional inputs, on iter 3 have 123 / 256
* * * * [misc]points:  Computing exacts on every 8 of 133 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 4 of 133 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 133 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 133 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 107 additional inputs, on iter 4 have 149 / 256
* * * * [misc]points:  Computing exacts on every 6 of 107 points 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 107 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 107 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 83 additional inputs, on iter 5 have 173 / 256
* * * * [misc]points:  Computing exacts on every 5 of 83 points 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 83 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 83 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 72 additional inputs, on iter 6 have 184 / 256
* * * * [misc]points:  Computing exacts on every 4 of 72 points 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 72 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 72 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 62 additional inputs, on iter 7 have 194 / 256
* * * * [misc]points:  Computing exacts on every 3 of 62 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 62 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 48 additional inputs, on iter 8 have 208 / 256
* * * * [misc]points:  Computing exacts on every 3 of 48 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 48 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 38 additional inputs, on iter 9 have 218 / 256
* * * * [misc]points:  Computing exacts on every 2 of 38 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 38 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 31 additional inputs, on iter 10 have 225 / 256
* * * * [misc]points:  Computing exacts for 31 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 26 additional inputs, on iter 11 have 230 / 256
* * * * [misc]points:  Computing exacts for 26 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 19 additional inputs, on iter 12 have 237 / 256
* * * * [misc]points:  Computing exacts for 19 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 16 additional inputs, on iter 13 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 13 additional inputs, on iter 14 have 243 / 256
* * * * [misc]points:  Computing exacts for 13 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 10 additional inputs, on iter 15 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 5 additional inputs, on iter 16 have 251 / 256
* * * * [misc]points:  Computing exacts for 5 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 17 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 18 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 19 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 20 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 21 have 253 / 256
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 22 have 253 / 256
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 23 have 253 / 256
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 24 have 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 25 have 254 / 256
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 26 have 255 / 256
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [exit]points:  Sampled 257 points with exact outputs
* * * [misc]progress:  [2/2] Setting up program.
* [misc]progress:  [Phase 2 of 3] Improving.
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (52 enodes)
* * [misc]simplify:  iters left: 2 (56 enodes)
* * [misc]simplify:  iters left: 1 (63 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))
* * [misc]progress:  iteration 1 / 4
* * * [misc]progress:  picking best candidate
"ALT DATA: "{"picked-error":0.6589912863283546,"picked":"(λ (k n) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))","all-alts":["#<alt-event (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>","#<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))>"],"best-fresh-alt-per-point":[[[5.091954821941639e-192,6.815392098658887e+143],1,1.0],[[1.9872779421557533e+180,1.8165707546862427e+45],0,0],[[7.416044817432175e-280,4.187534830574239e+90],0,0],[[8.952174144166139e-302,1.0956116997098222e-31],0,0],[[2.7602034085604025e+247,3.933007183466984e+176],0,0],[[4.691318136614946e-91,2.2211280072565116e-303],1,0],[[9.07067712653544e+121,1.1966070572230463e+134],0,0],[[2.534573079598786e+169,3.2634856808337097e+195],0,0],[[6.317640848359807e-38,7.108640458245273e-156],1,0],[[1.37963739668883e-251,1.9832537005473266e-262],0,0],[[2.2237477837114185e-204,3.5971048785615273e+27],0,0],[[2.0235103563137384e-245,3.186488674327569e-306],0,1.0],[[4.535662949534244e+218,1.0124765649019447e+298],0,0],[[3.548084498024942e-190,1.2458518796694574e+90],0,1.0],[[1.0707760413948923e-209,1.8155292668497655e+36],1,0],[[8.082647412227132e-211,1.4588918120519666e-114],0,1.0],[[5.13876683088187e-118,9.467488944393916e+142],0,0],[[2.2187340876406246e+300,4.0696348581298066e+30],0,0],[[4.737175196542416e-301,9.453454014910064e+271],0,0],[[1.090098977941039e-114,5.7243448441390635e+162],0,0],[[2.571403883587662e-39,2.725225610867578e+225],0,0],[[5.081095649164445e+286,2.6437596200790387e+281],0,0],[[6.85981085886286e-168,1.9805731700427848e-169],0,0],[[9.636536782052696e-111,2.985561979664205e+171],0,0],[[1.0838714812801137e-216,1.1791770071753556e+107],1,1.0],[[1.072386271012045e-235,9.15478951965041e+260],0,0],[[4.954601632348903e-272,5.651261930475929e+123],0,0],[[5.598692384845278e-151,2.0020470402494707e-128],0,1.0],[[3.828518244176968e-308,9.957124504840989e+307],0,51.208680506187314],[[7.811244882301027e-64,2.3660873791160076e+189],0,0],[[1.1253736853318525e-46,4.582462397892038e-300],1,0],[[2271813.2914643916,1.711246486837026e+16],0,0],[[2.6512646278212223e-277,2.991195561163922e+252],0,0],[[2.8722519575799174e-220,8.864398632472997e+128],0,0],[[6.898353156002884e+56,5.049169591478046e+301],0,0],[[5.795257109406676e+26,7.254471041027067e+34],0,0],[[1.9680527238636918e-165,6.602387235477923e-263],1,0],[[4.390126892195692e-258,5.153839259075024e-217],0,1.0],[[3.7270065251219893e-51,4.1091807334876805e+121],0,0],[[1.2718549924538793e-67,1.4997147168186959e-133],1,0],[[7.779411959735569e-290,2.9896016385939845e-66],1,0],[[2.8931224974199074e-84,1.9240432527476484e-289],0,0],[[1.6509703901493846e-82,1.0044867221158944e+300],0,0],[[7.040383581327078e-101,5.96146379570227e+197],0,0],[[1.607215854807525e-42,2.5297373356963796e-300],0,0],[[8.687912841852904e-95,5.412515287604772e-64],0,0],[[7.938025318271498e-112,7.539778260587032e+298],1,0],[[4.0890448857589815e-140,6.188431370265012e+93],0,0],[[1.808792063616234e-42,1.2249262287356375e+78],1,0],[[2.813778253825615e-191,3.478381051263039e+83],0,1.0],[[4.959269200917455e+89,2.713904493922986e+74],0,0],[[1.6527464762421886e-272,9.284612428163018e+257],0,0],[[2.694216768013651e-08,2.481730668881008e+205],0,5.459431618637297],[[1.105287263764627e+102,5.503874697732584e+83],0,0],[[3.616766753957493e-134,1.405468459858575e-82],0,0],[[3.4960229754986024e-44,4.978416266226015e-252],0,0],[[0.34727693217194866,5.903688889215572e+29],0,0],[[1.179890420337443e-05,1.2231257626976233e+37],0,3.3219280948873626],[[3.985430525999154e-166,3.256025304820758e-99],0,0],[[2.9695246403166212e+172,1.0507438437361721e+109],0,0],[[7.823934036267622e-77,4.7561975058596834e-110],0,1.0],[[1.1032765895259676e-126,5.131532610213896e-61],0,0],[[2.572749544642796e-298,5.3648379001218185e+144],0,0],[[2.3744727510983187e-21,2.603715830745381e+94],0,1.0],[[4.041802722110561e+273,1.9237484678401125e+296],0,0],[[2.2344486550694127e+303,7.274885059224707e+101],0,0],[[2.3862496869231733e+76,4.3947035780108717e+80],0,0],[[5.7761035984398696e+196,4.71159629772397e+71],0,0],[[6.285466073933269e-22,3.4674975748042185e-38],1,0],[[7.733012551117168e-122,1.1382437559720419e-95],0,1.0],[[7.904830930452407e+266,3.6582181035579515e+271],0,0],[[2.305585729830853e-134,5.145630715071899e+201],0,0],[[8.206730771606587e+43,12242.925111988056],0,0],[[2.693652367216071e-233,2.6617051987770008e+262],1,0],[[3.3852972616768538e-282,1.6281541302987446e-101],0,1.0],[[4.023984950841538e-207,1.672209984146438e-177],0,1.0],[[5.997642554579093e+226,8267761121118583.0],0,0],[[3.025865987124205e+48,1.1774375942605503e+37],0,0],[[1.7578451228930594e-74,2.489149382420679e+27],0,1.0],[[3.938884622122182e-132,1.011396351900011e-125],0,1.0],[[9.807783778428908e+281,8.750108477874464e+259],0,0],[[1.0213927801883013e-280,2.4118761560252843e-59],0,1.0],[[1.195916640070373e-91,1.1745784325466232e+243],0,0],[[7.335711770377127e-38,1.214621771874996e+281],0,0],[[7.26354692283978e-298,6.697902311356943e+127],0,0],[[1.2351743153928947e-17,1.1081913151635317e-281],0,4.954196310386876],[[8.845830180604385e+55,4.68925600491289e+144],0,0],[[1.4639565733772952e-243,4.1910390611535265e+279],0,0],[[1.6983735818136165e-150,4.057563235251733e-168],0,0],[[1.5987895001152558e-250,1.0362772075683598e+99],0,1.0],[[2.574015514786201e-195,4.120748433400853e+266],0,0],[[2.828506773801223e-34,1.3980028593340099e-80],0,0],[[7.10451338618339e-112,2.752384728131671e-298],0,0],[[5.3848532123061334e+141,4.101841091919989e+82],0,0],[[1.8880422706568598e-131,6.087242169493258e-74],1,0],[[1.6828341140646555e-168,2.8288040637518216e+97],1,0],[[2.4020959302167836e+173,4.276010429020236e+247],0,0],[[1.679279614673279e-17,7.802007187654651e-08],0,1.0],[[6.190907314532847e-276,1.745791372849607e+234],1,0],[[5.911713422365171e-224,1.0773053002356648e-277],0,0],[[6.326943736711642e+259,2.02315867891966e+129],0,0],[[7.946583410099056e-261,2.144814527894872e+96],0,0],[[1.0066412328328968e-127,6.619416378892868e-163],0,0],[[1.1159565897451056e-40,9.147384059902005e+52],0,1.0],[[1.1165161433358629e+279,6.875662873883236e+254],0,0],[[7.053265896579982e-111,2.7551492956412816e-291],0,1.0],[[1.792618476145051e+142,3.258027489034141e+228],0,0],[[2.3780466739014797e+260,7.6303811992955545e+112],0,0],[[2.5226551585558244e+149,4.479310754223626e+77],0,0],[[6.3759232335206e-291,3.5785496756947083e-76],0,0],[[3.8797234898178104e-266,6.295638798327878e-124],0,1.0],[[6.621128712488456e-94,3.152253828409111e+30],0,0],[[3.5260516775312726e-162,4.379941188803635e-139],0,0],[[1.6672047786154368e+54,6.224498176564759e+252],0,0],[[6.79091067430158e+35,7.230059261043331e+195],0,0],[[4.3750470153682443e+216,8.334409599853035e+119],0,0],[[5.317028386962457e+95,1.5305424059226277e+248],0,0],[[6.409528319039091e+96,2.932037839848625e+137],0,0],[[8.883362223957793e+93,1.0708005705289017e+244],0,0],[[5.053806292662203e-155,2.523406045226158e-210],0,0],[[3.6380611743774316e+28,4.3451652399410245e+66],0,0],[[5.5111229904756633e-36,1.6975346890789871e+105],0,0],[[9.95962237767467e+23,1.044537127877944e+107],0,0],[[1.2032276449725793e-85,1.3054961346651174e-44],0,1.0],[[2.3075398048335097e-269,3.594097673489053e+137],1,0],[[3.130685264260855e-76,9.058189937007456e-86],0,0],[[4.53732938437198e+150,1.4669818938577088e+222],0,0],[[4.302212151190092e+240,2.4335687807904273e+271],0,0],[[6.550539660350184e-98,2.959467597264242e-230],0,0],[[2.052107344086851e-70,7.509188631026346e+286],0,1.0],[[2.2721511366771778e-250,4.0477581754304153e-125],0,1.0],[[4.931733655566518e-258,1.554975231016035e+153],1,0],[[3.4461749360980795e-185,7.6218106112626015e+295],0,0],[[1.3987141013277275e+91,6.132373723862702e+252],0,0],[[2.4801215181567776e-295,5.2115166535835604e-169],0,0],[[5.907165300326855e+32,1.9267899651560147e+275],0,0],[[7.475270857526654e-304,1.0862105938569748e+148],0,0],[[4.380578158292964e+195,3.0321252530234052e+38],0,0],[[2.4655809623086505e-116,1.1536689796869952e-11],0,0],[[8.444294654343975e-240,3.513520042407809e+153],0,1.0],[[3.28610894527258e-300,3.973558968153068e+125],0,0],[[2.5394112430978073e-295,1.4298675637930828e+180],0,1.0],[[8.332917955185835e+296,6.741628989608122e+71],0,0],[[1.6232174805713086e+70,3.765990859086882e+52],0,0],[[9.373092063300388e+294,2.8072978291071996e+105],0,0],[[8.752592959491946e-33,2.9311591750368227e+22],0,0],[[3.0241599246809088e+252,3.184319790336394e+219],0,0],[[1.0760470830369276e-175,3.1675280578479312e-77],0,0],[[9.685450907847438e-63,1.537477220142015e-154],0,0],[[1.4316271455151301e-258,2.996770630299676e+274],0,0],[[1.6611161145230723e-191,714914460440.7544],0,0],[[9.206946233985896e+265,5.909438823195212e+35],0,0],[[4.3407560983206045e+110,1.0066329381452874e+195],0,0],[[2.300114102133609e+63,3.3520036437628364e+162],0,0],[[3.7952930805105457e-199,7.532023979359606e+99],0,1.5849625007211563],[[7.921938015189254e-17,1.6708793826459247e-57],0,3.9068905956085187],[[1023.2212474515807,2.9921045438694274e+227],0,0],[[0.0009065963481940791,3.905734270420228e+62],0,4.08746284125034],[[1.891116192597785e-215,6.110124011150757e+46],0,0],[[8.602881405868794e-32,4.340706048852671e-131],0,0],[[2.098983450835455e-256,7.299124485355855e+137],0,1.0],[[1.2757681535951056e+63,3.8712901591408457e+228],0,0],[[7.968357209160169e+93,6.567762824642581e+50],0,0],[[4.548601565249598e+188,2.083390534713302e+140],0,0],[[4.161272910469861e-301,4.4146411652973813e+21],0,0],[[6.4821321459802055e+193,1.7939351909740315e+68],0,0],[[2.7868826984034328e-297,6.274746106885988e-177],0,1.0],[[7.586534919343994e-75,1.6802148352573582e-128],0,1.0],[[9.491422824807354e-253,4.0739010895320517e+273],0,1.0],[[2.2415352671784828e-150,1.625167989850363e+119],0,1.0],[[7.01138751262021e-280,1.4841539461233504e+69],0,1.0],[[2.824709004194289e-77,3.4428899655780295e-69],0,0],[[1.1294315636198499e-278,5.86009335903585e-102],0,1.0],[[7.990408500607478e+225,7.43139844967742e+271],0,0],[[2.6148734958275445e-59,1.4522191998681414e+95],0,0],[[2.1746518322952078e-54,2.8875549970579304e+175],0,0],[[3.1487113596301893e-35,2.0573785747587795e-193],0,1.0],[[2.790368131936616e-145,6.479697484604152e-174],0,0],[[1.220285592766294e+307,3.861133926570598e+263],0,0],[[1.2654603057808926e-132,5.480340484157898e-137],0,1.0],[[3.9582185084442164e+58,1.0006915947365432e+290],0,0],[[2.2385341061737422e-125,1.1296035831317978e+178],0,0],[[1.9956859819988883e+208,1.3053442887826894e+292],0,0],[[1.3725216771543658e-17,7.122506379956216e-199],0,4.08746284125034],[[5.070205966511977e-66,2.1591257954674133e-112],0,0],[[1.9637167511580492e-290,4.1122590034758076e+161],0,0],[[6.289641429573477e-53,4.44964744501718e-303],0,1.0],[[4.921669299348463e+48,9.174188702008102e+144],0,0],[[1.0631632090197916e+200,5.699753770483561e+65],0,0],[[3.7304700864524026e-88,7.425542676714504e-84],0,0],[[4.592687610132483e+74,5.15900678827599e+24],0,0],[[3.2643753621921254e-59,9.955169418668015e-289],0,0],[[1.8079468232084944e-292,4.570078655862018e+54],0,0],[[11359488250023.906,1.6061320544606304e+202],0,0],[[1.3892861350443015e-223,4.641071766140853e-231],0,0],[[7.360110913281388e-12,2.8431063873980092e+116],0,0],[[4.0565095880949425e+280,6.675799068433044e+76],0,0],[[9.20664563196908e+294,1.3131400831400088e+86],0,0],[[1.0649783843865697e-107,2.193063794905827e+36],0,0],[[1.1535731528175885e-293,16122199543.85404],1,1.0],[[0.23158759667032142,2.174373890634123e+206],0,6.339850002884625],[[2.8576099148948687e+47,4.535106259884878e+127],0,0],[[4.76442930878223e-20,1.662443875692076e+190],0,1.0],[[1.7386181741597865e-117,2.2869715061523446e+282],0,1.0],[[1.8576198723851754e+267,1.4640464205690061e+181],0,0],[[1.0730971371295596e-35,1.3731090395442879e-244],0,0],[[5.8750151697224545e-09,3.2058797502881587e-47],0,3.5849625007211565],[[6.606104192306025e-76,2.1980904706831728e-104],0,0],[[1.1320100213914422e-197,9.218931403807496e-238],1,0],[[1.371076068469597e-276,3.7292018910669483e+61],0,1.0],[[7.468254766320453e-225,5.794033588679369e+140],0,0],[[3.2896013204457148e-279,1.1190715118628351e-13],0,1.0],[[1.855739410010682e-286,1.2449977298699466e-295],1,0],[[8.63596361370883e-168,3.1003420231048053e-198],0,1.0],[[1.4390244358772018e+249,2.9639589969742274e+281],0,0],[[2.0583492621633517e-132,1.73356572916747e+144],0,0],[[1.6662800714135864e-218,3.017825861340067e+260],0,0],[[1.7909913857676524e-234,4.184907550158769e-217],1,0],[[5.556148241691299e-119,1.5213816359492715e-307],0,0],[[3.486470059469502e+53,1.4785130640238136e+99],0,0],[[4.750171216619508e-73,1.0938841522691449e-182],0,1.0],[[9.94673708940353e+255,6.918320731214305e+101],0,0],[[5.706158108157338e+305,1.2638234743036793e+156],0,0],[[2.427769796556236e-78,7.21762410022307e+205],0,1.0],[[2.727021877346581e-178,1.860064553198903e-67],0,0],[[8.657759546694974e-157,2.0568784750151953e+96],0,0],[[1.0675856537644375e+279,5.0108195646214185e+182],0,0],[[2.412016495848343e-259,2.1622905926715047e-231],0,0],[[1.4157269095091182e+175,1.752320881957983e+240],0,0],[[7.474117465579979e+250,1.998141361266681e+100],0,0],[[1.542984322219514e-13,3.0489294036502483e-215],0,4.954196310386876],[[1.095382951219098e-121,4.4403690793251364e-66],0,1.0],[[3.0292511751059167e-285,4.774911884404591e+104],0,1.0],[[7366.597199336127,3.437966658215048e+175],0,0],[[1.013327533564468e-142,1.0958904515570749e+229],0,0],[[5.365396337730866e+62,5.564528795268944e+304],0,0],[[2.2999903268614278e-290,1.0741122062961354e-261],1,1.0],[[5.859557539322906e-140,12468368041124.15],0,1.0],[[3.29750078510446e+71,1.1536796494388956e+294],0,0],[[1.0050966216294641e+208,3094188499901330.5],0,0],[[2.486240422123665e+301,6.411662743035886e+150],0,0],[[1.1448971434422485e-274,1.3291916155898896e-54],1,0],[[5.99451935698111e-22,2.459533652847606e+166],0,0],[[5.471344172015073e-66,2.5497871706438334e+172],0,0],[[1.929136835934461e+126,1.4511860769870938e+51],0,0],[[1.6848563310412775e-81,1.8787633523770844e+304],0,0],[[2.9246728990313427e+289,4.038893686579631e+19],0,0],[[7.229157843683878e+19,7.0767085636431225e+53],0,0],[[1.5968409688876136e+240,1.6442404219839566e+41],0,0],[[1.2356592442417317e-130,2.7522555769102684e-277],0,1.0],[[2.0679460963453592e-53,3.5340357590538254e+140],0,1.0],[[1.0662100247031813e-43,2.521296463327911e+268],0,1.0],[[1.2229817874252346e-71,8.506337374180222e-99],0,0],[[2.3910560608115626e-11,2.932647945759088e-270],0,5.129283016944966],[[9.315042055884043e+48,4.0024068424625754e+43],0,0],[[1.43710899076724e+182,2.2997526865909637e+146],0,0]],"best-alt-per-point":[[[5.091954821941639e-192,6.815392098658887e+143],1,1.0],[[1.9872779421557533e+180,1.8165707546862427e+45],0,0],[[7.416044817432175e-280,4.187534830574239e+90],0,0],[[8.952174144166139e-302,1.0956116997098222e-31],0,0],[[2.7602034085604025e+247,3.933007183466984e+176],0,0],[[4.691318136614946e-91,2.2211280072565116e-303],1,0],[[9.07067712653544e+121,1.1966070572230463e+134],0,0],[[2.534573079598786e+169,3.2634856808337097e+195],0,0],[[6.317640848359807e-38,7.108640458245273e-156],1,0],[[1.37963739668883e-251,1.9832537005473266e-262],0,0],[[2.2237477837114185e-204,3.5971048785615273e+27],0,0],[[2.0235103563137384e-245,3.186488674327569e-306],0,1.0],[[4.535662949534244e+218,1.0124765649019447e+298],0,0],[[3.548084498024942e-190,1.2458518796694574e+90],0,1.0],[[1.0707760413948923e-209,1.8155292668497655e+36],1,0],[[8.082647412227132e-211,1.4588918120519666e-114],0,1.0],[[5.13876683088187e-118,9.467488944393916e+142],0,0],[[2.2187340876406246e+300,4.0696348581298066e+30],0,0],[[4.737175196542416e-301,9.453454014910064e+271],0,0],[[1.090098977941039e-114,5.7243448441390635e+162],0,0],[[2.571403883587662e-39,2.725225610867578e+225],0,0],[[5.081095649164445e+286,2.6437596200790387e+281],0,0],[[6.85981085886286e-168,1.9805731700427848e-169],0,0],[[9.636536782052696e-111,2.985561979664205e+171],0,0],[[1.0838714812801137e-216,1.1791770071753556e+107],1,1.0],[[1.072386271012045e-235,9.15478951965041e+260],0,0],[[4.954601632348903e-272,5.651261930475929e+123],0,0],[[5.598692384845278e-151,2.0020470402494707e-128],0,1.0],[[3.828518244176968e-308,9.957124504840989e+307],0,51.208680506187314],[[7.811244882301027e-64,2.3660873791160076e+189],0,0],[[1.1253736853318525e-46,4.582462397892038e-300],1,0],[[2271813.2914643916,1.711246486837026e+16],0,0],[[2.6512646278212223e-277,2.991195561163922e+252],0,0],[[2.8722519575799174e-220,8.864398632472997e+128],0,0],[[6.898353156002884e+56,5.049169591478046e+301],0,0],[[5.795257109406676e+26,7.254471041027067e+34],0,0],[[1.9680527238636918e-165,6.602387235477923e-263],1,0],[[4.390126892195692e-258,5.153839259075024e-217],0,1.0],[[3.7270065251219893e-51,4.1091807334876805e+121],0,0],[[1.2718549924538793e-67,1.4997147168186959e-133],1,0],[[7.779411959735569e-290,2.9896016385939845e-66],1,0],[[2.8931224974199074e-84,1.9240432527476484e-289],0,0],[[1.6509703901493846e-82,1.0044867221158944e+300],0,0],[[7.040383581327078e-101,5.96146379570227e+197],0,0],[[1.607215854807525e-42,2.5297373356963796e-300],0,0],[[8.687912841852904e-95,5.412515287604772e-64],0,0],[[7.938025318271498e-112,7.539778260587032e+298],1,0],[[4.0890448857589815e-140,6.188431370265012e+93],0,0],[[1.808792063616234e-42,1.2249262287356375e+78],1,0],[[2.813778253825615e-191,3.478381051263039e+83],0,1.0],[[4.959269200917455e+89,2.713904493922986e+74],0,0],[[1.6527464762421886e-272,9.284612428163018e+257],0,0],[[2.694216768013651e-08,2.481730668881008e+205],0,5.459431618637297],[[1.105287263764627e+102,5.503874697732584e+83],0,0],[[3.616766753957493e-134,1.405468459858575e-82],0,0],[[3.4960229754986024e-44,4.978416266226015e-252],0,0],[[0.34727693217194866,5.903688889215572e+29],0,0],[[1.179890420337443e-05,1.2231257626976233e+37],0,3.3219280948873626],[[3.985430525999154e-166,3.256025304820758e-99],0,0],[[2.9695246403166212e+172,1.0507438437361721e+109],0,0],[[7.823934036267622e-77,4.7561975058596834e-110],0,1.0],[[1.1032765895259676e-126,5.131532610213896e-61],0,0],[[2.572749544642796e-298,5.3648379001218185e+144],0,0],[[2.3744727510983187e-21,2.603715830745381e+94],0,1.0],[[4.041802722110561e+273,1.9237484678401125e+296],0,0],[[2.2344486550694127e+303,7.274885059224707e+101],0,0],[[2.3862496869231733e+76,4.3947035780108717e+80],0,0],[[5.7761035984398696e+196,4.71159629772397e+71],0,0],[[6.285466073933269e-22,3.4674975748042185e-38],1,0],[[7.733012551117168e-122,1.1382437559720419e-95],0,1.0],[[7.904830930452407e+266,3.6582181035579515e+271],0,0],[[2.305585729830853e-134,5.145630715071899e+201],0,0],[[8.206730771606587e+43,12242.925111988056],0,0],[[2.693652367216071e-233,2.6617051987770008e+262],1,0],[[3.3852972616768538e-282,1.6281541302987446e-101],0,1.0],[[4.023984950841538e-207,1.672209984146438e-177],0,1.0],[[5.997642554579093e+226,8267761121118583.0],0,0],[[3.025865987124205e+48,1.1774375942605503e+37],0,0],[[1.7578451228930594e-74,2.489149382420679e+27],0,1.0],[[3.938884622122182e-132,1.011396351900011e-125],0,1.0],[[9.807783778428908e+281,8.750108477874464e+259],0,0],[[1.0213927801883013e-280,2.4118761560252843e-59],0,1.0],[[1.195916640070373e-91,1.1745784325466232e+243],0,0],[[7.335711770377127e-38,1.214621771874996e+281],0,0],[[7.26354692283978e-298,6.697902311356943e+127],0,0],[[1.2351743153928947e-17,1.1081913151635317e-281],0,4.954196310386876],[[8.845830180604385e+55,4.68925600491289e+144],0,0],[[1.4639565733772952e-243,4.1910390611535265e+279],0,0],[[1.6983735818136165e-150,4.057563235251733e-168],0,0],[[1.5987895001152558e-250,1.0362772075683598e+99],0,1.0],[[2.574015514786201e-195,4.120748433400853e+266],0,0],[[2.828506773801223e-34,1.3980028593340099e-80],0,0],[[7.10451338618339e-112,2.752384728131671e-298],0,0],[[5.3848532123061334e+141,4.101841091919989e+82],0,0],[[1.8880422706568598e-131,6.087242169493258e-74],1,0],[[1.6828341140646555e-168,2.8288040637518216e+97],1,0],[[2.4020959302167836e+173,4.276010429020236e+247],0,0],[[1.679279614673279e-17,7.802007187654651e-08],0,1.0],[[6.190907314532847e-276,1.745791372849607e+234],1,0],[[5.911713422365171e-224,1.0773053002356648e-277],0,0],[[6.326943736711642e+259,2.02315867891966e+129],0,0],[[7.946583410099056e-261,2.144814527894872e+96],0,0],[[1.0066412328328968e-127,6.619416378892868e-163],0,0],[[1.1159565897451056e-40,9.147384059902005e+52],0,1.0],[[1.1165161433358629e+279,6.875662873883236e+254],0,0],[[7.053265896579982e-111,2.7551492956412816e-291],0,1.0],[[1.792618476145051e+142,3.258027489034141e+228],0,0],[[2.3780466739014797e+260,7.6303811992955545e+112],0,0],[[2.5226551585558244e+149,4.479310754223626e+77],0,0],[[6.3759232335206e-291,3.5785496756947083e-76],0,0],[[3.8797234898178104e-266,6.295638798327878e-124],0,1.0],[[6.621128712488456e-94,3.152253828409111e+30],0,0],[[3.5260516775312726e-162,4.379941188803635e-139],0,0],[[1.6672047786154368e+54,6.224498176564759e+252],0,0],[[6.79091067430158e+35,7.230059261043331e+195],0,0],[[4.3750470153682443e+216,8.334409599853035e+119],0,0],[[5.317028386962457e+95,1.5305424059226277e+248],0,0],[[6.409528319039091e+96,2.932037839848625e+137],0,0],[[8.883362223957793e+93,1.0708005705289017e+244],0,0],[[5.053806292662203e-155,2.523406045226158e-210],0,0],[[3.6380611743774316e+28,4.3451652399410245e+66],0,0],[[5.5111229904756633e-36,1.6975346890789871e+105],0,0],[[9.95962237767467e+23,1.044537127877944e+107],0,0],[[1.2032276449725793e-85,1.3054961346651174e-44],0,1.0],[[2.3075398048335097e-269,3.594097673489053e+137],1,0],[[3.130685264260855e-76,9.058189937007456e-86],0,0],[[4.53732938437198e+150,1.4669818938577088e+222],0,0],[[4.302212151190092e+240,2.4335687807904273e+271],0,0],[[6.550539660350184e-98,2.959467597264242e-230],0,0],[[2.052107344086851e-70,7.509188631026346e+286],0,1.0],[[2.2721511366771778e-250,4.0477581754304153e-125],0,1.0],[[4.931733655566518e-258,1.554975231016035e+153],1,0],[[3.4461749360980795e-185,7.6218106112626015e+295],0,0],[[1.3987141013277275e+91,6.132373723862702e+252],0,0],[[2.4801215181567776e-295,5.2115166535835604e-169],0,0],[[5.907165300326855e+32,1.9267899651560147e+275],0,0],[[7.475270857526654e-304,1.0862105938569748e+148],0,0],[[4.380578158292964e+195,3.0321252530234052e+38],0,0],[[2.4655809623086505e-116,1.1536689796869952e-11],0,0],[[8.444294654343975e-240,3.513520042407809e+153],0,1.0],[[3.28610894527258e-300,3.973558968153068e+125],0,0],[[2.5394112430978073e-295,1.4298675637930828e+180],0,1.0],[[8.332917955185835e+296,6.741628989608122e+71],0,0],[[1.6232174805713086e+70,3.765990859086882e+52],0,0],[[9.373092063300388e+294,2.8072978291071996e+105],0,0],[[8.752592959491946e-33,2.9311591750368227e+22],0,0],[[3.0241599246809088e+252,3.184319790336394e+219],0,0],[[1.0760470830369276e-175,3.1675280578479312e-77],0,0],[[9.685450907847438e-63,1.537477220142015e-154],0,0],[[1.4316271455151301e-258,2.996770630299676e+274],0,0],[[1.6611161145230723e-191,714914460440.7544],0,0],[[9.206946233985896e+265,5.909438823195212e+35],0,0],[[4.3407560983206045e+110,1.0066329381452874e+195],0,0],[[2.300114102133609e+63,3.3520036437628364e+162],0,0],[[3.7952930805105457e-199,7.532023979359606e+99],0,1.5849625007211563],[[7.921938015189254e-17,1.6708793826459247e-57],0,3.9068905956085187],[[1023.2212474515807,2.9921045438694274e+227],0,0],[[0.0009065963481940791,3.905734270420228e+62],0,4.08746284125034],[[1.891116192597785e-215,6.110124011150757e+46],0,0],[[8.602881405868794e-32,4.340706048852671e-131],0,0],[[2.098983450835455e-256,7.299124485355855e+137],0,1.0],[[1.2757681535951056e+63,3.8712901591408457e+228],0,0],[[7.968357209160169e+93,6.567762824642581e+50],0,0],[[4.548601565249598e+188,2.083390534713302e+140],0,0],[[4.161272910469861e-301,4.4146411652973813e+21],0,0],[[6.4821321459802055e+193,1.7939351909740315e+68],0,0],[[2.7868826984034328e-297,6.274746106885988e-177],0,1.0],[[7.586534919343994e-75,1.6802148352573582e-128],0,1.0],[[9.491422824807354e-253,4.0739010895320517e+273],0,1.0],[[2.2415352671784828e-150,1.625167989850363e+119],0,1.0],[[7.01138751262021e-280,1.4841539461233504e+69],0,1.0],[[2.824709004194289e-77,3.4428899655780295e-69],0,0],[[1.1294315636198499e-278,5.86009335903585e-102],0,1.0],[[7.990408500607478e+225,7.43139844967742e+271],0,0],[[2.6148734958275445e-59,1.4522191998681414e+95],0,0],[[2.1746518322952078e-54,2.8875549970579304e+175],0,0],[[3.1487113596301893e-35,2.0573785747587795e-193],0,1.0],[[2.790368131936616e-145,6.479697484604152e-174],0,0],[[1.220285592766294e+307,3.861133926570598e+263],0,0],[[1.2654603057808926e-132,5.480340484157898e-137],0,1.0],[[3.9582185084442164e+58,1.0006915947365432e+290],0,0],[[2.2385341061737422e-125,1.1296035831317978e+178],0,0],[[1.9956859819988883e+208,1.3053442887826894e+292],0,0],[[1.3725216771543658e-17,7.122506379956216e-199],0,4.08746284125034],[[5.070205966511977e-66,2.1591257954674133e-112],0,0],[[1.9637167511580492e-290,4.1122590034758076e+161],0,0],[[6.289641429573477e-53,4.44964744501718e-303],0,1.0],[[4.921669299348463e+48,9.174188702008102e+144],0,0],[[1.0631632090197916e+200,5.699753770483561e+65],0,0],[[3.7304700864524026e-88,7.425542676714504e-84],0,0],[[4.592687610132483e+74,5.15900678827599e+24],0,0],[[3.2643753621921254e-59,9.955169418668015e-289],0,0],[[1.8079468232084944e-292,4.570078655862018e+54],0,0],[[11359488250023.906,1.6061320544606304e+202],0,0],[[1.3892861350443015e-223,4.641071766140853e-231],0,0],[[7.360110913281388e-12,2.8431063873980092e+116],0,0],[[4.0565095880949425e+280,6.675799068433044e+76],0,0],[[9.20664563196908e+294,1.3131400831400088e+86],0,0],[[1.0649783843865697e-107,2.193063794905827e+36],0,0],[[1.1535731528175885e-293,16122199543.85404],1,1.0],[[0.23158759667032142,2.174373890634123e+206],0,6.339850002884625],[[2.8576099148948687e+47,4.535106259884878e+127],0,0],[[4.76442930878223e-20,1.662443875692076e+190],0,1.0],[[1.7386181741597865e-117,2.2869715061523446e+282],0,1.0],[[1.8576198723851754e+267,1.4640464205690061e+181],0,0],[[1.0730971371295596e-35,1.3731090395442879e-244],0,0],[[5.8750151697224545e-09,3.2058797502881587e-47],0,3.5849625007211565],[[6.606104192306025e-76,2.1980904706831728e-104],0,0],[[1.1320100213914422e-197,9.218931403807496e-238],1,0],[[1.371076068469597e-276,3.7292018910669483e+61],0,1.0],[[7.468254766320453e-225,5.794033588679369e+140],0,0],[[3.2896013204457148e-279,1.1190715118628351e-13],0,1.0],[[1.855739410010682e-286,1.2449977298699466e-295],1,0],[[8.63596361370883e-168,3.1003420231048053e-198],0,1.0],[[1.4390244358772018e+249,2.9639589969742274e+281],0,0],[[2.0583492621633517e-132,1.73356572916747e+144],0,0],[[1.6662800714135864e-218,3.017825861340067e+260],0,0],[[1.7909913857676524e-234,4.184907550158769e-217],1,0],[[5.556148241691299e-119,1.5213816359492715e-307],0,0],[[3.486470059469502e+53,1.4785130640238136e+99],0,0],[[4.750171216619508e-73,1.0938841522691449e-182],0,1.0],[[9.94673708940353e+255,6.918320731214305e+101],0,0],[[5.706158108157338e+305,1.2638234743036793e+156],0,0],[[2.427769796556236e-78,7.21762410022307e+205],0,1.0],[[2.727021877346581e-178,1.860064553198903e-67],0,0],[[8.657759546694974e-157,2.0568784750151953e+96],0,0],[[1.0675856537644375e+279,5.0108195646214185e+182],0,0],[[2.412016495848343e-259,2.1622905926715047e-231],0,0],[[1.4157269095091182e+175,1.752320881957983e+240],0,0],[[7.474117465579979e+250,1.998141361266681e+100],0,0],[[1.542984322219514e-13,3.0489294036502483e-215],0,4.954196310386876],[[1.095382951219098e-121,4.4403690793251364e-66],0,1.0],[[3.0292511751059167e-285,4.774911884404591e+104],0,1.0],[[7366.597199336127,3.437966658215048e+175],0,0],[[1.013327533564468e-142,1.0958904515570749e+229],0,0],[[5.365396337730866e+62,5.564528795268944e+304],0,0],[[2.2999903268614278e-290,1.0741122062961354e-261],1,1.0],[[5.859557539322906e-140,12468368041124.15],0,1.0],[[3.29750078510446e+71,1.1536796494388956e+294],0,0],[[1.0050966216294641e+208,3094188499901330.5],0,0],[[2.486240422123665e+301,6.411662743035886e+150],0,0],[[1.1448971434422485e-274,1.3291916155898896e-54],1,0],[[5.99451935698111e-22,2.459533652847606e+166],0,0],[[5.471344172015073e-66,2.5497871706438334e+172],0,0],[[1.929136835934461e+126,1.4511860769870938e+51],0,0],[[1.6848563310412775e-81,1.8787633523770844e+304],0,0],[[2.9246728990313427e+289,4.038893686579631e+19],0,0],[[7.229157843683878e+19,7.0767085636431225e+53],0,0],[[1.5968409688876136e+240,1.6442404219839566e+41],0,0],[[1.2356592442417317e-130,2.7522555769102684e-277],0,1.0],[[2.0679460963453592e-53,3.5340357590538254e+140],0,1.0],[[1.0662100247031813e-43,2.521296463327911e+268],0,1.0],[[1.2229817874252346e-71,8.506337374180222e-99],0,0],[[2.3910560608115626e-11,2.932647945759088e-270],0,5.129283016944966],[[9.315042055884043e+48,4.0024068424625754e+43],0,0],[[1.43710899076724e+182,2.2997526865909637e+146],0,0]],"fresh-alts":["#<alt-event (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>","#<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))>"]}* * * * [misc]pick:  Picked  #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 3 ] rewriting at (2 1)
* * * * [misc]progress:  [ 2 / 3 ] rewriting at (2 1 1)
* * * * [misc]progress:  [ 3 / 3 ] rewriting at (2)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 3 ] generating series at (2 1)
* [misc]approximate:  Taking taylor expansion of (pow (* 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:  [ 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)
* [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:  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)))
* * [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:  [ 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)))
* * [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:  [ 3 / 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:  [ 4 / 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:  [ 5 / 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:  [ 6 / 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:  [ 7 / 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:  [ 8 / 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:  [ 9 / 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:  [ 10 / 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:  [ 11 / 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:  [ 12 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* n (* PI 2)) (/ (- 1 k) 2)) 1) (sqrt k)))>
* * * * [misc]progress:  [ 13 / 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:  [ 14 / 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:  [ 15 / 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:  [ 16 / 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:  [ 17 / 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:  [ 18 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* 1 (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)))>
* * * * [misc]progress:  [ 19 / 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:  [ 20 / 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:  [ 21 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (pow (* n (* PI 2)) 1) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 22 / 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:  [ 23 / 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:  [ 24 / 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:  [ 25 / 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:  [ 26 / 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:  [ 27 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* 1 (* n (* PI 2))) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 28 / 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:  [ 29 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))>
* * * * [misc]progress:  [ 30 / 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:  [ 31 / 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:  [ 32 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (pow (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) 1))>
* * * * [misc]progress:  [ 33 / 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:  [ 34 / 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:  [ 35 / 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:  [ 36 / 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:  [ 37 / 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:  [ 38 / 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:  [ 39 / 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:  [ 40 / 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:  [ 41 / 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:  [ 42 / 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:  [ 43 / 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:  [ 44 / 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:  [ 45 / 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:  [ 46 / 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:  [ 47 / 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:  [ 48 / 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:  [ 49 / 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:  [ 50 / 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:  [ 51 / 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:  [ 52 / 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:  [ 53 / 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:  [ 54 / 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:  [ 55 / 74 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))>
* * * * [misc]progress:  [ 56 / 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:  [ 57 / 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:  [ 58 / 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:  [ 59 / 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:  [ 60 / 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:  [ 61 / 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:  [ 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)))) (/ (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:  [ 63 / 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:  [ 64 / 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:  [ 65 / 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:  [ 66 / 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:  [ 67 / 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:  [ 68 / 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:  [ 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) (- (+ (* +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:  [ 73 / 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:  [ 74 / 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:  adding candidates to table
* * [misc]progress:  iteration 2 / 4
* * * [misc]progress:  picking best candidate
"ALT DATA: "{"picked-error":0.4971798245227657,"picked":"(λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))","all-alts":["#<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>","#<alt-delta (λ (k n) (/ (+ (* (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (* (* k k) 1/8)) (+ (* (log n) (log n)) (* (log (* PI 2)) (log (* PI 2))))) (- (fma (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4)) (* (log (* PI 2)) (* (* k k) (log n))) (* (pow (* PI 2) 1/2) (pow n 1/2))) (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/2)) (fma k (log (* PI 2)) (* (log n) k))))) (sqrt k)))>","#<alt-delta (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>","#<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>","#<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>","#<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2)))))>","#<alt-event (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>","#<alt-delta (λ (k n) (/ (* (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k)))>","#<alt-delta (λ (k n) (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))>","#<alt-delta (λ (k n) (* (/ (* (cbrt (pow (* n (* 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) (* (* (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)))))>"],"best-fresh-alt-per-point":[[[5.091954821941639e-192,6.815392098658887e+143],0,0],[[1.9872779421557533e+180,1.8165707546862427e+45],0,0],[[7.416044817432175e-280,4.187534830574239e+90],1,0],[[8.952174144166139e-302,1.0956116997098222e-31],0,0],[[2.7602034085604025e+247,3.933007183466984e+176],0,0],[[4.691318136614946e-91,2.2211280072565116e-303],0,0],[[9.07067712653544e+121,1.1966070572230463e+134],0,0],[[2.534573079598786e+169,3.2634856808337097e+195],0,0],[[6.317640848359807e-38,7.108640458245273e-156],0,0],[[1.37963739668883e-251,1.9832537005473266e-262],0,0],[[2.2237477837114185e-204,3.5971048785615273e+27],6,0],[[2.0235103563137384e-245,3.186488674327569e-306],2,0],[[4.535662949534244e+218,1.0124765649019447e+298],0,0],[[3.548084498024942e-190,1.2458518796694574e+90],8,0],[[1.0707760413948923e-209,1.8155292668497655e+36],1,0],[[8.082647412227132e-211,1.4588918120519666e-114],8,0],[[5.13876683088187e-118,9.467488944393916e+142],5,0],[[2.2187340876406246e+300,4.0696348581298066e+30],0,0],[[4.737175196542416e-301,9.453454014910064e+271],1,0],[[1.090098977941039e-114,5.7243448441390635e+162],0,0],[[2.571403883587662e-39,2.725225610867578e+225],1,0],[[5.081095649164445e+286,2.6437596200790387e+281],0,0],[[6.85981085886286e-168,1.9805731700427848e-169],0,0],[[9.636536782052696e-111,2.985561979664205e+171],0,0],[[1.0838714812801137e-216,1.1791770071753556e+107],1,0],[[1.072386271012045e-235,9.15478951965041e+260],2,0],[[4.954601632348903e-272,5.651261930475929e+123],0,0],[[5.598692384845278e-151,2.0020470402494707e-128],7,0],[[3.828518244176968e-308,9.957124504840989e+307],2,1.0],[[7.811244882301027e-64,2.3660873791160076e+189],3,0],[[1.1253736853318525e-46,4.582462397892038e-300],0,0],[[2271813.2914643916,1.711246486837026e+16],0,0],[[2.6512646278212223e-277,2.991195561163922e+252],0,0],[[2.8722519575799174e-220,8.864398632472997e+128],0,0],[[6.898353156002884e+56,5.049169591478046e+301],0,0],[[5.795257109406676e+26,7.254471041027067e+34],0,0],[[1.9680527238636918e-165,6.602387235477923e-263],0,0],[[4.390126892195692e-258,5.153839259075024e-217],2,0],[[3.7270065251219893e-51,4.1091807334876805e+121],0,0],[[1.2718549924538793e-67,1.4997147168186959e-133],3,0],[[7.779411959735569e-290,2.9896016385939845e-66],0,0],[[2.8931224974199074e-84,1.9240432527476484e-289],6,0],[[1.6509703901493846e-82,1.0044867221158944e+300],6,0],[[7.040383581327078e-101,5.96146379570227e+197],1,0],[[1.607215854807525e-42,2.5297373356963796e-300],0,0],[[8.687912841852904e-95,5.412515287604772e-64],3,0],[[7.938025318271498e-112,7.539778260587032e+298],0,0],[[4.0890448857589815e-140,6.188431370265012e+93],0,0],[[1.808792063616234e-42,1.2249262287356375e+78],1,0],[[2.813778253825615e-191,3.478381051263039e+83],7,0],[[4.959269200917455e+89,2.713904493922986e+74],0,0],[[1.6527464762421886e-272,9.284612428163018e+257],5,0],[[2.694216768013651e-08,2.481730668881008e+205],1,0],[[1.105287263764627e+102,5.503874697732584e+83],0,0],[[3.616766753957493e-134,1.405468459858575e-82],0,0],[[3.4960229754986024e-44,4.978416266226015e-252],3,0],[[0.34727693217194866,5.903688889215572e+29],3,0],[[1.179890420337443e-05,1.2231257626976233e+37],3,0],[[3.985430525999154e-166,3.256025304820758e-99],2,0],[[2.9695246403166212e+172,1.0507438437361721e+109],0,0],[[7.823934036267622e-77,4.7561975058596834e-110],0,0],[[1.1032765895259676e-126,5.131532610213896e-61],2,0],[[2.572749544642796e-298,5.3648379001218185e+144],1,0],[[2.3744727510983187e-21,2.603715830745381e+94],7,0],[[4.041802722110561e+273,1.9237484678401125e+296],0,0],[[2.2344486550694127e+303,7.274885059224707e+101],0,0],[[2.3862496869231733e+76,4.3947035780108717e+80],0,0],[[5.7761035984398696e+196,4.71159629772397e+71],0,0],[[6.285466073933269e-22,3.4674975748042185e-38],1,0],[[7.733012551117168e-122,1.1382437559720419e-95],7,0],[[7.904830930452407e+266,3.6582181035579515e+271],0,0],[[2.305585729830853e-134,5.145630715071899e+201],0,0],[[8.206730771606587e+43,12242.925111988056],0,0],[[2.693652367216071e-233,2.6617051987770008e+262],1,0],[[3.3852972616768538e-282,1.6281541302987446e-101],9,0],[[4.023984950841538e-207,1.672209984146438e-177],0,0],[[5.997642554579093e+226,8267761121118583.0],0,0],[[3.025865987124205e+48,1.1774375942605503e+37],0,0],[[1.7578451228930594e-74,2.489149382420679e+27],7,0],[[3.938884622122182e-132,1.011396351900011e-125],2,0],[[9.807783778428908e+281,8.750108477874464e+259],0,0],[[1.0213927801883013e-280,2.4118761560252843e-59],7,0],[[1.195916640070373e-91,1.1745784325466232e+243],1,0],[[7.335711770377127e-38,1.214621771874996e+281],0,0],[[7.26354692283978e-298,6.697902311356943e+127],0,0],[[1.2351743153928947e-17,1.1081913151635317e-281],1,0],[[8.845830180604385e+55,4.68925600491289e+144],0,0],[[1.4639565733772952e-243,4.1910390611535265e+279],1,0],[[1.6983735818136165e-150,4.057563235251733e-168],0,0],[[1.5987895001152558e-250,1.0362772075683598e+99],0,0],[[2.574015514786201e-195,4.120748433400853e+266],0,0],[[2.828506773801223e-34,1.3980028593340099e-80],3,0],[[7.10451338618339e-112,2.752384728131671e-298],0,0],[[5.3848532123061334e+141,4.101841091919989e+82],0,0],[[1.8880422706568598e-131,6.087242169493258e-74],1,0],[[1.6828341140646555e-168,2.8288040637518216e+97],0,0],[[2.4020959302167836e+173,4.276010429020236e+247],0,0],[[1.679279614673279e-17,7.802007187654651e-08],0,0],[[6.190907314532847e-276,1.745791372849607e+234],3,0],[[5.911713422365171e-224,1.0773053002356648e-277],0,0],[[6.326943736711642e+259,2.02315867891966e+129],0,0],[[7.946583410099056e-261,2.144814527894872e+96],0,0],[[1.0066412328328968e-127,6.619416378892868e-163],3,0],[[1.1159565897451056e-40,9.147384059902005e+52],9,0],[[1.1165161433358629e+279,6.875662873883236e+254],0,0],[[7.053265896579982e-111,2.7551492956412816e-291],2,0],[[1.792618476145051e+142,3.258027489034141e+228],0,0],[[2.3780466739014797e+260,7.6303811992955545e+112],0,0],[[2.5226551585558244e+149,4.479310754223626e+77],0,0],[[6.3759232335206e-291,3.5785496756947083e-76],2,0],[[3.8797234898178104e-266,6.295638798327878e-124],1,0],[[6.621128712488456e-94,3.152253828409111e+30],4,0],[[3.5260516775312726e-162,4.379941188803635e-139],0,0],[[1.6672047786154368e+54,6.224498176564759e+252],0,0],[[6.79091067430158e+35,7.230059261043331e+195],0,0],[[4.3750470153682443e+216,8.334409599853035e+119],0,0],[[5.317028386962457e+95,1.5305424059226277e+248],0,0],[[6.409528319039091e+96,2.932037839848625e+137],0,0],[[8.883362223957793e+93,1.0708005705289017e+244],0,0],[[5.053806292662203e-155,2.523406045226158e-210],5,0],[[3.6380611743774316e+28,4.3451652399410245e+66],0,0],[[5.5111229904756633e-36,1.6975346890789871e+105],1,0],[[9.95962237767467e+23,1.044537127877944e+107],0,0],[[1.2032276449725793e-85,1.3054961346651174e-44],2,0],[[2.3075398048335097e-269,3.594097673489053e+137],0,0],[[3.130685264260855e-76,9.058189937007456e-86],0,0],[[4.53732938437198e+150,1.4669818938577088e+222],0,0],[[4.302212151190092e+240,2.4335687807904273e+271],0,0],[[6.550539660350184e-98,2.959467597264242e-230],0,0],[[2.052107344086851e-70,7.509188631026346e+286],5,0],[[2.2721511366771778e-250,4.0477581754304153e-125],2,0],[[4.931733655566518e-258,1.554975231016035e+153],3,0],[[3.4461749360980795e-185,7.6218106112626015e+295],0,0],[[1.3987141013277275e+91,6.132373723862702e+252],0,0],[[2.4801215181567776e-295,5.2115166535835604e-169],0,0],[[5.907165300326855e+32,1.9267899651560147e+275],0,0],[[7.475270857526654e-304,1.0862105938569748e+148],1,0],[[4.380578158292964e+195,3.0321252530234052e+38],0,0],[[2.4655809623086505e-116,1.1536689796869952e-11],6,0],[[8.444294654343975e-240,3.513520042407809e+153],5,0],[[3.28610894527258e-300,3.973558968153068e+125],2,0],[[2.5394112430978073e-295,1.4298675637930828e+180],0,0],[[8.332917955185835e+296,6.741628989608122e+71],0,0],[[1.6232174805713086e+70,3.765990859086882e+52],0,0],[[9.373092063300388e+294,2.8072978291071996e+105],0,0],[[8.752592959491946e-33,2.9311591750368227e+22],6,0],[[3.0241599246809088e+252,3.184319790336394e+219],0,0],[[1.0760470830369276e-175,3.1675280578479312e-77],0,0],[[9.685450907847438e-63,1.537477220142015e-154],3,0],[[1.4316271455151301e-258,2.996770630299676e+274],1,0],[[1.6611161145230723e-191,714914460440.7544],4,0],[[9.206946233985896e+265,5.909438823195212e+35],0,0],[[4.3407560983206045e+110,1.0066329381452874e+195],0,0],[[2.300114102133609e+63,3.3520036437628364e+162],0,0],[[3.7952930805105457e-199,7.532023979359606e+99],9,0],[[7.921938015189254e-17,1.6708793826459247e-57],1,1.5849625007211563],[[1023.2212474515807,2.9921045438694274e+227],0,0],[[0.0009065963481940791,3.905734270420228e+62],3,0],[[1.891116192597785e-215,6.110124011150757e+46],0,0],[[8.602881405868794e-32,4.340706048852671e-131],2,0],[[2.098983450835455e-256,7.299124485355855e+137],5,0],[[1.2757681535951056e+63,3.8712901591408457e+228],0,0],[[7.968357209160169e+93,6.567762824642581e+50],0,0],[[4.548601565249598e+188,2.083390534713302e+140],0,0],[[4.161272910469861e-301,4.4146411652973813e+21],3,0],[[6.4821321459802055e+193,1.7939351909740315e+68],0,0],[[2.7868826984034328e-297,6.274746106885988e-177],7,0],[[7.586534919343994e-75,1.6802148352573582e-128],0,0],[[9.491422824807354e-253,4.0739010895320517e+273],0,0],[[2.2415352671784828e-150,1.625167989850363e+119],0,0],[[7.01138751262021e-280,1.4841539461233504e+69],5,0],[[2.824709004194289e-77,3.4428899655780295e-69],6,0],[[1.1294315636198499e-278,5.86009335903585e-102],0,0],[[7.990408500607478e+225,7.43139844967742e+271],0,0],[[2.6148734958275445e-59,1.4522191998681414e+95],1,0],[[2.1746518322952078e-54,2.8875549970579304e+175],2,0],[[3.1487113596301893e-35,2.0573785747587795e-193],5,0],[[2.790368131936616e-145,6.479697484604152e-174],0,0],[[1.220285592766294e+307,3.861133926570598e+263],0,0],[[1.2654603057808926e-132,5.480340484157898e-137],0,0],[[3.9582185084442164e+58,1.0006915947365432e+290],0,0],[[2.2385341061737422e-125,1.1296035831317978e+178],1,0],[[1.9956859819988883e+208,1.3053442887826894e+292],0,0],[[1.3725216771543658e-17,7.122506379956216e-199],1,1.0],[[5.070205966511977e-66,2.1591257954674133e-112],0,0],[[1.9637167511580492e-290,4.1122590034758076e+161],3,0],[[6.289641429573477e-53,4.44964744501718e-303],10,0],[[4.921669299348463e+48,9.174188702008102e+144],0,0],[[1.0631632090197916e+200,5.699753770483561e+65],0,0],[[3.7304700864524026e-88,7.425542676714504e-84],1,0],[[4.592687610132483e+74,5.15900678827599e+24],0,0],[[3.2643753621921254e-59,9.955169418668015e-289],2,0],[[1.8079468232084944e-292,4.570078655862018e+54],3,0],[[11359488250023.906,1.6061320544606304e+202],0,0],[[1.3892861350443015e-223,4.641071766140853e-231],0,0],[[7.360110913281388e-12,2.8431063873980092e+116],6,0],[[4.0565095880949425e+280,6.675799068433044e+76],0,0],[[9.20664563196908e+294,1.3131400831400088e+86],0,0],[[1.0649783843865697e-107,2.193063794905827e+36],2,0],[[1.1535731528175885e-293,16122199543.85404],9,0],[[0.23158759667032142,2.174373890634123e+206],3,0],[[2.8576099148948687e+47,4.535106259884878e+127],0,0],[[4.76442930878223e-20,1.662443875692076e+190],2,0],[[1.7386181741597865e-117,2.2869715061523446e+282],2,0],[[1.8576198723851754e+267,1.4640464205690061e+181],0,0],[[1.0730971371295596e-35,1.3731090395442879e-244],0,0],[[5.8750151697224545e-09,3.2058797502881587e-47],1,0],[[6.606104192306025e-76,2.1980904706831728e-104],6,0],[[1.1320100213914422e-197,9.218931403807496e-238],1,0],[[1.371076068469597e-276,3.7292018910669483e+61],2,0],[[7.468254766320453e-225,5.794033588679369e+140],0,0],[[3.2896013204457148e-279,1.1190715118628351e-13],4,0],[[1.855739410010682e-286,1.2449977298699466e-295],0,0],[[8.63596361370883e-168,3.1003420231048053e-198],2,0],[[1.4390244358772018e+249,2.9639589969742274e+281],0,0],[[2.0583492621633517e-132,1.73356572916747e+144],1,0],[[1.6662800714135864e-218,3.017825861340067e+260],0,0],[[1.7909913857676524e-234,4.184907550158769e-217],0,0],[[5.556148241691299e-119,1.5213816359492715e-307],1,0],[[3.486470059469502e+53,1.4785130640238136e+99],0,0],[[4.750171216619508e-73,1.0938841522691449e-182],10,0],[[9.94673708940353e+255,6.918320731214305e+101],0,0],[[5.706158108157338e+305,1.2638234743036793e+156],0,0],[[2.427769796556236e-78,7.21762410022307e+205],2,0],[[2.727021877346581e-178,1.860064553198903e-67],0,0],[[8.657759546694974e-157,2.0568784750151953e+96],0,0],[[1.0675856537644375e+279,5.0108195646214185e+182],0,0],[[2.412016495848343e-259,2.1622905926715047e-231],0,0],[[1.4157269095091182e+175,1.752320881957983e+240],0,0],[[7.474117465579979e+250,1.998141361266681e+100],0,0],[[1.542984322219514e-13,3.0489294036502483e-215],3,0],[[1.095382951219098e-121,4.4403690793251364e-66],0,1.0],[[3.0292511751059167e-285,4.774911884404591e+104],8,0],[[7366.597199336127,3.437966658215048e+175],0,0],[[1.013327533564468e-142,1.0958904515570749e+229],0,0],[[5.365396337730866e+62,5.564528795268944e+304],0,0],[[2.2999903268614278e-290,1.0741122062961354e-261],0,0],[[5.859557539322906e-140,12468368041124.15],0,0],[[3.29750078510446e+71,1.1536796494388956e+294],0,0],[[1.0050966216294641e+208,3094188499901330.5],0,0],[[2.486240422123665e+301,6.411662743035886e+150],0,0],[[1.1448971434422485e-274,1.3291916155898896e-54],1,0],[[5.99451935698111e-22,2.459533652847606e+166],0,0],[[5.471344172015073e-66,2.5497871706438334e+172],3,0],[[1.929136835934461e+126,1.4511860769870938e+51],0,0],[[1.6848563310412775e-81,1.8787633523770844e+304],0,0],[[2.9246728990313427e+289,4.038893686579631e+19],0,0],[[7.229157843683878e+19,7.0767085636431225e+53],0,0],[[1.5968409688876136e+240,1.6442404219839566e+41],0,0],[[1.2356592442417317e-130,2.7522555769102684e-277],0,0],[[2.0679460963453592e-53,3.5340357590538254e+140],8,0],[[1.0662100247031813e-43,2.521296463327911e+268],4,0],[[1.2229817874252346e-71,8.506337374180222e-99],2,0],[[2.3910560608115626e-11,2.932647945759088e-270],1,0],[[9.315042055884043e+48,4.0024068424625754e+43],0,0],[[1.43710899076724e+182,2.2997526865909637e+146],0,0]],"best-alt-per-point":[[[5.091954821941639e-192,6.815392098658887e+143],0,0],[[1.9872779421557533e+180,1.8165707546862427e+45],0,0],[[7.416044817432175e-280,4.187534830574239e+90],1,0],[[8.952174144166139e-302,1.0956116997098222e-31],0,0],[[2.7602034085604025e+247,3.933007183466984e+176],0,0],[[4.691318136614946e-91,2.2211280072565116e-303],0,0],[[9.07067712653544e+121,1.1966070572230463e+134],0,0],[[2.534573079598786e+169,3.2634856808337097e+195],0,0],[[6.317640848359807e-38,7.108640458245273e-156],0,0],[[1.37963739668883e-251,1.9832537005473266e-262],0,0],[[2.2237477837114185e-204,3.5971048785615273e+27],6,0],[[2.0235103563137384e-245,3.186488674327569e-306],2,0],[[4.535662949534244e+218,1.0124765649019447e+298],0,0],[[3.548084498024942e-190,1.2458518796694574e+90],8,0],[[1.0707760413948923e-209,1.8155292668497655e+36],1,0],[[8.082647412227132e-211,1.4588918120519666e-114],8,0],[[5.13876683088187e-118,9.467488944393916e+142],5,0],[[2.2187340876406246e+300,4.0696348581298066e+30],0,0],[[4.737175196542416e-301,9.453454014910064e+271],1,0],[[1.090098977941039e-114,5.7243448441390635e+162],0,0],[[2.571403883587662e-39,2.725225610867578e+225],1,0],[[5.081095649164445e+286,2.6437596200790387e+281],0,0],[[6.85981085886286e-168,1.9805731700427848e-169],0,0],[[9.636536782052696e-111,2.985561979664205e+171],0,0],[[1.0838714812801137e-216,1.1791770071753556e+107],1,0],[[1.072386271012045e-235,9.15478951965041e+260],2,0],[[4.954601632348903e-272,5.651261930475929e+123],0,0],[[5.598692384845278e-151,2.0020470402494707e-128],7,0],[[3.828518244176968e-308,9.957124504840989e+307],2,1.0],[[7.811244882301027e-64,2.3660873791160076e+189],3,0],[[1.1253736853318525e-46,4.582462397892038e-300],0,0],[[2271813.2914643916,1.711246486837026e+16],0,0],[[2.6512646278212223e-277,2.991195561163922e+252],0,0],[[2.8722519575799174e-220,8.864398632472997e+128],0,0],[[6.898353156002884e+56,5.049169591478046e+301],0,0],[[5.795257109406676e+26,7.254471041027067e+34],0,0],[[1.9680527238636918e-165,6.602387235477923e-263],0,0],[[4.390126892195692e-258,5.153839259075024e-217],2,0],[[3.7270065251219893e-51,4.1091807334876805e+121],0,0],[[1.2718549924538793e-67,1.4997147168186959e-133],3,0],[[7.779411959735569e-290,2.9896016385939845e-66],0,0],[[2.8931224974199074e-84,1.9240432527476484e-289],6,0],[[1.6509703901493846e-82,1.0044867221158944e+300],6,0],[[7.040383581327078e-101,5.96146379570227e+197],1,0],[[1.607215854807525e-42,2.5297373356963796e-300],0,0],[[8.687912841852904e-95,5.412515287604772e-64],3,0],[[7.938025318271498e-112,7.539778260587032e+298],0,0],[[4.0890448857589815e-140,6.188431370265012e+93],0,0],[[1.808792063616234e-42,1.2249262287356375e+78],1,0],[[2.813778253825615e-191,3.478381051263039e+83],7,0],[[4.959269200917455e+89,2.713904493922986e+74],0,0],[[1.6527464762421886e-272,9.284612428163018e+257],5,0],[[2.694216768013651e-08,2.481730668881008e+205],1,0],[[1.105287263764627e+102,5.503874697732584e+83],0,0],[[3.616766753957493e-134,1.405468459858575e-82],0,0],[[3.4960229754986024e-44,4.978416266226015e-252],3,0],[[0.34727693217194866,5.903688889215572e+29],3,0],[[1.179890420337443e-05,1.2231257626976233e+37],3,0],[[3.985430525999154e-166,3.256025304820758e-99],2,0],[[2.9695246403166212e+172,1.0507438437361721e+109],0,0],[[7.823934036267622e-77,4.7561975058596834e-110],0,0],[[1.1032765895259676e-126,5.131532610213896e-61],2,0],[[2.572749544642796e-298,5.3648379001218185e+144],1,0],[[2.3744727510983187e-21,2.603715830745381e+94],7,0],[[4.041802722110561e+273,1.9237484678401125e+296],0,0],[[2.2344486550694127e+303,7.274885059224707e+101],0,0],[[2.3862496869231733e+76,4.3947035780108717e+80],0,0],[[5.7761035984398696e+196,4.71159629772397e+71],0,0],[[6.285466073933269e-22,3.4674975748042185e-38],1,0],[[7.733012551117168e-122,1.1382437559720419e-95],7,0],[[7.904830930452407e+266,3.6582181035579515e+271],0,0],[[2.305585729830853e-134,5.145630715071899e+201],0,0],[[8.206730771606587e+43,12242.925111988056],0,0],[[2.693652367216071e-233,2.6617051987770008e+262],1,0],[[3.3852972616768538e-282,1.6281541302987446e-101],9,0],[[4.023984950841538e-207,1.672209984146438e-177],0,0],[[5.997642554579093e+226,8267761121118583.0],0,0],[[3.025865987124205e+48,1.1774375942605503e+37],0,0],[[1.7578451228930594e-74,2.489149382420679e+27],7,0],[[3.938884622122182e-132,1.011396351900011e-125],2,0],[[9.807783778428908e+281,8.750108477874464e+259],0,0],[[1.0213927801883013e-280,2.4118761560252843e-59],7,0],[[1.195916640070373e-91,1.1745784325466232e+243],1,0],[[7.335711770377127e-38,1.214621771874996e+281],0,0],[[7.26354692283978e-298,6.697902311356943e+127],0,0],[[1.2351743153928947e-17,1.1081913151635317e-281],1,0],[[8.845830180604385e+55,4.68925600491289e+144],0,0],[[1.4639565733772952e-243,4.1910390611535265e+279],1,0],[[1.6983735818136165e-150,4.057563235251733e-168],0,0],[[1.5987895001152558e-250,1.0362772075683598e+99],0,0],[[2.574015514786201e-195,4.120748433400853e+266],0,0],[[2.828506773801223e-34,1.3980028593340099e-80],3,0],[[7.10451338618339e-112,2.752384728131671e-298],0,0],[[5.3848532123061334e+141,4.101841091919989e+82],0,0],[[1.8880422706568598e-131,6.087242169493258e-74],1,0],[[1.6828341140646555e-168,2.8288040637518216e+97],0,0],[[2.4020959302167836e+173,4.276010429020236e+247],0,0],[[1.679279614673279e-17,7.802007187654651e-08],0,0],[[6.190907314532847e-276,1.745791372849607e+234],3,0],[[5.911713422365171e-224,1.0773053002356648e-277],0,0],[[6.326943736711642e+259,2.02315867891966e+129],0,0],[[7.946583410099056e-261,2.144814527894872e+96],0,0],[[1.0066412328328968e-127,6.619416378892868e-163],3,0],[[1.1159565897451056e-40,9.147384059902005e+52],9,0],[[1.1165161433358629e+279,6.875662873883236e+254],0,0],[[7.053265896579982e-111,2.7551492956412816e-291],2,0],[[1.792618476145051e+142,3.258027489034141e+228],0,0],[[2.3780466739014797e+260,7.6303811992955545e+112],0,0],[[2.5226551585558244e+149,4.479310754223626e+77],0,0],[[6.3759232335206e-291,3.5785496756947083e-76],2,0],[[3.8797234898178104e-266,6.295638798327878e-124],1,0],[[6.621128712488456e-94,3.152253828409111e+30],4,0],[[3.5260516775312726e-162,4.379941188803635e-139],0,0],[[1.6672047786154368e+54,6.224498176564759e+252],0,0],[[6.79091067430158e+35,7.230059261043331e+195],0,0],[[4.3750470153682443e+216,8.334409599853035e+119],0,0],[[5.317028386962457e+95,1.5305424059226277e+248],0,0],[[6.409528319039091e+96,2.932037839848625e+137],0,0],[[8.883362223957793e+93,1.0708005705289017e+244],0,0],[[5.053806292662203e-155,2.523406045226158e-210],5,0],[[3.6380611743774316e+28,4.3451652399410245e+66],0,0],[[5.5111229904756633e-36,1.6975346890789871e+105],1,0],[[9.95962237767467e+23,1.044537127877944e+107],0,0],[[1.2032276449725793e-85,1.3054961346651174e-44],2,0],[[2.3075398048335097e-269,3.594097673489053e+137],0,0],[[3.130685264260855e-76,9.058189937007456e-86],0,0],[[4.53732938437198e+150,1.4669818938577088e+222],0,0],[[4.302212151190092e+240,2.4335687807904273e+271],0,0],[[6.550539660350184e-98,2.959467597264242e-230],0,0],[[2.052107344086851e-70,7.509188631026346e+286],5,0],[[2.2721511366771778e-250,4.0477581754304153e-125],2,0],[[4.931733655566518e-258,1.554975231016035e+153],3,0],[[3.4461749360980795e-185,7.6218106112626015e+295],0,0],[[1.3987141013277275e+91,6.132373723862702e+252],0,0],[[2.4801215181567776e-295,5.2115166535835604e-169],0,0],[[5.907165300326855e+32,1.9267899651560147e+275],0,0],[[7.475270857526654e-304,1.0862105938569748e+148],1,0],[[4.380578158292964e+195,3.0321252530234052e+38],0,0],[[2.4655809623086505e-116,1.1536689796869952e-11],6,0],[[8.444294654343975e-240,3.513520042407809e+153],5,0],[[3.28610894527258e-300,3.973558968153068e+125],2,0],[[2.5394112430978073e-295,1.4298675637930828e+180],0,0],[[8.332917955185835e+296,6.741628989608122e+71],0,0],[[1.6232174805713086e+70,3.765990859086882e+52],0,0],[[9.373092063300388e+294,2.8072978291071996e+105],0,0],[[8.752592959491946e-33,2.9311591750368227e+22],6,0],[[3.0241599246809088e+252,3.184319790336394e+219],0,0],[[1.0760470830369276e-175,3.1675280578479312e-77],0,0],[[9.685450907847438e-63,1.537477220142015e-154],3,0],[[1.4316271455151301e-258,2.996770630299676e+274],1,0],[[1.6611161145230723e-191,714914460440.7544],4,0],[[9.206946233985896e+265,5.909438823195212e+35],0,0],[[4.3407560983206045e+110,1.0066329381452874e+195],0,0],[[2.300114102133609e+63,3.3520036437628364e+162],0,0],[[3.7952930805105457e-199,7.532023979359606e+99],9,0],[[7.921938015189254e-17,1.6708793826459247e-57],1,1.5849625007211563],[[1023.2212474515807,2.9921045438694274e+227],0,0],[[0.0009065963481940791,3.905734270420228e+62],3,0],[[1.891116192597785e-215,6.110124011150757e+46],0,0],[[8.602881405868794e-32,4.340706048852671e-131],2,0],[[2.098983450835455e-256,7.299124485355855e+137],5,0],[[1.2757681535951056e+63,3.8712901591408457e+228],0,0],[[7.968357209160169e+93,6.567762824642581e+50],0,0],[[4.548601565249598e+188,2.083390534713302e+140],0,0],[[4.161272910469861e-301,4.4146411652973813e+21],3,0],[[6.4821321459802055e+193,1.7939351909740315e+68],0,0],[[2.7868826984034328e-297,6.274746106885988e-177],7,0],[[7.586534919343994e-75,1.6802148352573582e-128],0,0],[[9.491422824807354e-253,4.0739010895320517e+273],0,0],[[2.2415352671784828e-150,1.625167989850363e+119],0,0],[[7.01138751262021e-280,1.4841539461233504e+69],5,0],[[2.824709004194289e-77,3.4428899655780295e-69],6,0],[[1.1294315636198499e-278,5.86009335903585e-102],0,0],[[7.990408500607478e+225,7.43139844967742e+271],0,0],[[2.6148734958275445e-59,1.4522191998681414e+95],1,0],[[2.1746518322952078e-54,2.8875549970579304e+175],2,0],[[3.1487113596301893e-35,2.0573785747587795e-193],5,0],[[2.790368131936616e-145,6.479697484604152e-174],0,0],[[1.220285592766294e+307,3.861133926570598e+263],0,0],[[1.2654603057808926e-132,5.480340484157898e-137],0,0],[[3.9582185084442164e+58,1.0006915947365432e+290],0,0],[[2.2385341061737422e-125,1.1296035831317978e+178],1,0],[[1.9956859819988883e+208,1.3053442887826894e+292],0,0],[[1.3725216771543658e-17,7.122506379956216e-199],1,1.0],[[5.070205966511977e-66,2.1591257954674133e-112],0,0],[[1.9637167511580492e-290,4.1122590034758076e+161],3,0],[[6.289641429573477e-53,4.44964744501718e-303],10,0],[[4.921669299348463e+48,9.174188702008102e+144],0,0],[[1.0631632090197916e+200,5.699753770483561e+65],0,0],[[3.7304700864524026e-88,7.425542676714504e-84],1,0],[[4.592687610132483e+74,5.15900678827599e+24],0,0],[[3.2643753621921254e-59,9.955169418668015e-289],2,0],[[1.8079468232084944e-292,4.570078655862018e+54],3,0],[[11359488250023.906,1.6061320544606304e+202],0,0],[[1.3892861350443015e-223,4.641071766140853e-231],0,0],[[7.360110913281388e-12,2.8431063873980092e+116],6,0],[[4.0565095880949425e+280,6.675799068433044e+76],0,0],[[9.20664563196908e+294,1.3131400831400088e+86],0,0],[[1.0649783843865697e-107,2.193063794905827e+36],2,0],[[1.1535731528175885e-293,16122199543.85404],9,0],[[0.23158759667032142,2.174373890634123e+206],3,0],[[2.8576099148948687e+47,4.535106259884878e+127],0,0],[[4.76442930878223e-20,1.662443875692076e+190],2,0],[[1.7386181741597865e-117,2.2869715061523446e+282],2,0],[[1.8576198723851754e+267,1.4640464205690061e+181],0,0],[[1.0730971371295596e-35,1.3731090395442879e-244],0,0],[[5.8750151697224545e-09,3.2058797502881587e-47],1,0],[[6.606104192306025e-76,2.1980904706831728e-104],6,0],[[1.1320100213914422e-197,9.218931403807496e-238],1,0],[[1.371076068469597e-276,3.7292018910669483e+61],2,0],[[7.468254766320453e-225,5.794033588679369e+140],0,0],[[3.2896013204457148e-279,1.1190715118628351e-13],4,0],[[1.855739410010682e-286,1.2449977298699466e-295],0,0],[[8.63596361370883e-168,3.1003420231048053e-198],2,0],[[1.4390244358772018e+249,2.9639589969742274e+281],0,0],[[2.0583492621633517e-132,1.73356572916747e+144],1,0],[[1.6662800714135864e-218,3.017825861340067e+260],0,0],[[1.7909913857676524e-234,4.184907550158769e-217],0,0],[[5.556148241691299e-119,1.5213816359492715e-307],1,0],[[3.486470059469502e+53,1.4785130640238136e+99],0,0],[[4.750171216619508e-73,1.0938841522691449e-182],10,0],[[9.94673708940353e+255,6.918320731214305e+101],0,0],[[5.706158108157338e+305,1.2638234743036793e+156],0,0],[[2.427769796556236e-78,7.21762410022307e+205],2,0],[[2.727021877346581e-178,1.860064553198903e-67],0,0],[[8.657759546694974e-157,2.0568784750151953e+96],0,0],[[1.0675856537644375e+279,5.0108195646214185e+182],0,0],[[2.412016495848343e-259,2.1622905926715047e-231],0,0],[[1.4157269095091182e+175,1.752320881957983e+240],0,0],[[7.474117465579979e+250,1.998141361266681e+100],0,0],[[1.542984322219514e-13,3.0489294036502483e-215],3,0],[[1.095382951219098e-121,4.4403690793251364e-66],0,1.0],[[3.0292511751059167e-285,4.774911884404591e+104],8,0],[[7366.597199336127,3.437966658215048e+175],0,0],[[1.013327533564468e-142,1.0958904515570749e+229],0,0],[[5.365396337730866e+62,5.564528795268944e+304],0,0],[[2.2999903268614278e-290,1.0741122062961354e-261],0,0],[[5.859557539322906e-140,12468368041124.15],0,0],[[3.29750078510446e+71,1.1536796494388956e+294],0,0],[[1.0050966216294641e+208,3094188499901330.5],0,0],[[2.486240422123665e+301,6.411662743035886e+150],0,0],[[1.1448971434422485e-274,1.3291916155898896e-54],1,0],[[5.99451935698111e-22,2.459533652847606e+166],0,0],[[5.471344172015073e-66,2.5497871706438334e+172],3,0],[[1.929136835934461e+126,1.4511860769870938e+51],0,0],[[1.6848563310412775e-81,1.8787633523770844e+304],0,0],[[2.9246728990313427e+289,4.038893686579631e+19],0,0],[[7.229157843683878e+19,7.0767085636431225e+53],0,0],[[1.5968409688876136e+240,1.6442404219839566e+41],0,0],[[1.2356592442417317e-130,2.7522555769102684e-277],0,0],[[2.0679460963453592e-53,3.5340357590538254e+140],8,0],[[1.0662100247031813e-43,2.521296463327911e+268],4,0],[[1.2229817874252346e-71,8.506337374180222e-99],2,0],[[2.3910560608115626e-11,2.932647945759088e-270],1,0],[[9.315042055884043e+48,4.0024068424625754e+43],0,0],[[1.43710899076724e+182,2.2997526865909637e+146],0,0]],"fresh-alts":["#<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>","#<alt-delta (λ (k n) (/ (+ (* (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (* (* k k) 1/8)) (+ (* (log n) (log n)) (* (log (* PI 2)) (log (* PI 2))))) (- (fma (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4)) (* (log (* PI 2)) (* (* k k) (log n))) (* (pow (* PI 2) 1/2) (pow n 1/2))) (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/2)) (fma k (log (* PI 2)) (* (log n) k))))) (sqrt k)))>","#<alt-delta (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>","#<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>","#<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>","#<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2)))))>","#<alt-event (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>","#<alt-delta (λ (k n) (/ (* (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k)))>","#<alt-delta (λ (k n) (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))>","#<alt-delta (λ (k n) (* (/ (* (cbrt (pow (* n (* 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) (* (* (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)))))>"]}* * * * [misc]pick:  Picked  #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 4 ] rewriting at (2 1 1)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2 1 2 1)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2 1 1 1)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 4 ] generating series at (2 1 1)
* [misc]approximate:  Taking taylor expansion of (pow (* n (* PI 2)) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* n (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* n (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* n (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* n (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]approximate:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n)))))
* [misc]approximate:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* -2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* -2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* -2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 1)))) 24) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* -2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* -2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* -2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* -2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* -2 PI) 1)))) 120) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* -2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* -2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* -2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* -2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* -2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* -2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* -2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* -2 PI) 1)))) 720) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n)))))
* * * * [misc]progress:  [ 2 / 4 ] generating series at (2 1 2 1)
* [misc]approximate:  Taking taylor expansion of (* n (* PI 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) n) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
* * * * [misc]progress:  [ 3 / 4 ] generating series at (2 1 1 1)
* [misc]approximate:  Taking taylor expansion of (* n (* PI 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) n) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
* * * * [misc]progress:  [ 4 / 4 ] generating series at (2)
* [misc]approximate:  Taking taylor expansion of (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ 1 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* n (* PI 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* n (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in k
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of (* PI 2) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* n (* 2 PI)) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ k 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* n (* PI 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* n (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ k 2) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in k
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]taylor:  Taking taylor expansion of (* PI 2) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* n (* 2 PI)) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp 0) into 1
* [misc]backup-simplify:  Simplify (/ (pow (* 2 (* n PI)) 1/2) 1) into (sqrt (* n (* 2 PI)))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ (sqrt (* n (* 2 PI))) +nan.0) into (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* n (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* n (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* n (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* n (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 k) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* k (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (/ (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt k)) into (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* n (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* n (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* n (* PI 2)) (/ k 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ k 2) (log (* n (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ k 2) (log (* n (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ k 2) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ k 2) into (* 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* n (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 k) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* k (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (/ (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt k)) into (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (+ (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* k (+ (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 0 (+ (log (* 2 PI)) (log n))) into 0
* [misc]backup-simplify:  Simplify (* 1/2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (+ (log (* 2 PI)) (log n)))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (+ (log (* 2 PI)) (log n))) (* 0 0)) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))
* [misc]backup-simplify:  Simplify (exp 0) into 1
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 1) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) (/ 0 (sqrt k))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1) 1)))) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) +nan.0) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (+ (log (* 2 PI)) (log n))) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) 1)) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) +nan.0) (+ (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) +nan.0) (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) 0))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (+ (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (* 0 (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (+ (log (* 2 PI)) (log n))) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 3) 6)) (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2))))))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2)))))) 1)) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) (/ (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) 1)) (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (- (+ (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (log n)))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 3))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 3))) (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow (log n) 2))))))))
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) +nan.0) (+ (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) +nan.0) (+ (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) +nan.0) (* (- (+ (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (log n)))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 3))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 3))) (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow (log n) 2)))))))) 0)))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))))))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))))))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n))))))))))))))))))))))))
* [misc]approximate:  Taking taylor expansion of (/ (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (* PI 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (/ 1 n) into (/ 1 n)
* [misc]taylor:  Taking taylor expansion of (* PI 2) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) 1/2)
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (/ 1 n) into (/ 1 n)
* [misc]taylor:  Taking taylor expansion of (* PI 2) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))
* [misc]backup-simplify:  Simplify (/ (pow (* 2 (/ PI n)) 1/2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) into (* (sqrt (/ (* 2 PI) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ (* (sqrt (/ (* 2 PI) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) +nan.0) into (* +nan.0 (* (sqrt (/ PI n)) (/ (sqrt 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt (/ 1 k))) into (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 n) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 n) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ 1 k) 2) into (/ 1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 1 (* 2 PI)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt (/ 1 k))) into (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (- (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (- (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k
* [misc]taylor:  Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* k (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 3) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))))))))
* [misc]approximate:  Taking taylor expansion of (/ (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in k
* [misc]taylor:  Taking taylor expansion of (- n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (/ 1 (- n)) into (/ -1 n)
* [misc]taylor:  Taking taylor expansion of (* PI 2) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* -2 (/ PI n))))) into (pow (* -2 (/ PI n)) 1/2)
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in k
* [misc]taylor:  Taking taylor expansion of (- n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (/ 1 (- n)) into (/ -1 n)
* [misc]taylor:  Taking taylor expansion of (* PI 2) in k
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* -2 (/ PI n)))) into (* -1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))
* [misc]backup-simplify:  Simplify (/ (pow (* -2 (/ PI n)) 1/2) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) into (* (sqrt (/ (* PI -2) n)) (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ (* (sqrt (/ (* PI -2) n)) (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) +nan.0) into (* +nan.0 (/ (sqrt (* -2 (/ PI n))) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))
* [misc]taylor:  Taking taylor expansion of (/ (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 2) (log (* (/ 1 (- n)) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (/ 1 (- k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (/ (/ -1 k) 2) into (/ -1/2 k)
* [misc]taylor:  Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of (* PI 2) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (* PI 2) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* -1 (* 2 PI)) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))
* [misc]taylor:  Taking taylor expansion of (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (- (log (* -2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (- (log (* -2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* -2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* -2 PI) in k
* [misc]taylor:  Taking taylor expansion of -2 in k
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n))))
* [misc]taylor:  Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k
* [misc]taylor:  Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k
* [misc]taylor:  Taking taylor expansion of -1/2 in k
* [misc]backup-simplify:  Simplify -1/2 into -1/2
* [misc]taylor:  Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k
* [misc]taylor:  Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* -2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* -2 PI) in k
* [misc]taylor:  Taking taylor expansion of -2 in k
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* -1/2 (- (log (* -2 PI)) (log n))) into (* -1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ -1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ -1 k) in k
* [misc]taylor:  Taking taylor expansion of -1 in k
* [misc]backup-simplify:  Simplify -1 into -1
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ -1 1) into -1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) (/ 0 (sqrt (/ -1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))
* [misc]backup-simplify:  Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (+ (* (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))
* [misc]backup-simplify:  Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (+ (* (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))))
* * * [misc]progress:  simplifying candidates
* * * * [misc]progress:  [ 1 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (log1p (expm1 (pow (* n (* PI 2)) (/ 1 2)))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (expm1 (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (expm1 (pow (* (* PI n) 2) (/ 1 2)))
* * * * [misc]progress:  [ 2 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (expm1 (log1p (pow (* n (* PI 2)) (/ 1 2)))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (log1p (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (log1p (pow (* (* PI n) 2) (/ 1 2)))
* * * * [misc]progress:  [ 3 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (exp (* (log (* n (* PI 2))) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* n (* PI 2))) (/ 1 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (92 enodes)
* * [misc]simplify:  iters left: 2 (180 enodes)
* * [misc]simplify:  iters left: 1 (391 enodes)
* [exit]simplify:  Simplified to (fma (log (* 2 PI)) (/ 1 2) (/ (log n) 2))
* [exit]simplify:  Simplified to (fma (log (* 2 PI)) (/ 1 2) (/ (log n) 2))
* * * * [misc]progress:  [ 4 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (exp (* (log (* n (* PI 2))) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (log (* n (* PI 2))) (/ 1 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (92 enodes)
* * [misc]simplify:  iters left: 2 (180 enodes)
* * [misc]simplify:  iters left: 1 (391 enodes)
* [exit]simplify:  Simplified to (fma (log (* 2 PI)) (/ 1 2) (/ (log n) 2))
* [exit]simplify:  Simplified to (fma (log (* 2 PI)) (/ 1 2) (/ (log n) 2))
* * * * [misc]progress:  [ 5 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (* 1 (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* 1 (/ 1 2))
* * [misc]simplify:  iters left: 4 (4 enodes)
* * [misc]simplify:  iters left: 3 (9 enodes)
* [exit]simplify:  Simplified to (/ 1 2)
* [exit]simplify:  Simplified to (/ 1 2)
* * * * [misc]progress:  [ 6 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* n (* PI 2)) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) (cbrt (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (* PI 2)) (* (cbrt (/ 1 2)) (cbrt (/ 1 2))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (pow (* (* n 2) PI) (* (cbrt (/ 1 2)) (cbrt (/ 1 2))))
* [exit]simplify:  Simplified to (pow (* (* n 2) PI) (* (cbrt (/ 1 2)) (cbrt (/ 1 2))))
* * * * [misc]progress:  [ 7 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* n (* PI 2)) (sqrt (/ 1 2))) (sqrt (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (* PI 2)) (sqrt (/ 1 2)))
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* * [misc]simplify:  iters left: 3 (21 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (sqrt (/ 1 2)))
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (sqrt (/ 1 2)))
* * * * [misc]progress:  [ 8 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* n (* PI 2)) 1) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (* PI 2)) 1)
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (20 enodes)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* * * * [misc]progress:  [ 9 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* n (* PI 2)) 1) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow (* n (* PI 2)) 1)
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (20 enodes)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* [exit]simplify:  Simplified to (* (* PI n) 2)
* * * * [misc]progress:  [ 10 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (pow n (/ 1 2)) (pow (* PI 2) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (pow n (/ 1 2))
* * [misc]simplify:  iters left: 3 (5 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (pow n (/ 1 2))
* [exit]simplify:  Simplified to (pow n (/ 1 2))
* [enter]simplify:  Simplifying (pow (* PI 2) (/ 1 2))
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (9 enodes)
* [exit]simplify:  Simplified to (pow (* 2 PI) (/ 1 2))
* [exit]simplify:  Simplified to (pow (* 2 PI) (/ 1 2))
* * * * [misc]progress:  [ 11 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* n (* PI 2)) (/ 1 2)) 1) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 12 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (exp (log (pow (* n (* PI 2)) (/ 1 2)))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (72 enodes)
* * [misc]simplify:  iters left: 2 (182 enodes)
* * [misc]simplify:  iters left: 1 (429 enodes)
* [exit]simplify:  Simplified to (fma (log (* PI n)) (/ 1 2) (/ (log 2) 2))
* [exit]simplify:  Simplified to (fma (log (* PI n)) (/ 1 2) (/ (log 2) 2))
* * * * [misc]progress:  [ 13 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (log (exp (pow (* n (* PI 2)) (/ 1 2)))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (exp (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (exp (pow (* (* PI n) 2) (/ 1 2)))
* * * * [misc]progress:  [ 14 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2))))
* [enter]simplify:  Simplifying (cbrt (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (cbrt (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (cbrt (pow (* (* PI n) 2) (/ 1 2)))
* * * * [misc]progress:  [ 15 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (cbrt (* (* (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ 1 2)))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (pow (pow (* (* n 2) PI) (/ 1 2)) 3)
* [exit]simplify:  Simplified to (pow (pow (* (* n 2) PI) (/ 1 2)) 3)
* * * * [misc]progress:  [ 16 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ 1 2)))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2)))
* [enter]simplify:  Simplifying (sqrt (pow (* n (* PI 2)) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2)))
* * * * [misc]progress:  [ 17 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* 1 (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 18 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (log1p (expm1 (* n (* PI 2)))) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (expm1 (* (* n 2) PI))
* [exit]simplify:  Simplified to (expm1 (* (* n 2) PI))
* * * * [misc]progress:  [ 19 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (expm1 (log1p (* n (* PI 2)))) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (log1p (* (* n 2) PI))
* [exit]simplify:  Simplified to (log1p (* (* n 2) PI))
* * * * [misc]progress:  [ 20 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (pow (* n (* PI 2)) 1) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 21 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (exp (log (* n (* PI 2)))) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (log (* (* PI n) 2))
* [exit]simplify:  Simplified to (log (* (* PI n) 2))
* * * * [misc]progress:  [ 22 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (log (exp (* n (* PI 2)))) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* * [misc]simplify:  iters left: 2 (35 enodes)
* * [misc]simplify:  iters left: 1 (47 enodes)
* [exit]simplify:  Simplified to (pow (exp 2) (* PI n))
* [exit]simplify:  Simplified to (pow (exp 2) (* PI n))
* * * * [misc]progress:  [ 23 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (18 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2)))
* [exit]simplify:  Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2)))
* [enter]simplify:  Simplifying (cbrt (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (cbrt (* (* n 2) PI))
* [exit]simplify:  Simplified to (cbrt (* (* n 2) PI))
* * * * [misc]progress:  [ 24 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (cbrt (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (59 enodes)
* * [misc]simplify:  iters left: 3 (203 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) 3)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) 3)
* * * * [misc]progress:  [ 25 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* (sqrt (* n (* PI 2))) (sqrt (* n (* PI 2)))) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* [enter]simplify:  Simplifying (sqrt (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* * * * [misc]progress:  [ 26 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* 1 (* n (* PI 2))) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 27 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n PI)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* PI n)
* [exit]simplify:  Simplified to (* PI n)
* * * * [misc]progress:  [ 28 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* (* PI 2) n) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 29 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (log1p (expm1 (* n (* PI 2)))) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (expm1 (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (expm1 (* (* n 2) PI))
* [exit]simplify:  Simplified to (expm1 (* (* n 2) PI))
* * * * [misc]progress:  [ 30 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (expm1 (log1p (* n (* PI 2)))) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log1p (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (log1p (* (* n 2) PI))
* [exit]simplify:  Simplified to (log1p (* (* n 2) PI))
* * * * [misc]progress:  [ 31 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (pow (* n (* PI 2)) 1) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 32 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (exp (log (* n (* PI 2)))) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (log (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (41 enodes)
* [exit]simplify:  Simplified to (log (* (* PI n) 2))
* [exit]simplify:  Simplified to (log (* (* PI n) 2))
* * * * [misc]progress:  [ 33 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (log (exp (* n (* PI 2)))) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (exp (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* * [misc]simplify:  iters left: 2 (35 enodes)
* * [misc]simplify:  iters left: 1 (47 enodes)
* [exit]simplify:  Simplified to (pow (exp 2) (* PI n))
* [exit]simplify:  Simplified to (pow (exp 2) (* PI n))
* * * * [misc]progress:  [ 34 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (18 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2)))
* [exit]simplify:  Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2)))
* [enter]simplify:  Simplifying (cbrt (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (cbrt (* (* n 2) PI))
* [exit]simplify:  Simplified to (cbrt (* (* n 2) PI))
* * * * [misc]progress:  [ 35 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (cbrt (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2)))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (59 enodes)
* * [misc]simplify:  iters left: 3 (203 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) 3)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) 3)
* * * * [misc]progress:  [ 36 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (sqrt (* n (* PI 2))) (sqrt (* n (* PI 2)))) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (sqrt (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* [enter]simplify:  Simplifying (sqrt (* n (* PI 2)))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* [exit]simplify:  Simplified to (sqrt (* (* n 2) PI))
* * * * [misc]progress:  [ 37 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* 1 (* n (* PI 2))) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 38 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* n PI)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* PI n)
* [exit]simplify:  Simplified to (* PI n)
* * * * [misc]progress:  [ 39 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow (* (* PI 2) n) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* * * * [misc]progress:  [ 40 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (log1p (expm1 (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (expm1 (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (expm1 (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* [exit]simplify:  Simplified to (expm1 (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* * * * [misc]progress:  [ 41 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (expm1 (log1p (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (log1p (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (log1p (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* [exit]simplify:  Simplified to (log1p (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* * * * [misc]progress:  [ 42 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (pow (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) 1))>
* * * * [misc]progress:  [ 43 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (* (log (* n (* PI 2))) (/ 1 2)) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* n (* PI 2))) (/ 1 2)) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (97 enodes)
* * [misc]simplify:  iters left: 3 (307 enodes)
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 44 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (* (log (* n (* PI 2))) (/ 1 2)) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* n (* PI 2))) (/ 1 2)) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (97 enodes)
* * [misc]simplify:  iters left: 3 (307 enodes)
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 45 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (* (log (* n (* PI 2))) (/ 1 2)) (log (pow (* n (* PI 2)) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* n (* PI 2))) (/ 1 2)) (log (pow (* n (* PI 2)) (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (87 enodes)
* * [misc]simplify:  iters left: 3 (284 enodes)
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 46 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (* (log (* n (* PI 2))) (/ 1 2)) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* n (* PI 2))) (/ 1 2)) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (97 enodes)
* * [misc]simplify:  iters left: 3 (307 enodes)
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 47 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (* (log (* n (* PI 2))) (/ 1 2)) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* n (* PI 2))) (/ 1 2)) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (97 enodes)
* * [misc]simplify:  iters left: 3 (307 enodes)
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 48 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (* (log (* n (* PI 2))) (/ 1 2)) (log (pow (* n (* PI 2)) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (* (log (* n (* PI 2))) (/ 1 2)) (log (pow (* n (* PI 2)) (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (87 enodes)
* * [misc]simplify:  iters left: 3 (284 enodes)
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 49 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (log (pow (* n (* PI 2)) (/ 1 2))) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (log (pow (* n (* PI 2)) (/ 1 2))) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (90 enodes)
* * [misc]simplify:  iters left: 3 (263 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 50 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (log (pow (* n (* PI 2)) (/ 1 2))) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (log (pow (* n (* PI 2)) (/ 1 2))) (* (log (* n (* PI 2))) (/ k 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (90 enodes)
* * [misc]simplify:  iters left: 3 (263 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 51 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (- (log (pow (* n (* PI 2)) (/ 1 2))) (log (pow (* n (* PI 2)) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (- (log (pow (* n (* PI 2)) (/ 1 2))) (log (pow (* n (* PI 2)) (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (32 enodes)
* * [misc]simplify:  iters left: 4 (70 enodes)
* * [misc]simplify:  iters left: 3 (206 enodes)
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* n 2) PI)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* n 2) PI)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 52 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (exp (- (log (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (log (sqrt k)))))>
* [enter]simplify:  Simplifying (- (log (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (89 enodes)
* * [misc]simplify:  iters left: 2 (283 enodes)
* [exit]simplify:  Simplified to (fma (log (* 2 (* PI n))) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* 2 (* PI n))) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 53 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (exp (log (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (log (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (55 enodes)
* * [misc]simplify:  iters left: 2 (103 enodes)
* * [misc]simplify:  iters left: 1 (295 enodes)
* [exit]simplify:  Simplified to (fma (log (* (* 2 PI) n)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* (* 2 PI) n)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 54 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (log (exp (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (exp (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (exp (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* [exit]simplify:  Simplified to (exp (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* * * * [misc]progress:  [ 55 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (/ (/ (* (* (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ 1 2))) (* (* (pow (* n (* PI 2)) (/ k 2)) (pow (* n (* PI 2)) (/ k 2))) (pow (* n (* PI 2)) (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (* (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ 1 2))) (* (* (pow (* n (* PI 2)) (/ k 2)) (pow (* n (* PI 2)) (/ k 2))) (pow (* n (* PI 2)) (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (113 enodes)
* * [misc]simplify:  iters left: 3 (390 enodes)
* [exit]simplify:  Simplified to (/ (* (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (* (pow (* (* PI n) 2) (/ k 2)) (/ (* (sqrt k) k) (pow (* (* PI n) 2) (/ 1 2)))))
* [exit]simplify:  Simplified to (/ (* (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (* (pow (* (* PI n) 2) (/ k 2)) (/ (* (sqrt k) k) (pow (* (* PI n) 2) (/ 1 2)))))
* * * * [misc]progress:  [ 56 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (/ (* (* (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (* (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (39 enodes)
* * [misc]simplify:  iters left: 4 (96 enodes)
* * [misc]simplify:  iters left: 3 (266 enodes)
* [exit]simplify:  Simplified to (* (/ (pow (* PI (* n 2)) (/ 1 2)) (* (pow (* PI (* n 2)) (/ k 2)) (* (sqrt k) k))) (* (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))))
* [exit]simplify:  Simplified to (* (/ (pow (* PI (* n 2)) (/ 1 2)) (* (pow (* PI (* n 2)) (/ k 2)) (* (sqrt k) k))) (* (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))))
* * * * [misc]progress:  [ 57 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (cbrt (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))) (cbrt (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))) (cbrt (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (cbrt (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))) (cbrt (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))))
* [exit]simplify:  Simplified to (* (cbrt (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))))
* [enter]simplify:  Simplifying (cbrt (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* [exit]simplify:  Simplified to (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* * * * [misc]progress:  [ 58 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (* (* (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (* (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (69 enodes)
* * [misc]simplify:  iters left: 3 (196 enodes)
* [exit]simplify:  Simplified to (/ (/ (* (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ 1 2))) (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))) (/ (* k (pow (* (* 2 PI) n) (/ k 2))) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)))))
* [exit]simplify:  Simplified to (/ (/ (* (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ 1 2))) (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))) (/ (* k (pow (* (* 2 PI) n) (/ k 2))) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)))))
* * * * [misc]progress:  [ 59 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))) (sqrt (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (sqrt (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* [enter]simplify:  Simplifying (sqrt (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2)))))
* * * * [misc]progress:  [ 60 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (- (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (- (sqrt k))))>
* [enter]simplify:  Simplifying (- (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (- (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))
* [exit]simplify:  Simplified to (- (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))
* [enter]simplify:  Simplifying (- (sqrt k))
* * [misc]simplify:  iters left: 3 (3 enodes)
* [exit]simplify:  Simplified to (- (sqrt k))
* [exit]simplify:  Simplified to (- (sqrt k))
* * * * [misc]progress:  [ 61 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (* (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (45 enodes)
* * [misc]simplify:  iters left: 3 (49 enodes)
* * [misc]simplify:  iters left: 2 (52 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (* (/ (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 62 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (* (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 63 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (* (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))) 1) (/ (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))) 1)
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* * [misc]simplify:  iters left: 2 (52 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))))
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))))
* [enter]simplify:  Simplifying (/ (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k))
* [exit]simplify:  Simplified to (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k))
* * * * [misc]progress:  [ 64 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 65 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* n 2) PI) (/ 1 2)) (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 66 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) 1) (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) 1)
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))
* [enter]simplify:  Simplifying (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k))
* [exit]simplify:  Simplified to (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k))
* * * * [misc]progress:  [ 67 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* * [misc]simplify:  iters left: 2 (31 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (cbrt (sqrt k))) (pow (* 2 PI) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (cbrt (sqrt k))) (pow (* 2 PI) (/ k 2)))
* * * * [misc]progress:  [ 68 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) (sqrt (sqrt k))) (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (pow n (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (pow n (/ k 2)))
* [enter]simplify:  Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt (sqrt k))) (pow (* 2 PI) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt (sqrt k))) (pow (* 2 PI) (/ k 2)))
* * * * [misc]progress:  [ 69 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) 1) (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) 1)
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (21 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* [exit]simplify:  Simplified to (/ (pow n (/ 1 2)) (pow n (/ k 2)))
* [exit]simplify:  Simplified to (/ (pow n (/ 1 2)) (pow n (/ k 2)))
* [enter]simplify:  Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt k)) (pow (* 2 PI) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt k)) (pow (* 2 PI) (/ k 2)))
* * * * [misc]progress:  [ 70 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (46 enodes)
* * [misc]simplify:  iters left: 3 (60 enodes)
* * [misc]simplify:  iters left: 2 (72 enodes)
* * [misc]simplify:  iters left: 1 (75 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (pow (* n (* 2 PI)) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (pow (* n (* 2 PI)) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* (* n 2) PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* (* n 2) PI) (/ k 2))))
* * * * [misc]progress:  [ 71 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (38 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* * [misc]simplify:  iters left: 2 (48 enodes)
* [exit]simplify:  Simplified to (/ (/ (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* (* n 2) PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* (* n 2) PI) (/ k 2))))
* * * * [misc]progress:  [ 72 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) 1) (/ (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) 1)
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (42 enodes)
* * [misc]simplify:  iters left: 2 (47 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 73 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (45 enodes)
* * [misc]simplify:  iters left: 2 (46 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* n (* 2 PI)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* n (* 2 PI)) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2))))
* * * * [misc]progress:  [ 74 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) (/ (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2))))
* * * * [misc]progress:  [ 75 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) 1) (/ (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) 1)
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (37 enodes)
* [exit]simplify:  Simplified to (/ (pow n (/ 1 2)) (sqrt (pow (* n (* 2 PI)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (pow n (/ 1 2)) (sqrt (pow (* n (* 2 PI)) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 76 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow n (/ 1 2)) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (cbrt (sqrt k))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (pow n (/ 1 2)) (cbrt (sqrt k))) (cbrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (cbrt (sqrt k))) (pow (* PI (* n 2)) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (cbrt (sqrt k))) (pow (* PI (* n 2)) (/ k 2)))
* * * * [misc]progress:  [ 77 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) 1) (sqrt (sqrt k))) (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (pow n (/ 1 2)) 1) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* [exit]simplify:  Simplified to (/ (pow n (/ 1 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow n (/ 1 2)) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt (sqrt k))) (pow (* PI (* n 2)) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt (sqrt k))) (pow (* PI (* n 2)) (/ k 2)))
* * * * [misc]progress:  [ 78 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) 1) 1) (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (pow n (/ 1 2)) 1) 1)
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (11 enodes)
* [exit]simplify:  Simplified to (pow n (/ 1 2))
* [exit]simplify:  Simplified to (pow n (/ 1 2))
* [enter]simplify:  Simplifying (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt k)) (pow (* (* 2 PI) n) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ (pow (* 2 PI) (/ 1 2)) (sqrt k)) (pow (* (* 2 PI) n) (/ k 2)))
* * * * [misc]progress:  [ 79 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (50 enodes)
* * [misc]simplify:  iters left: 3 (86 enodes)
* * [misc]simplify:  iters left: 2 (124 enodes)
* * [misc]simplify:  iters left: 1 (143 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* 2 PI) n) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow n (/ k 2)) (cbrt (pow (* (* 2 PI) n) (/ 1 2)))))
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* 2 PI) n) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow n (/ k 2)) (cbrt (pow (* (* 2 PI) n) (/ 1 2)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* 2 PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* 2 PI) (/ k 2))))
* * * * [misc]progress:  [ 80 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (pow n (/ k 2))) (sqrt (sqrt k))) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (pow n (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (42 enodes)
* * [misc]simplify:  iters left: 3 (56 enodes)
* * [misc]simplify:  iters left: 2 (64 enodes)
* * [misc]simplify:  iters left: 1 (67 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (pow n (/ k 2))) (/ (sqrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ 1 2)))))
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (pow n (/ k 2))) (/ (sqrt (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ 1 2)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* 2 PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* 2 PI) (/ k 2))))
* * * * [misc]progress:  [ 81 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (pow n (/ k 2))) 1) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (pow n (/ k 2))) 1)
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (64 enodes)
* * [misc]simplify:  iters left: 2 (152 enodes)
* * [misc]simplify:  iters left: 1 (253 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* PI (* n 2)) (/ 1 2))) (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (pow n (/ k 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* PI (* n 2)) (/ 1 2))) (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (pow n (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (pow (* 2 PI) (/ k 2)) (sqrt k)))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (pow (* 2 PI) (/ k 2)) (sqrt k)))
* * * * [misc]progress:  [ 82 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (73 enodes)
* * [misc]simplify:  iters left: 3 (142 enodes)
* * [misc]simplify:  iters left: 2 (248 enodes)
* * [misc]simplify:  iters left: 1 (309 enodes)
* [exit]simplify:  Simplified to (* (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k))) (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (* (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k))) (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 83 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (59 enodes)
* * [misc]simplify:  iters left: 3 (92 enodes)
* * [misc]simplify:  iters left: 2 (127 enodes)
* * [misc]simplify:  iters left: 1 (145 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 84 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) 1) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) 1)
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (56 enodes)
* * [misc]simplify:  iters left: 3 (95 enodes)
* * [misc]simplify:  iters left: 2 (301 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))))
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 85 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (51 enodes)
* * [misc]simplify:  iters left: 3 (87 enodes)
* * [misc]simplify:  iters left: 2 (127 enodes)
* * [misc]simplify:  iters left: 1 (146 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (pow (* 2 (* PI n)) (/ 1 2)))))
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* 2 (* PI n)) (/ 1 2))) (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (pow (* 2 (* PI n)) (/ 1 2)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 86 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (57 enodes)
* * [misc]simplify:  iters left: 2 (65 enodes)
* * [misc]simplify:  iters left: 1 (68 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ 1 2)))))
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ 1 2)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 87 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) 1) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) 1)
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (65 enodes)
* * [misc]simplify:  iters left: 2 (157 enodes)
* * [misc]simplify:  iters left: 1 (277 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* 2 PI) n) (/ 1 2))) (/ (sqrt (pow (* (* 2 PI) n) (/ k 2))) (cbrt (pow (* (* 2 PI) n) (/ 1 2)))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* (* 2 PI) n) (/ 1 2))) (/ (sqrt (pow (* (* 2 PI) n) (/ k 2))) (cbrt (pow (* (* 2 PI) n) (/ 1 2)))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 88 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (56 enodes)
* * [misc]simplify:  iters left: 3 (102 enodes)
* * [misc]simplify:  iters left: 2 (238 enodes)
* * [misc]simplify:  iters left: 1 (272 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* 2 PI) n) (/ 1 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* 2 PI) n) (/ 1 2))) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* (* 2 PI) n) (/ 1 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* 2 PI) n) (/ 1 2))) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 89 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) 1) (sqrt (sqrt k))) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) 1) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (70 enodes)
* * [misc]simplify:  iters left: 2 (133 enodes)
* * [misc]simplify:  iters left: 1 (138 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* PI (* n 2)) (/ 1 2))) (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* PI (* n 2)) (/ 1 2))) (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 90 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) 1) 1) (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) 1) 1)
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* * [misc]simplify:  iters left: 2 (49 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2))))
* [enter]simplify:  Simplifying (/ (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (pow (* PI (* n 2)) (/ k 2)) (sqrt k)))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI (* n 2)) (/ 1 2))) (* (pow (* PI (* n 2)) (/ k 2)) (sqrt k)))
* * * * [misc]progress:  [ 91 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (45 enodes)
* * [misc]simplify:  iters left: 2 (46 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* 2 PI) n) (/ 1 2))) (* (pow n (/ k 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* 2 PI) n) (/ 1 2))) (* (pow n (/ k 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* 2 PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* 2 PI) (/ k 2))))
* * * * [misc]progress:  [ 92 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow n (/ k 2))) (sqrt (sqrt k))) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow n (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow n (/ k 2))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow n (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* 2 PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* 2 PI) (/ k 2))))
* * * * [misc]progress:  [ 93 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow n (/ k 2))) 1) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow n (/ k 2))) 1)
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (37 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow n (/ k 2)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (pow n (/ k 2)))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (pow (* 2 PI) (/ k 2)) (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (pow (* 2 PI) (/ k 2)) (sqrt k)))
* * * * [misc]progress:  [ 94 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (47 enodes)
* * [misc]simplify:  iters left: 3 (61 enodes)
* * [misc]simplify:  iters left: 2 (73 enodes)
* * [misc]simplify:  iters left: 1 (76 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* 2 (* PI n)) (/ 1 2))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (pow (* 2 (* PI n)) (/ k 2)))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 95 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* * [misc]simplify:  iters left: 2 (49 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 96 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) 1) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) 1)
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* * [misc]simplify:  iters left: 2 (48 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 97 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (46 enodes)
* * [misc]simplify:  iters left: 2 (47 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 98 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 99 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) 1) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) 1)
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* * [misc]simplify:  iters left: 2 (38 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 100 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (39 enodes)
* * [misc]simplify:  iters left: 3 (50 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (cbrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 101 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) 1) (sqrt (sqrt k))) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) 1) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ 1 2))) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (sqrt (sqrt k)) (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 102 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) 1) 1) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) 1) 1)
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2)))
* [enter]simplify:  Simplifying (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (pow (* PI (* n 2)) (/ k 2)) (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* PI (* n 2)) (/ 1 2))) (* (pow (* PI (* n 2)) (/ k 2)) (sqrt k)))
* * * * [misc]progress:  [ 103 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* PI 2) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (28 enodes)
* * [misc]simplify:  iters left: 2 (29 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (/ 1 (pow n (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* PI 2) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI (* n 2)) (/ 1 2)) (* (cbrt (sqrt k)) (pow (* 2 PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (pow (* PI (* n 2)) (/ 1 2)) (* (cbrt (sqrt k)) (pow (* 2 PI) (/ k 2))))
* * * * [misc]progress:  [ 104 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (pow n (/ k 2))) (sqrt (sqrt k))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* PI 2) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (pow n (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (14 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt (sqrt k))) (pow n (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt (sqrt k))) (pow n (/ k 2)))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* PI 2) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* 2 PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (pow (* PI (* n 2)) (/ 1 2)) (* (sqrt (sqrt k)) (pow (* 2 PI) (/ k 2))))
* * * * [misc]progress:  [ 105 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (pow n (/ k 2))) 1) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* PI 2) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ 1 (pow n (/ k 2))) 1)
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (12 enodes)
* * [misc]simplify:  iters left: 4 (15 enodes)
* * [misc]simplify:  iters left: 3 (18 enodes)
* [exit]simplify:  Simplified to (/ 1 (pow n (/ k 2)))
* [exit]simplify:  Simplified to (/ 1 (pow n (/ k 2)))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* PI 2) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ 1 2)) (* (sqrt k) (pow (* 2 PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ 1 2)) (* (sqrt k) (pow (* 2 PI) (/ k 2))))
* * * * [misc]progress:  [ 106 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (58 enodes)
* * [misc]simplify:  iters left: 2 (70 enodes)
* * [misc]simplify:  iters left: 1 (73 enodes)
* [exit]simplify:  Simplified to (/ (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (* (cbrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))))
* [exit]simplify:  Simplified to (/ (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (* (cbrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 107 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (46 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (* (sqrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (/ k 2)))))
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (* (sqrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (/ k 2)))))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 108 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) 1) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ 1 (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) 1)
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (39 enodes)
* * [misc]simplify:  iters left: 2 (40 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 109 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (25 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* * [misc]simplify:  iters left: 2 (44 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* (* 2 n) PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* (* 2 n) PI) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 110 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (pow (* 2 (* PI n)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (pow (* 2 (* PI n)) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 111 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (sqrt (pow (* n (* PI 2)) (/ k 2)))) 1) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ 1 (sqrt (pow (* n (* PI 2)) (/ k 2)))) 1)
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (pow (* n (* PI 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ 1 (sqrt (pow (* n (* PI 2)) (/ k 2))))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt k))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 112 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 113 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 1) (sqrt (sqrt k))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (/ 1 1) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 4 (6 enodes)
* * [misc]simplify:  iters left: 3 (8 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 114 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 1) 1) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ 1 1) 1)
* * [misc]simplify:  iters left: 4 (3 enodes)
* * [misc]simplify:  iters left: 3 (5 enodes)
* [exit]simplify:  Simplified to 1
* [exit]simplify:  Simplified to 1
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ 1 2)) (* (sqrt k) (pow (* (* n 2) PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ 1 2)) (* (sqrt k) (pow (* (* n 2) PI) (/ k 2))))
* * * * [misc]progress:  [ 115 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* [exit]simplify:  Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 116 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 117 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 1) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ 1 1)
* * [misc]simplify:  iters left: 2 (2 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to 1
* [exit]simplify:  Simplified to 1
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (32 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ 1 2)) (* (sqrt k) (pow (* (* n 2) PI) (/ k 2))))
* [exit]simplify:  Simplified to (/ (pow (* (* n 2) PI) (/ 1 2)) (* (sqrt k) (pow (* (* n 2) PI) (/ k 2))))
* * * * [misc]progress:  [ 118 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow (* n (* PI 2)) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ 1 (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (/ 1 (pow (* n (* PI 2)) (/ k 2))) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (31 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (sqrt k))) (pow (* n (* PI 2)) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ 1 (cbrt (sqrt k))) (pow (* n (* PI 2)) (/ k 2)))
* * * * [misc]progress:  [ 119 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (sqrt k))) (/ (/ 1 (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (/ 1 (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (31 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt (sqrt k))) (pow (* n (* PI 2)) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt (sqrt k))) (pow (* n (* PI 2)) (/ k 2)))
* * * * [misc]progress:  [ 120 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow (* n (* PI 2)) (/ 1 2)) 1) (/ (/ 1 (pow (* n (* PI 2)) (/ k 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow (* n (* PI 2)) (/ 1 2)) 1)
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (/ 1 2))
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (/ 1 2))
* [enter]simplify:  Simplifying (/ (/ 1 (pow (* n (* PI 2)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (30 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt k)) (pow (* n (* PI 2)) (/ k 2)))
* [exit]simplify:  Simplified to (/ (/ 1 (sqrt k)) (pow (* n (* PI 2)) (/ k 2)))
* * * * [misc]progress:  [ 121 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))))>
* * * * [misc]progress:  [ 122 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (/ 1 (sqrt k))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt k))
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (6 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt k))
* [exit]simplify:  Simplified to (/ 1 (sqrt k))
* * * * [misc]progress:  [ 123 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2)))
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2)))
* * * * [misc]progress:  [ 124 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (38 enodes)
* * [misc]simplify:  iters left: 3 (44 enodes)
* * [misc]simplify:  iters left: 2 (45 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 125 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 126 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) 1) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) 1)
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (37 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 127 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt k) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))))
* [exit]simplify:  Simplified to (/ (sqrt k) (cbrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))))
* * * * [misc]progress:  [ 128 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt k) (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (27 enodes)
* * [misc]simplify:  iters left: 3 (29 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (sqrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))))
* [exit]simplify:  Simplified to (/ (sqrt k) (sqrt (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))))
* * * * [misc]progress:  [ 129 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow n (/ 1 2)) (pow n (/ k 2))) (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2))))
* [exit]simplify:  Simplified to (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2))))
* * * * [misc]progress:  [ 130 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* PI 2) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* PI 2) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))
* * * * [misc]progress:  [ 131 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* PI 2) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2))))
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* PI 2) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2))))
* * * * [misc]progress:  [ 132 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (pow n (/ 1 2)) 1) (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* PI 2) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* PI 2) (/ 1 2))) (pow (* 2 (* n PI)) (/ k 2)))
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* PI 2) (/ 1 2))) (pow (* 2 (* n PI)) (/ k 2)))
* * * * [misc]progress:  [ 133 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (pow n (/ k 2))) (/ (sqrt k) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* PI 2) (/ k 2)) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ 1 2))))
* [exit]simplify:  Simplified to (/ (* (pow (* PI 2) (/ k 2)) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ 1 2))))
* * * * [misc]progress:  [ 134 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt k) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ 1 2))))
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ 1 2))))
* * * * [misc]progress:  [ 135 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt k) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* [exit]simplify:  Simplified to (/ (* (sqrt (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ 1 2))))
* [exit]simplify:  Simplified to (/ (* (sqrt (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (cbrt (pow (* n (* PI 2)) (/ 1 2))))
* * * * [misc]progress:  [ 136 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) 1) (/ (sqrt k) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* PI (* n 2)) (/ k 2)) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ 1 2))))
* [exit]simplify:  Simplified to (/ (* (pow (* PI (* n 2)) (/ k 2)) (sqrt k)) (cbrt (pow (* PI (* n 2)) (/ 1 2))))
* * * * [misc]progress:  [ 137 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow n (/ k 2))) (/ (sqrt k) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* PI 2) (/ k 2))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* PI 2) (/ k 2)) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ 1 2))))
* [exit]simplify:  Simplified to (/ (* (pow (* PI 2) (/ k 2)) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ 1 2))))
* * * * [misc]progress:  [ 138 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt k) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ 1 2))))
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ 1 2))))
* * * * [misc]progress:  [ 139 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt k) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (sqrt (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* [exit]simplify:  Simplified to (/ (* (sqrt (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ 1 2))))
* [exit]simplify:  Simplified to (/ (* (sqrt (pow (* n (* PI 2)) (/ k 2))) (sqrt k)) (sqrt (pow (* n (* PI 2)) (/ 1 2))))
* * * * [misc]progress:  [ 140 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) 1) (/ (sqrt k) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* PI (* n 2)) (/ k 2)) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ 1 2))))
* [exit]simplify:  Simplified to (/ (* (pow (* PI (* n 2)) (/ k 2)) (sqrt k)) (sqrt (pow (* PI (* n 2)) (/ 1 2))))
* * * * [misc]progress:  [ 141 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (pow n (/ k 2))) (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* PI 2) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* PI 2) (/ k 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* PI 2) (/ k 2)) (sqrt k)) (pow (* (* n 2) PI) (/ 1 2)))
* [exit]simplify:  Simplified to (/ (* (pow (* PI 2) (/ k 2)) (sqrt k)) (pow (* (* n 2) PI) (/ 1 2)))
* * * * [misc]progress:  [ 142 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* PI (* n 2)) (/ 1 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* PI (* n 2)) (/ 1 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 143 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* PI (* n 2)) (/ 1 2))) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* PI (* n 2)) (/ 1 2))) (sqrt (pow (* PI (* n 2)) (/ k 2))))
* * * * [misc]progress:  [ 144 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (/ 1 1) (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2)))
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2)))
* * * * [misc]progress:  [ 145 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2)))
* [exit]simplify:  Simplified to (* (/ (sqrt k) (pow (* (* n 2) PI) (/ 1 2))) (pow (* (* n 2) PI) (/ k 2)))
* * * * [misc]progress:  [ 146 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (/ (sqrt k) (/ 1 (pow (* n (* PI 2)) (/ k 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (/ 1 (pow (* n (* PI 2)) (/ k 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* * [misc]simplify:  iters left: 2 (43 enodes)
* * [misc]simplify:  iters left: 1 (48 enodes)
* [exit]simplify:  Simplified to (* (pow (* 2 (* n PI)) (/ k 2)) (sqrt k))
* [exit]simplify:  Simplified to (* (pow (* 2 (* n PI)) (/ k 2)) (sqrt k))
* * * * [misc]progress:  [ 147 / 159 ] simplifiying candidate #<alt-delta (λ (k n) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))>
* [enter]simplify:  Simplifying (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))
* [exit]simplify:  Simplified to (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))
* * * * [misc]progress:  [ 148 / 159 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (66 enodes)
* * [misc]simplify:  iters left: 3 (119 enodes)
* * [misc]simplify:  iters left: 2 (196 enodes)
* * [misc]simplify:  iters left: 1 (309 enodes)
* [exit]simplify:  Simplified to (/ (* (sqrt (* PI 2)) (/ (sqrt n) (sqrt k))) (pow (* n (* PI 2)) (/ k 2)))
* * * * [misc]progress:  [ 149 / 159 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (20 enodes)
* * [misc]simplify:  iters left: 5 (39 enodes)
* * [misc]simplify:  iters left: 4 (64 enodes)
* * [misc]simplify:  iters left: 3 (112 enodes)
* * [misc]simplify:  iters left: 2 (241 enodes)
* [exit]simplify:  Simplified to (/ (* (sqrt (* PI 2)) (/ (sqrt n) (sqrt k))) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 150 / 159 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (21 enodes)
* * [misc]simplify:  iters left: 5 (39 enodes)
* * [misc]simplify:  iters left: 4 (64 enodes)
* * [misc]simplify:  iters left: 3 (114 enodes)
* * [misc]simplify:  iters left: 2 (276 enodes)
* [exit]simplify:  Simplified to (/ (/ (/ (sqrt (* PI -2)) (pow (/ -1 n) 1/2)) (sqrt k)) (pow (* 2 (* PI n)) (/ k 2)))
* * * * [misc]progress:  [ 151 / 159 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 152 / 159 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 153 / 159 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* 2 (* n PI)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 154 / 159 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 155 / 159 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 156 / 159 ] simplifiying candidate #<alt-event (λ (k n) (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (/ (/ (pow (* 2 (* n PI)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (33 enodes)
* [exit]simplify:  Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) (pow (* (* PI n) 2) (/ k 2)))
* * * * [misc]progress:  [ 157 / 159 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n)))))))))))))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n))))))))))))))))))))))))
* * * * [misc]progress:  [ 158 / 159 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* k (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 3) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n)))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* k (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 3) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))))))))
* * * * [misc]progress:  [ 159 / 159 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))))
* * * [misc]progress:  adding candidates to table
* * [misc]progress:  iteration 3 / 4
* * * [misc]progress:  picking best candidate
"ALT DATA: "{"picked-error":0.6274372218162472,"picked":"(λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))","all-alts":["#<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))>","#<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>","#<alt-delta (λ (k n) (/ (+ (* (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (* (* k k) 1/8)) (+ (* (log n) (log n)) (* (log (* PI 2)) (log (* PI 2))))) (- (fma (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4)) (* (log (* PI 2)) (* (* k k) (log n))) (* (pow (* PI 2) 1/2) (pow n 1/2))) (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/2)) (fma k (log (* PI 2)) (* (log n) k))))) (sqrt k)))>","#<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>","#<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))>","#<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>","#<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2)))))>","#<alt-event (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>","#<alt-delta (λ (k n) (/ (* (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k)))>","#<alt-delta (λ (k n) (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))>","#<alt-delta (λ (k n) (* (/ (* (cbrt (pow (* n (* 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) (* (* (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)))))>"],"best-fresh-alt-per-point":[[[5.091954821941639e-192,6.815392098658887e+143],1,0],[[1.9872779421557533e+180,1.8165707546862427e+45],0,0],[[7.416044817432175e-280,4.187534830574239e+90],2,0],[[8.952174144166139e-302,1.0956116997098222e-31],1,0],[[2.7602034085604025e+247,3.933007183466984e+176],0,0],[[4.691318136614946e-91,2.2211280072565116e-303],1,0],[[9.07067712653544e+121,1.1966070572230463e+134],0,0],[[2.534573079598786e+169,3.2634856808337097e+195],0,0],[[6.317640848359807e-38,7.108640458245273e-156],1,0],[[1.37963739668883e-251,1.9832537005473266e-262],1,0],[[2.2237477837114185e-204,3.5971048785615273e+27],6,0],[[2.0235103563137384e-245,3.186488674327569e-306],0,0],[[4.535662949534244e+218,1.0124765649019447e+298],0,0],[[3.548084498024942e-190,1.2458518796694574e+90],8,0],[[1.0707760413948923e-209,1.8155292668497655e+36],2,0],[[8.082647412227132e-211,1.4588918120519666e-114],3,0],[[5.13876683088187e-118,9.467488944393916e+142],5,0],[[2.2187340876406246e+300,4.0696348581298066e+30],0,0],[[4.737175196542416e-301,9.453454014910064e+271],2,0],[[1.090098977941039e-114,5.7243448441390635e+162],1,0],[[2.571403883587662e-39,2.725225610867578e+225],0,0],[[5.081095649164445e+286,2.6437596200790387e+281],0,0],[[6.85981085886286e-168,1.9805731700427848e-169],1,0],[[9.636536782052696e-111,2.985561979664205e+171],1,0],[[1.0838714812801137e-216,1.1791770071753556e+107],2,0],[[1.072386271012045e-235,9.15478951965041e+260],0,0],[[4.954601632348903e-272,5.651261930475929e+123],1,0],[[5.598692384845278e-151,2.0020470402494707e-128],7,0],[[3.828518244176968e-308,9.957124504840989e+307],4,1.0],[[7.811244882301027e-64,2.3660873791160076e+189],4,0],[[1.1253736853318525e-46,4.582462397892038e-300],1,0],[[2271813.2914643916,1.711246486837026e+16],0,0],[[2.6512646278212223e-277,2.991195561163922e+252],1,0],[[2.8722519575799174e-220,8.864398632472997e+128],1,0],[[6.898353156002884e+56,5.049169591478046e+301],0,0],[[5.795257109406676e+26,7.254471041027067e+34],0,0],[[1.9680527238636918e-165,6.602387235477923e-263],0,0],[[4.390126892195692e-258,5.153839259075024e-217],0,0],[[3.7270065251219893e-51,4.1091807334876805e+121],0,0],[[1.2718549924538793e-67,1.4997147168186959e-133],3,0],[[7.779411959735569e-290,2.9896016385939845e-66],1,0],[[2.8931224974199074e-84,1.9240432527476484e-289],6,0],[[1.6509703901493846e-82,1.0044867221158944e+300],6,0],[[7.040383581327078e-101,5.96146379570227e+197],0,0],[[1.607215854807525e-42,2.5297373356963796e-300],0,0],[[8.687912841852904e-95,5.412515287604772e-64],3,0],[[7.938025318271498e-112,7.539778260587032e+298],0,0],[[4.0890448857589815e-140,6.188431370265012e+93],1,0],[[1.808792063616234e-42,1.2249262287356375e+78],2,0],[[2.813778253825615e-191,3.478381051263039e+83],7,0],[[4.959269200917455e+89,2.713904493922986e+74],0,0],[[1.6527464762421886e-272,9.284612428163018e+257],5,0],[[2.694216768013651e-08,2.481730668881008e+205],2,0],[[1.105287263764627e+102,5.503874697732584e+83],0,0],[[3.616766753957493e-134,1.405468459858575e-82],0,0],[[3.4960229754986024e-44,4.978416266226015e-252],4,0],[[0.34727693217194866,5.903688889215572e+29],4,0],[[1.179890420337443e-05,1.2231257626976233e+37],0,1.0],[[3.985430525999154e-166,3.256025304820758e-99],0,0],[[2.9695246403166212e+172,1.0507438437361721e+109],0,0],[[7.823934036267622e-77,4.7561975058596834e-110],0,0],[[1.1032765895259676e-126,5.131532610213896e-61],0,0],[[2.572749544642796e-298,5.3648379001218185e+144],2,0],[[2.3744727510983187e-21,2.603715830745381e+94],7,0],[[4.041802722110561e+273,1.9237484678401125e+296],0,0],[[2.2344486550694127e+303,7.274885059224707e+101],0,0],[[2.3862496869231733e+76,4.3947035780108717e+80],0,0],[[5.7761035984398696e+196,4.71159629772397e+71],0,0],[[6.285466073933269e-22,3.4674975748042185e-38],0,0],[[7.733012551117168e-122,1.1382437559720419e-95],7,0],[[7.904830930452407e+266,3.6582181035579515e+271],0,0],[[2.305585729830853e-134,5.145630715071899e+201],1,0],[[8.206730771606587e+43,12242.925111988056],0,0],[[2.693652367216071e-233,2.6617051987770008e+262],0,0],[[3.3852972616768538e-282,1.6281541302987446e-101],9,0],[[4.023984950841538e-207,1.672209984146438e-177],1,0],[[5.997642554579093e+226,8267761121118583.0],0,0],[[3.025865987124205e+48,1.1774375942605503e+37],0,0],[[1.7578451228930594e-74,2.489149382420679e+27],7,0],[[3.938884622122182e-132,1.011396351900011e-125],0,0],[[9.807783778428908e+281,8.750108477874464e+259],0,0],[[1.0213927801883013e-280,2.4118761560252843e-59],7,0],[[1.195916640070373e-91,1.1745784325466232e+243],2,0],[[7.335711770377127e-38,1.214621771874996e+281],1,0],[[7.26354692283978e-298,6.697902311356943e+127],1,0],[[1.2351743153928947e-17,1.1081913151635317e-281],2,0],[[8.845830180604385e+55,4.68925600491289e+144],0,0],[[1.4639565733772952e-243,4.1910390611535265e+279],2,0],[[1.6983735818136165e-150,4.057563235251733e-168],1,0],[[1.5987895001152558e-250,1.0362772075683598e+99],1,0],[[2.574015514786201e-195,4.120748433400853e+266],1,0],[[2.828506773801223e-34,1.3980028593340099e-80],5,0],[[7.10451338618339e-112,2.752384728131671e-298],1,0],[[5.3848532123061334e+141,4.101841091919989e+82],0,0],[[1.8880422706568598e-131,6.087242169493258e-74],2,0],[[1.6828341140646555e-168,2.8288040637518216e+97],1,0],[[2.4020959302167836e+173,4.276010429020236e+247],0,0],[[1.679279614673279e-17,7.802007187654651e-08],1,0],[[6.190907314532847e-276,1.745791372849607e+234],5,0],[[5.911713422365171e-224,1.0773053002356648e-277],1,0],[[6.326943736711642e+259,2.02315867891966e+129],0,0],[[7.946583410099056e-261,2.144814527894872e+96],0,0],[[1.0066412328328968e-127,6.619416378892868e-163],4,0],[[1.1159565897451056e-40,9.147384059902005e+52],9,0],[[1.1165161433358629e+279,6.875662873883236e+254],0,0],[[7.053265896579982e-111,2.7551492956412816e-291],0,0],[[1.792618476145051e+142,3.258027489034141e+228],0,0],[[2.3780466739014797e+260,7.6303811992955545e+112],0,0],[[2.5226551585558244e+149,4.479310754223626e+77],0,0],[[6.3759232335206e-291,3.5785496756947083e-76],0,0],[[3.8797234898178104e-266,6.295638798327878e-124],2,0],[[6.621128712488456e-94,3.152253828409111e+30],4,0],[[3.5260516775312726e-162,4.379941188803635e-139],1,0],[[1.6672047786154368e+54,6.224498176564759e+252],0,0],[[6.79091067430158e+35,7.230059261043331e+195],0,0],[[4.3750470153682443e+216,8.334409599853035e+119],0,0],[[5.317028386962457e+95,1.5305424059226277e+248],0,0],[[6.409528319039091e+96,2.932037839848625e+137],0,0],[[8.883362223957793e+93,1.0708005705289017e+244],0,0],[[5.053806292662203e-155,2.523406045226158e-210],5,0],[[3.6380611743774316e+28,4.3451652399410245e+66],0,0],[[5.5111229904756633e-36,1.6975346890789871e+105],0,0],[[9.95962237767467e+23,1.044537127877944e+107],0,0],[[1.2032276449725793e-85,1.3054961346651174e-44],0,0],[[2.3075398048335097e-269,3.594097673489053e+137],1,0],[[3.130685264260855e-76,9.058189937007456e-86],1,0],[[4.53732938437198e+150,1.4669818938577088e+222],0,0],[[4.302212151190092e+240,2.4335687807904273e+271],0,0],[[6.550539660350184e-98,2.959467597264242e-230],1,0],[[2.052107344086851e-70,7.509188631026346e+286],5,0],[[2.2721511366771778e-250,4.0477581754304153e-125],0,0],[[4.931733655566518e-258,1.554975231016035e+153],5,0],[[3.4461749360980795e-185,7.6218106112626015e+295],1,0],[[1.3987141013277275e+91,6.132373723862702e+252],0,0],[[2.4801215181567776e-295,5.2115166535835604e-169],1,0],[[5.907165300326855e+32,1.9267899651560147e+275],0,0],[[7.475270857526654e-304,1.0862105938569748e+148],2,0],[[4.380578158292964e+195,3.0321252530234052e+38],0,0],[[2.4655809623086505e-116,1.1536689796869952e-11],6,0],[[8.444294654343975e-240,3.513520042407809e+153],3,0],[[3.28610894527258e-300,3.973558968153068e+125],0,0],[[2.5394112430978073e-295,1.4298675637930828e+180],1,0],[[8.332917955185835e+296,6.741628989608122e+71],0,0],[[1.6232174805713086e+70,3.765990859086882e+52],0,0],[[9.373092063300388e+294,2.8072978291071996e+105],0,0],[[8.752592959491946e-33,2.9311591750368227e+22],6,0],[[3.0241599246809088e+252,3.184319790336394e+219],0,0],[[1.0760470830369276e-175,3.1675280578479312e-77],1,0],[[9.685450907847438e-63,1.537477220142015e-154],6,0],[[1.4316271455151301e-258,2.996770630299676e+274],0,0],[[1.6611161145230723e-191,714914460440.7544],4,0],[[9.206946233985896e+265,5.909438823195212e+35],0,0],[[4.3407560983206045e+110,1.0066329381452874e+195],0,0],[[2.300114102133609e+63,3.3520036437628364e+162],0,0],[[3.7952930805105457e-199,7.532023979359606e+99],9,0],[[7.921938015189254e-17,1.6708793826459247e-57],0,0],[[1023.2212474515807,2.9921045438694274e+227],0,0],[[0.0009065963481940791,3.905734270420228e+62],0,0],[[1.891116192597785e-215,6.110124011150757e+46],1,0],[[8.602881405868794e-32,4.340706048852671e-131],0,0],[[2.098983450835455e-256,7.299124485355855e+137],3,0],[[1.2757681535951056e+63,3.8712901591408457e+228],0,0],[[7.968357209160169e+93,6.567762824642581e+50],0,0],[[4.548601565249598e+188,2.083390534713302e+140],0,0],[[4.161272910469861e-301,4.4146411652973813e+21],4,0],[[6.4821321459802055e+193,1.7939351909740315e+68],0,0],[[2.7868826984034328e-297,6.274746106885988e-177],7,0],[[7.586534919343994e-75,1.6802148352573582e-128],1,0],[[9.491422824807354e-253,4.0739010895320517e+273],0,0],[[2.2415352671784828e-150,1.625167989850363e+119],1,0],[[7.01138751262021e-280,1.4841539461233504e+69],5,0],[[2.824709004194289e-77,3.4428899655780295e-69],6,0],[[1.1294315636198499e-278,5.86009335903585e-102],0,0],[[7.990408500607478e+225,7.43139844967742e+271],0,0],[[2.6148734958275445e-59,1.4522191998681414e+95],2,0],[[2.1746518322952078e-54,2.8875549970579304e+175],0,0],[[3.1487113596301893e-35,2.0573785747587795e-193],5,0],[[2.790368131936616e-145,6.479697484604152e-174],1,0],[[1.220285592766294e+307,3.861133926570598e+263],0,0],[[1.2654603057808926e-132,5.480340484157898e-137],1,0],[[3.9582185084442164e+58,1.0006915947365432e+290],0,0],[[2.2385341061737422e-125,1.1296035831317978e+178],0,0],[[1.9956859819988883e+208,1.3053442887826894e+292],0,0],[[1.3725216771543658e-17,7.122506379956216e-199],3,0],[[5.070205966511977e-66,2.1591257954674133e-112],0,0],[[1.9637167511580492e-290,4.1122590034758076e+161],6,0],[[6.289641429573477e-53,4.44964744501718e-303],10,0],[[4.921669299348463e+48,9.174188702008102e+144],0,0],[[1.0631632090197916e+200,5.699753770483561e+65],0,0],[[3.7304700864524026e-88,7.425542676714504e-84],2,0],[[4.592687610132483e+74,5.15900678827599e+24],0,0],[[3.2643753621921254e-59,9.955169418668015e-289],0,0],[[1.8079468232084944e-292,4.570078655862018e+54],3,0],[[11359488250023.906,1.6061320544606304e+202],0,0],[[1.3892861350443015e-223,4.641071766140853e-231],1,0],[[7.360110913281388e-12,2.8431063873980092e+116],6,0],[[4.0565095880949425e+280,6.675799068433044e+76],0,0],[[9.20664563196908e+294,1.3131400831400088e+86],0,0],[[1.0649783843865697e-107,2.193063794905827e+36],0,0],[[1.1535731528175885e-293,16122199543.85404],9,0],[[0.23158759667032142,2.174373890634123e+206],0,1.0],[[2.8576099148948687e+47,4.535106259884878e+127],0,0],[[4.76442930878223e-20,1.662443875692076e+190],0,0],[[1.7386181741597865e-117,2.2869715061523446e+282],0,0],[[1.8576198723851754e+267,1.4640464205690061e+181],0,0],[[1.0730971371295596e-35,1.3731090395442879e-244],0,0],[[5.8750151697224545e-09,3.2058797502881587e-47],2,0],[[6.606104192306025e-76,2.1980904706831728e-104],6,0],[[1.1320100213914422e-197,9.218931403807496e-238],2,0],[[1.371076068469597e-276,3.7292018910669483e+61],0,0],[[7.468254766320453e-225,5.794033588679369e+140],1,0],[[3.2896013204457148e-279,1.1190715118628351e-13],4,0],[[1.855739410010682e-286,1.2449977298699466e-295],0,0],[[8.63596361370883e-168,3.1003420231048053e-198],0,0],[[1.4390244358772018e+249,2.9639589969742274e+281],0,0],[[2.0583492621633517e-132,1.73356572916747e+144],2,0],[[1.6662800714135864e-218,3.017825861340067e+260],1,0],[[1.7909913857676524e-234,4.184907550158769e-217],0,0],[[5.556148241691299e-119,1.5213816359492715e-307],0,0],[[3.486470059469502e+53,1.4785130640238136e+99],0,0],[[4.750171216619508e-73,1.0938841522691449e-182],10,0],[[9.94673708940353e+255,6.918320731214305e+101],0,0],[[5.706158108157338e+305,1.2638234743036793e+156],0,0],[[2.427769796556236e-78,7.21762410022307e+205],0,0],[[2.727021877346581e-178,1.860064553198903e-67],0,0],[[8.657759546694974e-157,2.0568784750151953e+96],0,0],[[1.0675856537644375e+279,5.0108195646214185e+182],0,0],[[2.412016495848343e-259,2.1622905926715047e-231],0,0],[[1.4157269095091182e+175,1.752320881957983e+240],0,0],[[7.474117465579979e+250,1.998141361266681e+100],0,0],[[1.542984322219514e-13,3.0489294036502483e-215],3,0],[[1.095382951219098e-121,4.4403690793251364e-66],1,1.0],[[3.0292511751059167e-285,4.774911884404591e+104],8,0],[[7366.597199336127,3.437966658215048e+175],0,0],[[1.013327533564468e-142,1.0958904515570749e+229],1,0],[[5.365396337730866e+62,5.564528795268944e+304],0,0],[[2.2999903268614278e-290,1.0741122062961354e-261],1,0],[[5.859557539322906e-140,12468368041124.15],1,0],[[3.29750078510446e+71,1.1536796494388956e+294],0,0],[[1.0050966216294641e+208,3094188499901330.5],0,0],[[2.486240422123665e+301,6.411662743035886e+150],0,0],[[1.1448971434422485e-274,1.3291916155898896e-54],0,0],[[5.99451935698111e-22,2.459533652847606e+166],1,0],[[5.471344172015073e-66,2.5497871706438334e+172],5,0],[[1.929136835934461e+126,1.4511860769870938e+51],0,0],[[1.6848563310412775e-81,1.8787633523770844e+304],1,0],[[2.9246728990313427e+289,4.038893686579631e+19],0,0],[[7.229157843683878e+19,7.0767085636431225e+53],0,0],[[1.5968409688876136e+240,1.6442404219839566e+41],0,0],[[1.2356592442417317e-130,2.7522555769102684e-277],1,0],[[2.0679460963453592e-53,3.5340357590538254e+140],8,0],[[1.0662100247031813e-43,2.521296463327911e+268],4,0],[[1.2229817874252346e-71,8.506337374180222e-99],0,0],[[2.3910560608115626e-11,2.932647945759088e-270],2,0],[[9.315042055884043e+48,4.0024068424625754e+43],0,0],[[1.43710899076724e+182,2.2997526865909637e+146],0,0]],"best-alt-per-point":[[[5.091954821941639e-192,6.815392098658887e+143],1,0],[[1.9872779421557533e+180,1.8165707546862427e+45],0,0],[[7.416044817432175e-280,4.187534830574239e+90],2,0],[[8.952174144166139e-302,1.0956116997098222e-31],1,0],[[2.7602034085604025e+247,3.933007183466984e+176],0,0],[[4.691318136614946e-91,2.2211280072565116e-303],1,0],[[9.07067712653544e+121,1.1966070572230463e+134],0,0],[[2.534573079598786e+169,3.2634856808337097e+195],0,0],[[6.317640848359807e-38,7.108640458245273e-156],1,0],[[1.37963739668883e-251,1.9832537005473266e-262],1,0],[[2.2237477837114185e-204,3.5971048785615273e+27],7,0],[[2.0235103563137384e-245,3.186488674327569e-306],0,0],[[4.535662949534244e+218,1.0124765649019447e+298],0,0],[[3.548084498024942e-190,1.2458518796694574e+90],9,0],[[1.0707760413948923e-209,1.8155292668497655e+36],2,0],[[8.082647412227132e-211,1.4588918120519666e-114],4,0],[[5.13876683088187e-118,9.467488944393916e+142],6,0],[[2.2187340876406246e+300,4.0696348581298066e+30],0,0],[[4.737175196542416e-301,9.453454014910064e+271],2,0],[[1.090098977941039e-114,5.7243448441390635e+162],1,0],[[2.571403883587662e-39,2.725225610867578e+225],0,0],[[5.081095649164445e+286,2.6437596200790387e+281],0,0],[[6.85981085886286e-168,1.9805731700427848e-169],1,0],[[9.636536782052696e-111,2.985561979664205e+171],1,0],[[1.0838714812801137e-216,1.1791770071753556e+107],2,0],[[1.072386271012045e-235,9.15478951965041e+260],0,0],[[4.954601632348903e-272,5.651261930475929e+123],1,0],[[5.598692384845278e-151,2.0020470402494707e-128],8,0],[[3.828518244176968e-308,9.957124504840989e+307],5,1.0],[[7.811244882301027e-64,2.3660873791160076e+189],3,0],[[1.1253736853318525e-46,4.582462397892038e-300],1,0],[[2271813.2914643916,1.711246486837026e+16],0,0],[[2.6512646278212223e-277,2.991195561163922e+252],1,0],[[2.8722519575799174e-220,8.864398632472997e+128],1,0],[[6.898353156002884e+56,5.049169591478046e+301],0,0],[[5.795257109406676e+26,7.254471041027067e+34],0,0],[[1.9680527238636918e-165,6.602387235477923e-263],0,0],[[4.390126892195692e-258,5.153839259075024e-217],0,0],[[3.7270065251219893e-51,4.1091807334876805e+121],0,0],[[1.2718549924538793e-67,1.4997147168186959e-133],3,0],[[7.779411959735569e-290,2.9896016385939845e-66],1,0],[[2.8931224974199074e-84,1.9240432527476484e-289],7,0],[[1.6509703901493846e-82,1.0044867221158944e+300],7,0],[[7.040383581327078e-101,5.96146379570227e+197],0,0],[[1.607215854807525e-42,2.5297373356963796e-300],0,0],[[8.687912841852904e-95,5.412515287604772e-64],3,0],[[7.938025318271498e-112,7.539778260587032e+298],0,0],[[4.0890448857589815e-140,6.188431370265012e+93],1,0],[[1.808792063616234e-42,1.2249262287356375e+78],2,0],[[2.813778253825615e-191,3.478381051263039e+83],8,0],[[4.959269200917455e+89,2.713904493922986e+74],0,0],[[1.6527464762421886e-272,9.284612428163018e+257],6,0],[[2.694216768013651e-08,2.481730668881008e+205],2,0],[[1.105287263764627e+102,5.503874697732584e+83],0,0],[[3.616766753957493e-134,1.405468459858575e-82],0,0],[[3.4960229754986024e-44,4.978416266226015e-252],3,0],[[0.34727693217194866,5.903688889215572e+29],3,0],[[1.179890420337443e-05,1.2231257626976233e+37],3,0],[[3.985430525999154e-166,3.256025304820758e-99],0,0],[[2.9695246403166212e+172,1.0507438437361721e+109],0,0],[[7.823934036267622e-77,4.7561975058596834e-110],0,0],[[1.1032765895259676e-126,5.131532610213896e-61],0,0],[[2.572749544642796e-298,5.3648379001218185e+144],2,0],[[2.3744727510983187e-21,2.603715830745381e+94],8,0],[[4.041802722110561e+273,1.9237484678401125e+296],0,0],[[2.2344486550694127e+303,7.274885059224707e+101],0,0],[[2.3862496869231733e+76,4.3947035780108717e+80],0,0],[[5.7761035984398696e+196,4.71159629772397e+71],0,0],[[6.285466073933269e-22,3.4674975748042185e-38],0,0],[[7.733012551117168e-122,1.1382437559720419e-95],8,0],[[7.904830930452407e+266,3.6582181035579515e+271],0,0],[[2.305585729830853e-134,5.145630715071899e+201],1,0],[[8.206730771606587e+43,12242.925111988056],0,0],[[2.693652367216071e-233,2.6617051987770008e+262],0,0],[[3.3852972616768538e-282,1.6281541302987446e-101],10,0],[[4.023984950841538e-207,1.672209984146438e-177],1,0],[[5.997642554579093e+226,8267761121118583.0],0,0],[[3.025865987124205e+48,1.1774375942605503e+37],0,0],[[1.7578451228930594e-74,2.489149382420679e+27],8,0],[[3.938884622122182e-132,1.011396351900011e-125],0,0],[[9.807783778428908e+281,8.750108477874464e+259],0,0],[[1.0213927801883013e-280,2.4118761560252843e-59],8,0],[[1.195916640070373e-91,1.1745784325466232e+243],2,0],[[7.335711770377127e-38,1.214621771874996e+281],1,0],[[7.26354692283978e-298,6.697902311356943e+127],1,0],[[1.2351743153928947e-17,1.1081913151635317e-281],2,0],[[8.845830180604385e+55,4.68925600491289e+144],0,0],[[1.4639565733772952e-243,4.1910390611535265e+279],2,0],[[1.6983735818136165e-150,4.057563235251733e-168],1,0],[[1.5987895001152558e-250,1.0362772075683598e+99],1,0],[[2.574015514786201e-195,4.120748433400853e+266],1,0],[[2.828506773801223e-34,1.3980028593340099e-80],3,0],[[7.10451338618339e-112,2.752384728131671e-298],1,0],[[5.3848532123061334e+141,4.101841091919989e+82],0,0],[[1.8880422706568598e-131,6.087242169493258e-74],2,0],[[1.6828341140646555e-168,2.8288040637518216e+97],1,0],[[2.4020959302167836e+173,4.276010429020236e+247],0,0],[[1.679279614673279e-17,7.802007187654651e-08],1,0],[[6.190907314532847e-276,1.745791372849607e+234],3,0],[[5.911713422365171e-224,1.0773053002356648e-277],1,0],[[6.326943736711642e+259,2.02315867891966e+129],0,0],[[7.946583410099056e-261,2.144814527894872e+96],0,0],[[1.0066412328328968e-127,6.619416378892868e-163],3,0],[[1.1159565897451056e-40,9.147384059902005e+52],10,0],[[1.1165161433358629e+279,6.875662873883236e+254],0,0],[[7.053265896579982e-111,2.7551492956412816e-291],0,0],[[1.792618476145051e+142,3.258027489034141e+228],0,0],[[2.3780466739014797e+260,7.6303811992955545e+112],0,0],[[2.5226551585558244e+149,4.479310754223626e+77],0,0],[[6.3759232335206e-291,3.5785496756947083e-76],0,0],[[3.8797234898178104e-266,6.295638798327878e-124],2,0],[[6.621128712488456e-94,3.152253828409111e+30],5,0],[[3.5260516775312726e-162,4.379941188803635e-139],1,0],[[1.6672047786154368e+54,6.224498176564759e+252],0,0],[[6.79091067430158e+35,7.230059261043331e+195],0,0],[[4.3750470153682443e+216,8.334409599853035e+119],0,0],[[5.317028386962457e+95,1.5305424059226277e+248],0,0],[[6.409528319039091e+96,2.932037839848625e+137],0,0],[[8.883362223957793e+93,1.0708005705289017e+244],0,0],[[5.053806292662203e-155,2.523406045226158e-210],6,0],[[3.6380611743774316e+28,4.3451652399410245e+66],0,0],[[5.5111229904756633e-36,1.6975346890789871e+105],0,0],[[9.95962237767467e+23,1.044537127877944e+107],0,0],[[1.2032276449725793e-85,1.3054961346651174e-44],0,0],[[2.3075398048335097e-269,3.594097673489053e+137],1,0],[[3.130685264260855e-76,9.058189937007456e-86],1,0],[[4.53732938437198e+150,1.4669818938577088e+222],0,0],[[4.302212151190092e+240,2.4335687807904273e+271],0,0],[[6.550539660350184e-98,2.959467597264242e-230],1,0],[[2.052107344086851e-70,7.509188631026346e+286],6,0],[[2.2721511366771778e-250,4.0477581754304153e-125],0,0],[[4.931733655566518e-258,1.554975231016035e+153],3,0],[[3.4461749360980795e-185,7.6218106112626015e+295],1,0],[[1.3987141013277275e+91,6.132373723862702e+252],0,0],[[2.4801215181567776e-295,5.2115166535835604e-169],1,0],[[5.907165300326855e+32,1.9267899651560147e+275],0,0],[[7.475270857526654e-304,1.0862105938569748e+148],2,0],[[4.380578158292964e+195,3.0321252530234052e+38],0,0],[[2.4655809623086505e-116,1.1536689796869952e-11],7,0],[[8.444294654343975e-240,3.513520042407809e+153],4,0],[[3.28610894527258e-300,3.973558968153068e+125],0,0],[[2.5394112430978073e-295,1.4298675637930828e+180],1,0],[[8.332917955185835e+296,6.741628989608122e+71],0,0],[[1.6232174805713086e+70,3.765990859086882e+52],0,0],[[9.373092063300388e+294,2.8072978291071996e+105],0,0],[[8.752592959491946e-33,2.9311591750368227e+22],7,0],[[3.0241599246809088e+252,3.184319790336394e+219],0,0],[[1.0760470830369276e-175,3.1675280578479312e-77],1,0],[[9.685450907847438e-63,1.537477220142015e-154],3,0],[[1.4316271455151301e-258,2.996770630299676e+274],0,0],[[1.6611161145230723e-191,714914460440.7544],5,0],[[9.206946233985896e+265,5.909438823195212e+35],0,0],[[4.3407560983206045e+110,1.0066329381452874e+195],0,0],[[2.300114102133609e+63,3.3520036437628364e+162],0,0],[[3.7952930805105457e-199,7.532023979359606e+99],10,0],[[7.921938015189254e-17,1.6708793826459247e-57],0,0],[[1023.2212474515807,2.9921045438694274e+227],0,0],[[0.0009065963481940791,3.905734270420228e+62],0,0],[[1.891116192597785e-215,6.110124011150757e+46],1,0],[[8.602881405868794e-32,4.340706048852671e-131],0,0],[[2.098983450835455e-256,7.299124485355855e+137],4,0],[[1.2757681535951056e+63,3.8712901591408457e+228],0,0],[[7.968357209160169e+93,6.567762824642581e+50],0,0],[[4.548601565249598e+188,2.083390534713302e+140],0,0],[[4.161272910469861e-301,4.4146411652973813e+21],3,0],[[6.4821321459802055e+193,1.7939351909740315e+68],0,0],[[2.7868826984034328e-297,6.274746106885988e-177],8,0],[[7.586534919343994e-75,1.6802148352573582e-128],1,0],[[9.491422824807354e-253,4.0739010895320517e+273],0,0],[[2.2415352671784828e-150,1.625167989850363e+119],1,0],[[7.01138751262021e-280,1.4841539461233504e+69],6,0],[[2.824709004194289e-77,3.4428899655780295e-69],7,0],[[1.1294315636198499e-278,5.86009335903585e-102],0,0],[[7.990408500607478e+225,7.43139844967742e+271],0,0],[[2.6148734958275445e-59,1.4522191998681414e+95],2,0],[[2.1746518322952078e-54,2.8875549970579304e+175],0,0],[[3.1487113596301893e-35,2.0573785747587795e-193],6,0],[[2.790368131936616e-145,6.479697484604152e-174],1,0],[[1.220285592766294e+307,3.861133926570598e+263],0,0],[[1.2654603057808926e-132,5.480340484157898e-137],1,0],[[3.9582185084442164e+58,1.0006915947365432e+290],0,0],[[2.2385341061737422e-125,1.1296035831317978e+178],0,0],[[1.9956859819988883e+208,1.3053442887826894e+292],0,0],[[1.3725216771543658e-17,7.122506379956216e-199],4,0],[[5.070205966511977e-66,2.1591257954674133e-112],0,0],[[1.9637167511580492e-290,4.1122590034758076e+161],3,0],[[6.289641429573477e-53,4.44964744501718e-303],11,0],[[4.921669299348463e+48,9.174188702008102e+144],0,0],[[1.0631632090197916e+200,5.699753770483561e+65],0,0],[[3.7304700864524026e-88,7.425542676714504e-84],2,0],[[4.592687610132483e+74,5.15900678827599e+24],0,0],[[3.2643753621921254e-59,9.955169418668015e-289],0,0],[[1.8079468232084944e-292,4.570078655862018e+54],3,0],[[11359488250023.906,1.6061320544606304e+202],0,0],[[1.3892861350443015e-223,4.641071766140853e-231],1,0],[[7.360110913281388e-12,2.8431063873980092e+116],7,0],[[4.0565095880949425e+280,6.675799068433044e+76],0,0],[[9.20664563196908e+294,1.3131400831400088e+86],0,0],[[1.0649783843865697e-107,2.193063794905827e+36],0,0],[[1.1535731528175885e-293,16122199543.85404],10,0],[[0.23158759667032142,2.174373890634123e+206],3,0],[[2.8576099148948687e+47,4.535106259884878e+127],0,0],[[4.76442930878223e-20,1.662443875692076e+190],0,0],[[1.7386181741597865e-117,2.2869715061523446e+282],0,0],[[1.8576198723851754e+267,1.4640464205690061e+181],0,0],[[1.0730971371295596e-35,1.3731090395442879e-244],0,0],[[5.8750151697224545e-09,3.2058797502881587e-47],2,0],[[6.606104192306025e-76,2.1980904706831728e-104],7,0],[[1.1320100213914422e-197,9.218931403807496e-238],2,0],[[1.371076068469597e-276,3.7292018910669483e+61],0,0],[[7.468254766320453e-225,5.794033588679369e+140],1,0],[[3.2896013204457148e-279,1.1190715118628351e-13],5,0],[[1.855739410010682e-286,1.2449977298699466e-295],0,0],[[8.63596361370883e-168,3.1003420231048053e-198],0,0],[[1.4390244358772018e+249,2.9639589969742274e+281],0,0],[[2.0583492621633517e-132,1.73356572916747e+144],2,0],[[1.6662800714135864e-218,3.017825861340067e+260],1,0],[[1.7909913857676524e-234,4.184907550158769e-217],0,0],[[5.556148241691299e-119,1.5213816359492715e-307],0,0],[[3.486470059469502e+53,1.4785130640238136e+99],0,0],[[4.750171216619508e-73,1.0938841522691449e-182],11,0],[[9.94673708940353e+255,6.918320731214305e+101],0,0],[[5.706158108157338e+305,1.2638234743036793e+156],0,0],[[2.427769796556236e-78,7.21762410022307e+205],0,0],[[2.727021877346581e-178,1.860064553198903e-67],0,0],[[8.657759546694974e-157,2.0568784750151953e+96],0,0],[[1.0675856537644375e+279,5.0108195646214185e+182],0,0],[[2.412016495848343e-259,2.1622905926715047e-231],0,0],[[1.4157269095091182e+175,1.752320881957983e+240],0,0],[[7.474117465579979e+250,1.998141361266681e+100],0,0],[[1.542984322219514e-13,3.0489294036502483e-215],3,0],[[1.095382951219098e-121,4.4403690793251364e-66],1,1.0],[[3.0292511751059167e-285,4.774911884404591e+104],9,0],[[7366.597199336127,3.437966658215048e+175],0,0],[[1.013327533564468e-142,1.0958904515570749e+229],1,0],[[5.365396337730866e+62,5.564528795268944e+304],0,0],[[2.2999903268614278e-290,1.0741122062961354e-261],1,0],[[5.859557539322906e-140,12468368041124.15],1,0],[[3.29750078510446e+71,1.1536796494388956e+294],0,0],[[1.0050966216294641e+208,3094188499901330.5],0,0],[[2.486240422123665e+301,6.411662743035886e+150],0,0],[[1.1448971434422485e-274,1.3291916155898896e-54],0,0],[[5.99451935698111e-22,2.459533652847606e+166],1,0],[[5.471344172015073e-66,2.5497871706438334e+172],3,0],[[1.929136835934461e+126,1.4511860769870938e+51],0,0],[[1.6848563310412775e-81,1.8787633523770844e+304],1,0],[[2.9246728990313427e+289,4.038893686579631e+19],0,0],[[7.229157843683878e+19,7.0767085636431225e+53],0,0],[[1.5968409688876136e+240,1.6442404219839566e+41],0,0],[[1.2356592442417317e-130,2.7522555769102684e-277],1,0],[[2.0679460963453592e-53,3.5340357590538254e+140],9,0],[[1.0662100247031813e-43,2.521296463327911e+268],5,0],[[1.2229817874252346e-71,8.506337374180222e-99],0,0],[[2.3910560608115626e-11,2.932647945759088e-270],2,0],[[9.315042055884043e+48,4.0024068424625754e+43],0,0],[[1.43710899076724e+182,2.2997526865909637e+146],0,0]],"fresh-alts":["#<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))>","#<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>","#<alt-delta (λ (k n) (/ (+ (* (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (* (* k k) 1/8)) (+ (* (log n) (log n)) (* (log (* PI 2)) (log (* PI 2))))) (- (fma (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4)) (* (log (* PI 2)) (* (* k k) (log n))) (* (pow (* PI 2) 1/2) (pow n 1/2))) (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/2)) (fma k (log (* PI 2)) (* (log n) k))))) (sqrt k)))>","#<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))>","#<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>","#<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2)))))>","#<alt-event (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>","#<alt-delta (λ (k n) (/ (* (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k)))>","#<alt-delta (λ (k n) (/ (pow (* (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2)))) (/ (- 1 k) 2)) (sqrt k)))>","#<alt-delta (λ (k n) (* (/ (* (cbrt (pow (* n (* 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) (* (* (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)))))>"]}* * * * [misc]pick:  Picked  #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 4 ] rewriting at (2 2 1)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2 2)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2 1)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 4 ] generating series at (2 2 1)
* [misc]approximate:  Taking taylor expansion of (pow (* PI 2) (/ (- 1 k) 2)) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* PI 2) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 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 (* PI 2)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2)
* [misc]taylor:  Taking taylor expansion of (pow (* PI 2) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 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 (* PI 2)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2)
* [misc]backup-simplify:  Simplify (pow (* 2 PI) 1/2) into (pow (* 2 PI) 1/2)
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 1) 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 PI)))) into (- (* 1/2 (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* 2 PI)) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (* -1/2 (* (sqrt (* 2 PI)) (log (* 2 PI)))) into (* -1/2 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 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 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* 2 PI)) (pow (log (* 2 PI)) 2)))
* [misc]backup-simplify:  Simplify (* 1/8 (* (sqrt (* 2 PI)) (pow (log (* 2 PI)) 2))) into (* 1/8 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (sqrt 2))))
* [misc]backup-simplify:  Simplify (+ (* (* 1/8 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (pow k 2)) (+ (* (* -1/2 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2)))) k) (pow (* 2 PI) 1/2))) into (- (+ (pow (* 2 PI) 1/2) (* 1/8 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (* (pow k 2) (sqrt 2)))))) (* 1/2 (* (sqrt PI) (* (log (* 2 PI)) (* k (sqrt 2))))))
* [misc]approximate:  Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 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 (* PI 2)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI 2)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 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 (* PI 2)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI 2)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))
* [misc]approximate:  Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 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 (* PI 2)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI 2)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 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 (* PI 2)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI 2)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))
* * * * [misc]progress:  [ 2 / 4 ] generating series at (2 2)
* [misc]approximate:  Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (pow (* PI 2) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 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 (* PI 2)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 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 PI) 1/2) +nan.0) into (* +nan.0 (sqrt (* 2 PI)))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (pow (* PI 2) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 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 (* PI 2)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 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 PI) 1/2) +nan.0) into (* +nan.0 (sqrt (* 2 PI)))
* [misc]backup-simplify:  Simplify (* +nan.0 (sqrt (* 2 PI))) into (* +nan.0 (* (sqrt PI) (sqrt 2)))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 1) 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 PI)))) into (- (* 1/2 (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* 2 PI)) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ (* -1/2 (* (sqrt (* 2 PI)) (log (* 2 PI)))) +nan.0) (+ (* (* +nan.0 (sqrt (* 2 PI))) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2)))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2))))))) into (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2)))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 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 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* 2 PI)) (pow (log (* 2 PI)) 2)))
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ (* 1/8 (* (sqrt (* 2 PI)) (pow (log (* 2 PI)) 2))) +nan.0) (+ (* (* +nan.0 (sqrt (* 2 PI))) (/ +nan.0 +nan.0)) (* (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2))))))) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2)))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2))))))))) into (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2)))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2))))))))) k) (+ (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2))))))) (* (* +nan.0 (* (sqrt PI) (sqrt 2))) (/ 1 k)))) into (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (+ (* +nan.0 (* (sqrt PI) (* k (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (* k (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt PI) (/ (sqrt 2) k))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (* k (sqrt 2))))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2)))))))))))))))
* [misc]approximate:  Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 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 (* PI 2)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI 2)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 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 (* PI 2)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI 2)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))
* [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)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))))) (pow (/ 1 k) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI))))))) (/ 1 k)) (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI)))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)))))))
* [misc]approximate:  Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 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 (* PI 2)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI 2)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking 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))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 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 (* PI 2)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI 2)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking 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))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 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)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (log (* 2 PI))))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (log (* 2 PI))))))) (/ 1 (- k))) (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (log (* 2 PI)))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)))))))
* * * * [misc]progress:  [ 3 / 4 ] generating series at (2)
* [misc]approximate:  Taking taylor expansion of (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) in k
* [misc]taylor:  Taking taylor expansion of (pow n (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 k) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (* 1/2 (log n)) into (* 1/2 (log n))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log n))) into (pow n 1/2)
* [misc]taylor:  Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (pow (* PI 2) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 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 (* PI 2)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 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 PI) 1/2) +nan.0) into (* +nan.0 (sqrt (* 2 PI)))
* [misc]taylor:  Taking taylor expansion of (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) in n
* [misc]taylor:  Taking taylor expansion of (pow n (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log n))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log n)) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (+ 1 (- k)) into (- 1 k)
* [misc]backup-simplify:  Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k))
* [misc]taylor:  Taking taylor expansion of (log n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (log 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) 0) into (log n)
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (log n)) into (* 1/2 (* (- 1 k) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 k) (log n)))) into (exp (* 1/2 (* (- 1 k) (log n))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (pow (* PI 2) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 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 (* PI 2)) in n
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (log (* 2 PI))) into (* 1/2 (* (- 1 k) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt k)) into (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) in n
* [misc]taylor:  Taking taylor expansion of (pow n (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log n))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log n)) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (+ 1 (- k)) into (- 1 k)
* [misc]backup-simplify:  Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k))
* [misc]taylor:  Taking taylor expansion of (log n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (log 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) 0) into (log n)
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (log n)) into (* 1/2 (* (- 1 k) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 k) (log n)))) into (exp (* 1/2 (* (- 1 k) (log n))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (pow (* PI 2) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* 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 (* PI 2)) in n
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (log (* 2 PI))) into (* 1/2 (* (- 1 k) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt k)) into (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt (/ 1 k)))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt (/ 1 k)))) into (* (* (exp (* 1/2 (* (- 1 k) (log n)))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (sqrt (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (* (* (exp (* 1/2 (* (- 1 k) (log n)))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (* (exp (* 1/2 (* (- 1 k) (log n)))) (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 k) (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 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 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 (* 1 (log n)) into (log n)
* [misc]backup-simplify:  Simplify (* 1/2 (log n)) into (* 1/2 (log n))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log n))) into (pow n 1/2)
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 k) (log (* 2 PI)))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (- 1 k) (log (* 2 PI))) in k
* [misc]taylor:  Taking taylor expansion of (- 1 k) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (* 1 (log (* 2 PI))) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2)
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (* (pow n 1/2) (pow (* 2 PI) 1/2)) into (sqrt (* n (* 2 PI)))
* [misc]backup-simplify:  Simplify (* (sqrt (* n (* 2 PI))) 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 (/ (* (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 (+ (* (* 1/2 (- 1 k)) 0) (* 0 (log (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt (/ 1 k))) (/ 0 (sqrt k))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) 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)) 0) into (log n)
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (log n))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (- 1 k) (log n)))) 0) (* 0 (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (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 (+ (* 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) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* -1 (log (* 2 PI)))) into (- (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (- (log (* 2 PI)))) (* 0 (log (* 2 PI)))) into (- (* 1/2 (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* 2 PI)) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* -1 (log n))) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (- (log n))) (* 0 (log n))) into (- (* 1/2 (log n)))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n)))
* [misc]backup-simplify:  Simplify (+ (* (pow n 1/2) (* -1/2 (* (sqrt (* 2 PI)) (log (* 2 PI))))) (* (* -1/2 (* (sqrt n) (log n))) (pow (* 2 PI) 1/2))) into (- (+ (* 1/2 (* (sqrt (* n PI)) (* (log (* 2 PI)) (sqrt 2)))) (* 1/2 (* (sqrt (* n PI)) (* (log n) (sqrt 2))))))
* [misc]backup-simplify:  Simplify (+ (* (sqrt (* n (* 2 PI))) +nan.0) (* (- (+ (* 1/2 (* (sqrt (* n PI)) (* (log (* 2 PI)) (sqrt 2)))) (* 1/2 (* (sqrt (* n PI)) (* (log n) (sqrt 2)))))) 0)) into (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))) into (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt (/ 1 k))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) 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)) 0) into (log n)
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (- 1 k) (log n)))) 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (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 (- (+ (* 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 (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (- (log (* 2 PI)))) (* 0 (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* 2 PI)) (pow (log (* 2 PI)) 2)))
* [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 0) (+ (* -1 0) (* 0 (log n)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (- (log n))) (* 0 (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2)))
* [misc]backup-simplify:  Simplify (+ (* (pow n 1/2) (* 1/8 (* (sqrt (* 2 PI)) (pow (log (* 2 PI)) 2)))) (+ (* (* -1/2 (* (sqrt n) (log n))) (* -1/2 (* (sqrt (* 2 PI)) (log (* 2 PI))))) (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (pow (* 2 PI) 1/2)))) into (+ (* 1/8 (* (sqrt (* n PI)) (* (pow (log n) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* (log n) (sqrt 2)))))))
* [misc]backup-simplify:  Simplify (+ (* (sqrt (* n (* 2 PI))) +nan.0) (+ (* (- (+ (* 1/2 (* (sqrt (* n PI)) (* (log (* 2 PI)) (sqrt 2)))) (* 1/2 (* (sqrt (* n PI)) (* (log n) (sqrt 2)))))) +nan.0) (* (+ (* 1/8 (* (sqrt (* n PI)) (* (pow (log n) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* (log n) (sqrt 2))))))) 0))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (sqrt 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (sqrt 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (sqrt 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt k)) (+ (* (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt (/ 1 k))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) 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)) 0) into (log n)
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (- 1 k) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (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 (- (+ (* 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 (- 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)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (log (* 2 PI)))) (* 0 (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* 2 PI)) (pow (log (* 2 PI)) 3)))
* [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 0) (+ (* -1 0) (+ (* 0 0) (* 0 (log n))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (log n))) (* 0 (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 3) 6)) (* (/ (pow (- (* 1/2 (log n))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt n) (pow (log n) 3)))
* [misc]backup-simplify:  Simplify (+ (* (pow n 1/2) (* -1/48 (* (sqrt (* 2 PI)) (pow (log (* 2 PI)) 3)))) (+ (* (* -1/2 (* (sqrt n) (log n))) (* 1/8 (* (sqrt (* 2 PI)) (pow (log (* 2 PI)) 2)))) (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (* -1/2 (* (sqrt (* 2 PI)) (log (* 2 PI))))) (* (* -1/48 (* (sqrt n) (pow (log n) 3))) (pow (* 2 PI) 1/2))))) into (- (+ (* 1/48 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 3) (sqrt 2)))) (+ (* 1/16 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* (pow (log n) 2) (sqrt 2))))) (+ (* 1/16 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 2) (* (log n) (sqrt 2))))) (* 1/48 (* (sqrt (* n PI)) (* (pow (log n) 3) (sqrt 2))))))))
* [misc]backup-simplify:  Simplify (+ (* (sqrt (* n (* 2 PI))) +nan.0) (+ (* (- (+ (* 1/2 (* (sqrt (* n PI)) (* (log (* 2 PI)) (sqrt 2)))) (* 1/2 (* (sqrt (* n PI)) (* (log n) (sqrt 2)))))) +nan.0) (+ (* (+ (* 1/8 (* (sqrt (* n PI)) (* (pow (log n) 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (* 1/4 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* (log n) (sqrt 2))))))) +nan.0) (* (- (+ (* 1/48 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 3) (sqrt 2)))) (+ (* 1/16 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* (pow (log n) 2) (sqrt 2))))) (+ (* 1/16 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 2) (* (log n) (sqrt 2))))) (* 1/48 (* (sqrt (* n PI)) (* (pow (log n) 3) (sqrt 2)))))))) 0)))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log n) 2) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* (log n) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (sqrt 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))))))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log n) 2) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* (log n) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (sqrt 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))))))))))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log n) 2) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* (log n) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (sqrt 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))))))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log n) 2) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 2) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* (log n) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (sqrt 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (sqrt 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))))) (* k 1)) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (* k (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 2) (* (pow k 2) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow k 2) (* (log n) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* (pow k 2) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* k (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* k (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow k 2) (* (pow (log n) 2) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow k 2) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (* (log (* 2 PI)) (* (pow k 2) (log n)))))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))))))))))))))))))))
* [misc]approximate:  Taking taylor expansion of (* (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) (/ (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (* (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) (/ (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (/ 1 n)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (/ 1 n) into (/ 1 n)
* [misc]backup-simplify:  Simplify (log (/ 1 n)) into (log (/ 1 n))
* [misc]backup-simplify:  Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n)))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 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 (* PI 2)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI 2)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))
* [misc]taylor:  Taking taylor expansion of (* (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) (/ (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (/ 1 n)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (log 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log n))) into (* -1/2 (* (- 1 (/ 1 k)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 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 (* PI 2)) in n
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) into (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
* [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))))) (sqrt (/ 1 k))) into (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))
* [misc]taylor:  Taking taylor expansion of (* (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) (/ (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (/ 1 n)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (log 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log n))) into (* -1/2 (* (- 1 (/ 1 k)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* 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 (* PI 2)) in n
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 PI))) into (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
* [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))))) (sqrt (/ 1 k))) into (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))) into (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))) (sqrt k))
* [misc]taylor:  Taking taylor expansion of (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))) (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 PI))) 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)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (* -1 (log (* 2 PI))) into (* -1 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (* -1 (log (* 2 PI)))) into (* -1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* -1/2 (* (- 1 (/ 1 k)) (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 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 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 (* -1 (log n)) into (* -1 (log n))
* [misc]backup-simplify:  Simplify (* -1/2 (* -1 (log n))) into (* 1/2 (log n))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (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))))) (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))) into (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))
* [misc]backup-simplify:  Simplify (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) 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 (/ (* (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 (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (log (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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)) 0) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (* 0 (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) 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))))) 0) (* 0 (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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)) 0) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (+ (* 0 0) (* 0 (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))))) 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))))) 0) (+ (* 0 0) (* 0 (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log (* 2 PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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)) 0) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))))) 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))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI)))))))) into (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 PI))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 (/ 1 k))) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 (/ 1 k))) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (* (exp (* -1/2 (* (- 1 (/ 1 (/ 1 k))) (log (/ 1 n))))) (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (log (* 2 PI)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* -1/2 (* (- 1 k) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* -1/2 (* (- 1 k) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* -1/2 (* (- 1 k) (log (/ 1 n)))))) (pow k 3))))))))
* [misc]approximate:  Taking taylor expansion of (* (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) (/ (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (* (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) (/ (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) in k
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- -1) into 1
* [misc]backup-simplify:  Simplify (+ 0 1) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (/ 1 (- n))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in k
* [misc]taylor:  Taking taylor expansion of (- n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (/ 1 (- n)) into (/ -1 n)
* [misc]backup-simplify:  Simplify (log (/ -1 n)) into (log (/ -1 n))
* [misc]backup-simplify:  Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (/ -1 n)))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI 2)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 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 (* PI 2)) in k
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI 2)))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking 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))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))
* [misc]taylor:  Taking taylor expansion of (* (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) (/ (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) in n
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ -1 k)) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (/ 1 (- n))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (log -1) into (log -1)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log -1) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n)))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 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 (* PI 2)) in n
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ 1 (/ 1 k))) (log (* 2 PI))) into (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))
* [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))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) (sqrt (/ -1 k)))
* [misc]taylor:  Taking taylor expansion of (* (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) (/ (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k))))) in n
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ -1 k)) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (/ 1 (- n))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (log -1) into (log -1)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log -1) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n)))))
* [misc]taylor:  Taking taylor expansion of (/ (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (pow (* PI 2) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* PI 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* 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 (* PI 2)) in n
* [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 (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ 1 (/ 1 k))) (log (* 2 PI))) into (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))
* [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))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) (sqrt (/ -1 k)))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) (sqrt (/ -1 k)))) into (/ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))) (sqrt (/ -1 k)))
* [misc]taylor:  Taking taylor expansion of (/ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))) (sqrt (/ -1 k))) in k
* [misc]taylor:  Taking taylor expansion of (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))) in k
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (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 -1) (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 -1) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log -1) in k
* [misc]taylor:  Taking taylor expansion of -1 in k
* [misc]backup-simplify:  Simplify -1 into -1
* [misc]backup-simplify:  Simplify (log -1) into (log -1)
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (+ 0 1) into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n))
* [misc]backup-simplify:  Simplify (* 1 (- (log -1) (log n))) into (- (log -1) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n)))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* 2 PI))) 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)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ 0 1) into 1
* [misc]backup-simplify:  Simplify (* 1 (log (* 2 PI))) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))
* [misc]taylor:  Taking taylor expansion of (sqrt (/ -1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ -1 k) in k
* [misc]taylor:  Taking taylor expansion of -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 -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))) into (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))
* [misc]backup-simplify:  Simplify (/ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))) +nan.0) into (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))) into (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (* 0 2)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (log (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 -1)) into (- (log -1) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log -1) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) 0) (* 0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) (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 -1) (log n))))) 0) (* 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))) 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 -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))))
* [misc]backup-simplify:  Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (log (* 2 PI))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 -1)) into (- (log -1) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) 0) (+ (* 0 0) (* 0 (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))) (sqrt (/ -1 k)))))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))))) 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 -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI)))))))) into (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* 2 PI))))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log -1) (log (/ 1 (- n))))))) (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (log (* 2 PI)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log -1) (log (/ 1 (- n))))))) (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (log (* 2 PI)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (* (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log -1) (log (/ 1 (- n))))))) (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n))))))) k)) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n))))))) (pow k 2))) (- (* +nan.0 (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))))))))))
* * * * [misc]progress:  [ 4 / 4 ] generating series at (2 1)
* [misc]approximate:  Taking taylor expansion of (pow n (/ (- 1 k) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow n (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 k) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (* 1/2 (log n)) into (* 1/2 (log n))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log n))) into (pow n 1/2)
* [misc]taylor:  Taking taylor expansion of (pow n (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log n))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log n)) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (+ 1 (- k)) into (- 1 k)
* [misc]backup-simplify:  Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k))
* [misc]taylor:  Taking taylor expansion of (log n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (log 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) 0) into (log n)
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (log n)) into (* 1/2 (* (- 1 k) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 k) (log n)))) into (exp (* 1/2 (* (- 1 k) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow n (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log n))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log n)) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (+ 1 (- k)) into (- 1 k)
* [misc]backup-simplify:  Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k))
* [misc]taylor:  Taking taylor expansion of (log n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (log 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) 0) into (log n)
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (log n)) into (* 1/2 (* (- 1 k) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 k) (log n)))) into (exp (* 1/2 (* (- 1 k) (log n))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 k) (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 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 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 (* 1 (log n)) into (log n)
* [misc]backup-simplify:  Simplify (* 1/2 (log n)) into (* 1/2 (log n))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log n))) into (pow n 1/2)
* [misc]backup-simplify:  Simplify (pow n 1/2) into (pow n 1/2)
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 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)) 0) into (log n)
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (log n))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* -1 (log n))) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (- (log n))) (* 0 (log n))) into (- (* 1/2 (log n)))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n)))
* [misc]backup-simplify:  Simplify (* -1/2 (* (sqrt n) (log n))) into (* -1/2 (* (sqrt n) (log n)))
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 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)) 0) into (log n)
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 k) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 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 0) (+ (* -1 0) (* 0 (log n)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (- (log n))) (* 0 (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2)))
* [misc]backup-simplify:  Simplify (* 1/8 (* (sqrt n) (pow (log n) 2))) into (* 1/8 (* (sqrt n) (pow (log n) 2)))
* [misc]backup-simplify:  Simplify (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (pow (* k 1) 2)) (+ (* (* -1/2 (* (sqrt n) (log n))) (* k 1)) (pow n 1/2))) into (- (+ (* 1/8 (* (sqrt n) (* (pow (log n) 2) (pow k 2)))) (pow n 1/2)) (* 1/2 (* (sqrt n) (* (log n) k))))
* [misc]approximate:  Taking taylor expansion of (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (/ 1 n)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (/ 1 n) into (/ 1 n)
* [misc]backup-simplify:  Simplify (log (/ 1 n)) into (log (/ 1 n))
* [misc]backup-simplify:  Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ 1 n)))))
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (/ 1 n)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (log 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log n))) into (* -1/2 (* (- 1 (/ 1 k)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 n) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (/ 1 n))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (/ 1 n)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (log 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log n))) into (* -1/2 (* (- 1 (/ 1 k)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
* [misc]taylor:  Taking taylor expansion of (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of (* -1/2 (* (- 1 (/ 1 k)) (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 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 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 (* -1 (log n)) into (* -1 (log n))
* [misc]backup-simplify:  Simplify (* -1/2 (* -1 (log n))) into (* 1/2 (log n))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) into (exp (* -1/2 (* (- 1 (/ 1 k)) (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 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)) 0) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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)) 0) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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)) 0) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* -1/2 (* (- 1 (/ 1 k)) (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 (/ 1 n))))) into (exp (* -1/2 (* (- 1 k) (log (/ 1 n)))))
* [misc]approximate:  Taking taylor expansion of (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- -1) into 1
* [misc]backup-simplify:  Simplify (+ 0 1) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (/ 1 (- n))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in k
* [misc]taylor:  Taking taylor expansion of (- n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (/ 1 (- n)) into (/ -1 n)
* [misc]backup-simplify:  Simplify (log (/ -1 n)) into (log (/ -1 n))
* [misc]backup-simplify:  Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n)))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (/ -1 n)))))
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ -1 k)) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (/ 1 (- n))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (log -1) into (log -1)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log -1) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n)))))
* [misc]taylor:  Taking taylor expansion of (pow (/ 1 (- n)) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (/ 1 (- n)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ -1 k)) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (/ 1 (- n))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (log -1) into (log -1)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log -1) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n)))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (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 -1) (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 -1) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log -1) in k
* [misc]taylor:  Taking taylor expansion of -1 in k
* [misc]backup-simplify:  Simplify -1 into -1
* [misc]backup-simplify:  Simplify (log -1) into (log -1)
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (+ 0 1) into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n))
* [misc]backup-simplify:  Simplify (* 1 (- (log -1) (log n))) into (- (log -1) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n)))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 -1)) into (- (log -1) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log -1) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 -1)) into (- (log -1) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -1 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) 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 -1)) into (- (log -1) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -1) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log -1) (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 -1) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n))))))
* * * [misc]progress:  simplifying candidates
* * * * [misc]progress:  [ 1 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (log1p (expm1 (pow (* PI 2) (/ (- 1 k) 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (expm1 (pow (* PI 2) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (expm1 (pow (* 2 PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (expm1 (pow (* 2 PI) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 2 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (expm1 (log1p (pow (* PI 2) (/ (- 1 k) 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (log1p (pow (* PI 2) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (log1p (pow (* 2 PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (log1p (pow (* 2 PI) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 3 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (exp (* (log (* PI 2)) (/ (- 1 k) 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (* (log (* PI 2)) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (105 enodes)
* * [misc]simplify:  iters left: 2 (395 enodes)
* [exit]simplify:  Simplified to (* (log (* 2 PI)) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (* (log (* 2 PI)) (/ (- 1 k) 2))
* * * * [misc]progress:  [ 4 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (exp (* (log (* PI 2)) (/ (- 1 k) 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (* (log (* PI 2)) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (105 enodes)
* * [misc]simplify:  iters left: 2 (395 enodes)
* [exit]simplify:  Simplified to (* (log (* 2 PI)) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (* (log (* 2 PI)) (/ (- 1 k) 2))
* * * * [misc]progress:  [ 5 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* 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:  [ 6 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (/ (pow (* PI 2) (/ 1 2)) (pow (* PI 2) (/ k 2))) (sqrt k))))>
* [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))
* [enter]simplify:  Simplifying (pow (* PI 2) (/ k 2))
* * [misc]simplify:  iters left: 3 (6 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (pow (* 2 PI) (/ k 2))
* [exit]simplify:  Simplified to (pow (* 2 PI) (/ k 2))
* * * * [misc]progress:  [ 7 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* PI 2) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (pow (* PI 2) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* [exit]simplify:  Simplified to (pow (* 2 PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (pow (* 2 PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 8 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* PI 2) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (pow (* PI 2) (sqrt (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (pow (* 2 PI) (sqrt (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (pow (* 2 PI) (sqrt (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 9 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* PI 2) 1) (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (pow (* PI 2) 1)
* * [misc]simplify:  iters left: 3 (5 enodes)
* * [misc]simplify:  iters left: 2 (8 enodes)
* [exit]simplify:  Simplified to (* 2 PI)
* [exit]simplify:  Simplified to (* 2 PI)
* * * * [misc]progress:  [ 10 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* PI 2) (- 1 k)) (/ 1 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (pow (* PI 2) (- 1 k))
* * [misc]simplify:  iters left: 3 (7 enodes)
* * [misc]simplify:  iters left: 2 (12 enodes)
* * [misc]simplify:  iters left: 1 (13 enodes)
* [exit]simplify:  Simplified to (pow (* 2 PI) (- 1 k))
* [exit]simplify:  Simplified to (pow (* 2 PI) (- 1 k))
* * * * [misc]progress:  [ 11 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (* (pow PI (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (pow PI (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (17 enodes)
* * [misc]simplify:  iters left: 2 (19 enodes)
* [exit]simplify:  Simplified to (pow PI (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow PI (/ (- 1 k) 2))
* [enter]simplify:  Simplifying (pow 2 (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (pow 2 (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow 2 (/ (- 1 k) 2))
* * * * [misc]progress:  [ 12 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* PI 2) (/ (- 1 k) 2)) 1) (sqrt k))))>
* * * * [misc]progress:  [ 13 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (exp (log (pow (* PI 2) (/ (- 1 k) 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (log (pow (* PI 2) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (57 enodes)
* * [misc]simplify:  iters left: 2 (132 enodes)
* * [misc]simplify:  iters left: 1 (490 enodes)
* [exit]simplify:  Simplified to (* (log (* 2 PI)) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (* (log (* 2 PI)) (/ (- 1 k) 2))
* * * * [misc]progress:  [ 14 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (log (exp (pow (* PI 2) (/ (- 1 k) 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (exp (pow (* PI 2) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (exp (pow (* 2 PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (exp (pow (* 2 PI) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 15 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (* (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (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 (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2))))
* [enter]simplify:  Simplifying (cbrt (pow (* PI 2) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 16 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (cbrt (* (* (pow (* PI 2) (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2))) (pow (* PI 2) (/ (- 1 k) 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (* (* (pow (* PI 2) (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2))) (pow (* PI 2) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (19 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (26 enodes)
* [exit]simplify:  Simplified to (pow (pow (* 2 PI) (/ (- 1 k) 2)) 3)
* [exit]simplify:  Simplified to (pow (pow (* 2 PI) (/ (- 1 k) 2)) 3)
* * * * [misc]progress:  [ 17 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (* (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (pow (* PI 2) (/ (- 1 k) 2)))) (sqrt k))))>
* [enter]simplify:  Simplifying (sqrt (pow (* PI 2) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* 2 PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* 2 PI) (/ (- 1 k) 2)))
* [enter]simplify:  Simplifying (sqrt (pow (* PI 2) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* 2 PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* 2 PI) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 18 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (* 1 (pow (* PI 2) (/ (- 1 k) 2))) (sqrt k))))>
* * * * [misc]progress:  [ 19 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (log1p (expm1 (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (expm1 (/ (pow (* PI 2) (/ (- 1 k) 2)) (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 (expm1 (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (expm1 (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 20 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (expm1 (log1p (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (log1p (/ (pow (* PI 2) (/ (- 1 k) 2)) (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 (log1p (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (log1p (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 21 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (pow (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) 1)))>
* * * * [misc]progress:  [ 22 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (exp (- (* (log (* PI 2)) (/ (- 1 k) 2)) (log (sqrt k))))))>
* [enter]simplify:  Simplifying (- (* (log (* PI 2)) (/ (- 1 k) 2)) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (51 enodes)
* * [misc]simplify:  iters left: 3 (125 enodes)
* * [misc]simplify:  iters left: 2 (455 enodes)
* [exit]simplify:  Simplified to (- (/ (log (* 2 PI)) (/ 2 (- 1 k))) (log (sqrt k)))
* [exit]simplify:  Simplified to (- (/ (log (* 2 PI)) (/ 2 (- 1 k))) (log (sqrt k)))
* * * * [misc]progress:  [ 23 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (exp (- (* (log (* PI 2)) (/ (- 1 k) 2)) (log (sqrt k))))))>
* [enter]simplify:  Simplifying (- (* (log (* PI 2)) (/ (- 1 k) 2)) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (51 enodes)
* * [misc]simplify:  iters left: 3 (125 enodes)
* * [misc]simplify:  iters left: 2 (455 enodes)
* [exit]simplify:  Simplified to (- (/ (log (* 2 PI)) (/ 2 (- 1 k))) (log (sqrt k)))
* [exit]simplify:  Simplified to (- (/ (log (* 2 PI)) (/ 2 (- 1 k))) (log (sqrt k)))
* * * * [misc]progress:  [ 24 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (exp (- (log (pow (* PI 2) (/ (- 1 k) 2))) (log (sqrt k))))))>
* [enter]simplify:  Simplifying (- (log (pow (* PI 2) (/ (- 1 k) 2))) (log (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (36 enodes)
* * [misc]simplify:  iters left: 3 (65 enodes)
* * [misc]simplify:  iters left: 2 (176 enodes)
* [exit]simplify:  Simplified to (- (/ (log (* 2 PI)) (/ 2 (- 1 k))) (log (sqrt k)))
* [exit]simplify:  Simplified to (- (/ (log (* 2 PI)) (/ 2 (- 1 k))) (log (sqrt k)))
* * * * [misc]progress:  [ 25 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (exp (log (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (log (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (29 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (69 enodes)
* * [misc]simplify:  iters left: 1 (192 enodes)
* [exit]simplify:  Simplified to (- (/ (log (* 2 PI)) (/ 2 (- 1 k))) (log (sqrt k)))
* [exit]simplify:  Simplified to (- (/ (log (* 2 PI)) (/ 2 (- 1 k))) (log (sqrt k)))
* * * * [misc]progress:  [ 26 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (log (exp (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (exp (/ (pow (* PI 2) (/ (- 1 k) 2)) (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 (exp (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (exp (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 27 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (cbrt (/ (* (* (pow (* PI 2) (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2))) (pow (* PI 2) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (* (* (pow (* PI 2) (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2))) (pow (* PI 2) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (62 enodes)
* * [misc]simplify:  iters left: 3 (120 enodes)
* * [misc]simplify:  iters left: 2 (204 enodes)
* * [misc]simplify:  iters left: 1 (341 enodes)
* [exit]simplify:  Simplified to (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (* k (sqrt k))) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (* k (sqrt k))) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 28 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (* (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (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 (* (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))
* [enter]simplify:  Simplifying (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (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 (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (cbrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 29 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (cbrt (* (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (50 enodes)
* * [misc]simplify:  iters left: 3 (77 enodes)
* * [misc]simplify:  iters left: 2 (112 enodes)
* * [misc]simplify:  iters left: 1 (143 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* 2 PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* 2 PI) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 30 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (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 (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))
* [enter]simplify:  Simplifying (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (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 (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 31 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (- (pow (* PI 2) (/ (- 1 k) 2))) (- (sqrt k)))))>
* [enter]simplify:  Simplifying (- (pow (* PI 2) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (- (pow (* 2 PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (- (pow (* 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:  [ 32 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (pow PI (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow 2 (/ (- 1 k) 2)) (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow PI (/ (- 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 PI (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow PI (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (pow 2 (/ (- 1 k) 2)) (cbrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* * [misc]simplify:  iters left: 3 (21 enodes)
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 33 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* * [misc]simplify:  iters left: 3 (21 enodes)
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 34 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (pow PI (/ (- 1 k) 2)) 1) (/ (pow 2 (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow PI (/ (- 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 PI (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow PI (/ (- 1 k) 2))
* [enter]simplify:  Simplifying (/ (pow 2 (/ (- 1 k) 2)) (sqrt k))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt k))
* [exit]simplify:  Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 35 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (40 enodes)
* * [misc]simplify:  iters left: 3 (45 enodes)
* * [misc]simplify:  iters left: 2 (48 enodes)
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (* (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (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 (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 36 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (28 enodes)
* * [misc]simplify:  iters left: 3 (31 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (cbrt (pow (* 2 PI) (/ (- 1 k) 2)))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 37 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) 1) (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) 1)
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* * [misc]simplify:  iters left: 2 (48 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (pow (* 2 PI) (/ (- 1 k) 2))))
* [enter]simplify:  Simplifying (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (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 (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k))
* * * * [misc]progress:  [ 38 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (26 enodes)
* * [misc]simplify:  iters left: 3 (28 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (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 (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (cbrt (sqrt k)))
* * * * [misc]progress:  [ 39 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (sqrt k))))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
* * * * [misc]progress:  [ 40 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) 1) (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) 1)
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* 2 PI) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* 2 PI) (/ (- 1 k) 2)))
* [enter]simplify:  Simplifying (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (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 (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k))
* * * * [misc]progress:  [ 41 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 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 (* 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:  [ 42 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* 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 (* 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:  [ 43 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (/ 1 1) (/ (pow (* 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 (* 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:  [ 44 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (* 1 (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 45 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (pow (* 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:  [ 46 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ 1 (/ (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:  [ 47 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (/ (pow (* PI 2) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (/ (pow (* PI 2) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (27 enodes)
* [exit]simplify:  Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 48 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) (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:  [ 49 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (/ (pow (* PI 2) (/ (- 1 k) 2)) 1) (sqrt k))))>
* [enter]simplify:  Simplifying (/ (pow (* PI 2) (/ (- 1 k) 2)) 1)
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (pow (* 2 PI) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow (* 2 PI) (/ (- 1 k) 2))
* * * * [misc]progress:  [ 50 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* [exit]simplify:  Simplified to (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 51 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) (/ (sqrt k) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (cbrt (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 k) (cbrt (pow (* PI 2) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (sqrt k) (cbrt (pow (* PI 2) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 52 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* PI 2) (/ (- 1 k) 2)))))))>
* [enter]simplify:  Simplifying (/ (sqrt k) (sqrt (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 k) (sqrt (pow (* PI 2) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (sqrt k) (sqrt (pow (* PI 2) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 53 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ 1 (/ (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:  [ 54 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ 1 2)) (* (sqrt k) (pow (* PI 2) (/ k 2))))))>
* [enter]simplify:  Simplifying (* (sqrt k) (pow (* PI 2) (/ k 2)))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* [exit]simplify:  Simplified to (* (pow (* PI 2) (/ k 2)) (sqrt k))
* [exit]simplify:  Simplified to (* (pow (* PI 2) (/ k 2)) (sqrt k))
* * * * [misc]progress:  [ 55 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (log1p (expm1 (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (expm1 (* (pow n (/ (- 1 k) 2)) (/ (pow (* 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 (32 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 (expm1 (* (/ (pow n (/ (- 1 k) 2)) (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (expm1 (* (/ (pow n (/ (- 1 k) 2)) (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 56 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (expm1 (log1p (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (log1p (* (pow n (/ (- 1 k) 2)) (/ (pow (* 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 (32 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 (log1p (* (/ (pow n (/ (- 1 k) 2)) (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (log1p (* (/ (pow n (/ (- 1 k) 2)) (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 57 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (pow (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) 1))>
* * * * [misc]progress:  [ 58 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (* (log n) (/ (- 1 k) 2)) (- (* (log (* PI 2)) (/ (- 1 k) 2)) (log (sqrt k))))))>
* [enter]simplify:  Simplifying (+ (* (log n) (/ (- 1 k) 2)) (- (* (log (* PI 2)) (/ (- 1 k) 2)) (log (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (82 enodes)
* * [misc]simplify:  iters left: 3 (242 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (+ (log n) (log (* PI 2))) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (+ (log n) (log (* PI 2))) (- (log (sqrt k))))
* * * * [misc]progress:  [ 59 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (* (log n) (/ (- 1 k) 2)) (- (* (log (* PI 2)) (/ (- 1 k) 2)) (log (sqrt k))))))>
* [enter]simplify:  Simplifying (+ (* (log n) (/ (- 1 k) 2)) (- (* (log (* PI 2)) (/ (- 1 k) 2)) (log (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (40 enodes)
* * [misc]simplify:  iters left: 4 (82 enodes)
* * [misc]simplify:  iters left: 3 (242 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (+ (log n) (log (* PI 2))) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (+ (log n) (log (* PI 2))) (- (log (sqrt k))))
* * * * [misc]progress:  [ 60 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (* (log n) (/ (- 1 k) 2)) (- (log (pow (* PI 2) (/ (- 1 k) 2))) (log (sqrt k))))))>
* [enter]simplify:  Simplifying (+ (* (log n) (/ (- 1 k) 2)) (- (log (pow (* PI 2) (/ (- 1 k) 2))) (log (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (35 enodes)
* * [misc]simplify:  iters left: 4 (68 enodes)
* * [misc]simplify:  iters left: 3 (171 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (+ (log n) (log (* PI 2))) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (+ (log n) (log (* PI 2))) (- (log (sqrt k))))
* * * * [misc]progress:  [ 61 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (* (log n) (/ (- 1 k) 2)) (log (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (+ (* (log n) (/ (- 1 k) 2)) (log (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (53 enodes)
* * [misc]simplify:  iters left: 3 (117 enodes)
* * [misc]simplify:  iters left: 2 (313 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (+ (log (* PI 2)) (log n)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (+ (log (* PI 2)) (log n)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 62 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (log (pow n (/ (- 1 k) 2))) (- (* (log (* PI 2)) (/ (- 1 k) 2)) (log (sqrt k))))))>
* [enter]simplify:  Simplifying (+ (log (pow n (/ (- 1 k) 2))) (- (* (log (* PI 2)) (/ (- 1 k) 2)) (log (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (38 enodes)
* * [misc]simplify:  iters left: 4 (73 enodes)
* * [misc]simplify:  iters left: 3 (194 enodes)
* [exit]simplify:  Simplified to (fma (+ (log n) (log (* PI 2))) (/ (- 1 k) 2) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (+ (log n) (log (* PI 2))) (/ (- 1 k) 2) (- (log (sqrt k))))
* * * * [misc]progress:  [ 63 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (log (pow n (/ (- 1 k) 2))) (- (* (log (* PI 2)) (/ (- 1 k) 2)) (log (sqrt k))))))>
* [enter]simplify:  Simplifying (+ (log (pow n (/ (- 1 k) 2))) (- (* (log (* PI 2)) (/ (- 1 k) 2)) (log (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (38 enodes)
* * [misc]simplify:  iters left: 4 (73 enodes)
* * [misc]simplify:  iters left: 3 (194 enodes)
* [exit]simplify:  Simplified to (fma (+ (log n) (log (* PI 2))) (/ (- 1 k) 2) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (+ (log n) (log (* PI 2))) (/ (- 1 k) 2) (- (log (sqrt k))))
* * * * [misc]progress:  [ 64 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (log (pow n (/ (- 1 k) 2))) (- (log (pow (* PI 2) (/ (- 1 k) 2))) (log (sqrt k))))))>
* [enter]simplify:  Simplifying (+ (log (pow n (/ (- 1 k) 2))) (- (log (pow (* PI 2) (/ (- 1 k) 2))) (log (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (58 enodes)
* * [misc]simplify:  iters left: 3 (122 enodes)
* * [misc]simplify:  iters left: 2 (388 enodes)
* [exit]simplify:  Simplified to (fma (+ (log n) (log (* PI 2))) (/ (- 1 k) 2) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (+ (log n) (log (* PI 2))) (/ (- 1 k) 2) (- (log (sqrt k))))
* * * * [misc]progress:  [ 65 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (log (pow n (/ (- 1 k) 2))) (log (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (+ (log (pow n (/ (- 1 k) 2))) (log (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (79 enodes)
* * [misc]simplify:  iters left: 2 (196 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (+ (log (* PI 2)) (log n)) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (+ (log (* PI 2)) (log n)) (- (log (sqrt k))))
* * * * [misc]progress:  [ 66 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (exp (log (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (log (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (62 enodes)
* * [misc]simplify:  iters left: 2 (110 enodes)
* * [misc]simplify:  iters left: 1 (289 enodes)
* [exit]simplify:  Simplified to (fma (+ (log (* PI 2)) (log n)) (/ (- 1 k) 2) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (+ (log (* PI 2)) (log n)) (/ (- 1 k) 2) (- (log (sqrt k))))
* * * * [misc]progress:  [ 67 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (log (exp (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (exp (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* * [misc]simplify:  iters left: 2 (40 enodes)
* * [misc]simplify:  iters left: 1 (41 enodes)
* [exit]simplify:  Simplified to (pow (exp (pow n (/ (- 1 k) 2))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (pow (exp (pow n (/ (- 1 k) 2))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 68 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (* (* (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (/ (* (* (pow (* PI 2) (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2))) (pow (* PI 2) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (* (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (/ (* (* (pow (* PI 2) (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2))) (pow (* PI 2) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (42 enodes)
* * [misc]simplify:  iters left: 4 (118 enodes)
* * [misc]simplify:  iters left: 3 (448 enodes)
* [exit]simplify:  Simplified to (* (/ (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (/ k (pow n (/ (- 1 k) 2)))) (/ (* (pow (* PI 2) (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2))) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))))
* [exit]simplify:  Simplified to (* (/ (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (/ k (pow n (/ (- 1 k) 2)))) (/ (* (pow (* PI 2) (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2))) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 69 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (* (* (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (* (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (* (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (* (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (38 enodes)
* * [misc]simplify:  iters left: 4 (94 enodes)
* * [misc]simplify:  iters left: 3 (232 enodes)
* [exit]simplify:  Simplified to (* (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (/ (* (pow (* PI 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (/ k (pow (* PI 2) (/ (- 1 k) 2)))))
* [exit]simplify:  Simplified to (* (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))) (/ (* (pow (* PI 2) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (/ k (pow (* PI 2) (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 70 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (cbrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))) (cbrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (cbrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* 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 (33 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 (* (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (/ (sqrt k) (pow n (/ (- 1 k) 2))))) (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (/ (sqrt k) (pow n (/ (- 1 k) 2))))))
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (/ (sqrt k) (pow n (/ (- 1 k) 2))))) (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (/ (sqrt k) (pow n (/ (- 1 k) 2))))))
* [enter]simplify:  Simplifying (cbrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* 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 (32 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (38 enodes)
* * [misc]simplify:  iters left: 1 (39 enodes)
* [exit]simplify:  Simplified to (cbrt (* (/ (pow n (/ (- 1 k) 2)) (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (cbrt (* (/ (pow n (/ (- 1 k) 2)) (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 71 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (* (* (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (* (* (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (74 enodes)
* * [misc]simplify:  iters left: 3 (195 enodes)
* [exit]simplify:  Simplified to (pow (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))) 3)
* [exit]simplify:  Simplified to (pow (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))) 3)
* * * * [misc]progress:  [ 72 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))))>
* [enter]simplify:  Simplifying (sqrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* 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 (32 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 (* (/ (pow n (/ (- 1 k) 2)) (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (sqrt (* (/ (pow n (/ (- 1 k) 2)) (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2))))
* [enter]simplify:  Simplifying (sqrt (* (pow n (/ (- 1 k) 2)) (/ (pow (* 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 (32 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 (* (/ (pow n (/ (- 1 k) 2)) (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (sqrt (* (/ (pow n (/ (- 1 k) 2)) (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 73 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow n (/ 1 2)) (pow (* PI 2) (/ (- 1 k) 2))) (* (pow n (/ k 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (* (pow n (/ 1 2)) (pow (* PI 2) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))
* [exit]simplify:  Simplified to (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ 1 2)))
* [enter]simplify:  Simplifying (* (pow n (/ k 2)) (sqrt k))
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (8 enodes)
* [exit]simplify:  Simplified to (* (sqrt k) (pow n (/ k 2)))
* [exit]simplify:  Simplified to (* (sqrt k) (pow n (/ k 2)))
* * * * [misc]progress:  [ 74 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))))>
* * * * [misc]progress:  [ 75 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (* (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))) (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (pow n (/ (- 1 k) 2)) (* (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* 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 (31 enodes)
* * [misc]simplify:  iters left: 3 (33 enodes)
* [exit]simplify:  Simplified to (* (* (pow n (/ (- 1 k) 2)) (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (* (pow n (/ (- 1 k) 2)) (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 76 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (pow n (/ (- 1 k) 2)) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (26 enodes)
* * [misc]simplify:  iters left: 3 (28 enodes)
* [exit]simplify:  Simplified to (* (pow n (/ (- 1 k) 2)) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (pow n (/ (- 1 k) 2)) (sqrt (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))
* * * * [misc]progress:  [ 77 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow 2 (/ (- 1 k) 2)) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (pow n (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (41 enodes)
* * [misc]simplify:  iters left: 3 (53 enodes)
* * [misc]simplify:  iters left: 2 (61 enodes)
* * [misc]simplify:  iters left: 1 (69 enodes)
* [exit]simplify:  Simplified to (/ (* (pow PI (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ (* (pow PI (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 78 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k)))) (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (pow n (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* * [misc]simplify:  iters left: 2 (36 enodes)
* * [misc]simplify:  iters left: 1 (37 enodes)
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) (/ (sqrt (sqrt k)) (pow PI (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (pow n (/ (- 1 k) 2)) (/ (sqrt (sqrt k)) (pow PI (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 79 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) 1)) (/ (pow 2 (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (* (pow n (/ (- 1 k) 2)) (/ (pow PI (/ (- 1 k) 2)) 1))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (43 enodes)
* * [misc]simplify:  iters left: 1 (49 enodes)
* [exit]simplify:  Simplified to (* (pow PI (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (* (pow PI (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 80 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (pow n (/ (- 1 k) 2)) (/ (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (34 enodes)
* * [misc]simplify:  iters left: 4 (67 enodes)
* * [misc]simplify:  iters left: 3 (106 enodes)
* * [misc]simplify:  iters left: 2 (150 enodes)
* * [misc]simplify:  iters left: 1 (176 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))))
* [exit]simplify:  Simplified to (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))))
* * * * [misc]progress:  [ 81 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) (sqrt (sqrt k)))) (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (pow n (/ (- 1 k) 2)) (/ (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (57 enodes)
* * [misc]simplify:  iters left: 2 (73 enodes)
* * [misc]simplify:  iters left: 1 (76 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))))
* * * * [misc]progress:  [ 82 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) 1)) (/ (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (* (pow n (/ (- 1 k) 2)) (/ (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2)))) 1))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (66 enodes)
* * [misc]simplify:  iters left: 2 (153 enodes)
* * [misc]simplify:  iters left: 1 (297 enodes)
* [exit]simplify:  Simplified to (* (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (* (* (cbrt (pow (* PI 2) (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))) (cbrt (pow (* PI 2) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 83 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (pow n (/ (- 1 k) 2)) (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (16 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (56 enodes)
* * [misc]simplify:  iters left: 2 (64 enodes)
* * [misc]simplify:  iters left: 1 (72 enodes)
* [exit]simplify:  Simplified to (* (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* PI 2) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (* (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* PI 2) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 84 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))) (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (pow n (/ (- 1 k) 2)) (/ (sqrt (pow (* 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 (33 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 (pow (* PI 2) (/ (- 1 k) 2))) (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))))
* [exit]simplify:  Simplified to (* (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))))
* * * * [misc]progress:  [ 85 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) 1)) (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (sqrt k))))>
* [enter]simplify:  Simplifying (* (pow n (/ (- 1 k) 2)) (/ (sqrt (pow (* PI 2) (/ (- 1 k) 2))) 1))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (37 enodes)
* * [misc]simplify:  iters left: 3 (43 enodes)
* * [misc]simplify:  iters left: 2 (46 enodes)
* * [misc]simplify:  iters left: 1 (52 enodes)
* [exit]simplify:  Simplified to (* (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (* (sqrt (pow (* PI 2) (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 86 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (pow n (/ (- 1 k) 2)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (41 enodes)
* * [misc]simplify:  iters left: 3 (65 enodes)
* * [misc]simplify:  iters left: 2 (105 enodes)
* * [misc]simplify:  iters left: 1 (129 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))))
* * * * [misc]progress:  [ 87 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ 1 (sqrt (sqrt k)))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
* [enter]simplify:  Simplifying (* (pow n (/ (- 1 k) 2)) (/ 1 (sqrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (54 enodes)
* * [misc]simplify:  iters left: 1 (55 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:  [ 88 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (/ 1 1)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (* (pow n (/ (- 1 k) 2)) (/ 1 1))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (20 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (pow n (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow n (/ (- 1 k) 2))
* * * * [misc]progress:  [ 89 / 123 ] 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 (16 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* [exit]simplify:  Simplified to (pow n (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow n (/ (- 1 k) 2))
* * * * [misc]progress:  [ 90 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2))) (/ 1 (sqrt k))))>
* [enter]simplify:  Simplifying (* (pow n (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (* (pow n (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (* (pow n (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 91 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (cbrt (pow n (/ (- 1 k) 2))) (cbrt (pow n (/ (- 1 k) 2)))) (* (cbrt (pow n (/ (- 1 k) 2))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (cbrt (pow n (/ (- 1 k) 2))) (/ (pow (* 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 (32 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (38 enodes)
* * [misc]simplify:  iters left: 1 (39 enodes)
* [exit]simplify:  Simplified to (/ (cbrt (pow n (/ (- 1 k) 2))) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (cbrt (pow n (/ (- 1 k) 2))) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 92 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (pow n (/ (- 1 k) 2))) (* (sqrt (pow n (/ (- 1 k) 2))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (sqrt (pow n (/ (- 1 k) 2))) (/ (pow (* 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 (32 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 (pow n (/ (- 1 k) 2))) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (sqrt (pow n (/ (- 1 k) 2))) (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 93 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))))>
* [enter]simplify:  Simplifying (* (pow n (/ (- 1 k) 2)) (/ (pow (* 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 (31 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* * [misc]simplify:  iters left: 2 (37 enodes)
* * [misc]simplify:  iters left: 1 (38 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI 2) (/ (- 1 k) 2)) (/ (sqrt k) (pow n (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (pow (* PI 2) (/ (- 1 k) 2)) (/ (sqrt k) (pow n (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 94 / 123 ] 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)) (pow (* PI 2) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (20 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (* (pow n (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (* (pow n (/ (- 1 k) 2)) (pow (* PI 2) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 95 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (pow n (/ 1 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))) (pow n (/ k 2))))>
* [enter]simplify:  Simplifying (* (pow n (/ 1 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* * [misc]simplify:  iters left: 2 (37 enodes)
* * [misc]simplify:  iters left: 1 (38 enodes)
* [exit]simplify:  Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (/ (sqrt k) (pow n (/ 1 2))))
* [exit]simplify:  Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (/ (sqrt k) (pow n (/ 1 2))))
* * * * [misc]progress:  [ 96 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) (pow n (/ (- 1 k) 2))))>
* * * * [misc]progress:  [ 97 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (log1p (expm1 (pow n (/ (- 1 k) 2)))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (expm1 (pow n (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* [exit]simplify:  Simplified to (expm1 (pow n (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (expm1 (pow n (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 98 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (expm1 (log1p (pow n (/ (- 1 k) 2)))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (log1p (pow n (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* [exit]simplify:  Simplified to (log1p (pow n (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (log1p (pow n (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 99 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (exp (* (log n) (/ (- 1 k) 2))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (* (log n) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (73 enodes)
* * [misc]simplify:  iters left: 2 (161 enodes)
* * [misc]simplify:  iters left: 1 (345 enodes)
* [exit]simplify:  Simplified to (* (/ (log n) 2) (- 1 k))
* [exit]simplify:  Simplified to (* (/ (log n) 2) (- 1 k))
* * * * [misc]progress:  [ 100 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (pow n (/ 1 2)) (pow n (/ k 2))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (pow n (/ 1 2))
* * [misc]simplify:  iters left: 3 (5 enodes)
* * [misc]simplify:  iters left: 2 (7 enodes)
* [exit]simplify:  Simplified to (pow n (/ 1 2))
* [exit]simplify:  Simplified to (pow n (/ 1 2))
* [enter]simplify:  Simplifying (pow n (/ k 2))
* * [misc]simplify:  iters left: 3 (5 enodes)
* [exit]simplify:  Simplified to (pow n (/ k 2))
* [exit]simplify:  Simplified to (pow n (/ k 2))
* * * * [misc]progress:  [ 101 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow (pow n (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (pow n (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* * [misc]simplify:  iters left: 3 (21 enodes)
* [exit]simplify:  Simplified to (pow n (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (pow n (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 102 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow (pow n (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (pow n (sqrt (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* [exit]simplify:  Simplified to (pow n (sqrt (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (pow n (sqrt (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 103 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow (pow n 1) (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (pow n 1)
* * [misc]simplify:  iters left: 1 (3 enodes)
* [exit]simplify:  Simplified to n
* [exit]simplify:  Simplified to n
* * * * [misc]progress:  [ 104 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow (pow n (- 1 k)) (/ 1 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (pow n (- 1 k))
* * [misc]simplify:  iters left: 3 (5 enodes)
* * [misc]simplify:  iters left: 2 (9 enodes)
* * [misc]simplify:  iters left: 1 (10 enodes)
* [exit]simplify:  Simplified to (pow n (- 1 k))
* [exit]simplify:  Simplified to (pow n (- 1 k))
* * * * [misc]progress:  [ 105 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow (pow n (/ (- 1 k) 2)) 1) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>
* * * * [misc]progress:  [ 106 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (exp (log (pow n (/ (- 1 k) 2)))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (log (pow n (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (23 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* * [misc]simplify:  iters left: 2 (58 enodes)
* * [misc]simplify:  iters left: 1 (128 enodes)
* [exit]simplify:  Simplified to (/ (* (- 1 k) (log n)) 2)
* [exit]simplify:  Simplified to (/ (* (- 1 k) (log n)) 2)
* * * * [misc]progress:  [ 107 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (log (exp (pow n (/ (- 1 k) 2)))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (exp (pow n (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* [exit]simplify:  Simplified to (exp (pow n (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (exp (pow n (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 108 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (* (cbrt (pow n (/ (- 1 k) 2))) (cbrt (pow n (/ (- 1 k) 2)))) (cbrt (pow n (/ (- 1 k) 2)))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (* (cbrt (pow n (/ (- 1 k) 2))) (cbrt (pow n (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (19 enodes)
* * [misc]simplify:  iters left: 3 (21 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow n (/ (- 1 k) 2))) (cbrt (pow n (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow n (/ (- 1 k) 2))) (cbrt (pow n (/ (- 1 k) 2))))
* [enter]simplify:  Simplifying (cbrt (pow n (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* [exit]simplify:  Simplified to (cbrt (pow n (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (cbrt (pow n (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 109 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (cbrt (* (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2)))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (* (* (pow n (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (17 enodes)
* * [misc]simplify:  iters left: 4 (22 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* [exit]simplify:  Simplified to (pow (pow n (/ (- 1 k) 2)) 3)
* [exit]simplify:  Simplified to (pow (pow n (/ (- 1 k) 2)) 3)
* * * * [misc]progress:  [ 110 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (pow n (/ (- 1 k) 2))) (sqrt (pow n (/ (- 1 k) 2)))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (sqrt (pow n (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* [exit]simplify:  Simplified to (sqrt (pow n (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (sqrt (pow n (/ (- 1 k) 2)))
* [enter]simplify:  Simplifying (sqrt (pow n (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (8 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (18 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* [exit]simplify:  Simplified to (sqrt (pow n (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (sqrt (pow n (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 111 / 123 ] simplifiying candidate #<alt-delta (λ (k n) (* (* 1 (pow n (/ (- 1 k) 2))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>
* * * * [misc]progress:  [ 112 / 123 ] simplifiying candidate #<alt-event (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (- (+ (pow (* 2 PI) 1/2) (* 1/8 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (* (pow k 2) (sqrt 2)))))) (* 1/2 (* (sqrt PI) (* (log (* 2 PI)) (* k (sqrt 2)))))) (sqrt k))))>
* [enter]simplify:  Simplifying (* (pow n (/ (- 1 k) 2)) (/ (- (+ (pow (* 2 PI) 1/2) (* 1/8 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (* (pow k 2) (sqrt 2)))))) (* 1/2 (* (sqrt PI) (* (log (* 2 PI)) (* k (sqrt 2)))))) (sqrt k)))
* * [misc]simplify:  iters left: 6 (30 enodes)
* * [misc]simplify:  iters left: 5 (75 enodes)
* * [misc]simplify:  iters left: 4 (227 enodes)
* [exit]simplify:  Simplified to (* (/ (pow n (/ (- 1 k) 2)) (sqrt k)) (fma (* (* 1/8 (sqrt PI)) (* (log (* PI 2)) (log (* PI 2)))) (* (sqrt 2) (* k k)) (- (sqrt (* PI 2)) (* (log (* PI 2)) (* (sqrt PI) (* (sqrt 2) (* k 1/2)))))))
* * * * [misc]progress:  [ 113 / 123 ] simplifiying candidate #<alt-event (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt k))))>
* [enter]simplify:  Simplifying (* (pow n (/ (- 1 k) 2)) (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (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 (167 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI 2) (- 1/2 (* 1/2 k))) (/ (sqrt k) (pow n (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 114 / 123 ] simplifiying candidate #<alt-event (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (sqrt k))))>
* [enter]simplify:  Simplifying (* (pow n (/ (- 1 k) 2)) (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (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 (167 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI 2) (- 1/2 (* 1/2 k))) (/ (sqrt k) (pow n (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 115 / 123 ] simplifiying candidate #<alt-event (λ (k n) (* (pow n (/ (- 1 k) 2)) (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (+ (* +nan.0 (* (sqrt PI) (* k (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (* k (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt PI) (/ (sqrt 2) k))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (* k (sqrt 2))))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2)))))))))))))))))>
* [enter]simplify:  Simplifying (* (pow n (/ (- 1 k) 2)) (- (+ (* +nan.0 (* (sqrt PI) (sqrt 2))) (- (+ (* +nan.0 (* (sqrt PI) (* k (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (* k (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt PI) (/ (sqrt 2) k))) (- (+ (* +nan.0 (* (sqrt PI) (* (pow (log (* 2 PI)) 2) (* k (sqrt 2))))) (- (* +nan.0 (* (sqrt PI) (* (log (* 2 PI)) (sqrt 2))))))))))))))))
* * * * [misc]progress:  [ 116 / 123 ] simplifiying candidate #<alt-event (λ (k n) (* (pow n (/ (- 1 k) 2)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)))))))))>
* [enter]simplify:  Simplifying (* (pow n (/ (- 1 k) 2)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k))))))))
* * * * [misc]progress:  [ 117 / 123 ] simplifiying candidate #<alt-event (λ (k n) (* (pow n (/ (- 1 k) 2)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k)))))))))>
* [enter]simplify:  Simplifying (* (pow n (/ (- 1 k) 2)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (log (* 2 PI)))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) k))))))))
* * * * [misc]progress:  [ 118 / 123 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (* k (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 2) (* (pow k 2) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow k 2) (* (log n) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* (pow k 2) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* k (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* k (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow k 2) (* (pow (log n) 2) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow k 2) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (* (log (* 2 PI)) (* (pow k 2) (log n)))))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))))))))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (* k (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log (* 2 PI)) 2) (* (pow k 2) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow k 2) (* (log n) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* (pow k 2) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log (* 2 PI)) (* k (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* k (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow k 2) (* (pow (log n) 2) (sqrt 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow k 2) (sqrt 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (* (log (* 2 PI)) (* (pow k 2) (log n)))))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))))))))))))))))))))
* * * * [misc]progress:  [ 119 / 123 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* -1/2 (* (- 1 k) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* -1/2 (* (- 1 k) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* -1/2 (* (- 1 k) (log (/ 1 n)))))) (pow k 3)))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* -1/2 (* (- 1 k) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* -1/2 (* (- 1 k) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* -1/2 (* (- 1 k) (log (/ 1 n)))))) (pow k 3))))))))
* * * * [misc]progress:  [ 120 / 123 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n))))))) k)) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n))))))) (pow k 2))) (- (* +nan.0 (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n))))))) k)) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n))))))) (pow k 2))) (- (* +nan.0 (* (exp (* 1/2 (* (- 1 k) (log (* 2 PI))))) (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))))))))))
* * * * [misc]progress:  [ 121 / 123 ] simplifiying candidate #<alt-event (λ (k n) (* (- (+ (* 1/8 (* (sqrt n) (* (pow (log n) 2) (pow k 2)))) (pow n 1/2)) (* 1/2 (* (sqrt n) (* (log n) k)))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (* (- (+ (* 1/8 (* (sqrt n) (* (pow (log n) 2) (pow k 2)))) (pow n 1/2)) (* 1/2 (* (sqrt n) (* (log n) k)))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (27 enodes)
* * [misc]simplify:  iters left: 5 (60 enodes)
* * [misc]simplify:  iters left: 4 (159 enodes)
* [exit]simplify:  Simplified to (* (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) (fma (- 1/2) (* (* (sqrt n) (log n)) k) (fma 1/8 (* (* (sqrt n) (log n)) (* (log n) (* k k))) (sqrt n))))
* * * * [misc]progress:  [ 122 / 123 ] simplifiying candidate #<alt-event (λ (k n) (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (* (exp (* -1/2 (* (- 1 k) (log (/ 1 n))))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (39 enodes)
* * [misc]simplify:  iters left: 4 (71 enodes)
* * [misc]simplify:  iters left: 3 (155 enodes)
* [exit]simplify:  Simplified to (/ (pow (/ 1 n) (- -1/2 (* -1/2 k))) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 123 / 123 ] simplifiying candidate #<alt-event (λ (k n) (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>
* [enter]simplify:  Simplifying (* (exp (* 1/2 (* (- 1 k) (- (log -1) (log (/ -1 n)))))) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)))
* * [misc]simplify:  iters left: 6 (21 enodes)
* * [misc]simplify:  iters left: 5 (42 enodes)
* * [misc]simplify:  iters left: 4 (84 enodes)
* * [misc]simplify:  iters left: 3 (232 enodes)
* [exit]simplify:  Simplified to (* (/ (pow (exp (log n)) (- 1/2 (* 1/2 k))) (sqrt k)) (pow (* PI 2) (/ (- 1 k) 2)))
* * * [misc]progress:  adding candidates to table
* * [misc]progress:  iteration 4 / 4
* * * [misc]progress:  picking best candidate
"ALT DATA: "{"picked-error":0.6717154575888729,"picked":"(λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))","all-alts":["#<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))>","#<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>","#<alt-delta (λ (k n) (/ (+ (* (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (* (* k k) 1/8)) (+ (* (log n) (log n)) (* (log (* PI 2)) (log (* PI 2))))) (- (fma (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4)) (* (log (* PI 2)) (* (* k k) (log n))) (* (pow (* PI 2) 1/2) (pow n 1/2))) (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/2)) (fma k (log (* PI 2)) (* (log n) k))))) (sqrt k)))>","#<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>","#<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))>","#<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* PI 2) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (sqrt k))))>","#<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))>","#<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2)))))>","#<alt-event (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>","#<alt-delta (λ (k n) (/ (* (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (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)))))>"],"best-fresh-alt-per-point":[[[5.091954821941639e-192,6.815392098658887e+143],1,0],[[1.9872779421557533e+180,1.8165707546862427e+45],0,0],[[7.416044817432175e-280,4.187534830574239e+90],2,0],[[8.952174144166139e-302,1.0956116997098222e-31],1,0],[[2.7602034085604025e+247,3.933007183466984e+176],0,0],[[4.691318136614946e-91,2.2211280072565116e-303],1,0],[[9.07067712653544e+121,1.1966070572230463e+134],0,0],[[2.534573079598786e+169,3.2634856808337097e+195],0,0],[[6.317640848359807e-38,7.108640458245273e-156],1,0],[[1.37963739668883e-251,1.9832537005473266e-262],1,0],[[2.2237477837114185e-204,3.5971048785615273e+27],4,0],[[2.0235103563137384e-245,3.186488674327569e-306],0,0],[[4.535662949534244e+218,1.0124765649019447e+298],0,0],[[3.548084498024942e-190,1.2458518796694574e+90],4,0],[[1.0707760413948923e-209,1.8155292668497655e+36],2,0],[[8.082647412227132e-211,1.4588918120519666e-114],3,0],[[5.13876683088187e-118,9.467488944393916e+142],5,0],[[2.2187340876406246e+300,4.0696348581298066e+30],0,0],[[4.737175196542416e-301,9.453454014910064e+271],2,0],[[1.090098977941039e-114,5.7243448441390635e+162],1,0],[[2.571403883587662e-39,2.725225610867578e+225],0,0],[[5.081095649164445e+286,2.6437596200790387e+281],0,0],[[6.85981085886286e-168,1.9805731700427848e-169],1,0],[[9.636536782052696e-111,2.985561979664205e+171],1,0],[[1.0838714812801137e-216,1.1791770071753556e+107],2,0],[[1.072386271012045e-235,9.15478951965041e+260],0,0],[[4.954601632348903e-272,5.651261930475929e+123],1,0],[[5.598692384845278e-151,2.0020470402494707e-128],4,0],[[3.828518244176968e-308,9.957124504840989e+307],4,0],[[7.811244882301027e-64,2.3660873791160076e+189],4,0],[[1.1253736853318525e-46,4.582462397892038e-300],1,0],[[2271813.2914643916,1.711246486837026e+16],0,0],[[2.6512646278212223e-277,2.991195561163922e+252],1,0],[[2.8722519575799174e-220,8.864398632472997e+128],1,0],[[6.898353156002884e+56,5.049169591478046e+301],0,0],[[5.795257109406676e+26,7.254471041027067e+34],0,0],[[1.9680527238636918e-165,6.602387235477923e-263],0,0],[[4.390126892195692e-258,5.153839259075024e-217],0,0],[[3.7270065251219893e-51,4.1091807334876805e+121],0,0],[[1.2718549924538793e-67,1.4997147168186959e-133],3,0],[[7.779411959735569e-290,2.9896016385939845e-66],1,0],[[2.8931224974199074e-84,1.9240432527476484e-289],4,0],[[1.6509703901493846e-82,1.0044867221158944e+300],4,0],[[7.040383581327078e-101,5.96146379570227e+197],0,0],[[1.607215854807525e-42,2.5297373356963796e-300],0,0],[[8.687912841852904e-95,5.412515287604772e-64],3,0],[[7.938025318271498e-112,7.539778260587032e+298],0,0],[[4.0890448857589815e-140,6.188431370265012e+93],1,0],[[1.808792063616234e-42,1.2249262287356375e+78],2,0],[[2.813778253825615e-191,3.478381051263039e+83],7,0],[[4.959269200917455e+89,2.713904493922986e+74],0,0],[[1.6527464762421886e-272,9.284612428163018e+257],4,0],[[2.694216768013651e-08,2.481730668881008e+205],2,0],[[1.105287263764627e+102,5.503874697732584e+83],0,0],[[3.616766753957493e-134,1.405468459858575e-82],0,0],[[3.4960229754986024e-44,4.978416266226015e-252],5,0],[[0.34727693217194866,5.903688889215572e+29],4,0],[[1.179890420337443e-05,1.2231257626976233e+37],0,1.0],[[3.985430525999154e-166,3.256025304820758e-99],0,0],[[2.9695246403166212e+172,1.0507438437361721e+109],0,0],[[7.823934036267622e-77,4.7561975058596834e-110],0,0],[[1.1032765895259676e-126,5.131532610213896e-61],0,0],[[2.572749544642796e-298,5.3648379001218185e+144],2,0],[[2.3744727510983187e-21,2.603715830745381e+94],7,0],[[4.041802722110561e+273,1.9237484678401125e+296],0,0],[[2.2344486550694127e+303,7.274885059224707e+101],0,0],[[2.3862496869231733e+76,4.3947035780108717e+80],0,0],[[5.7761035984398696e+196,4.71159629772397e+71],0,0],[[6.285466073933269e-22,3.4674975748042185e-38],0,0],[[7.733012551117168e-122,1.1382437559720419e-95],4,0],[[7.904830930452407e+266,3.6582181035579515e+271],0,0],[[2.305585729830853e-134,5.145630715071899e+201],1,0],[[8.206730771606587e+43,12242.925111988056],0,0],[[2.693652367216071e-233,2.6617051987770008e+262],0,0],[[3.3852972616768538e-282,1.6281541302987446e-101],4,0],[[4.023984950841538e-207,1.672209984146438e-177],1,0],[[5.997642554579093e+226,8267761121118583.0],0,0],[[3.025865987124205e+48,1.1774375942605503e+37],0,0],[[1.7578451228930594e-74,2.489149382420679e+27],4,0],[[3.938884622122182e-132,1.011396351900011e-125],0,0],[[9.807783778428908e+281,8.750108477874464e+259],0,0],[[1.0213927801883013e-280,2.4118761560252843e-59],7,0],[[1.195916640070373e-91,1.1745784325466232e+243],2,0],[[7.335711770377127e-38,1.214621771874996e+281],1,0],[[7.26354692283978e-298,6.697902311356943e+127],1,0],[[1.2351743153928947e-17,1.1081913151635317e-281],2,0],[[8.845830180604385e+55,4.68925600491289e+144],0,0],[[1.4639565733772952e-243,4.1910390611535265e+279],2,0],[[1.6983735818136165e-150,4.057563235251733e-168],1,0],[[1.5987895001152558e-250,1.0362772075683598e+99],1,0],[[2.574015514786201e-195,4.120748433400853e+266],1,0],[[2.828506773801223e-34,1.3980028593340099e-80],5,0],[[7.10451338618339e-112,2.752384728131671e-298],1,0],[[5.3848532123061334e+141,4.101841091919989e+82],0,0],[[1.8880422706568598e-131,6.087242169493258e-74],2,0],[[1.6828341140646555e-168,2.8288040637518216e+97],1,0],[[2.4020959302167836e+173,4.276010429020236e+247],0,0],[[1.679279614673279e-17,7.802007187654651e-08],1,0],[[6.190907314532847e-276,1.745791372849607e+234],4,0],[[5.911713422365171e-224,1.0773053002356648e-277],1,0],[[6.326943736711642e+259,2.02315867891966e+129],0,0],[[7.946583410099056e-261,2.144814527894872e+96],0,0],[[1.0066412328328968e-127,6.619416378892868e-163],6,0],[[1.1159565897451056e-40,9.147384059902005e+52],4,0],[[1.1165161433358629e+279,6.875662873883236e+254],0,0],[[7.053265896579982e-111,2.7551492956412816e-291],0,0],[[1.792618476145051e+142,3.258027489034141e+228],0,0],[[2.3780466739014797e+260,7.6303811992955545e+112],0,0],[[2.5226551585558244e+149,4.479310754223626e+77],0,0],[[6.3759232335206e-291,3.5785496756947083e-76],0,0],[[3.8797234898178104e-266,6.295638798327878e-124],2,0],[[6.621128712488456e-94,3.152253828409111e+30],6,0],[[3.5260516775312726e-162,4.379941188803635e-139],1,0],[[1.6672047786154368e+54,6.224498176564759e+252],0,0],[[6.79091067430158e+35,7.230059261043331e+195],0,0],[[4.3750470153682443e+216,8.334409599853035e+119],0,0],[[5.317028386962457e+95,1.5305424059226277e+248],0,0],[[6.409528319039091e+96,2.932037839848625e+137],0,0],[[8.883362223957793e+93,1.0708005705289017e+244],0,0],[[5.053806292662203e-155,2.523406045226158e-210],4,0],[[3.6380611743774316e+28,4.3451652399410245e+66],0,0],[[5.5111229904756633e-36,1.6975346890789871e+105],0,0],[[9.95962237767467e+23,1.044537127877944e+107],0,0],[[1.2032276449725793e-85,1.3054961346651174e-44],0,0],[[2.3075398048335097e-269,3.594097673489053e+137],1,0],[[3.130685264260855e-76,9.058189937007456e-86],1,0],[[4.53732938437198e+150,1.4669818938577088e+222],0,0],[[4.302212151190092e+240,2.4335687807904273e+271],0,0],[[6.550539660350184e-98,2.959467597264242e-230],1,0],[[2.052107344086851e-70,7.509188631026346e+286],4,0],[[2.2721511366771778e-250,4.0477581754304153e-125],0,0],[[4.931733655566518e-258,1.554975231016035e+153],4,0],[[3.4461749360980795e-185,7.6218106112626015e+295],1,0],[[1.3987141013277275e+91,6.132373723862702e+252],0,0],[[2.4801215181567776e-295,5.2115166535835604e-169],1,0],[[5.907165300326855e+32,1.9267899651560147e+275],0,0],[[7.475270857526654e-304,1.0862105938569748e+148],2,0],[[4.380578158292964e+195,3.0321252530234052e+38],0,0],[[2.4655809623086505e-116,1.1536689796869952e-11],6,0],[[8.444294654343975e-240,3.513520042407809e+153],3,0],[[3.28610894527258e-300,3.973558968153068e+125],0,0],[[2.5394112430978073e-295,1.4298675637930828e+180],1,0],[[8.332917955185835e+296,6.741628989608122e+71],0,0],[[1.6232174805713086e+70,3.765990859086882e+52],0,0],[[9.373092063300388e+294,2.8072978291071996e+105],0,0],[[8.752592959491946e-33,2.9311591750368227e+22],6,0],[[3.0241599246809088e+252,3.184319790336394e+219],0,0],[[1.0760470830369276e-175,3.1675280578479312e-77],1,0],[[9.685450907847438e-63,1.537477220142015e-154],4,0],[[1.4316271455151301e-258,2.996770630299676e+274],0,0],[[1.6611161145230723e-191,714914460440.7544],6,0],[[9.206946233985896e+265,5.909438823195212e+35],0,0],[[4.3407560983206045e+110,1.0066329381452874e+195],0,0],[[2.300114102133609e+63,3.3520036437628364e+162],0,0],[[3.7952930805105457e-199,7.532023979359606e+99],4,0],[[7.921938015189254e-17,1.6708793826459247e-57],0,0],[[1023.2212474515807,2.9921045438694274e+227],0,0],[[0.0009065963481940791,3.905734270420228e+62],0,0],[[1.891116192597785e-215,6.110124011150757e+46],1,0],[[8.602881405868794e-32,4.340706048852671e-131],0,0],[[2.098983450835455e-256,7.299124485355855e+137],3,0],[[1.2757681535951056e+63,3.8712901591408457e+228],0,0],[[7.968357209160169e+93,6.567762824642581e+50],0,0],[[4.548601565249598e+188,2.083390534713302e+140],0,0],[[4.161272910469861e-301,4.4146411652973813e+21],5,0],[[6.4821321459802055e+193,1.7939351909740315e+68],0,0],[[2.7868826984034328e-297,6.274746106885988e-177],4,0],[[7.586534919343994e-75,1.6802148352573582e-128],1,0],[[9.491422824807354e-253,4.0739010895320517e+273],0,0],[[2.2415352671784828e-150,1.625167989850363e+119],1,0],[[7.01138751262021e-280,1.4841539461233504e+69],5,0],[[2.824709004194289e-77,3.4428899655780295e-69],4,0],[[1.1294315636198499e-278,5.86009335903585e-102],0,0],[[7.990408500607478e+225,7.43139844967742e+271],0,0],[[2.6148734958275445e-59,1.4522191998681414e+95],2,0],[[2.1746518322952078e-54,2.8875549970579304e+175],0,0],[[3.1487113596301893e-35,2.0573785747587795e-193],5,0],[[2.790368131936616e-145,6.479697484604152e-174],1,0],[[1.220285592766294e+307,3.861133926570598e+263],0,0],[[1.2654603057808926e-132,5.480340484157898e-137],1,0],[[3.9582185084442164e+58,1.0006915947365432e+290],0,0],[[2.2385341061737422e-125,1.1296035831317978e+178],0,0],[[1.9956859819988883e+208,1.3053442887826894e+292],0,0],[[1.3725216771543658e-17,7.122506379956216e-199],3,0],[[5.070205966511977e-66,2.1591257954674133e-112],0,0],[[1.9637167511580492e-290,4.1122590034758076e+161],6,0],[[6.289641429573477e-53,4.44964744501718e-303],4,0],[[4.921669299348463e+48,9.174188702008102e+144],0,0],[[1.0631632090197916e+200,5.699753770483561e+65],0,0],[[3.7304700864524026e-88,7.425542676714504e-84],2,0],[[4.592687610132483e+74,5.15900678827599e+24],0,0],[[3.2643753621921254e-59,9.955169418668015e-289],0,0],[[1.8079468232084944e-292,4.570078655862018e+54],3,0],[[11359488250023.906,1.6061320544606304e+202],0,0],[[1.3892861350443015e-223,4.641071766140853e-231],1,0],[[7.360110913281388e-12,2.8431063873980092e+116],6,0],[[4.0565095880949425e+280,6.675799068433044e+76],0,0],[[9.20664563196908e+294,1.3131400831400088e+86],0,0],[[1.0649783843865697e-107,2.193063794905827e+36],0,0],[[1.1535731528175885e-293,16122199543.85404],8,0],[[0.23158759667032142,2.174373890634123e+206],0,1.0],[[2.8576099148948687e+47,4.535106259884878e+127],0,0],[[4.76442930878223e-20,1.662443875692076e+190],0,0],[[1.7386181741597865e-117,2.2869715061523446e+282],0,0],[[1.8576198723851754e+267,1.4640464205690061e+181],0,0],[[1.0730971371295596e-35,1.3731090395442879e-244],0,0],[[5.8750151697224545e-09,3.2058797502881587e-47],2,0],[[6.606104192306025e-76,2.1980904706831728e-104],4,0],[[1.1320100213914422e-197,9.218931403807496e-238],2,0],[[1.371076068469597e-276,3.7292018910669483e+61],0,0],[[7.468254766320453e-225,5.794033588679369e+140],1,0],[[3.2896013204457148e-279,1.1190715118628351e-13],4,0],[[1.855739410010682e-286,1.2449977298699466e-295],0,0],[[8.63596361370883e-168,3.1003420231048053e-198],0,0],[[1.4390244358772018e+249,2.9639589969742274e+281],0,0],[[2.0583492621633517e-132,1.73356572916747e+144],2,0],[[1.6662800714135864e-218,3.017825861340067e+260],1,0],[[1.7909913857676524e-234,4.184907550158769e-217],0,0],[[5.556148241691299e-119,1.5213816359492715e-307],0,0],[[3.486470059469502e+53,1.4785130640238136e+99],0,0],[[4.750171216619508e-73,1.0938841522691449e-182],4,0],[[9.94673708940353e+255,6.918320731214305e+101],0,0],[[5.706158108157338e+305,1.2638234743036793e+156],0,0],[[2.427769796556236e-78,7.21762410022307e+205],0,0],[[2.727021877346581e-178,1.860064553198903e-67],0,0],[[8.657759546694974e-157,2.0568784750151953e+96],0,0],[[1.0675856537644375e+279,5.0108195646214185e+182],0,0],[[2.412016495848343e-259,2.1622905926715047e-231],0,0],[[1.4157269095091182e+175,1.752320881957983e+240],0,0],[[7.474117465579979e+250,1.998141361266681e+100],0,0],[[1.542984322219514e-13,3.0489294036502483e-215],3,0],[[1.095382951219098e-121,4.4403690793251364e-66],4,0],[[3.0292511751059167e-285,4.774911884404591e+104],4,0],[[7366.597199336127,3.437966658215048e+175],0,0],[[1.013327533564468e-142,1.0958904515570749e+229],1,0],[[5.365396337730866e+62,5.564528795268944e+304],0,0],[[2.2999903268614278e-290,1.0741122062961354e-261],1,0],[[5.859557539322906e-140,12468368041124.15],1,0],[[3.29750078510446e+71,1.1536796494388956e+294],0,0],[[1.0050966216294641e+208,3094188499901330.5],0,0],[[2.486240422123665e+301,6.411662743035886e+150],0,0],[[1.1448971434422485e-274,1.3291916155898896e-54],0,0],[[5.99451935698111e-22,2.459533652847606e+166],1,0],[[5.471344172015073e-66,2.5497871706438334e+172],4,0],[[1.929136835934461e+126,1.4511860769870938e+51],0,0],[[1.6848563310412775e-81,1.8787633523770844e+304],1,0],[[2.9246728990313427e+289,4.038893686579631e+19],0,0],[[7.229157843683878e+19,7.0767085636431225e+53],0,0],[[1.5968409688876136e+240,1.6442404219839566e+41],0,0],[[1.2356592442417317e-130,2.7522555769102684e-277],1,0],[[2.0679460963453592e-53,3.5340357590538254e+140],4,0],[[1.0662100247031813e-43,2.521296463327911e+268],0,1.0],[[1.2229817874252346e-71,8.506337374180222e-99],0,0],[[2.3910560608115626e-11,2.932647945759088e-270],2,0],[[9.315042055884043e+48,4.0024068424625754e+43],0,0],[[1.43710899076724e+182,2.2997526865909637e+146],0,0]],"best-alt-per-point":[[[5.091954821941639e-192,6.815392098658887e+143],1,0],[[1.9872779421557533e+180,1.8165707546862427e+45],0,0],[[7.416044817432175e-280,4.187534830574239e+90],2,0],[[8.952174144166139e-302,1.0956116997098222e-31],1,0],[[2.7602034085604025e+247,3.933007183466984e+176],0,0],[[4.691318136614946e-91,2.2211280072565116e-303],1,0],[[9.07067712653544e+121,1.1966070572230463e+134],0,0],[[2.534573079598786e+169,3.2634856808337097e+195],0,0],[[6.317640848359807e-38,7.108640458245273e-156],1,0],[[1.37963739668883e-251,1.9832537005473266e-262],1,0],[[2.2237477837114185e-204,3.5971048785615273e+27],5,0],[[2.0235103563137384e-245,3.186488674327569e-306],0,0],[[4.535662949534244e+218,1.0124765649019447e+298],0,0],[[3.548084498024942e-190,1.2458518796694574e+90],5,0],[[1.0707760413948923e-209,1.8155292668497655e+36],2,0],[[8.082647412227132e-211,1.4588918120519666e-114],4,0],[[5.13876683088187e-118,9.467488944393916e+142],7,0],[[2.2187340876406246e+300,4.0696348581298066e+30],0,0],[[4.737175196542416e-301,9.453454014910064e+271],2,0],[[1.090098977941039e-114,5.7243448441390635e+162],1,0],[[2.571403883587662e-39,2.725225610867578e+225],0,0],[[5.081095649164445e+286,2.6437596200790387e+281],0,0],[[6.85981085886286e-168,1.9805731700427848e-169],1,0],[[9.636536782052696e-111,2.985561979664205e+171],1,0],[[1.0838714812801137e-216,1.1791770071753556e+107],2,0],[[1.072386271012045e-235,9.15478951965041e+260],0,0],[[4.954601632348903e-272,5.651261930475929e+123],1,0],[[5.598692384845278e-151,2.0020470402494707e-128],5,0],[[3.828518244176968e-308,9.957124504840989e+307],5,0],[[7.811244882301027e-64,2.3660873791160076e+189],3,0],[[1.1253736853318525e-46,4.582462397892038e-300],1,0],[[2271813.2914643916,1.711246486837026e+16],0,0],[[2.6512646278212223e-277,2.991195561163922e+252],1,0],[[2.8722519575799174e-220,8.864398632472997e+128],1,0],[[6.898353156002884e+56,5.049169591478046e+301],0,0],[[5.795257109406676e+26,7.254471041027067e+34],0,0],[[1.9680527238636918e-165,6.602387235477923e-263],0,0],[[4.390126892195692e-258,5.153839259075024e-217],0,0],[[3.7270065251219893e-51,4.1091807334876805e+121],0,0],[[1.2718549924538793e-67,1.4997147168186959e-133],3,0],[[7.779411959735569e-290,2.9896016385939845e-66],1,0],[[2.8931224974199074e-84,1.9240432527476484e-289],5,0],[[1.6509703901493846e-82,1.0044867221158944e+300],5,0],[[7.040383581327078e-101,5.96146379570227e+197],0,0],[[1.607215854807525e-42,2.5297373356963796e-300],0,0],[[8.687912841852904e-95,5.412515287604772e-64],3,0],[[7.938025318271498e-112,7.539778260587032e+298],0,0],[[4.0890448857589815e-140,6.188431370265012e+93],1,0],[[1.808792063616234e-42,1.2249262287356375e+78],2,0],[[2.813778253825615e-191,3.478381051263039e+83],9,0],[[4.959269200917455e+89,2.713904493922986e+74],0,0],[[1.6527464762421886e-272,9.284612428163018e+257],5,0],[[2.694216768013651e-08,2.481730668881008e+205],2,0],[[1.105287263764627e+102,5.503874697732584e+83],0,0],[[3.616766753957493e-134,1.405468459858575e-82],0,0],[[3.4960229754986024e-44,4.978416266226015e-252],3,0],[[0.34727693217194866,5.903688889215572e+29],3,0],[[1.179890420337443e-05,1.2231257626976233e+37],3,0],[[3.985430525999154e-166,3.256025304820758e-99],0,0],[[2.9695246403166212e+172,1.0507438437361721e+109],0,0],[[7.823934036267622e-77,4.7561975058596834e-110],0,0],[[1.1032765895259676e-126,5.131532610213896e-61],0,0],[[2.572749544642796e-298,5.3648379001218185e+144],2,0],[[2.3744727510983187e-21,2.603715830745381e+94],9,0],[[4.041802722110561e+273,1.9237484678401125e+296],0,0],[[2.2344486550694127e+303,7.274885059224707e+101],0,0],[[2.3862496869231733e+76,4.3947035780108717e+80],0,0],[[5.7761035984398696e+196,4.71159629772397e+71],0,0],[[6.285466073933269e-22,3.4674975748042185e-38],0,0],[[7.733012551117168e-122,1.1382437559720419e-95],5,0],[[7.904830930452407e+266,3.6582181035579515e+271],0,0],[[2.305585729830853e-134,5.145630715071899e+201],1,0],[[8.206730771606587e+43,12242.925111988056],0,0],[[2.693652367216071e-233,2.6617051987770008e+262],0,0],[[3.3852972616768538e-282,1.6281541302987446e-101],5,0],[[4.023984950841538e-207,1.672209984146438e-177],1,0],[[5.997642554579093e+226,8267761121118583.0],0,0],[[3.025865987124205e+48,1.1774375942605503e+37],0,0],[[1.7578451228930594e-74,2.489149382420679e+27],5,0],[[3.938884622122182e-132,1.011396351900011e-125],0,0],[[9.807783778428908e+281,8.750108477874464e+259],0,0],[[1.0213927801883013e-280,2.4118761560252843e-59],9,0],[[1.195916640070373e-91,1.1745784325466232e+243],2,0],[[7.335711770377127e-38,1.214621771874996e+281],1,0],[[7.26354692283978e-298,6.697902311356943e+127],1,0],[[1.2351743153928947e-17,1.1081913151635317e-281],2,0],[[8.845830180604385e+55,4.68925600491289e+144],0,0],[[1.4639565733772952e-243,4.1910390611535265e+279],2,0],[[1.6983735818136165e-150,4.057563235251733e-168],1,0],[[1.5987895001152558e-250,1.0362772075683598e+99],1,0],[[2.574015514786201e-195,4.120748433400853e+266],1,0],[[2.828506773801223e-34,1.3980028593340099e-80],3,0],[[7.10451338618339e-112,2.752384728131671e-298],1,0],[[5.3848532123061334e+141,4.101841091919989e+82],0,0],[[1.8880422706568598e-131,6.087242169493258e-74],2,0],[[1.6828341140646555e-168,2.8288040637518216e+97],1,0],[[2.4020959302167836e+173,4.276010429020236e+247],0,0],[[1.679279614673279e-17,7.802007187654651e-08],1,0],[[6.190907314532847e-276,1.745791372849607e+234],3,0],[[5.911713422365171e-224,1.0773053002356648e-277],1,0],[[6.326943736711642e+259,2.02315867891966e+129],0,0],[[7.946583410099056e-261,2.144814527894872e+96],0,0],[[1.0066412328328968e-127,6.619416378892868e-163],3,0],[[1.1159565897451056e-40,9.147384059902005e+52],5,0],[[1.1165161433358629e+279,6.875662873883236e+254],0,0],[[7.053265896579982e-111,2.7551492956412816e-291],0,0],[[1.792618476145051e+142,3.258027489034141e+228],0,0],[[2.3780466739014797e+260,7.6303811992955545e+112],0,0],[[2.5226551585558244e+149,4.479310754223626e+77],0,0],[[6.3759232335206e-291,3.5785496756947083e-76],0,0],[[3.8797234898178104e-266,6.295638798327878e-124],2,0],[[6.621128712488456e-94,3.152253828409111e+30],6,0],[[3.5260516775312726e-162,4.379941188803635e-139],1,0],[[1.6672047786154368e+54,6.224498176564759e+252],0,0],[[6.79091067430158e+35,7.230059261043331e+195],0,0],[[4.3750470153682443e+216,8.334409599853035e+119],0,0],[[5.317028386962457e+95,1.5305424059226277e+248],0,0],[[6.409528319039091e+96,2.932037839848625e+137],0,0],[[8.883362223957793e+93,1.0708005705289017e+244],0,0],[[5.053806292662203e-155,2.523406045226158e-210],5,0],[[3.6380611743774316e+28,4.3451652399410245e+66],0,0],[[5.5111229904756633e-36,1.6975346890789871e+105],0,0],[[9.95962237767467e+23,1.044537127877944e+107],0,0],[[1.2032276449725793e-85,1.3054961346651174e-44],0,0],[[2.3075398048335097e-269,3.594097673489053e+137],1,0],[[3.130685264260855e-76,9.058189937007456e-86],1,0],[[4.53732938437198e+150,1.4669818938577088e+222],0,0],[[4.302212151190092e+240,2.4335687807904273e+271],0,0],[[6.550539660350184e-98,2.959467597264242e-230],1,0],[[2.052107344086851e-70,7.509188631026346e+286],5,0],[[2.2721511366771778e-250,4.0477581754304153e-125],0,0],[[4.931733655566518e-258,1.554975231016035e+153],3,0],[[3.4461749360980795e-185,7.6218106112626015e+295],1,0],[[1.3987141013277275e+91,6.132373723862702e+252],0,0],[[2.4801215181567776e-295,5.2115166535835604e-169],1,0],[[5.907165300326855e+32,1.9267899651560147e+275],0,0],[[7.475270857526654e-304,1.0862105938569748e+148],2,0],[[4.380578158292964e+195,3.0321252530234052e+38],0,0],[[2.4655809623086505e-116,1.1536689796869952e-11],8,0],[[8.444294654343975e-240,3.513520042407809e+153],4,0],[[3.28610894527258e-300,3.973558968153068e+125],0,0],[[2.5394112430978073e-295,1.4298675637930828e+180],1,0],[[8.332917955185835e+296,6.741628989608122e+71],0,0],[[1.6232174805713086e+70,3.765990859086882e+52],0,0],[[9.373092063300388e+294,2.8072978291071996e+105],0,0],[[8.752592959491946e-33,2.9311591750368227e+22],8,0],[[3.0241599246809088e+252,3.184319790336394e+219],0,0],[[1.0760470830369276e-175,3.1675280578479312e-77],1,0],[[9.685450907847438e-63,1.537477220142015e-154],3,0],[[1.4316271455151301e-258,2.996770630299676e+274],0,0],[[1.6611161145230723e-191,714914460440.7544],6,0],[[9.206946233985896e+265,5.909438823195212e+35],0,0],[[4.3407560983206045e+110,1.0066329381452874e+195],0,0],[[2.300114102133609e+63,3.3520036437628364e+162],0,0],[[3.7952930805105457e-199,7.532023979359606e+99],5,0],[[7.921938015189254e-17,1.6708793826459247e-57],0,0],[[1023.2212474515807,2.9921045438694274e+227],0,0],[[0.0009065963481940791,3.905734270420228e+62],0,0],[[1.891116192597785e-215,6.110124011150757e+46],1,0],[[8.602881405868794e-32,4.340706048852671e-131],0,0],[[2.098983450835455e-256,7.299124485355855e+137],4,0],[[1.2757681535951056e+63,3.8712901591408457e+228],0,0],[[7.968357209160169e+93,6.567762824642581e+50],0,0],[[4.548601565249598e+188,2.083390534713302e+140],0,0],[[4.161272910469861e-301,4.4146411652973813e+21],3,0],[[6.4821321459802055e+193,1.7939351909740315e+68],0,0],[[2.7868826984034328e-297,6.274746106885988e-177],5,0],[[7.586534919343994e-75,1.6802148352573582e-128],1,0],[[9.491422824807354e-253,4.0739010895320517e+273],0,0],[[2.2415352671784828e-150,1.625167989850363e+119],1,0],[[7.01138751262021e-280,1.4841539461233504e+69],7,0],[[2.824709004194289e-77,3.4428899655780295e-69],5,0],[[1.1294315636198499e-278,5.86009335903585e-102],0,0],[[7.990408500607478e+225,7.43139844967742e+271],0,0],[[2.6148734958275445e-59,1.4522191998681414e+95],2,0],[[2.1746518322952078e-54,2.8875549970579304e+175],0,0],[[3.1487113596301893e-35,2.0573785747587795e-193],7,0],[[2.790368131936616e-145,6.479697484604152e-174],1,0],[[1.220285592766294e+307,3.861133926570598e+263],0,0],[[1.2654603057808926e-132,5.480340484157898e-137],1,0],[[3.9582185084442164e+58,1.0006915947365432e+290],0,0],[[2.2385341061737422e-125,1.1296035831317978e+178],0,0],[[1.9956859819988883e+208,1.3053442887826894e+292],0,0],[[1.3725216771543658e-17,7.122506379956216e-199],4,0],[[5.070205966511977e-66,2.1591257954674133e-112],0,0],[[1.9637167511580492e-290,4.1122590034758076e+161],3,0],[[6.289641429573477e-53,4.44964744501718e-303],5,0],[[4.921669299348463e+48,9.174188702008102e+144],0,0],[[1.0631632090197916e+200,5.699753770483561e+65],0,0],[[3.7304700864524026e-88,7.425542676714504e-84],2,0],[[4.592687610132483e+74,5.15900678827599e+24],0,0],[[3.2643753621921254e-59,9.955169418668015e-289],0,0],[[1.8079468232084944e-292,4.570078655862018e+54],3,0],[[11359488250023.906,1.6061320544606304e+202],0,0],[[1.3892861350443015e-223,4.641071766140853e-231],1,0],[[7.360110913281388e-12,2.8431063873980092e+116],8,0],[[4.0565095880949425e+280,6.675799068433044e+76],0,0],[[9.20664563196908e+294,1.3131400831400088e+86],0,0],[[1.0649783843865697e-107,2.193063794905827e+36],0,0],[[1.1535731528175885e-293,16122199543.85404],10,0],[[0.23158759667032142,2.174373890634123e+206],3,0],[[2.8576099148948687e+47,4.535106259884878e+127],0,0],[[4.76442930878223e-20,1.662443875692076e+190],0,0],[[1.7386181741597865e-117,2.2869715061523446e+282],0,0],[[1.8576198723851754e+267,1.4640464205690061e+181],0,0],[[1.0730971371295596e-35,1.3731090395442879e-244],0,0],[[5.8750151697224545e-09,3.2058797502881587e-47],2,0],[[6.606104192306025e-76,2.1980904706831728e-104],5,0],[[1.1320100213914422e-197,9.218931403807496e-238],2,0],[[1.371076068469597e-276,3.7292018910669483e+61],0,0],[[7.468254766320453e-225,5.794033588679369e+140],1,0],[[3.2896013204457148e-279,1.1190715118628351e-13],5,0],[[1.855739410010682e-286,1.2449977298699466e-295],0,0],[[8.63596361370883e-168,3.1003420231048053e-198],0,0],[[1.4390244358772018e+249,2.9639589969742274e+281],0,0],[[2.0583492621633517e-132,1.73356572916747e+144],2,0],[[1.6662800714135864e-218,3.017825861340067e+260],1,0],[[1.7909913857676524e-234,4.184907550158769e-217],0,0],[[5.556148241691299e-119,1.5213816359492715e-307],0,0],[[3.486470059469502e+53,1.4785130640238136e+99],0,0],[[4.750171216619508e-73,1.0938841522691449e-182],5,0],[[9.94673708940353e+255,6.918320731214305e+101],0,0],[[5.706158108157338e+305,1.2638234743036793e+156],0,0],[[2.427769796556236e-78,7.21762410022307e+205],0,0],[[2.727021877346581e-178,1.860064553198903e-67],0,0],[[8.657759546694974e-157,2.0568784750151953e+96],0,0],[[1.0675856537644375e+279,5.0108195646214185e+182],0,0],[[2.412016495848343e-259,2.1622905926715047e-231],0,0],[[1.4157269095091182e+175,1.752320881957983e+240],0,0],[[7.474117465579979e+250,1.998141361266681e+100],0,0],[[1.542984322219514e-13,3.0489294036502483e-215],3,0],[[1.095382951219098e-121,4.4403690793251364e-66],5,0],[[3.0292511751059167e-285,4.774911884404591e+104],5,0],[[7366.597199336127,3.437966658215048e+175],0,0],[[1.013327533564468e-142,1.0958904515570749e+229],1,0],[[5.365396337730866e+62,5.564528795268944e+304],0,0],[[2.2999903268614278e-290,1.0741122062961354e-261],1,0],[[5.859557539322906e-140,12468368041124.15],1,0],[[3.29750078510446e+71,1.1536796494388956e+294],0,0],[[1.0050966216294641e+208,3094188499901330.5],0,0],[[2.486240422123665e+301,6.411662743035886e+150],0,0],[[1.1448971434422485e-274,1.3291916155898896e-54],0,0],[[5.99451935698111e-22,2.459533652847606e+166],1,0],[[5.471344172015073e-66,2.5497871706438334e+172],3,0],[[1.929136835934461e+126,1.4511860769870938e+51],0,0],[[1.6848563310412775e-81,1.8787633523770844e+304],1,0],[[2.9246728990313427e+289,4.038893686579631e+19],0,0],[[7.229157843683878e+19,7.0767085636431225e+53],0,0],[[1.5968409688876136e+240,1.6442404219839566e+41],0,0],[[1.2356592442417317e-130,2.7522555769102684e-277],1,0],[[2.0679460963453592e-53,3.5340357590538254e+140],5,0],[[1.0662100247031813e-43,2.521296463327911e+268],6,0],[[1.2229817874252346e-71,8.506337374180222e-99],0,0],[[2.3910560608115626e-11,2.932647945759088e-270],2,0],[[9.315042055884043e+48,4.0024068424625754e+43],0,0],[[1.43710899076724e+182,2.2997526865909637e+146],0,0]],"fresh-alts":["#<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))>","#<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))>","#<alt-delta (λ (k n) (/ (+ (* (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (* (* k k) 1/8)) (+ (* (log n) (log n)) (* (log (* PI 2)) (log (* PI 2))))) (- (fma (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4)) (* (log (* PI 2)) (* (* k k) (log n))) (* (pow (* PI 2) 1/2) (pow n 1/2))) (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/2)) (fma k (log (* PI 2)) (* (log n) k))))) (sqrt k)))>","#<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))>","#<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* PI 2) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (sqrt k))))>","#<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2)))))>","#<alt-event (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>","#<alt-delta (λ (k n) (/ (* (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (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)))))>"]}* * * * [misc]pick:  Picked  #<alt-event (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* * * [misc]progress:  localizing error
* * * [misc]progress:  generating rewritten candidates
* * * * [misc]progress:  [ 1 / 4 ] rewriting at (2 2)
* * * * [misc]progress:  [ 2 / 4 ] rewriting at (2 2 1)
* * * * [misc]progress:  [ 3 / 4 ] rewriting at (2 1)
* * * * [misc]progress:  [ 4 / 4 ] rewriting at (2)
* * * [misc]progress:  generating series expansions
* * * * [misc]progress:  [ 1 / 4 ] generating series at (2 2)
* [misc]approximate:  Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 k) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) n)) in k
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) n) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) n) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (+ 1 (- k)) into (- 1 k)
* [misc]backup-simplify:  Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k))
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) n)) in n
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) n) in n
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 1) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (+ 1 (- k)) into (- 1 k)
* [misc]backup-simplify:  Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k))
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) n)) in n
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) n) in n
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 1) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (- 1 k) (+ (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (- 1 k) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1 (+ (log (* 2 PI)) (log n))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 1) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (+ (* 1 0) (* -1 (+ (log (* 2 PI)) (log n)))) into (- (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))
* [misc]backup-simplify:  Simplify (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))))
* [misc]backup-simplify:  Simplify (+ (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k)))))
* [misc]approximate:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in k
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (/ 1 n) into (/ 1 n)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in n
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) 1) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in n
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) 1) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* 2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (* 0 1)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 1))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
* [misc]approximate:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in (n k) around 0
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- -1) into 1
* [misc]backup-simplify:  Simplify (+ 0 1) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in k
* [misc]taylor:  Taking taylor expansion of (- n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (/ 1 (- n)) into (/ -1 n)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ -1 n)) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ -1 k)) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) -1) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ -1 k)) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) -1) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) in k
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) in k
* [misc]taylor:  Taking taylor expansion of 1/2 in k
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) in k
* [misc]taylor:  Taking taylor expansion of (+ 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
* [misc]taylor:  Taking taylor expansion of (log (* -2 PI)) in k
* [misc]taylor:  Taking taylor expansion of (* -2 PI) in k
* [misc]taylor:  Taking taylor expansion of -2 in k
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]taylor:  Taking taylor expansion of (log n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (log n) into (log n)
* [misc]backup-simplify:  Simplify (+ 0 1) into 1
* [misc]backup-simplify:  Simplify (- (log n)) into (- (log n))
* [misc]backup-simplify:  Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (* 0 -1)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 -1))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
* [misc]taylor:  Taking taylor expansion of 0 in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
* * * * [misc]progress:  [ 2 / 4 ] generating series at (2 2 1)
* [misc]approximate:  Taking taylor expansion of (* (* 2 PI) n) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) n) in n
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) n) in n
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 1) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 1) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) n) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) 1) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (* 0 1)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 1))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
* [misc]approximate:  Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in (n) around 0
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) -1) into (* -2 PI)
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (* 0 -1)) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 -1))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
* * * * [misc]progress:  [ 3 / 4 ] generating series at (2 1)
* [misc]approximate:  Taking taylor expansion of (/ 1 (sqrt k)) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (- +nan.0) into (- +nan.0)
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (- +nan.0) into (- +nan.0)
* [misc]backup-simplify:  Simplify (+ (* (- +nan.0) k) (+ (- +nan.0) (* +nan.0 (/ 1 k)))) into (- (+ +nan.0 (- (+ (* +nan.0 k) (- (* +nan.0 (/ 1 k)))))))
* [misc]approximate:  Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (- +nan.0) into (- +nan.0)
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (- +nan.0) into (- +nan.0)
* [misc]backup-simplify:  Simplify (+ (* (- +nan.0) (pow (/ 1 k) 2)) (+ (* (- +nan.0) (/ 1 k)) +nan.0)) into (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2))))))))
* [misc]approximate:  Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in (k) around 0
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (- +nan.0) into (- +nan.0)
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (- +nan.0) into (- +nan.0)
* [misc]backup-simplify:  Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2))))))))
* * * * [misc]progress:  [ 4 / 4 ] generating series at (2)
* [misc]approximate:  Taking taylor expansion of (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt k)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (sqrt k) into (sqrt k)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt k))) into 0
* [misc]backup-simplify:  Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k))
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 k) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (+ 1 (- k)) into (- 1 k)
* [misc]backup-simplify:  Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k))
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) n)) in n
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) n) in n
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 1) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 k) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) n)) in k
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) n) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) n) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt k)) in k
* [misc]taylor:  Taking taylor expansion of (sqrt k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 k) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 k) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 1 0) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) n)) in k
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) n) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) n) into (* 2 (* n PI))
* [misc]backup-simplify:  Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
* [misc]backup-simplify:  Simplify (* +nan.0 (pow (* 2 (* n PI)) 1/2)) into (* +nan.0 (sqrt (* n (* 2 PI))))
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (sqrt (* n (* 2 PI)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (sqrt (* n (* 2 PI))) in n
* [misc]taylor:  Taking taylor expansion of (* n (* 2 PI)) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* 0 (* 2 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI)
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ (* 2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (* 0 n)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (- (/ -1 2) (+ (* 1/2 (/ 0 2)))) into -1/2
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI)))))
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI)))))) (* (- +nan.0) (pow (* 2 (* n PI)) 1/2))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))))
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI))))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (* n PI)) (sqrt 2)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (sqrt 2) (+ (log (* 2 PI)) (log n))) into (* (+ (log (* 2 PI)) (log n)) (sqrt 2))
* [misc]backup-simplify:  Simplify (* 0 (* (+ (log (* 2 PI)) (log n)) (sqrt 2))) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (* 0 (sqrt 2)) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 PI))
* [misc]backup-simplify:  Simplify (- (* +nan.0 PI)) into (- (* +nan.0 PI))
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 n))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* n (* 2 PI))) (pow (log (* 2 (* n PI))) 2)))
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (* 1/8 (* (sqrt (* n (* 2 PI))) (pow (log (* 2 (* n PI))) 2)))) (+ (* (- +nan.0) (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI)))))) (* (- +nan.0) (pow (* 2 (* n PI)) 1/2)))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))))))
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI))))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))) in n
* [misc]taylor:  Taking taylor expansion of (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]taylor:  Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n
* [misc]taylor:  Taking taylor expansion of (exp (* 2 (log (log (* 2 (* n PI)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (log (log (* 2 (* n PI))))) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (log (log (* 2 (* n PI)))) in n
* [misc]taylor:  Taking taylor expansion of (log (* 2 (* n PI))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (* 2 0) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (log (+ (log (* 2 PI)) (log n))) into (log (+ (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 2 (log (+ (log (* 2 PI)) (log n)))) into (* 2 (log (+ (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 2 (log (+ (log (* 2 PI)) (log n))))) into (pow (+ (log (* 2 PI)) (log n)) 2)
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (* (sqrt (* n PI)) (sqrt 2)) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (* n PI)) in n
* [misc]taylor:  Taking taylor expansion of (* n PI) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]backup-simplify:  Simplify (* 0 PI) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* 1 PI)) into PI
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
* [misc]taylor:  Taking taylor expansion of (sqrt 2) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (sqrt 2) into (sqrt 2)
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt 2))) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (sqrt 2) (+ (log (* 2 PI)) (log n))) into (* (+ (log (* 2 PI)) (log n)) (sqrt 2))
* [misc]backup-simplify:  Simplify (* 0 (* (+ (log (* 2 PI)) (log n)) (sqrt 2))) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (* (sqrt 2) (pow (+ (log (* 2 PI)) (log n)) 2)) into (* (pow (+ (log (* 2 PI)) (log n)) 2) (sqrt 2))
* [misc]backup-simplify:  Simplify (* 0 (* (pow (+ (log (* 2 PI)) (log n)) 2) (sqrt 2))) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (* 0 (sqrt 2)) into 0
* [misc]backup-simplify:  Simplify (* +nan.0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* (* +nan.0 PI) (* (+ (log (* 2 PI)) (log n)) (sqrt 2)))) into (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))) (* 0 0)) into (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))
* [misc]backup-simplify:  Simplify (+ (* 0 0) (* (* +nan.0 PI) (sqrt 2))) into (- (* +nan.0 (* PI (sqrt 2))))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (- (* +nan.0 (* PI (sqrt 2))))) (* 0 0)) into (- (* +nan.0 (* PI (sqrt 2))))
* [misc]backup-simplify:  Simplify (- (- (* +nan.0 (* PI (sqrt 2))))) into (- (* +nan.0 (* PI (sqrt 2))))
* [misc]backup-simplify:  Simplify (+ (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))) (- (* +nan.0 (* PI (sqrt 2))))) into (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))))
* [misc]backup-simplify:  Simplify (- (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))))) into (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))))
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))))) into (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))))
* [misc]backup-simplify:  Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
* [misc]backup-simplify:  Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
* [misc]backup-simplify:  Simplify (+ (* +nan.0 (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (pow PI 2)))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (pow PI 2))) into (- (* +nan.0 (pow PI 2)))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (pow PI 2))) (* (pow n 2) (/ 1 k))) (+ (* (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))))) (* n 1)) (* (- (* +nan.0 PI)) (* n (/ 1 k))))) into (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) k)) (- (+ (* +nan.0 (* n (* PI (sqrt 2)))) (- (+ (* +nan.0 (/ (* n PI) k)) (- (+ (* +nan.0 (* n (* PI (* (log n) (sqrt 2))))) (- (* +nan.0 (* n (* PI (* (log (* 2 PI)) (sqrt 2))))))))))))))
* [misc]approximate:  Taking taylor expansion of (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k)
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in n
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) 1) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in k
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (/ 1 n) into (/ 1 n)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ 1 1) into 1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (+ 0 -1) into -1
* [misc]backup-simplify:  Simplify (/ -1 2) into -1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in k
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (/ 1 n) into (/ 1 n)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) into (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (log (* 2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (* (- (log (* 2 PI)) (log n)) (- 1 (/ 1 k))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (+ (* +nan.0 0) (* (- +nan.0) (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (log (* 2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (* (- (log (* 2 PI)) (log n)) (- 1 (/ 1 k))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (+ (* (- (log (* 2 PI)) (log n)) 0) (* 0 (- 1 (/ 1 k)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (+ (* +nan.0 0) (+ (* (- +nan.0) 0) (* (- +nan.0) (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))) in n
* [misc]taylor:  Taking taylor expansion of (log (* 2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (log (* 2 PI)) into (log (* 2 PI))
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
* [misc]backup-simplify:  Simplify (- (/ 1 k)) into (- (/ 1 k))
* [misc]backup-simplify:  Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (* (- (log (* 2 PI)) (log n)) (- 1 (/ 1 k))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))) (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)))))))
* [misc]approximate:  Taking taylor expansion of (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) in (k n) around 0
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in n
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]backup-simplify:  Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0
* [misc]backup-simplify:  Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
* [misc]backup-simplify:  Simplify (/ 1 (sqrt (/ -1 k))) into (/ 1 (sqrt (/ -1 k)))
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in n
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in n
* [misc]taylor:  Taking taylor expansion of (- k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (- k) into (- k)
* [misc]backup-simplify:  Simplify (/ 1 (- k)) into (/ -1 k)
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- (/ -1 k)) into (/ 1 k)
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k)))
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in n
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in n
* [misc]taylor:  Taking taylor expansion of 2 in n
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in n
* [misc]taylor:  Taking taylor expansion of (- n) in n
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) -1) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- -1) into 1
* [misc]backup-simplify:  Simplify (+ 0 1) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in k
* [misc]taylor:  Taking taylor expansion of (- n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (/ 1 (- n)) into (/ -1 n)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ -1 n)) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))
* [misc]taylor:  Taking taylor expansion of (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in k
* [misc]taylor:  Taking taylor expansion of (sqrt (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]backup-simplify:  Simplify (sqrt 0) into 0
* [misc]backup-simplify:  Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
* [misc]backup-simplify:  Simplify (/ 1 +nan.0) into +nan.0
* [misc]taylor:  Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in k
* [misc]taylor:  Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in k
* [misc]taylor:  Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in k
* [misc]taylor:  Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k
* [misc]taylor:  Taking taylor expansion of (- 1 (/ 1 (- k))) in k
* [misc]taylor:  Taking taylor expansion of 1 in k
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 (- k)) in k
* [misc]taylor:  Taking taylor expansion of (- k) in k
* [misc]taylor:  Taking taylor expansion of k in k
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (/ 1 -1) into -1
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]backup-simplify:  Simplify (- -1) into 1
* [misc]backup-simplify:  Simplify (+ 0 1) into 1
* [misc]backup-simplify:  Simplify (/ 1 2) into 1/2
* [misc]taylor:  Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in k
* [misc]taylor:  Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in k
* [misc]taylor:  Taking taylor expansion of (* 2 PI) in k
* [misc]taylor:  Taking taylor expansion of 2 in k
* [misc]backup-simplify:  Simplify 2 into 2
* [misc]taylor:  Taking taylor expansion of PI in k
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of (/ 1 (- n)) in k
* [misc]taylor:  Taking taylor expansion of (- n) in k
* [misc]taylor:  Taking taylor expansion of n in k
* [misc]backup-simplify:  Simplify n into n
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (- n) into (- n)
* [misc]backup-simplify:  Simplify (/ 1 (- n)) into (/ -1 n)
* [misc]backup-simplify:  Simplify (* 2 PI) into (* 2 PI)
* [misc]backup-simplify:  Simplify (* (* 2 PI) (/ -1 n)) into (* -2 (/ PI n))
* [misc]backup-simplify:  Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
* [misc]backup-simplify:  Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
* [misc]backup-simplify:  Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (+ 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log (* -2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -2 in n
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) into (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (+ (* +nan.0 0) (* (- +nan.0) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (+ 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log (* -2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -2 in n
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) into (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* -2 0) (* 0 PI)) into 0
* [misc]backup-simplify:  Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
* [misc]backup-simplify:  Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
* [misc]backup-simplify:  Simplify (+ 0 0) into 0
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (+ (* (+ 1 (/ 1 k)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
* [misc]backup-simplify:  Simplify (+ (* 1/2 0) (* 0 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into 0
* [misc]backup-simplify:  Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
* [misc]backup-simplify:  Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into 0
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- 0) into 0
* [misc]backup-simplify:  Simplify (- 1) into -1
* [misc]backup-simplify:  Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0
* [misc]backup-simplify:  Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
* [misc]backup-simplify:  Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
* [misc]backup-simplify:  Simplify (+ (* +nan.0 0) (+ (* (- +nan.0) 0) (* (- +nan.0) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))
* [misc]taylor:  Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) in n
* [misc]taylor:  Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) in n
* [misc]taylor:  Taking taylor expansion of +nan.0 in n
* [misc]backup-simplify:  Simplify +nan.0 into +nan.0
* [misc]taylor:  Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n
* [misc]taylor:  Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n
* [misc]taylor:  Taking taylor expansion of 1/2 in n
* [misc]backup-simplify:  Simplify 1/2 into 1/2
* [misc]taylor:  Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) in n
* [misc]taylor:  Taking taylor expansion of (+ 1 (/ 1 k)) in n
* [misc]taylor:  Taking taylor expansion of 1 in n
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]taylor:  Taking taylor expansion of (/ 1 k) in n
* [misc]taylor:  Taking taylor expansion of k in n
* [misc]backup-simplify:  Simplify k into k
* [misc]backup-simplify:  Simplify (/ 1 k) into (/ 1 k)
* [misc]taylor:  Taking taylor expansion of (log (* -2 (/ PI n))) in n
* [misc]taylor:  Taking taylor expansion of (* -2 (/ PI n)) in n
* [misc]taylor:  Taking taylor expansion of -2 in n
* [misc]backup-simplify:  Simplify -2 into -2
* [misc]taylor:  Taking taylor expansion of (/ PI n) in n
* [misc]taylor:  Taking taylor expansion of PI in n
* [misc]backup-simplify:  Simplify PI into PI
* [misc]taylor:  Taking taylor expansion of n in n
* [misc]backup-simplify:  Simplify 0 into 0
* [misc]backup-simplify:  Simplify 1 into 1
* [misc]backup-simplify:  Simplify (/ PI 1) into PI
* [misc]backup-simplify:  Simplify (* -2 PI) into (* -2 PI)
* [misc]backup-simplify:  Simplify (log (* -2 PI)) into (log (* -2 PI))
* [misc]backup-simplify:  Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k))
* [misc]backup-simplify:  Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
* [misc]backup-simplify:  Simplify (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) into (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))
* [misc]backup-simplify:  Simplify (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))
* [misc]backup-simplify:  Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))
* [misc]backup-simplify:  Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))))
* [misc]backup-simplify:  Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))))))))
* * * [misc]progress:  simplifying candidates
* * * * [misc]progress:  [ 1 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (log1p (expm1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (expm1 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (expm1 (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (expm1 (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 2 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (expm1 (log1p (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (log1p (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (log1p (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (log1p (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 3 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (58 enodes)
* * [misc]simplify:  iters left: 3 (145 enodes)
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2))))
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2))))
* * * * [misc]progress:  [ 4 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (58 enodes)
* * [misc]simplify:  iters left: 3 (145 enodes)
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2))))
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2))))
* * * * [misc]progress:  [ 5 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* 1 (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (30 enodes)
* * [misc]simplify:  iters left: 3 (51 enodes)
* * [misc]simplify:  iters left: 2 (66 enodes)
* * [misc]simplify:  iters left: 1 (81 enodes)
* [exit]simplify:  Simplified to (/ (- 1 k) 2)
* [exit]simplify:  Simplified to (/ (- 1 k) 2)
* * * * [misc]progress:  [ 6 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)))))>
* [enter]simplify:  Simplifying (pow (* (* 2 PI) n) (/ 1 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (20 enodes)
* * [misc]simplify:  iters left: 2 (22 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI 2) n) (/ 1 2))
* [exit]simplify:  Simplified to (pow (* (* PI 2) n) (/ 1 2))
* [enter]simplify:  Simplifying (pow (* (* 2 PI) n) (/ k 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (18 enodes)
* * [misc]simplify:  iters left: 2 (20 enodes)
* [exit]simplify:  Simplified to (pow (* 2 (* n PI)) (/ k 2))
* [exit]simplify:  Simplified to (pow (* 2 (* n PI)) (/ k 2))
* * * * [misc]progress:  [ 7 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 8 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI 2) n) (sqrt (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (pow (* (* PI 2) n) (sqrt (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 9 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (pow (* (* 2 PI) n) 1)
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (20 enodes)
* [exit]simplify:  Simplified to (* (* n PI) 2)
* [exit]simplify:  Simplified to (* (* n PI) 2)
* * * * [misc]progress:  [ 10 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (- 1 k)) (/ 1 2))))>
* [enter]simplify:  Simplifying (pow (* (* 2 PI) n) (- 1 k))
* * [misc]simplify:  iters left: 5 (9 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (25 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI 2) n) (- 1 k))
* [exit]simplify:  Simplified to (pow (* (* PI 2) n) (- 1 k))
* * * * [misc]progress:  [ 11 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (pow (* 2 PI) (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (16 enodes)
* * [misc]simplify:  iters left: 3 (19 enodes)
* * [misc]simplify:  iters left: 2 (21 enodes)
* [exit]simplify:  Simplified to (pow (* PI 2) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow (* PI 2) (/ (- 1 k) 2))
* [enter]simplify:  Simplifying (pow n (/ (- 1 k) 2))
* * [misc]simplify:  iters left: 5 (7 enodes)
* * [misc]simplify:  iters left: 4 (14 enodes)
* * [misc]simplify:  iters left: 3 (17 enodes)
* * [misc]simplify:  iters left: 2 (19 enodes)
* [exit]simplify:  Simplified to (pow n (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow n (/ (- 1 k) 2))
* * * * [misc]progress:  [ 12 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (- 1 k) 2)) 1)))>
* * * * [misc]progress:  [ 13 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (exp (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (90 enodes)
* * [misc]simplify:  iters left: 2 (246 enodes)
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
* [exit]simplify:  Simplified to (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
* * * * [misc]progress:  [ 14 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (log (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (exp (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (exp (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 15 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (* (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (35 enodes)
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
* [enter]simplify:  Simplifying (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 16 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (cbrt (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (24 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (pow (pow (* PI (* n 2)) (/ (- 1 k) 2)) 3)
* [exit]simplify:  Simplified to (pow (pow (* PI (* n 2)) (/ (- 1 k) 2)) 3)
* * * * [misc]progress:  [ 17 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (* (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* [enter]simplify:  Simplifying (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (31 enodes)
* * [misc]simplify:  iters left: 3 (34 enodes)
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 18 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
* * * * [misc]progress:  [ 19 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (log1p (expm1 (* (* 2 PI) n))) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (expm1 (* (* 2 PI) n))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (expm1 (* 2 (* n PI)))
* [exit]simplify:  Simplified to (expm1 (* 2 (* n PI)))
* * * * [misc]progress:  [ 20 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (expm1 (log1p (* (* 2 PI) n))) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (log1p (* (* 2 PI) n))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (log1p (* 2 (* n PI)))
* [exit]simplify:  Simplified to (log1p (* 2 (* n PI)))
* * * * [misc]progress:  [ 21 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
* * * * [misc]progress:  [ 22 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (log (* (* 2 PI) n))) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (log (* (* 2 PI) n))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (13 enodes)
* * [misc]simplify:  iters left: 3 (24 enodes)
* * [misc]simplify:  iters left: 2 (40 enodes)
* [exit]simplify:  Simplified to (log (* (* n PI) 2))
* [exit]simplify:  Simplified to (log (* (* n PI) 2))
* * * * [misc]progress:  [ 23 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (log (exp (* (* 2 PI) n))) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (exp (* (* 2 PI) n))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* * [misc]simplify:  iters left: 3 (23 enodes)
* * [misc]simplify:  iters left: 2 (29 enodes)
* * [misc]simplify:  iters left: 1 (40 enodes)
* [exit]simplify:  Simplified to (pow (exp PI) (* n 2))
* [exit]simplify:  Simplified to (pow (exp PI) (* n 2))
* * * * [misc]progress:  [ 24 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n))) (cbrt (* (* 2 PI) n))) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n)))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (11 enodes)
* * [misc]simplify:  iters left: 4 (17 enodes)
* * [misc]simplify:  iters left: 3 (18 enodes)
* [exit]simplify:  Simplified to (* (cbrt (* (* n PI) 2)) (cbrt (* (* n PI) 2)))
* [exit]simplify:  Simplified to (* (cbrt (* (* n PI) 2)) (cbrt (* (* n PI) 2)))
* [enter]simplify:  Simplifying (cbrt (* (* 2 PI) n))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (cbrt (* 2 (* n PI)))
* [exit]simplify:  Simplified to (cbrt (* 2 (* n PI)))
* * * * [misc]progress:  [ 25 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))
* * [misc]simplify:  iters left: 6 (7 enodes)
* * [misc]simplify:  iters left: 5 (18 enodes)
* * [misc]simplify:  iters left: 4 (53 enodes)
* * [misc]simplify:  iters left: 3 (168 enodes)
* [exit]simplify:  Simplified to (pow (* (* n 2) PI) 3)
* [exit]simplify:  Simplified to (pow (* (* n 2) PI) 3)
* * * * [misc]progress:  [ 26 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (* (sqrt (* (* 2 PI) n)) (sqrt (* (* 2 PI) n))) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (sqrt (* (* 2 PI) n))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (sqrt (* 2 (* n PI)))
* [exit]simplify:  Simplified to (sqrt (* 2 (* n PI)))
* [enter]simplify:  Simplifying (sqrt (* (* 2 PI) n))
* * [misc]simplify:  iters left: 5 (6 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* * [misc]simplify:  iters left: 3 (16 enodes)
* * [misc]simplify:  iters left: 2 (18 enodes)
* [exit]simplify:  Simplified to (sqrt (* 2 (* n PI)))
* [exit]simplify:  Simplified to (sqrt (* 2 (* n PI)))
* * * * [misc]progress:  [ 27 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (* 1 (* (* 2 PI) n)) (/ (- 1 k) 2))))>
* * * * [misc]progress:  [ 28 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* PI n)) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* PI n)
* * [misc]simplify:  iters left: 2 (3 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (* n PI)
* [exit]simplify:  Simplified to (* n PI)
* * * * [misc]progress:  [ 29 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))>
* * * * [misc]progress:  [ 30 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (log1p (expm1 (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (expm1 (/ 1 (sqrt k)))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* [exit]simplify:  Simplified to (expm1 (/ 1 (sqrt k)))
* [exit]simplify:  Simplified to (expm1 (/ 1 (sqrt k)))
* * * * [misc]progress:  [ 31 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (expm1 (log1p (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (log1p (/ 1 (sqrt k)))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* [exit]simplify:  Simplified to (log1p (/ 1 (sqrt k)))
* [exit]simplify:  Simplified to (log1p (/ 1 (sqrt k)))
* * * * [misc]progress:  [ 32 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow (sqrt k) -1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* * * * [misc]progress:  [ 33 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (- 1/2)
* * [misc]simplify:  iters left: 2 (2 enodes)
* [exit]simplify:  Simplified to (- 1/2)
* [exit]simplify:  Simplified to (- 1/2)
* * * * [misc]progress:  [ 34 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow (sqrt k) (- 1)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (- 1)
* * [misc]simplify:  iters left: 2 (2 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (- 1)
* [exit]simplify:  Simplified to (- 1)
* * * * [misc]progress:  [ 35 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow (/ 1 (sqrt k)) 1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* * * * [misc]progress:  [ 36 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (exp (- (log (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (- (log (sqrt k)))
* * [misc]simplify:  iters left: 4 (4 enodes)
* [exit]simplify:  Simplified to (- (log (sqrt k)))
* [exit]simplify:  Simplified to (- (log (sqrt k)))
* * * * [misc]progress:  [ 37 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (exp (log (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (log (/ 1 (sqrt k)))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (11 enodes)
* * [misc]simplify:  iters left: 2 (12 enodes)
* * [misc]simplify:  iters left: 1 (16 enodes)
* [exit]simplify:  Simplified to (- (log (sqrt k)))
* [exit]simplify:  Simplified to (- (log (sqrt k)))
* * * * [misc]progress:  [ 38 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (log (exp (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (exp (/ 1 (sqrt k)))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* [exit]simplify:  Simplified to (exp (/ 1 (sqrt k)))
* [exit]simplify:  Simplified to (exp (/ 1 (sqrt k)))
* * * * [misc]progress:  [ 39 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (cbrt (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (8 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k))))
* [exit]simplify:  Simplified to (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k))))
* [enter]simplify:  Simplifying (cbrt (/ 1 (sqrt k)))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* [exit]simplify:  Simplified to (cbrt (/ 1 (sqrt k)))
* [exit]simplify:  Simplified to (cbrt (/ 1 (sqrt k)))
* * * * [misc]progress:  [ 40 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (cbrt (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (25 enodes)
* * [misc]simplify:  iters left: 3 (36 enodes)
* * [misc]simplify:  iters left: 2 (60 enodes)
* * [misc]simplify:  iters left: 1 (79 enodes)
* [exit]simplify:  Simplified to (/ (/ 1 k) (sqrt k))
* [exit]simplify:  Simplified to (/ (/ 1 k) (sqrt k))
* * * * [misc]progress:  [ 41 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (sqrt (/ 1 (sqrt k)))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* [exit]simplify:  Simplified to (sqrt (/ 1 (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ 1 (sqrt k)))
* [enter]simplify:  Simplifying (sqrt (/ 1 (sqrt k)))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* [exit]simplify:  Simplified to (sqrt (/ 1 (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ 1 (sqrt k)))
* * * * [misc]progress:  [ 42 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (- 1) (- (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (- 1)
* * [misc]simplify:  iters left: 2 (2 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to (- 1)
* [exit]simplify:  Simplified to (- 1)
* [enter]simplify:  Simplifying (- (sqrt k))
* * [misc]simplify:  iters left: 3 (3 enodes)
* [exit]simplify:  Simplified to (- (sqrt k))
* [exit]simplify:  Simplified to (- (sqrt k))
* * * * [misc]progress:  [ 43 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (* 1 (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* * * * [misc]progress:  [ 44 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (* 1 (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt k))
* * [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:  [ 45 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ 1 (/ (sqrt k) 1)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (/ (sqrt k) 1)
* * [misc]simplify:  iters left: 3 (4 enodes)
* * [misc]simplify:  iters left: 2 (6 enodes)
* * [misc]simplify:  iters left: 1 (8 enodes)
* [exit]simplify:  Simplified to (sqrt k)
* [exit]simplify:  Simplified to (sqrt k)
* * * * [misc]progress:  [ 46 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * [misc]simplify:  iters left: 6 (6 enodes)
* * [misc]simplify:  iters left: 5 (10 enodes)
* [exit]simplify:  Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* [exit]simplify:  Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
* * * * [misc]progress:  [ 47 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (/ 1 (sqrt (sqrt k)))
* * [misc]simplify:  iters left: 4 (5 enodes)
* * [misc]simplify:  iters left: 3 (7 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* [exit]simplify:  Simplified to (/ 1 (sqrt (sqrt k)))
* * * * [misc]progress:  [ 48 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (/ (/ 1 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (/ 1 1)
* * [misc]simplify:  iters left: 2 (2 enodes)
* * [misc]simplify:  iters left: 1 (4 enodes)
* [exit]simplify:  Simplified to 1
* [exit]simplify:  Simplified to 1
* * * * [misc]progress:  [ 49 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (log1p (expm1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (expm1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (53 enodes)
* * [misc]simplify:  iters left: 2 (57 enodes)
* * [misc]simplify:  iters left: 1 (64 enodes)
* [exit]simplify:  Simplified to (expm1 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (expm1 (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 50 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (expm1 (log1p (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (log1p (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (53 enodes)
* * [misc]simplify:  iters left: 2 (57 enodes)
* * [misc]simplify:  iters left: 1 (64 enodes)
* [exit]simplify:  Simplified to (log1p (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (log1p (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 51 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (pow (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1))>
* * * * [misc]progress:  [ 52 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (66 enodes)
* * [misc]simplify:  iters left: 3 (164 enodes)
* [exit]simplify:  Simplified to (fma (log (* n (* PI 2))) (/ (- 1 k) 2) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* n (* PI 2))) (/ (- 1 k) 2) (- (log (sqrt k))))
* * * * [misc]progress:  [ 53 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (66 enodes)
* * [misc]simplify:  iters left: 3 (164 enodes)
* [exit]simplify:  Simplified to (fma (log (* n (* PI 2))) (/ (- 1 k) 2) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* n (* PI 2))) (/ (- 1 k) 2) (- (log (sqrt k))))
* * * * [misc]progress:  [ 54 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (- (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (+ (- (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (50 enodes)
* * [misc]simplify:  iters left: 3 (98 enodes)
* * [misc]simplify:  iters left: 2 (302 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* PI (* n 2))) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* PI (* n 2))) (- (log (sqrt k))))
* * * * [misc]progress:  [ 55 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (75 enodes)
* * [misc]simplify:  iters left: 3 (195 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k))))
* * * * [misc]progress:  [ 56 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (37 enodes)
* * [misc]simplify:  iters left: 4 (75 enodes)
* * [misc]simplify:  iters left: 3 (195 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k))))
* * * * [misc]progress:  [ 57 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (+ (log (/ 1 (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (33 enodes)
* * [misc]simplify:  iters left: 4 (59 enodes)
* * [misc]simplify:  iters left: 3 (120 enodes)
* * [misc]simplify:  iters left: 2 (436 enodes)
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (/ (- 1 k) 2) (log (* n (* PI 2))) (- (log (sqrt k))))
* * * * [misc]progress:  [ 58 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (exp (log (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (log (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (56 enodes)
* * [misc]simplify:  iters left: 3 (103 enodes)
* * [misc]simplify:  iters left: 2 (193 enodes)
* [exit]simplify:  Simplified to (fma (log (* PI (* n 2))) (/ (- 1 k) 2) (- (log (sqrt k))))
* [exit]simplify:  Simplified to (fma (log (* PI (* n 2))) (/ (- 1 k) 2) (- (log (sqrt k))))
* * * * [misc]progress:  [ 59 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (log (exp (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (exp (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (30 enodes)
* * [misc]simplify:  iters left: 4 (46 enodes)
* * [misc]simplify:  iters left: 3 (55 enodes)
* * [misc]simplify:  iters left: 2 (59 enodes)
* * [misc]simplify:  iters left: 1 (68 enodes)
* [exit]simplify:  Simplified to (pow (exp (/ 1 (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (pow (exp (/ 1 (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 60 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (17 enodes)
* * [misc]simplify:  iters left: 5 (41 enodes)
* * [misc]simplify:  iters left: 4 (97 enodes)
* * [misc]simplify:  iters left: 3 (179 enodes)
* * [misc]simplify:  iters left: 2 (347 enodes)
* [exit]simplify:  Simplified to (* (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (* k (sqrt k))))
* [exit]simplify:  Simplified to (* (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (* k (sqrt k))))
* * * * [misc]progress:  [ 61 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (* (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (29 enodes)
* * [misc]simplify:  iters left: 4 (45 enodes)
* * [misc]simplify:  iters left: 3 (54 enodes)
* * [misc]simplify:  iters left: 2 (58 enodes)
* * [misc]simplify:  iters left: 1 (65 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* [exit]simplify:  Simplified to (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))))
* [enter]simplify:  Simplifying (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (53 enodes)
* * [misc]simplify:  iters left: 2 (57 enodes)
* * [misc]simplify:  iters left: 1 (64 enodes)
* [exit]simplify:  Simplified to (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 62 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (cbrt (* (* (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (* (* (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (36 enodes)
* * [misc]simplify:  iters left: 4 (94 enodes)
* * [misc]simplify:  iters left: 3 (202 enodes)
* * [misc]simplify:  iters left: 2 (465 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* [exit]simplify:  Simplified to (/ (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* n (* PI 2)) (/ (- 1 k) 2))))
* * * * [misc]progress:  [ 63 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
* [enter]simplify:  Simplifying (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (53 enodes)
* * [misc]simplify:  iters left: 2 (57 enodes)
* * [misc]simplify:  iters left: 1 (64 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* [enter]simplify:  Simplifying (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (53 enodes)
* * [misc]simplify:  iters left: 2 (57 enodes)
* * [misc]simplify:  iters left: 1 (64 enodes)
* [exit]simplify:  Simplified to (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* [exit]simplify:  Simplified to (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))
* * * * [misc]progress:  [ 64 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* 1 (pow (* (* 2 PI) n) (/ 1 2))) (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))))>
* [enter]simplify:  Simplifying (* 1 (pow (* (* 2 PI) n) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (9 enodes)
* * [misc]simplify:  iters left: 5 (16 enodes)
* * [misc]simplify:  iters left: 4 (24 enodes)
* * [misc]simplify:  iters left: 3 (25 enodes)
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (/ 1 2))
* [exit]simplify:  Simplified to (pow (* (* PI n) 2) (/ 1 2))
* [enter]simplify:  Simplifying (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))
* * [misc]simplify:  iters left: 6 (10 enodes)
* * [misc]simplify:  iters left: 5 (15 enodes)
* * [misc]simplify:  iters left: 4 (21 enodes)
* * [misc]simplify:  iters left: 3 (22 enodes)
* [exit]simplify:  Simplified to (* (sqrt k) (pow (* 2 (* PI n)) (/ k 2)))
* [exit]simplify:  Simplified to (* (sqrt k) (pow (* 2 (* PI n)) (/ k 2)))
* * * * [misc]progress:  [ 65 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
* * * * [misc]progress:  [ 66 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (22 enodes)
* * [misc]simplify:  iters left: 4 (32 enodes)
* * [misc]simplify:  iters left: 3 (40 enodes)
* * [misc]simplify:  iters left: 2 (44 enodes)
* * [misc]simplify:  iters left: 1 (51 enodes)
* [exit]simplify:  Simplified to (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))
* [exit]simplify:  Simplified to (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 67 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt k)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))
* * [misc]simplify:  iters left: 6 (15 enodes)
* * [misc]simplify:  iters left: 5 (31 enodes)
* * [misc]simplify:  iters left: 4 (48 enodes)
* * [misc]simplify:  iters left: 3 (74 enodes)
* * [misc]simplify:  iters left: 2 (102 enodes)
* * [misc]simplify:  iters left: 1 (106 enodes)
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k))
* [exit]simplify:  Simplified to (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k))
* * * * [misc]progress:  [ 68 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (28 enodes)
* * [misc]simplify:  iters left: 4 (44 enodes)
* * [misc]simplify:  iters left: 3 (53 enodes)
* * [misc]simplify:  iters left: 2 (57 enodes)
* * [misc]simplify:  iters left: 1 (64 enodes)
* [exit]simplify:  Simplified to (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))
* [exit]simplify:  Simplified to (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k))
* * * * [misc]progress:  [ 69 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (/ 1 (sqrt k)) 1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) 1)
* * [misc]simplify:  iters left: 5 (5 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* [exit]simplify:  Simplified to (/ 1 (sqrt k))
* [exit]simplify:  Simplified to (/ 1 (sqrt k))
* * * * [misc]progress:  [ 70 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (* (cbrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* (cbrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (* (cbrt (/ 1 (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (* (cbrt (/ 1 (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 71 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (sqrt (/ 1 (sqrt k))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (14 enodes)
* * [misc]simplify:  iters left: 5 (26 enodes)
* * [misc]simplify:  iters left: 4 (35 enodes)
* * [misc]simplify:  iters left: 3 (38 enodes)
* [exit]simplify:  Simplified to (* (sqrt (/ 1 (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2)))
* [exit]simplify:  Simplified to (* (sqrt (/ 1 (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 72 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (52 enodes)
* * [misc]simplify:  iters left: 2 (56 enodes)
* * [misc]simplify:  iters left: 1 (63 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))
* [exit]simplify:  Simplified to (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 73 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (52 enodes)
* * [misc]simplify:  iters left: 2 (56 enodes)
* * [misc]simplify:  iters left: 1 (63 enodes)
* [exit]simplify:  Simplified to (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))
* [exit]simplify:  Simplified to (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 74 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2))) (pow (* (* 2 PI) n) (/ k 2))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2)))
* * [misc]simplify:  iters left: 6 (12 enodes)
* * [misc]simplify:  iters left: 5 (21 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (41 enodes)
* * [misc]simplify:  iters left: 2 (45 enodes)
* * [misc]simplify:  iters left: 1 (52 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k))
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k))
* * * * [misc]progress:  [ 75 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (/ (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt k)))>
* [enter]simplify:  Simplifying (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (11 enodes)
* * [misc]simplify:  iters left: 5 (23 enodes)
* * [misc]simplify:  iters left: 4 (34 enodes)
* * [misc]simplify:  iters left: 3 (37 enodes)
* [exit]simplify:  Simplified to (pow (* (* 2 n) PI) (/ (- 1 k) 2))
* [exit]simplify:  Simplified to (pow (* (* 2 n) PI) (/ (- 1 k) 2))
* * * * [misc]progress:  [ 76 / 88 ] simplifiying candidate #<alt-delta (λ (k n) (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
* * * * [misc]progress:  [ 77 / 88 ] simplifiying candidate #<alt-event (λ (k n) (* (/ 1 (sqrt k)) (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k)))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))))))
* * [misc]simplify:  iters left: 6 (41 enodes)
* * [misc]simplify:  iters left: 5 (117 enodes)
* * [misc]simplify:  iters left: 4 (405 enodes)
* [exit]simplify:  Simplified to (/ (+ (* (* (* k k) (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/8))) (+ (* (log (* PI 2)) (log (* PI 2))) (* (log n) (log n)))) (- (fma (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4)) (* (* (log n) (* k k)) (log (* PI 2))) (* (pow n 1/2) (pow (* PI 2) 1/2))) (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/2)) (fma (log (* PI 2)) k (* (log n) k))))) (sqrt k))
* * * * [misc]progress:  [ 78 / 88 ] simplifiying candidate #<alt-event (λ (k n) (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))))
* * [misc]simplify:  iters left: 6 (18 enodes)
* * [misc]simplify:  iters left: 5 (41 enodes)
* * [misc]simplify:  iters left: 4 (86 enodes)
* * [misc]simplify:  iters left: 3 (293 enodes)
* [exit]simplify:  Simplified to (/ (* (pow (* PI 2) (- 1/2 (* k 1/2))) (pow n (- 1/2 (* k 1/2)))) (sqrt k))
* * * * [misc]progress:  [ 79 / 88 ] simplifiying candidate #<alt-event (λ (k n) (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))
* * [misc]simplify:  iters left: 6 (19 enodes)
* * [misc]simplify:  iters left: 5 (41 enodes)
* * [misc]simplify:  iters left: 4 (86 enodes)
* * [misc]simplify:  iters left: 3 (307 enodes)
* [exit]simplify:  Simplified to (/ (pow (pow (exp 1/2) (- 1 k)) (- (log (* PI -2)) (log (/ -1 n)))) (sqrt k))
* * * * [misc]progress:  [ 80 / 88 ] simplifiying candidate #<alt-event (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (52 enodes)
* * [misc]simplify:  iters left: 2 (56 enodes)
* * [misc]simplify:  iters left: 1 (63 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 81 / 88 ] simplifiying candidate #<alt-event (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (52 enodes)
* * [misc]simplify:  iters left: 2 (56 enodes)
* * [misc]simplify:  iters left: 1 (63 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 82 / 88 ] simplifiying candidate #<alt-event (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2)))
* * [misc]simplify:  iters left: 6 (13 enodes)
* * [misc]simplify:  iters left: 5 (27 enodes)
* * [misc]simplify:  iters left: 4 (43 enodes)
* * [misc]simplify:  iters left: 3 (52 enodes)
* * [misc]simplify:  iters left: 2 (56 enodes)
* * [misc]simplify:  iters left: 1 (63 enodes)
* [exit]simplify:  Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))
* * * * [misc]progress:  [ 83 / 88 ] simplifiying candidate #<alt-event (λ (k n) (* (- (+ +nan.0 (- (+ (* +nan.0 k) (- (* +nan.0 (/ 1 k))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* (- (+ +nan.0 (- (+ (* +nan.0 k) (- (* +nan.0 (/ 1 k))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 84 / 88 ] simplifiying candidate #<alt-event (λ (k n) (* (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2)))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2)))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 85 / 88 ] simplifiying candidate #<alt-event (λ (k n) (* (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2)))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
* [enter]simplify:  Simplifying (* (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2)))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
* * * * [misc]progress:  [ 86 / 88 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) k)) (- (+ (* +nan.0 (* n (* PI (sqrt 2)))) (- (+ (* +nan.0 (/ (* n PI) k)) (- (+ (* +nan.0 (* n (* PI (* (log n) (sqrt 2))))) (- (* +nan.0 (* n (* PI (* (log (* 2 PI)) (sqrt 2)))))))))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) k)) (- (+ (* +nan.0 (* n (* PI (sqrt 2)))) (- (+ (* +nan.0 (/ (* n PI) k)) (- (+ (* +nan.0 (* n (* PI (* (log n) (sqrt 2))))) (- (* +nan.0 (* n (* PI (* (log (* 2 PI)) (sqrt 2))))))))))))))
* * * * [misc]progress:  [ 87 / 88 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)))))))
* * * * [misc]progress:  [ 88 / 88 ] simplifiying candidate #<alt-event (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))))>
* [enter]simplify:  Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))))))))
* * * [misc]progress:  adding candidates to table
* [misc]progress:  [Phase 3 of 3] Extracting.
* * [misc]regime-changes:  Finding splitpoints for: (#<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (pow (* PI 2) (/ 1 2)) (cbrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt k)))))> #<alt-delta (λ (k n) (* (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))))> #<alt-delta (λ (k n) (/ (+ (* (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (* (* k k) 1/8)) (+ (* (log n) (log n)) (* (log (* PI 2)) (log (* PI 2))))) (- (fma (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4)) (* (log (* PI 2)) (* (* k k) (log n))) (* (pow (* PI 2) 1/2) (pow n 1/2))) (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/2)) (fma k (log (* PI 2)) (* (log n) k))))) (sqrt k)))> #<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))> #<alt-delta (λ (k n) (* (/ (/ (pow n (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* PI 2) (/ 1 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt k)))))> #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (pow (* PI 2) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (sqrt k))))> #<alt-delta (λ (k n) (* (pow n (/ (- 1 k) 2)) (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))))> #<alt-delta (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2)))))> #<alt-event (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt-delta (λ (k n) (/ (* (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt (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)))))>)
* [misc]regimes:  Found splitpoints: (#s(sp 0 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) +nan.0)) , with alts (#<alt-delta (λ (k n) (/ (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) (sqrt k)))>)
* [enter]simplify:  Simplifying (pow (* n (* PI 2)) (/ 1 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (12 enodes)
* [exit]simplify:  Simplified to (pow (* (* 2 PI) n) (/ 1 2))
* [exit]simplify:  Simplified to (pow (* (* 2 PI) n) (/ 1 2))
* [enter]simplify:  Simplifying (pow (* n (* PI 2)) (/ k 2))
* * [misc]simplify:  iters left: 5 (8 enodes)
* * [misc]simplify:  iters left: 4 (10 enodes)
* [exit]simplify:  Simplified to (pow (* (* 2 PI) n) (/ k 2))
* [exit]simplify:  Simplified to (pow (* (* 2 PI) n) (/ k 2))
* * * * [misc]points:  Sampling 8000 additional inputs, on iter 0 have 0 / 8000
* * * * [misc]points:  Computing exacts on every 500 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 250 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 125 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 62 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 31 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 15 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 7 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 3 of 8000 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 8000 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 6533 additional inputs, on iter 1 have 1467 / 8000
* * * * [misc]points:  Computing exacts on every 408 of 6533 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 204 of 6533 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 102 of 6533 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 51 of 6533 points 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 6533 points 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 6533 points 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 6533 points 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 6533 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 6533 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 5303 additional inputs, on iter 2 have 2697 / 8000
* * * * [misc]points:  Computing exacts on every 331 of 5303 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 165 of 5303 points 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 5303 points 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 5303 points 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 5303 points 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 5303 points 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 5303 points 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 5303 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 5303 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4289 additional inputs, on iter 3 have 3711 / 8000
* * * * [misc]points:  Computing exacts on every 268 of 4289 points 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 4289 points 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 4289 points 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 4289 points 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 4289 points 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 4289 points 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 4289 points 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 4289 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 4289 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 3506 additional inputs, on iter 4 have 4494 / 8000
* * * * [misc]points:  Computing exacts on every 219 of 3506 points 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 3506 points 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 3506 points 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 3506 points 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 3506 points 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 3506 points 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 3506 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 3506 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 2864 additional inputs, on iter 5 have 5136 / 8000
* * * * [misc]points:  Computing exacts on every 179 of 2864 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 89 of 2864 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 44 of 2864 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 22 of 2864 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 11 of 2864 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 5 of 2864 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 2864 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 2864 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 2335 additional inputs, on iter 6 have 5665 / 8000
* * * * [misc]points:  Computing exacts on every 145 of 2335 points 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 2335 points 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 2335 points 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 2335 points 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 2335 points 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 2335 points 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 2335 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 2335 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 1868 additional inputs, on iter 7 have 6132 / 8000
* * * * [misc]points:  Computing exacts on every 116 of 1868 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 58 of 1868 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 29 of 1868 points 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 1868 points 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 1868 points 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 1868 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1868 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 1511 additional inputs, on iter 8 have 6489 / 8000
* * * * [misc]points:  Computing exacts on every 94 of 1511 points 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 1511 points 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 1511 points 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 1511 points 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 1511 points 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 1511 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1511 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 1213 additional inputs, on iter 9 have 6787 / 8000
* * * * [misc]points:  Computing exacts on every 75 of 1213 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 37 of 1213 points 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 1213 points 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 1213 points 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 1213 points 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 1213 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 1213 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 979 additional inputs, on iter 10 have 7021 / 8000
* * * * [misc]points:  Computing exacts on every 61 of 979 points 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 979 points 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 979 points 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 979 points 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 979 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 979 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 807 additional inputs, on iter 11 have 7193 / 8000
* * * * [misc]points:  Computing exacts on every 50 of 807 points 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 807 points 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 807 points 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 807 points 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 807 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 807 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 645 additional inputs, on iter 12 have 7355 / 8000
* * * * [misc]points:  Computing exacts on every 40 of 645 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 20 of 645 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 10 of 645 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 5 of 645 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 645 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 645 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 549 additional inputs, on iter 13 have 7451 / 8000
* * * * [misc]points:  Computing exacts on every 34 of 549 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 17 of 549 points 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 549 points 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 549 points 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 549 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 549 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 445 additional inputs, on iter 14 have 7555 / 8000
* * * * [misc]points:  Computing exacts on every 27 of 445 points 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 445 points 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 445 points 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 445 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 445 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 363 additional inputs, on iter 15 have 7637 / 8000
* * * * [misc]points:  Computing exacts on every 22 of 363 points 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 363 points 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 363 points 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 363 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 363 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 303 additional inputs, on iter 16 have 7697 / 8000
* * * * [misc]points:  Computing exacts on every 18 of 303 points 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 303 points 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 303 points 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 303 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 303 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 257 additional inputs, on iter 17 have 7743 / 8000
* * * * [misc]points:  Computing exacts on every 16 of 257 points 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 257 points 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 257 points 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 257 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 257 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 211 additional inputs, on iter 18 have 7789 / 8000
* * * * [misc]points:  Computing exacts on every 13 of 211 points 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 211 points 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 211 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 211 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 177 additional inputs, on iter 19 have 7823 / 8000
* * * * [misc]points:  Computing exacts on every 11 of 177 points 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 177 points 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 177 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 177 points
* * * * [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 20 have 7852 / 8000
* * * * [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 123 additional inputs, on iter 21 have 7877 / 8000
* * * * [misc]points:  Computing exacts on every 7 of 123 points 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 123 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 123 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 99 additional inputs, on iter 22 have 7901 / 8000
* * * * [misc]points:  Computing exacts on every 6 of 99 points 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 99 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 99 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 79 additional inputs, on iter 23 have 7921 / 8000
* * * * [misc]points:  Computing exacts on every 4 of 79 points 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 79 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 79 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 65 additional inputs, on iter 24 have 7935 / 8000
* * * * [misc]points:  Computing exacts on every 4 of 65 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts on every 2 of 65 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 65 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 53 additional inputs, on iter 25 have 7947 / 8000
* * * * [misc]points:  Computing exacts on every 3 of 53 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 53 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 46 additional inputs, on iter 26 have 7954 / 8000
* * * * [misc]points:  Computing exacts on every 2 of 46 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 46 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 37 additional inputs, on iter 27 have 7963 / 8000
* * * * [misc]points:  Computing exacts on every 2 of 37 points to ramp up precision
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Computing exacts for 37 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 30 additional inputs, on iter 28 have 7970 / 8000
* * * * [misc]points:  Computing exacts for 30 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 25 additional inputs, on iter 29 have 7975 / 8000
* * * * [misc]points:  Computing exacts for 25 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 20 additional inputs, on iter 30 have 7980 / 8000
* * * * [misc]points:  Computing exacts for 20 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 17 additional inputs, on iter 31 have 7983 / 8000
* * * * [misc]points:  Computing exacts for 17 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 15 additional inputs, on iter 32 have 7985 / 8000
* * * * [misc]points:  Computing exacts for 15 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 12 additional inputs, on iter 33 have 7988 / 8000
* * * * [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 34 have 7990 / 8000
* * * * [misc]points:  Computing exacts for 10 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 7 additional inputs, on iter 35 have 7993 / 8000
* * * * [misc]points:  Computing exacts for 7 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 6 additional inputs, on iter 36 have 7994 / 8000
* * * * [misc]points:  Computing exacts for 6 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 5 additional inputs, on iter 37 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 38 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 39 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 40 have 7997 / 8000
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [misc]points:  Sampling 4 additional inputs, on iter 41 have 7999 / 8000
* * * * [misc]points:  Computing exacts for 4 points
* * * * [misc]points:  Setting MPFR precision to 1088
* * * * [misc]points:  Setting MPFR precision to 1344
* * * * [misc]points:  Filtering points with unrepresentable outputs
* * * * [exit]points:  Sampled 8000 points with exact outputs