57.367 * [progress]: [Phase 1 of 3] Setting up. 0.002 * * * [progress]: [1/2] Preparing points 0.153 * * * [progress]: [2/2] Setting up program. 0.158 * [progress]: [Phase 2 of 3] Improving. 0.158 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.159 * * [simplify]: Extracting # 0 : cost 0 0.159 * * [simplify]: Extracting # 1 : cost 0 0.159 * * [simplify]: Extracting # 2 : cost 0 0.159 * * [simplify]: Extracting # 3 : cost 0 0.159 * * [simplify]: Extracting # 4 : cost 0 0.159 * * [simplify]: Extracting # 5 : cost 0 0.159 * * [simplify]: Extracting # 6 : cost 0 0.159 * * [simplify]: Extracting # 7 : cost 0 0.159 * * [simplify]: iteration 0 : 13 enodes (cost 16 ) 0.162 * * [simplify]: Extracting # 0 : cost 0 0.162 * * [simplify]: Extracting # 1 : cost 0 0.162 * * [simplify]: Extracting # 2 : cost 0 0.162 * * [simplify]: Extracting # 3 : cost 0 0.162 * * [simplify]: Extracting # 4 : cost 0 0.162 * * [simplify]: Extracting # 5 : cost 0 0.162 * * [simplify]: iteration 1 : 29 enodes (cost 16 ) 0.197 * * [simplify]: Extracting # 0 : cost 0 0.197 * * [simplify]: Extracting # 1 : cost 0 0.197 * * [simplify]: Extracting # 2 : cost 0 0.198 * * [simplify]: Extracting # 3 : cost 0 0.198 * * [simplify]: Extracting # 4 : cost 0 0.198 * * [simplify]: iteration 2 : 59 enodes (cost 16 ) 0.228 * * [simplify]: Extracting # 0 : cost 0 0.228 * * [simplify]: Extracting # 1 : cost 0 0.228 * * [simplify]: Extracting # 2 : cost 0 0.228 * * [simplify]: Extracting # 3 : cost 0 0.229 * * [simplify]: Extracting # 4 : cost 0 0.229 * * [simplify]: iteration 3 : 119 enodes (cost 16 ) 0.268 * * [simplify]: Extracting # 0 : cost 0 0.268 * * [simplify]: Extracting # 1 : cost 0 0.269 * * [simplify]: Extracting # 2 : cost 0 0.269 * * [simplify]: Extracting # 3 : cost 0 0.269 * * [simplify]: Extracting # 4 : cost 0 0.270 * * [simplify]: iteration 4 : 313 enodes (cost 16 ) 0.506 * * [simplify]: Extracting # 0 : cost 0 0.508 * * [simplify]: Extracting # 1 : cost 0 0.510 * * [simplify]: Extracting # 2 : cost 0 0.511 * * [simplify]: Extracting # 3 : cost 0 0.513 * * [simplify]: Extracting # 4 : cost 0 0.514 * * [simplify]: iteration 5 : 853 enodes (cost 16 ) 2.210 * * [simplify]: Extracting # 0 : cost 0 2.214 * * [simplify]: Extracting # 1 : cost 0 2.218 * * [simplify]: Extracting # 2 : cost 0 2.220 * * [simplify]: Extracting # 3 : cost 0 2.225 * * [simplify]: Extracting # 4 : cost 0 2.230 * * [simplify]: iteration 6 : 3196 enodes (cost 16 ) 3.979 * * [simplify]: Extracting # 0 : cost 0 3.990 * * [simplify]: Extracting # 1 : cost 0 3.995 * * [simplify]: Extracting # 2 : cost 0 4.000 * * [simplify]: Extracting # 3 : cost 0 4.005 * * [simplify]: Extracting # 4 : cost 0 4.009 * * [simplify]: iteration done: 5001 enodes (cost 16 ) 4.010 * [simplify]: Simplified to: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 4.010 * * [progress]: iteration 1 / 4 4.010 * * * [progress]: picking best candidate 4.012 * * * * [pick]: Picked # 4.012 * * * [progress]: localizing error 4.045 * * * [progress]: generating rewritten candidates 4.045 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 4.084 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 4.090 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 4.113 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 4.215 * * * [progress]: generating series expansions 4.215 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 4.217 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 4.217 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 4.217 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 4.217 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.217 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.218 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 4.218 * [taylor]: Taking taylor expansion of 0.5 in k 4.218 * [backup-simplify]: Simplify 0.5 into 0.5 4.218 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.218 * [taylor]: Taking taylor expansion of 1.0 in k 4.218 * [backup-simplify]: Simplify 1.0 into 1.0 4.218 * [taylor]: Taking taylor expansion of k in k 4.218 * [backup-simplify]: Simplify 0 into 0 4.218 * [backup-simplify]: Simplify 1 into 1 4.218 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.218 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.218 * [taylor]: Taking taylor expansion of 2.0 in k 4.218 * [backup-simplify]: Simplify 2.0 into 2.0 4.218 * [taylor]: Taking taylor expansion of (* n PI) in k 4.218 * [taylor]: Taking taylor expansion of n in k 4.218 * [backup-simplify]: Simplify n into n 4.218 * [taylor]: Taking taylor expansion of PI in k 4.218 * [backup-simplify]: Simplify PI into PI 4.218 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.218 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.218 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.219 * [backup-simplify]: Simplify (- 0) into 0 4.219 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.220 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 4.220 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 4.220 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 4.220 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.220 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.220 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.220 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.220 * [taylor]: Taking taylor expansion of 0.5 in n 4.220 * [backup-simplify]: Simplify 0.5 into 0.5 4.220 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.220 * [taylor]: Taking taylor expansion of 1.0 in n 4.220 * [backup-simplify]: Simplify 1.0 into 1.0 4.220 * [taylor]: Taking taylor expansion of k in n 4.220 * [backup-simplify]: Simplify k into k 4.220 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.220 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.220 * [taylor]: Taking taylor expansion of 2.0 in n 4.221 * [backup-simplify]: Simplify 2.0 into 2.0 4.221 * [taylor]: Taking taylor expansion of (* n PI) in n 4.221 * [taylor]: Taking taylor expansion of n in n 4.221 * [backup-simplify]: Simplify 0 into 0 4.221 * [backup-simplify]: Simplify 1 into 1 4.221 * [taylor]: Taking taylor expansion of PI in n 4.221 * [backup-simplify]: Simplify PI into PI 4.221 * [backup-simplify]: Simplify (* 0 PI) into 0 4.222 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.223 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.225 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.226 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.226 * [backup-simplify]: Simplify (- k) into (- k) 4.226 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.226 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 4.228 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.229 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.230 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.230 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.230 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.230 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.230 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.231 * [taylor]: Taking taylor expansion of 0.5 in n 4.231 * [backup-simplify]: Simplify 0.5 into 0.5 4.231 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.231 * [taylor]: Taking taylor expansion of 1.0 in n 4.231 * [backup-simplify]: Simplify 1.0 into 1.0 4.231 * [taylor]: Taking taylor expansion of k in n 4.231 * [backup-simplify]: Simplify k into k 4.231 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.231 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.231 * [taylor]: Taking taylor expansion of 2.0 in n 4.231 * [backup-simplify]: Simplify 2.0 into 2.0 4.231 * [taylor]: Taking taylor expansion of (* n PI) in n 4.231 * [taylor]: Taking taylor expansion of n in n 4.231 * [backup-simplify]: Simplify 0 into 0 4.231 * [backup-simplify]: Simplify 1 into 1 4.231 * [taylor]: Taking taylor expansion of PI in n 4.231 * [backup-simplify]: Simplify PI into PI 4.232 * [backup-simplify]: Simplify (* 0 PI) into 0 4.232 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.234 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.235 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.235 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.235 * [backup-simplify]: Simplify (- k) into (- k) 4.235 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.236 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 4.236 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.237 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.238 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.238 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.238 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.238 * [taylor]: Taking taylor expansion of 0.5 in k 4.238 * [backup-simplify]: Simplify 0.5 into 0.5 4.238 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.238 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.238 * [taylor]: Taking taylor expansion of 1.0 in k 4.238 * [backup-simplify]: Simplify 1.0 into 1.0 4.238 * [taylor]: Taking taylor expansion of k in k 4.238 * [backup-simplify]: Simplify 0 into 0 4.238 * [backup-simplify]: Simplify 1 into 1 4.238 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.238 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.238 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.238 * [taylor]: Taking taylor expansion of 2.0 in k 4.238 * [backup-simplify]: Simplify 2.0 into 2.0 4.238 * [taylor]: Taking taylor expansion of PI in k 4.238 * [backup-simplify]: Simplify PI into PI 4.239 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.239 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.239 * [taylor]: Taking taylor expansion of (log n) in k 4.239 * [taylor]: Taking taylor expansion of n in k 4.239 * [backup-simplify]: Simplify n into n 4.240 * [backup-simplify]: Simplify (log n) into (log n) 4.240 * [backup-simplify]: Simplify (- 0) into 0 4.240 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.241 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 4.241 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 4.242 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 4.243 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 4.244 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 4.244 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.245 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.246 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.246 * [backup-simplify]: Simplify (- 0) into 0 4.246 * [backup-simplify]: Simplify (+ 0 0) into 0 4.247 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 4.248 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.248 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 4.250 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.250 * [taylor]: Taking taylor expansion of 0 in k 4.250 * [backup-simplify]: Simplify 0 into 0 4.250 * [backup-simplify]: Simplify 0 into 0 4.250 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.251 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.252 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.252 * [backup-simplify]: Simplify (+ 0 0) into 0 4.252 * [backup-simplify]: Simplify (- 1) into -1 4.252 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.253 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 4.255 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 4.257 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 4.259 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 4.259 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.260 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.262 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.263 * [backup-simplify]: Simplify (- 0) into 0 4.263 * [backup-simplify]: Simplify (+ 0 0) into 0 4.263 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 4.269 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.270 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.272 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.272 * [taylor]: Taking taylor expansion of 0 in k 4.272 * [backup-simplify]: Simplify 0 into 0 4.272 * [backup-simplify]: Simplify 0 into 0 4.273 * [backup-simplify]: Simplify 0 into 0 4.274 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.278 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.280 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.280 * [backup-simplify]: Simplify (+ 0 0) into 0 4.280 * [backup-simplify]: Simplify (- 0) into 0 4.281 * [backup-simplify]: Simplify (+ 0 0) into 0 4.283 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.285 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 4.289 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 4.295 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 4.306 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 4.307 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 4.307 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 4.307 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 4.307 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.307 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.307 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 4.307 * [taylor]: Taking taylor expansion of 0.5 in k 4.307 * [backup-simplify]: Simplify 0.5 into 0.5 4.307 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.307 * [taylor]: Taking taylor expansion of 1.0 in k 4.307 * [backup-simplify]: Simplify 1.0 into 1.0 4.307 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.307 * [taylor]: Taking taylor expansion of k in k 4.307 * [backup-simplify]: Simplify 0 into 0 4.307 * [backup-simplify]: Simplify 1 into 1 4.308 * [backup-simplify]: Simplify (/ 1 1) into 1 4.308 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.308 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.308 * [taylor]: Taking taylor expansion of 2.0 in k 4.308 * [backup-simplify]: Simplify 2.0 into 2.0 4.308 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.308 * [taylor]: Taking taylor expansion of PI in k 4.308 * [backup-simplify]: Simplify PI into PI 4.308 * [taylor]: Taking taylor expansion of n in k 4.308 * [backup-simplify]: Simplify n into n 4.308 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.308 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.308 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.309 * [backup-simplify]: Simplify (- 1) into -1 4.309 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.309 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 4.310 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 4.310 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 4.310 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 4.310 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.310 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.310 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 4.310 * [taylor]: Taking taylor expansion of 0.5 in n 4.310 * [backup-simplify]: Simplify 0.5 into 0.5 4.310 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.310 * [taylor]: Taking taylor expansion of 1.0 in n 4.310 * [backup-simplify]: Simplify 1.0 into 1.0 4.310 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.310 * [taylor]: Taking taylor expansion of k in n 4.310 * [backup-simplify]: Simplify k into k 4.311 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.311 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.311 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.311 * [taylor]: Taking taylor expansion of 2.0 in n 4.311 * [backup-simplify]: Simplify 2.0 into 2.0 4.311 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.311 * [taylor]: Taking taylor expansion of PI in n 4.311 * [backup-simplify]: Simplify PI into PI 4.311 * [taylor]: Taking taylor expansion of n in n 4.311 * [backup-simplify]: Simplify 0 into 0 4.311 * [backup-simplify]: Simplify 1 into 1 4.312 * [backup-simplify]: Simplify (/ PI 1) into PI 4.312 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.313 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.313 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.314 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.314 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 4.315 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.316 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.318 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.318 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 4.318 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.318 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.318 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 4.318 * [taylor]: Taking taylor expansion of 0.5 in n 4.318 * [backup-simplify]: Simplify 0.5 into 0.5 4.318 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.318 * [taylor]: Taking taylor expansion of 1.0 in n 4.318 * [backup-simplify]: Simplify 1.0 into 1.0 4.318 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.318 * [taylor]: Taking taylor expansion of k in n 4.318 * [backup-simplify]: Simplify k into k 4.318 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.318 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.318 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.318 * [taylor]: Taking taylor expansion of 2.0 in n 4.318 * [backup-simplify]: Simplify 2.0 into 2.0 4.318 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.318 * [taylor]: Taking taylor expansion of PI in n 4.318 * [backup-simplify]: Simplify PI into PI 4.318 * [taylor]: Taking taylor expansion of n in n 4.318 * [backup-simplify]: Simplify 0 into 0 4.318 * [backup-simplify]: Simplify 1 into 1 4.319 * [backup-simplify]: Simplify (/ PI 1) into PI 4.319 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.321 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.321 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.321 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.321 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 4.322 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.324 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.325 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.325 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.325 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.325 * [taylor]: Taking taylor expansion of 0.5 in k 4.325 * [backup-simplify]: Simplify 0.5 into 0.5 4.326 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.326 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.326 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.326 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.326 * [taylor]: Taking taylor expansion of 2.0 in k 4.326 * [backup-simplify]: Simplify 2.0 into 2.0 4.326 * [taylor]: Taking taylor expansion of PI in k 4.326 * [backup-simplify]: Simplify PI into PI 4.326 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.327 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.327 * [taylor]: Taking taylor expansion of (log n) in k 4.327 * [taylor]: Taking taylor expansion of n in k 4.327 * [backup-simplify]: Simplify n into n 4.328 * [backup-simplify]: Simplify (log n) into (log n) 4.328 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.328 * [taylor]: Taking taylor expansion of 1.0 in k 4.328 * [backup-simplify]: Simplify 1.0 into 1.0 4.328 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.328 * [taylor]: Taking taylor expansion of k in k 4.328 * [backup-simplify]: Simplify 0 into 0 4.328 * [backup-simplify]: Simplify 1 into 1 4.328 * [backup-simplify]: Simplify (/ 1 1) into 1 4.328 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.329 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 4.330 * [backup-simplify]: Simplify (- 1) into -1 4.330 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.331 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 4.332 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 4.334 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.335 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.336 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.337 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.339 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.339 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.340 * [backup-simplify]: Simplify (- 0) into 0 4.340 * [backup-simplify]: Simplify (+ 0 0) into 0 4.340 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.342 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.343 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 4.345 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.345 * [taylor]: Taking taylor expansion of 0 in k 4.345 * [backup-simplify]: Simplify 0 into 0 4.345 * [backup-simplify]: Simplify 0 into 0 4.345 * [backup-simplify]: Simplify 0 into 0 4.346 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.348 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.351 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.351 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.352 * [backup-simplify]: Simplify (- 0) into 0 4.352 * [backup-simplify]: Simplify (+ 0 0) into 0 4.353 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 4.354 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.356 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 4.359 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.359 * [taylor]: Taking taylor expansion of 0 in k 4.359 * [backup-simplify]: Simplify 0 into 0 4.359 * [backup-simplify]: Simplify 0 into 0 4.359 * [backup-simplify]: Simplify 0 into 0 4.359 * [backup-simplify]: Simplify 0 into 0 4.360 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.361 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.367 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 4.367 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.368 * [backup-simplify]: Simplify (- 0) into 0 4.368 * [backup-simplify]: Simplify (+ 0 0) into 0 4.369 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 4.371 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.373 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 4.376 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.376 * [taylor]: Taking taylor expansion of 0 in k 4.377 * [backup-simplify]: Simplify 0 into 0 4.377 * [backup-simplify]: Simplify 0 into 0 4.378 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 4.379 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 4.379 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 4.379 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 4.379 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.379 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.379 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 4.379 * [taylor]: Taking taylor expansion of 0.5 in k 4.379 * [backup-simplify]: Simplify 0.5 into 0.5 4.379 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.379 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.379 * [taylor]: Taking taylor expansion of k in k 4.379 * [backup-simplify]: Simplify 0 into 0 4.379 * [backup-simplify]: Simplify 1 into 1 4.380 * [backup-simplify]: Simplify (/ 1 1) into 1 4.380 * [taylor]: Taking taylor expansion of 1.0 in k 4.380 * [backup-simplify]: Simplify 1.0 into 1.0 4.380 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.380 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.380 * [taylor]: Taking taylor expansion of -2.0 in k 4.380 * [backup-simplify]: Simplify -2.0 into -2.0 4.380 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.380 * [taylor]: Taking taylor expansion of PI in k 4.380 * [backup-simplify]: Simplify PI into PI 4.380 * [taylor]: Taking taylor expansion of n in k 4.380 * [backup-simplify]: Simplify n into n 4.380 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.380 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.380 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.381 * [backup-simplify]: Simplify (+ 1 0) into 1 4.381 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 4.381 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 4.381 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 4.382 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 4.382 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.382 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.382 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 4.382 * [taylor]: Taking taylor expansion of 0.5 in n 4.382 * [backup-simplify]: Simplify 0.5 into 0.5 4.382 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.382 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.382 * [taylor]: Taking taylor expansion of k in n 4.382 * [backup-simplify]: Simplify k into k 4.382 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.382 * [taylor]: Taking taylor expansion of 1.0 in n 4.382 * [backup-simplify]: Simplify 1.0 into 1.0 4.382 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.382 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.382 * [taylor]: Taking taylor expansion of -2.0 in n 4.382 * [backup-simplify]: Simplify -2.0 into -2.0 4.382 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.382 * [taylor]: Taking taylor expansion of PI in n 4.382 * [backup-simplify]: Simplify PI into PI 4.382 * [taylor]: Taking taylor expansion of n in n 4.382 * [backup-simplify]: Simplify 0 into 0 4.382 * [backup-simplify]: Simplify 1 into 1 4.383 * [backup-simplify]: Simplify (/ PI 1) into PI 4.383 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.384 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.384 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.385 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 4.386 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.387 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.389 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.389 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 4.389 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.389 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.389 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 4.389 * [taylor]: Taking taylor expansion of 0.5 in n 4.389 * [backup-simplify]: Simplify 0.5 into 0.5 4.389 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.389 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.389 * [taylor]: Taking taylor expansion of k in n 4.389 * [backup-simplify]: Simplify k into k 4.389 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.389 * [taylor]: Taking taylor expansion of 1.0 in n 4.389 * [backup-simplify]: Simplify 1.0 into 1.0 4.389 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.389 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.389 * [taylor]: Taking taylor expansion of -2.0 in n 4.389 * [backup-simplify]: Simplify -2.0 into -2.0 4.389 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.389 * [taylor]: Taking taylor expansion of PI in n 4.389 * [backup-simplify]: Simplify PI into PI 4.389 * [taylor]: Taking taylor expansion of n in n 4.389 * [backup-simplify]: Simplify 0 into 0 4.389 * [backup-simplify]: Simplify 1 into 1 4.390 * [backup-simplify]: Simplify (/ PI 1) into PI 4.390 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.391 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.391 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.392 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 4.393 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.395 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.396 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.396 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.396 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.396 * [taylor]: Taking taylor expansion of 0.5 in k 4.396 * [backup-simplify]: Simplify 0.5 into 0.5 4.396 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.396 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.396 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.396 * [taylor]: Taking taylor expansion of k in k 4.396 * [backup-simplify]: Simplify 0 into 0 4.396 * [backup-simplify]: Simplify 1 into 1 4.397 * [backup-simplify]: Simplify (/ 1 1) into 1 4.397 * [taylor]: Taking taylor expansion of 1.0 in k 4.397 * [backup-simplify]: Simplify 1.0 into 1.0 4.397 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.397 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.397 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.397 * [taylor]: Taking taylor expansion of -2.0 in k 4.397 * [backup-simplify]: Simplify -2.0 into -2.0 4.397 * [taylor]: Taking taylor expansion of PI in k 4.397 * [backup-simplify]: Simplify PI into PI 4.398 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.399 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.399 * [taylor]: Taking taylor expansion of (log n) in k 4.399 * [taylor]: Taking taylor expansion of n in k 4.399 * [backup-simplify]: Simplify n into n 4.399 * [backup-simplify]: Simplify (log n) into (log n) 4.400 * [backup-simplify]: Simplify (+ 1 0) into 1 4.400 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.401 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 4.402 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 4.403 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 4.405 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.406 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.407 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.408 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.410 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.410 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.411 * [backup-simplify]: Simplify (+ 0 0) into 0 4.412 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 4.413 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.414 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.417 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.417 * [taylor]: Taking taylor expansion of 0 in k 4.417 * [backup-simplify]: Simplify 0 into 0 4.417 * [backup-simplify]: Simplify 0 into 0 4.417 * [backup-simplify]: Simplify 0 into 0 4.418 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.419 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.429 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 4.430 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.430 * [backup-simplify]: Simplify (+ 0 0) into 0 4.431 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 4.433 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.435 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 4.437 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.437 * [taylor]: Taking taylor expansion of 0 in k 4.437 * [backup-simplify]: Simplify 0 into 0 4.437 * [backup-simplify]: Simplify 0 into 0 4.437 * [backup-simplify]: Simplify 0 into 0 4.438 * [backup-simplify]: Simplify 0 into 0 4.439 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.440 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.447 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 4.447 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.448 * [backup-simplify]: Simplify (+ 0 0) into 0 4.449 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 4.449 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.451 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 4.452 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.452 * [taylor]: Taking taylor expansion of 0 in k 4.452 * [backup-simplify]: Simplify 0 into 0 4.452 * [backup-simplify]: Simplify 0 into 0 4.453 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 4.453 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 4.453 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 4.454 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 4.454 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.454 * [taylor]: Taking taylor expansion of 1.0 in k 4.454 * [backup-simplify]: Simplify 1.0 into 1.0 4.454 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.454 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.454 * [taylor]: Taking taylor expansion of k in k 4.454 * [backup-simplify]: Simplify 0 into 0 4.454 * [backup-simplify]: Simplify 1 into 1 4.454 * [backup-simplify]: Simplify (/ 1 1) into 1 4.454 * [backup-simplify]: Simplify (sqrt 0) into 0 4.455 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.455 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.455 * [taylor]: Taking taylor expansion of 1.0 in k 4.455 * [backup-simplify]: Simplify 1.0 into 1.0 4.455 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.455 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.455 * [taylor]: Taking taylor expansion of k in k 4.455 * [backup-simplify]: Simplify 0 into 0 4.455 * [backup-simplify]: Simplify 1 into 1 4.456 * [backup-simplify]: Simplify (/ 1 1) into 1 4.456 * [backup-simplify]: Simplify (sqrt 0) into 0 4.457 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.457 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.457 * [backup-simplify]: Simplify 0 into 0 4.458 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.458 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.459 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 4.460 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.462 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.462 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.462 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.465 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.466 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.466 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.467 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 4.467 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 4.467 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 4.467 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.467 * [taylor]: Taking taylor expansion of 1.0 in k 4.467 * [backup-simplify]: Simplify 1.0 into 1.0 4.467 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.467 * [taylor]: Taking taylor expansion of k in k 4.467 * [backup-simplify]: Simplify 0 into 0 4.467 * [backup-simplify]: Simplify 1 into 1 4.468 * [backup-simplify]: Simplify (sqrt 0) into 0 4.468 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.469 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.469 * [taylor]: Taking taylor expansion of 1.0 in k 4.469 * [backup-simplify]: Simplify 1.0 into 1.0 4.469 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.469 * [taylor]: Taking taylor expansion of k in k 4.469 * [backup-simplify]: Simplify 0 into 0 4.469 * [backup-simplify]: Simplify 1 into 1 4.469 * [backup-simplify]: Simplify (sqrt 0) into 0 4.470 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.470 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.470 * [backup-simplify]: Simplify 0 into 0 4.471 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.471 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.473 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.474 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.474 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.477 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.478 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.478 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.479 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 4.480 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 4.480 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 4.480 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.480 * [taylor]: Taking taylor expansion of 1.0 in k 4.480 * [backup-simplify]: Simplify 1.0 into 1.0 4.480 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.480 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.480 * [taylor]: Taking taylor expansion of -1 in k 4.480 * [backup-simplify]: Simplify -1 into -1 4.480 * [taylor]: Taking taylor expansion of k in k 4.480 * [backup-simplify]: Simplify 0 into 0 4.480 * [backup-simplify]: Simplify 1 into 1 4.480 * [backup-simplify]: Simplify (/ -1 1) into -1 4.480 * [backup-simplify]: Simplify (sqrt 0) into 0 4.481 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.481 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.481 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.481 * [taylor]: Taking taylor expansion of 1.0 in k 4.482 * [backup-simplify]: Simplify 1.0 into 1.0 4.482 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.482 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.482 * [taylor]: Taking taylor expansion of -1 in k 4.482 * [backup-simplify]: Simplify -1 into -1 4.482 * [taylor]: Taking taylor expansion of k in k 4.482 * [backup-simplify]: Simplify 0 into 0 4.482 * [backup-simplify]: Simplify 1 into 1 4.482 * [backup-simplify]: Simplify (/ -1 1) into -1 4.482 * [backup-simplify]: Simplify (sqrt 0) into 0 4.483 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.483 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.483 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.484 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.486 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.487 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 4.488 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.488 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.490 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.493 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 4.493 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.494 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 4.494 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 4.495 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 4.495 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 4.495 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.495 * [taylor]: Taking taylor expansion of 2.0 in n 4.495 * [backup-simplify]: Simplify 2.0 into 2.0 4.495 * [taylor]: Taking taylor expansion of (* n PI) in n 4.495 * [taylor]: Taking taylor expansion of n in n 4.495 * [backup-simplify]: Simplify 0 into 0 4.495 * [backup-simplify]: Simplify 1 into 1 4.495 * [taylor]: Taking taylor expansion of PI in n 4.495 * [backup-simplify]: Simplify PI into PI 4.495 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.495 * [taylor]: Taking taylor expansion of 2.0 in n 4.495 * [backup-simplify]: Simplify 2.0 into 2.0 4.495 * [taylor]: Taking taylor expansion of (* n PI) in n 4.495 * [taylor]: Taking taylor expansion of n in n 4.495 * [backup-simplify]: Simplify 0 into 0 4.495 * [backup-simplify]: Simplify 1 into 1 4.495 * [taylor]: Taking taylor expansion of PI in n 4.495 * [backup-simplify]: Simplify PI into PI 4.496 * [backup-simplify]: Simplify (* 0 PI) into 0 4.496 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.496 * [backup-simplify]: Simplify 0 into 0 4.498 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.499 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.500 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.501 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.502 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.502 * [backup-simplify]: Simplify 0 into 0 4.503 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.504 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.504 * [backup-simplify]: Simplify 0 into 0 4.505 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.507 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 4.507 * [backup-simplify]: Simplify 0 into 0 4.508 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.510 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 4.510 * [backup-simplify]: Simplify 0 into 0 4.511 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.513 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 4.513 * [backup-simplify]: Simplify 0 into 0 4.515 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 4.517 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 4.517 * [backup-simplify]: Simplify 0 into 0 4.518 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 4.518 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 4.518 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 4.518 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.518 * [taylor]: Taking taylor expansion of 2.0 in n 4.518 * [backup-simplify]: Simplify 2.0 into 2.0 4.518 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.518 * [taylor]: Taking taylor expansion of PI in n 4.518 * [backup-simplify]: Simplify PI into PI 4.518 * [taylor]: Taking taylor expansion of n in n 4.518 * [backup-simplify]: Simplify 0 into 0 4.518 * [backup-simplify]: Simplify 1 into 1 4.519 * [backup-simplify]: Simplify (/ PI 1) into PI 4.519 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.519 * [taylor]: Taking taylor expansion of 2.0 in n 4.519 * [backup-simplify]: Simplify 2.0 into 2.0 4.519 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.519 * [taylor]: Taking taylor expansion of PI in n 4.519 * [backup-simplify]: Simplify PI into PI 4.519 * [taylor]: Taking taylor expansion of n in n 4.519 * [backup-simplify]: Simplify 0 into 0 4.519 * [backup-simplify]: Simplify 1 into 1 4.520 * [backup-simplify]: Simplify (/ PI 1) into PI 4.520 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.521 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.522 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.522 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.522 * [backup-simplify]: Simplify 0 into 0 4.524 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.525 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.525 * [backup-simplify]: Simplify 0 into 0 4.526 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.527 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.527 * [backup-simplify]: Simplify 0 into 0 4.528 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.530 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.530 * [backup-simplify]: Simplify 0 into 0 4.531 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.533 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.533 * [backup-simplify]: Simplify 0 into 0 4.534 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.536 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.536 * [backup-simplify]: Simplify 0 into 0 4.537 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 4.537 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 4.537 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 4.537 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.538 * [taylor]: Taking taylor expansion of -2.0 in n 4.538 * [backup-simplify]: Simplify -2.0 into -2.0 4.538 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.538 * [taylor]: Taking taylor expansion of PI in n 4.538 * [backup-simplify]: Simplify PI into PI 4.538 * [taylor]: Taking taylor expansion of n in n 4.538 * [backup-simplify]: Simplify 0 into 0 4.538 * [backup-simplify]: Simplify 1 into 1 4.538 * [backup-simplify]: Simplify (/ PI 1) into PI 4.538 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.538 * [taylor]: Taking taylor expansion of -2.0 in n 4.538 * [backup-simplify]: Simplify -2.0 into -2.0 4.538 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.538 * [taylor]: Taking taylor expansion of PI in n 4.539 * [backup-simplify]: Simplify PI into PI 4.539 * [taylor]: Taking taylor expansion of n in n 4.539 * [backup-simplify]: Simplify 0 into 0 4.539 * [backup-simplify]: Simplify 1 into 1 4.539 * [backup-simplify]: Simplify (/ PI 1) into PI 4.540 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.540 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.541 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.542 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.542 * [backup-simplify]: Simplify 0 into 0 4.543 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.543 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.543 * [backup-simplify]: Simplify 0 into 0 4.544 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.922 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.922 * [backup-simplify]: Simplify 0 into 0 4.924 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.925 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.925 * [backup-simplify]: Simplify 0 into 0 4.926 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.928 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.928 * [backup-simplify]: Simplify 0 into 0 4.929 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.931 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.931 * [backup-simplify]: Simplify 0 into 0 4.935 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 4.935 * * * * [progress]: [ 4 / 4 ] generating series at (2) 4.936 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) 4.936 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in (k n) around 0 4.936 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 4.936 * [taylor]: Taking taylor expansion of 1.0 in n 4.936 * [backup-simplify]: Simplify 1.0 into 1.0 4.936 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 4.936 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 4.936 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.936 * [taylor]: Taking taylor expansion of k in n 4.936 * [backup-simplify]: Simplify k into k 4.936 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.936 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 4.936 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.937 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 4.937 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.937 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.937 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.937 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.937 * [taylor]: Taking taylor expansion of 0.5 in n 4.937 * [backup-simplify]: Simplify 0.5 into 0.5 4.937 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.937 * [taylor]: Taking taylor expansion of 1.0 in n 4.937 * [backup-simplify]: Simplify 1.0 into 1.0 4.937 * [taylor]: Taking taylor expansion of k in n 4.937 * [backup-simplify]: Simplify k into k 4.937 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.937 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.937 * [taylor]: Taking taylor expansion of 2.0 in n 4.937 * [backup-simplify]: Simplify 2.0 into 2.0 4.937 * [taylor]: Taking taylor expansion of (* n PI) in n 4.937 * [taylor]: Taking taylor expansion of n in n 4.937 * [backup-simplify]: Simplify 0 into 0 4.937 * [backup-simplify]: Simplify 1 into 1 4.937 * [taylor]: Taking taylor expansion of PI in n 4.937 * [backup-simplify]: Simplify PI into PI 4.938 * [backup-simplify]: Simplify (* 0 PI) into 0 4.938 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.940 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.942 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.943 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.943 * [backup-simplify]: Simplify (- k) into (- k) 4.943 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.943 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 4.944 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.946 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.947 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.947 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 4.947 * [taylor]: Taking taylor expansion of 1.0 in k 4.947 * [backup-simplify]: Simplify 1.0 into 1.0 4.947 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 4.947 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.947 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.947 * [taylor]: Taking taylor expansion of k in k 4.947 * [backup-simplify]: Simplify 0 into 0 4.947 * [backup-simplify]: Simplify 1 into 1 4.948 * [backup-simplify]: Simplify (/ 1 1) into 1 4.948 * [backup-simplify]: Simplify (sqrt 0) into 0 4.949 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.949 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 4.949 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.950 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.950 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 4.950 * [taylor]: Taking taylor expansion of 0.5 in k 4.950 * [backup-simplify]: Simplify 0.5 into 0.5 4.950 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.950 * [taylor]: Taking taylor expansion of 1.0 in k 4.950 * [backup-simplify]: Simplify 1.0 into 1.0 4.950 * [taylor]: Taking taylor expansion of k in k 4.950 * [backup-simplify]: Simplify 0 into 0 4.950 * [backup-simplify]: Simplify 1 into 1 4.950 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.950 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.950 * [taylor]: Taking taylor expansion of 2.0 in k 4.950 * [backup-simplify]: Simplify 2.0 into 2.0 4.950 * [taylor]: Taking taylor expansion of (* n PI) in k 4.950 * [taylor]: Taking taylor expansion of n in k 4.950 * [backup-simplify]: Simplify n into n 4.950 * [taylor]: Taking taylor expansion of PI in k 4.950 * [backup-simplify]: Simplify PI into PI 4.950 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.950 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.950 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.951 * [backup-simplify]: Simplify (- 0) into 0 4.951 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.952 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 4.952 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 4.952 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 4.952 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 4.952 * [taylor]: Taking taylor expansion of 1.0 in k 4.952 * [backup-simplify]: Simplify 1.0 into 1.0 4.952 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 4.952 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.952 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.952 * [taylor]: Taking taylor expansion of k in k 4.952 * [backup-simplify]: Simplify 0 into 0 4.952 * [backup-simplify]: Simplify 1 into 1 4.953 * [backup-simplify]: Simplify (/ 1 1) into 1 4.953 * [backup-simplify]: Simplify (sqrt 0) into 0 4.955 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.955 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 4.955 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.955 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.955 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 4.955 * [taylor]: Taking taylor expansion of 0.5 in k 4.955 * [backup-simplify]: Simplify 0.5 into 0.5 4.955 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.955 * [taylor]: Taking taylor expansion of 1.0 in k 4.955 * [backup-simplify]: Simplify 1.0 into 1.0 4.955 * [taylor]: Taking taylor expansion of k in k 4.955 * [backup-simplify]: Simplify 0 into 0 4.955 * [backup-simplify]: Simplify 1 into 1 4.955 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.955 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.955 * [taylor]: Taking taylor expansion of 2.0 in k 4.955 * [backup-simplify]: Simplify 2.0 into 2.0 4.955 * [taylor]: Taking taylor expansion of (* n PI) in k 4.955 * [taylor]: Taking taylor expansion of n in k 4.955 * [backup-simplify]: Simplify n into n 4.955 * [taylor]: Taking taylor expansion of PI in k 4.955 * [backup-simplify]: Simplify PI into PI 4.955 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.955 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.956 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.956 * [backup-simplify]: Simplify (- 0) into 0 4.956 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.957 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 4.957 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 4.957 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 4.958 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 4.958 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.958 * [taylor]: Taking taylor expansion of 0 in n 4.958 * [backup-simplify]: Simplify 0 into 0 4.958 * [backup-simplify]: Simplify 0 into 0 4.959 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 4.959 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 4.960 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 4.960 * [backup-simplify]: Simplify (- 1) into -1 4.961 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.962 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 4.963 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 4.964 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1)))) into (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.966 * [backup-simplify]: Simplify (+ (* 0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 4.968 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.968 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n 4.968 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 4.968 * [taylor]: Taking taylor expansion of +nan.0 in n 4.968 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.968 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 4.968 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 4.968 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 4.968 * [taylor]: Taking taylor expansion of 0.5 in n 4.968 * [backup-simplify]: Simplify 0.5 into 0.5 4.968 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 4.968 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 4.968 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.968 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.968 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.968 * [taylor]: Taking taylor expansion of 1.0 in n 4.968 * [backup-simplify]: Simplify 1.0 into 1.0 4.968 * [taylor]: Taking taylor expansion of (log PI) in n 4.968 * [taylor]: Taking taylor expansion of PI in n 4.968 * [backup-simplify]: Simplify PI into PI 4.969 * [backup-simplify]: Simplify (log PI) into (log PI) 4.970 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.972 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.972 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 4.972 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.972 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.972 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.972 * [taylor]: Taking taylor expansion of 1.0 in n 4.972 * [backup-simplify]: Simplify 1.0 into 1.0 4.972 * [taylor]: Taking taylor expansion of (log n) in n 4.972 * [taylor]: Taking taylor expansion of n in n 4.972 * [backup-simplify]: Simplify 0 into 0 4.972 * [backup-simplify]: Simplify 1 into 1 4.973 * [backup-simplify]: Simplify (log 1) into 0 4.973 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.973 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.973 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.973 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.973 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.973 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.973 * [taylor]: Taking taylor expansion of 1.0 in n 4.973 * [backup-simplify]: Simplify 1.0 into 1.0 4.974 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.974 * [taylor]: Taking taylor expansion of 2.0 in n 4.974 * [backup-simplify]: Simplify 2.0 into 2.0 4.974 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.975 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.976 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.977 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 4.978 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 4.979 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 4.980 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 4.981 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 4.982 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 4.983 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 4.983 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.984 * [backup-simplify]: Simplify 0 into 0 4.984 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 4.985 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 4.986 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 2) into 0 4.986 * [backup-simplify]: Simplify (- 0) into 0 4.986 * [backup-simplify]: Simplify (+ 0 0) into 0 4.987 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 4.987 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 4.988 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.989 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 4.991 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.993 * [backup-simplify]: Simplify (+ (* 0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5)))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) 4.996 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) 4.996 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) in n 4.996 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))) in n 4.996 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 4.996 * [taylor]: Taking taylor expansion of +nan.0 in n 4.996 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.996 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 4.996 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 4.996 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 4.996 * [taylor]: Taking taylor expansion of 0.5 in n 4.996 * [backup-simplify]: Simplify 0.5 into 0.5 4.996 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 4.996 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 4.997 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.997 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.997 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.997 * [taylor]: Taking taylor expansion of 1.0 in n 4.997 * [backup-simplify]: Simplify 1.0 into 1.0 4.997 * [taylor]: Taking taylor expansion of (log PI) in n 4.997 * [taylor]: Taking taylor expansion of PI in n 4.997 * [backup-simplify]: Simplify PI into PI 4.997 * [backup-simplify]: Simplify (log PI) into (log PI) 4.998 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.999 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.999 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 4.999 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.999 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.999 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.999 * [taylor]: Taking taylor expansion of 1.0 in n 4.999 * [backup-simplify]: Simplify 1.0 into 1.0 4.999 * [taylor]: Taking taylor expansion of (log n) in n 4.999 * [taylor]: Taking taylor expansion of n in n 4.999 * [backup-simplify]: Simplify 0 into 0 4.999 * [backup-simplify]: Simplify 1 into 1 4.999 * [backup-simplify]: Simplify (log 1) into 0 4.999 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.999 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.999 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.999 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.999 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.999 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 5.000 * [taylor]: Taking taylor expansion of 1.0 in n 5.000 * [backup-simplify]: Simplify 1.0 into 1.0 5.000 * [taylor]: Taking taylor expansion of (log 2.0) in n 5.000 * [taylor]: Taking taylor expansion of 2.0 in n 5.000 * [backup-simplify]: Simplify 2.0 into 2.0 5.000 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 5.000 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 5.001 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 5.002 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 5.003 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 5.003 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 5.004 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 5.005 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 5.005 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))) in n 5.005 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 5.005 * [taylor]: Taking taylor expansion of +nan.0 in n 5.005 * [backup-simplify]: Simplify +nan.0 into +nan.0 5.005 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 5.005 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 5.005 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 5.005 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 5.005 * [taylor]: Taking taylor expansion of 0.5 in n 5.005 * [backup-simplify]: Simplify 0.5 into 0.5 5.005 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 5.005 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 5.005 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 5.005 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 5.005 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 5.006 * [taylor]: Taking taylor expansion of 1.0 in n 5.006 * [backup-simplify]: Simplify 1.0 into 1.0 5.006 * [taylor]: Taking taylor expansion of (log 2.0) in n 5.006 * [taylor]: Taking taylor expansion of 2.0 in n 5.006 * [backup-simplify]: Simplify 2.0 into 2.0 5.006 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 5.007 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 5.008 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 5.008 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 5.008 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 5.008 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 5.008 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 5.008 * [taylor]: Taking taylor expansion of 1.0 in n 5.008 * [backup-simplify]: Simplify 1.0 into 1.0 5.008 * [taylor]: Taking taylor expansion of (log PI) in n 5.008 * [taylor]: Taking taylor expansion of PI in n 5.008 * [backup-simplify]: Simplify PI into PI 5.009 * [backup-simplify]: Simplify (log PI) into (log PI) 5.010 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 5.011 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 5.011 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 5.011 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 5.011 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 5.012 * [taylor]: Taking taylor expansion of 1.0 in n 5.012 * [backup-simplify]: Simplify 1.0 into 1.0 5.012 * [taylor]: Taking taylor expansion of (log n) in n 5.012 * [taylor]: Taking taylor expansion of n in n 5.012 * [backup-simplify]: Simplify 0 into 0 5.012 * [backup-simplify]: Simplify 1 into 1 5.012 * [backup-simplify]: Simplify (log 1) into 0 5.012 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 5.013 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 5.013 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 5.013 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 5.015 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 5.016 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 5.017 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 5.019 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 5.019 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 5.019 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 5.019 * [taylor]: Taking taylor expansion of 2.0 in n 5.019 * [backup-simplify]: Simplify 2.0 into 2.0 5.019 * [taylor]: Taking taylor expansion of (* n PI) in n 5.019 * [taylor]: Taking taylor expansion of n in n 5.019 * [backup-simplify]: Simplify 0 into 0 5.019 * [backup-simplify]: Simplify 1 into 1 5.019 * [taylor]: Taking taylor expansion of PI in n 5.019 * [backup-simplify]: Simplify PI into PI 5.019 * [backup-simplify]: Simplify (* 0 PI) into 0 5.020 * [backup-simplify]: Simplify (* 2.0 0) into 0 5.021 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 5.023 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 5.024 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.026 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 5.027 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 5.030 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 5.032 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 5.035 * [backup-simplify]: Simplify (- (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))) 5.041 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 5.047 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 5.054 * [backup-simplify]: Simplify (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 5.056 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 5.057 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 5.058 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 5.060 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 5.060 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 5.061 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 5.062 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 5.070 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 5.072 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 5.074 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 5.076 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 5.077 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 5.080 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1)))) 1) into 0 5.081 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)))) into 0 5.084 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 5.086 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5))) into 0 5.086 * [backup-simplify]: Simplify (- 0) into 0 5.087 * [backup-simplify]: Simplify 0 into 0 5.088 * [backup-simplify]: Simplify 0 into 0 5.089 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 5.090 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 5.094 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 6) into 0 5.094 * [backup-simplify]: Simplify (- 0) into 0 5.094 * [backup-simplify]: Simplify (+ 0 0) into 0 5.096 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 5.097 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 5.099 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 5.100 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.104 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 5.110 * [backup-simplify]: Simplify (+ (* 0 (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 5.121 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))) (+ (* 0 (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 5.121 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) in n 5.121 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))) in n 5.121 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) in n 5.121 * [taylor]: Taking taylor expansion of +nan.0 in n 5.121 * [backup-simplify]: Simplify +nan.0 into +nan.0 5.121 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 5.121 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 5.121 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 5.121 * [taylor]: Taking taylor expansion of 0.5 in n 5.121 * [backup-simplify]: Simplify 0.5 into 0.5 5.121 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 5.121 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 5.122 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 5.122 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 5.122 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 5.122 * [taylor]: Taking taylor expansion of 1.0 in n 5.122 * [backup-simplify]: Simplify 1.0 into 1.0 5.122 * [taylor]: Taking taylor expansion of (log 2.0) in n 5.122 * [taylor]: Taking taylor expansion of 2.0 in n 5.122 * [backup-simplify]: Simplify 2.0 into 2.0 5.122 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 5.123 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 5.125 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 5.125 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 5.125 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 5.125 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 5.125 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 5.125 * [taylor]: Taking taylor expansion of 1.0 in n 5.125 * [backup-simplify]: Simplify 1.0 into 1.0 5.125 * [taylor]: Taking taylor expansion of (log n) in n 5.125 * [taylor]: Taking taylor expansion of n in n 5.125 * [backup-simplify]: Simplify 0 into 0 5.125 * [backup-simplify]: Simplify 1 into 1 5.125 * [backup-simplify]: Simplify (log 1) into 0 5.126 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 5.126 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 5.126 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 5.126 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 5.126 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 5.126 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 5.126 * [taylor]: Taking taylor expansion of 1.0 in n 5.126 * [backup-simplify]: Simplify 1.0 into 1.0 5.126 * [taylor]: Taking taylor expansion of (log PI) in n 5.126 * [taylor]: Taking taylor expansion of PI in n 5.126 * [backup-simplify]: Simplify PI into PI 5.127 * [backup-simplify]: Simplify (log PI) into (log PI) 5.128 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 5.129 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 5.130 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 5.131 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 5.133 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 5.134 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 5.136 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 5.136 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))) in n 5.136 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) in n 5.136 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 5.136 * [taylor]: Taking taylor expansion of +nan.0 in n 5.136 * [backup-simplify]: Simplify +nan.0 into +nan.0 5.136 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 5.136 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 5.136 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 5.136 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 5.136 * [taylor]: Taking taylor expansion of 0.5 in n 5.136 * [backup-simplify]: Simplify 0.5 into 0.5 5.136 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 5.136 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 5.136 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 5.136 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 5.137 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 5.137 * [taylor]: Taking taylor expansion of 1.0 in n 5.137 * [backup-simplify]: Simplify 1.0 into 1.0 5.137 * [taylor]: Taking taylor expansion of (log 2.0) in n 5.137 * [taylor]: Taking taylor expansion of 2.0 in n 5.137 * [backup-simplify]: Simplify 2.0 into 2.0 5.137 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 5.138 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 5.140 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 5.140 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 5.140 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 5.140 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 5.140 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 5.140 * [taylor]: Taking taylor expansion of 1.0 in n 5.140 * [backup-simplify]: Simplify 1.0 into 1.0 5.140 * [taylor]: Taking taylor expansion of (log PI) in n 5.140 * [taylor]: Taking taylor expansion of PI in n 5.140 * [backup-simplify]: Simplify PI into PI 5.140 * [backup-simplify]: Simplify (log PI) into (log PI) 5.141 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 5.143 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 5.143 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 5.143 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 5.143 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 5.143 * [taylor]: Taking taylor expansion of 1.0 in n 5.143 * [backup-simplify]: Simplify 1.0 into 1.0 5.143 * [taylor]: Taking taylor expansion of (log n) in n 5.143 * [taylor]: Taking taylor expansion of n in n 5.144 * [backup-simplify]: Simplify 0 into 0 5.144 * [backup-simplify]: Simplify 1 into 1 5.144 * [backup-simplify]: Simplify (log 1) into 0 5.144 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 5.144 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 5.145 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 5.145 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 5.147 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 5.148 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 5.149 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 5.151 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 5.151 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 5.151 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 5.151 * [taylor]: Taking taylor expansion of 2.0 in n 5.151 * [backup-simplify]: Simplify 2.0 into 2.0 5.151 * [taylor]: Taking taylor expansion of (* n PI) in n 5.151 * [taylor]: Taking taylor expansion of n in n 5.151 * [backup-simplify]: Simplify 0 into 0 5.151 * [backup-simplify]: Simplify 1 into 1 5.152 * [taylor]: Taking taylor expansion of PI in n 5.152 * [backup-simplify]: Simplify PI into PI 5.152 * [backup-simplify]: Simplify (* 0 PI) into 0 5.152 * [backup-simplify]: Simplify (* 2.0 0) into 0 5.154 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 5.156 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 5.157 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.157 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) in n 5.157 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n 5.157 * [taylor]: Taking taylor expansion of +nan.0 in n 5.157 * [backup-simplify]: Simplify +nan.0 into +nan.0 5.157 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n 5.157 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 5.157 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 5.157 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 5.157 * [taylor]: Taking taylor expansion of 0.5 in n 5.157 * [backup-simplify]: Simplify 0.5 into 0.5 5.157 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 5.157 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 5.157 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 5.157 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 5.157 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 5.157 * [taylor]: Taking taylor expansion of 1.0 in n 5.158 * [backup-simplify]: Simplify 1.0 into 1.0 5.158 * [taylor]: Taking taylor expansion of (log 2.0) in n 5.158 * [taylor]: Taking taylor expansion of 2.0 in n 5.158 * [backup-simplify]: Simplify 2.0 into 2.0 5.158 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 5.159 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 5.160 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 5.160 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 5.161 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 5.161 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 5.161 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 5.161 * [taylor]: Taking taylor expansion of 1.0 in n 5.161 * [backup-simplify]: Simplify 1.0 into 1.0 5.161 * [taylor]: Taking taylor expansion of (log PI) in n 5.161 * [taylor]: Taking taylor expansion of PI in n 5.161 * [backup-simplify]: Simplify PI into PI 5.161 * [backup-simplify]: Simplify (log PI) into (log PI) 5.162 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 5.164 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 5.164 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 5.164 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 5.164 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 5.164 * [taylor]: Taking taylor expansion of 1.0 in n 5.164 * [backup-simplify]: Simplify 1.0 into 1.0 5.164 * [taylor]: Taking taylor expansion of (log n) in n 5.164 * [taylor]: Taking taylor expansion of n in n 5.164 * [backup-simplify]: Simplify 0 into 0 5.164 * [backup-simplify]: Simplify 1 into 1 5.164 * [backup-simplify]: Simplify (log 1) into 0 5.165 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 5.165 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 5.165 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 5.166 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 5.167 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 5.168 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 5.170 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 5.171 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 5.171 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 5.171 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 5.171 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 5.171 * [taylor]: Taking taylor expansion of 2.0 in n 5.171 * [backup-simplify]: Simplify 2.0 into 2.0 5.171 * [taylor]: Taking taylor expansion of (* n PI) in n 5.171 * [taylor]: Taking taylor expansion of n in n 5.171 * [backup-simplify]: Simplify 0 into 0 5.171 * [backup-simplify]: Simplify 1 into 1 5.172 * [taylor]: Taking taylor expansion of PI in n 5.172 * [backup-simplify]: Simplify PI into PI 5.172 * [backup-simplify]: Simplify (* 0 PI) into 0 5.172 * [backup-simplify]: Simplify (* 2.0 0) into 0 5.174 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 5.176 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 5.177 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.178 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 5.180 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 5.181 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 5.184 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 5.187 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 5.188 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 5.190 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 5.192 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 5.195 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)) into (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 5.198 * [backup-simplify]: Simplify (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 5.201 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 5.212 * [backup-simplify]: Simplify (+ (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)))))))))))) 5.228 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))) 5.250 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 5.267 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 5.277 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 5.292 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) (pow (* 1 k) 2)) (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) (* 1 k)) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) into (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) 5.293 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 k))) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) into (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) 5.293 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in (k n) around 0 5.293 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 5.293 * [taylor]: Taking taylor expansion of 1.0 in n 5.293 * [backup-simplify]: Simplify 1.0 into 1.0 5.293 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 5.293 * [taylor]: Taking taylor expansion of (sqrt k) in n 5.293 * [taylor]: Taking taylor expansion of k in n 5.293 * [backup-simplify]: Simplify k into k 5.293 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 5.293 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 5.293 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 5.293 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 5.294 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 5.294 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 5.294 * [taylor]: Taking taylor expansion of 0.5 in n 5.294 * [backup-simplify]: Simplify 0.5 into 0.5 5.294 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 5.294 * [taylor]: Taking taylor expansion of 1.0 in n 5.294 * [backup-simplify]: Simplify 1.0 into 1.0 5.294 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.294 * [taylor]: Taking taylor expansion of k in n 5.294 * [backup-simplify]: Simplify k into k 5.294 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.294 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 5.294 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 5.294 * [taylor]: Taking taylor expansion of 2.0 in n 5.294 * [backup-simplify]: Simplify 2.0 into 2.0 5.294 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.294 * [taylor]: Taking taylor expansion of PI in n 5.294 * [backup-simplify]: Simplify PI into PI 5.294 * [taylor]: Taking taylor expansion of n in n 5.294 * [backup-simplify]: Simplify 0 into 0 5.294 * [backup-simplify]: Simplify 1 into 1 5.294 * [backup-simplify]: Simplify (/ PI 1) into PI 5.295 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 5.296 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.296 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 5.296 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 5.296 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 5.298 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 5.299 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 5.300 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 5.300 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 5.300 * [taylor]: Taking taylor expansion of 1.0 in k 5.301 * [backup-simplify]: Simplify 1.0 into 1.0 5.301 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 5.301 * [taylor]: Taking taylor expansion of (sqrt k) in k 5.301 * [taylor]: Taking taylor expansion of k in k 5.301 * [backup-simplify]: Simplify 0 into 0 5.301 * [backup-simplify]: Simplify 1 into 1 5.301 * [backup-simplify]: Simplify (sqrt 0) into 0 5.303 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 5.303 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 5.303 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 5.303 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 5.303 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 5.303 * [taylor]: Taking taylor expansion of 0.5 in k 5.303 * [backup-simplify]: Simplify 0.5 into 0.5 5.303 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 5.303 * [taylor]: Taking taylor expansion of 1.0 in k 5.303 * [backup-simplify]: Simplify 1.0 into 1.0 5.303 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.303 * [taylor]: Taking taylor expansion of k in k 5.303 * [backup-simplify]: Simplify 0 into 0 5.303 * [backup-simplify]: Simplify 1 into 1 5.303 * [backup-simplify]: Simplify (/ 1 1) into 1 5.303 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 5.303 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 5.303 * [taylor]: Taking taylor expansion of 2.0 in k 5.304 * [backup-simplify]: Simplify 2.0 into 2.0 5.304 * [taylor]: Taking taylor expansion of (/ PI n) in k 5.304 * [taylor]: Taking taylor expansion of PI in k 5.304 * [backup-simplify]: Simplify PI into PI 5.304 * [taylor]: Taking taylor expansion of n in k 5.304 * [backup-simplify]: Simplify n into n 5.304 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 5.304 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 5.304 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 5.305 * [backup-simplify]: Simplify (- 1) into -1 5.305 * [backup-simplify]: Simplify (+ 0 -1) into -1 5.305 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 5.306 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 5.306 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 5.306 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 5.306 * [taylor]: Taking taylor expansion of 1.0 in k 5.306 * [backup-simplify]: Simplify 1.0 into 1.0 5.306 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 5.306 * [taylor]: Taking taylor expansion of (sqrt k) in k 5.306 * [taylor]: Taking taylor expansion of k in k 5.306 * [backup-simplify]: Simplify 0 into 0 5.306 * [backup-simplify]: Simplify 1 into 1 5.307 * [backup-simplify]: Simplify (sqrt 0) into 0 5.308 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 5.308 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 5.308 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 5.308 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 5.308 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 5.308 * [taylor]: Taking taylor expansion of 0.5 in k 5.308 * [backup-simplify]: Simplify 0.5 into 0.5 5.308 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 5.308 * [taylor]: Taking taylor expansion of 1.0 in k 5.308 * [backup-simplify]: Simplify 1.0 into 1.0 5.308 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.308 * [taylor]: Taking taylor expansion of k in k 5.308 * [backup-simplify]: Simplify 0 into 0 5.308 * [backup-simplify]: Simplify 1 into 1 5.309 * [backup-simplify]: Simplify (/ 1 1) into 1 5.309 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 5.309 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 5.309 * [taylor]: Taking taylor expansion of 2.0 in k 5.309 * [backup-simplify]: Simplify 2.0 into 2.0 5.309 * [taylor]: Taking taylor expansion of (/ PI n) in k 5.309 * [taylor]: Taking taylor expansion of PI in k 5.309 * [backup-simplify]: Simplify PI into PI 5.309 * [taylor]: Taking taylor expansion of n in k 5.309 * [backup-simplify]: Simplify n into n 5.309 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 5.309 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 5.309 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 5.310 * [backup-simplify]: Simplify (- 1) into -1 5.310 * [backup-simplify]: Simplify (+ 0 -1) into -1 5.311 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 5.311 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 5.311 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 5.312 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 5.312 * [backup-simplify]: Simplify (* 1.0 0) into 0 5.312 * [taylor]: Taking taylor expansion of 0 in n 5.312 * [backup-simplify]: Simplify 0 into 0 5.312 * [backup-simplify]: Simplify 0 into 0 5.313 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 5.314 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 5.314 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 5.314 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 5.314 * [taylor]: Taking taylor expansion of +nan.0 in n 5.314 * [backup-simplify]: Simplify +nan.0 into +nan.0 5.314 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 5.314 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 5.314 * [taylor]: Taking taylor expansion of 0.5 in n 5.314 * [backup-simplify]: Simplify 0.5 into 0.5 5.314 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 5.314 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 5.314 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 5.314 * [taylor]: Taking taylor expansion of 2.0 in n 5.314 * [backup-simplify]: Simplify 2.0 into 2.0 5.314 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.314 * [taylor]: Taking taylor expansion of PI in n 5.314 * [backup-simplify]: Simplify PI into PI 5.314 * [taylor]: Taking taylor expansion of n in n 5.314 * [backup-simplify]: Simplify 0 into 0 5.314 * [backup-simplify]: Simplify 1 into 1 5.315 * [backup-simplify]: Simplify (/ PI 1) into PI 5.315 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 5.316 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.316 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 5.316 * [taylor]: Taking taylor expansion of 1.0 in n 5.316 * [backup-simplify]: Simplify 1.0 into 1.0 5.316 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.316 * [taylor]: Taking taylor expansion of k in n 5.316 * [backup-simplify]: Simplify k into k 5.317 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.318 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 5.318 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 5.318 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 5.319 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 5.321 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 5.322 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 5.323 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 5.325 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 5.326 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 5.326 * [backup-simplify]: Simplify 0 into 0 5.329 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 5.330 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 5.331 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 5.332 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 5.332 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 5.332 * [taylor]: Taking taylor expansion of +nan.0 in n 5.332 * [backup-simplify]: Simplify +nan.0 into +nan.0 5.332 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 5.332 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 5.332 * [taylor]: Taking taylor expansion of 0.5 in n 5.332 * [backup-simplify]: Simplify 0.5 into 0.5 5.332 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 5.332 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 5.332 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 5.332 * [taylor]: Taking taylor expansion of 2.0 in n 5.332 * [backup-simplify]: Simplify 2.0 into 2.0 5.332 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.332 * [taylor]: Taking taylor expansion of PI in n 5.332 * [backup-simplify]: Simplify PI into PI 5.332 * [taylor]: Taking taylor expansion of n in n 5.332 * [backup-simplify]: Simplify 0 into 0 5.332 * [backup-simplify]: Simplify 1 into 1 5.333 * [backup-simplify]: Simplify (/ PI 1) into PI 5.333 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 5.334 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.334 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 5.334 * [taylor]: Taking taylor expansion of 1.0 in n 5.334 * [backup-simplify]: Simplify 1.0 into 1.0 5.334 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.334 * [taylor]: Taking taylor expansion of k in n 5.335 * [backup-simplify]: Simplify k into k 5.335 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.336 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 5.336 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 5.336 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 5.338 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 5.339 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 5.340 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 5.342 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 5.343 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 5.345 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 5.346 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 5.346 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 5.347 * [backup-simplify]: Simplify (- 0) into 0 5.347 * [backup-simplify]: Simplify (+ 0 0) into 0 5.348 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 5.349 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 5.351 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 5.352 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 5.354 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 5.356 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 5.358 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 5.358 * [backup-simplify]: Simplify (- 0) into 0 5.358 * [backup-simplify]: Simplify 0 into 0 5.358 * [backup-simplify]: Simplify 0 into 0 5.363 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 5.364 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 5.366 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 5.366 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 5.366 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 5.366 * [taylor]: Taking taylor expansion of +nan.0 in n 5.366 * [backup-simplify]: Simplify +nan.0 into +nan.0 5.366 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 5.366 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 5.366 * [taylor]: Taking taylor expansion of 0.5 in n 5.366 * [backup-simplify]: Simplify 0.5 into 0.5 5.366 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 5.366 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 5.366 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 5.366 * [taylor]: Taking taylor expansion of 2.0 in n 5.366 * [backup-simplify]: Simplify 2.0 into 2.0 5.366 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.366 * [taylor]: Taking taylor expansion of PI in n 5.366 * [backup-simplify]: Simplify PI into PI 5.366 * [taylor]: Taking taylor expansion of n in n 5.366 * [backup-simplify]: Simplify 0 into 0 5.366 * [backup-simplify]: Simplify 1 into 1 5.370 * [backup-simplify]: Simplify (/ PI 1) into PI 5.370 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 5.371 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.371 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 5.371 * [taylor]: Taking taylor expansion of 1.0 in n 5.371 * [backup-simplify]: Simplify 1.0 into 1.0 5.371 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.371 * [taylor]: Taking taylor expansion of k in n 5.371 * [backup-simplify]: Simplify k into k 5.371 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.372 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 5.372 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 5.372 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 5.373 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 5.374 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 5.375 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 5.375 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 5.376 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 5.377 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 5.380 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) 5.381 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 5.381 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k n) around 0 5.381 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 5.381 * [taylor]: Taking taylor expansion of 1.0 in n 5.381 * [backup-simplify]: Simplify 1.0 into 1.0 5.381 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 5.381 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 5.381 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 5.381 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 5.381 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 5.381 * [taylor]: Taking taylor expansion of 0.5 in n 5.381 * [backup-simplify]: Simplify 0.5 into 0.5 5.381 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 5.381 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.381 * [taylor]: Taking taylor expansion of k in n 5.381 * [backup-simplify]: Simplify k into k 5.381 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.381 * [taylor]: Taking taylor expansion of 1.0 in n 5.381 * [backup-simplify]: Simplify 1.0 into 1.0 5.381 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 5.381 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 5.381 * [taylor]: Taking taylor expansion of -2.0 in n 5.381 * [backup-simplify]: Simplify -2.0 into -2.0 5.381 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.381 * [taylor]: Taking taylor expansion of PI in n 5.381 * [backup-simplify]: Simplify PI into PI 5.381 * [taylor]: Taking taylor expansion of n in n 5.381 * [backup-simplify]: Simplify 0 into 0 5.381 * [backup-simplify]: Simplify 1 into 1 5.382 * [backup-simplify]: Simplify (/ PI 1) into PI 5.382 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 5.382 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 5.383 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 5.383 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 5.384 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.384 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 5.385 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 5.385 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 5.385 * [taylor]: Taking taylor expansion of (/ -1 k) in n 5.385 * [taylor]: Taking taylor expansion of -1 in n 5.385 * [backup-simplify]: Simplify -1 into -1 5.385 * [taylor]: Taking taylor expansion of k in n 5.385 * [backup-simplify]: Simplify k into k 5.385 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 5.385 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 5.385 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 5.385 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 5.386 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) 5.386 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 5.386 * [taylor]: Taking taylor expansion of 1.0 in k 5.386 * [backup-simplify]: Simplify 1.0 into 1.0 5.386 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 5.386 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 5.386 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 5.386 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 5.386 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 5.386 * [taylor]: Taking taylor expansion of 0.5 in k 5.387 * [backup-simplify]: Simplify 0.5 into 0.5 5.387 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 5.387 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.387 * [taylor]: Taking taylor expansion of k in k 5.387 * [backup-simplify]: Simplify 0 into 0 5.387 * [backup-simplify]: Simplify 1 into 1 5.387 * [backup-simplify]: Simplify (/ 1 1) into 1 5.387 * [taylor]: Taking taylor expansion of 1.0 in k 5.387 * [backup-simplify]: Simplify 1.0 into 1.0 5.387 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 5.387 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 5.387 * [taylor]: Taking taylor expansion of -2.0 in k 5.387 * [backup-simplify]: Simplify -2.0 into -2.0 5.387 * [taylor]: Taking taylor expansion of (/ PI n) in k 5.387 * [taylor]: Taking taylor expansion of PI in k 5.387 * [backup-simplify]: Simplify PI into PI 5.387 * [taylor]: Taking taylor expansion of n in k 5.387 * [backup-simplify]: Simplify n into n 5.387 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 5.387 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 5.387 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 5.388 * [backup-simplify]: Simplify (+ 1 0) into 1 5.388 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 5.388 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 5.388 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 5.388 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 5.388 * [taylor]: Taking taylor expansion of (/ -1 k) in k 5.388 * [taylor]: Taking taylor expansion of -1 in k 5.388 * [backup-simplify]: Simplify -1 into -1 5.388 * [taylor]: Taking taylor expansion of k in k 5.388 * [backup-simplify]: Simplify 0 into 0 5.388 * [backup-simplify]: Simplify 1 into 1 5.388 * [backup-simplify]: Simplify (/ -1 1) into -1 5.389 * [backup-simplify]: Simplify (sqrt 0) into 0 5.390 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 5.390 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 5.390 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 5.390 * [taylor]: Taking taylor expansion of 1.0 in k 5.390 * [backup-simplify]: Simplify 1.0 into 1.0 5.390 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 5.390 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 5.390 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 5.390 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 5.390 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 5.390 * [taylor]: Taking taylor expansion of 0.5 in k 5.390 * [backup-simplify]: Simplify 0.5 into 0.5 5.390 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 5.390 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.390 * [taylor]: Taking taylor expansion of k in k 5.390 * [backup-simplify]: Simplify 0 into 0 5.390 * [backup-simplify]: Simplify 1 into 1 5.390 * [backup-simplify]: Simplify (/ 1 1) into 1 5.390 * [taylor]: Taking taylor expansion of 1.0 in k 5.390 * [backup-simplify]: Simplify 1.0 into 1.0 5.390 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 5.390 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 5.390 * [taylor]: Taking taylor expansion of -2.0 in k 5.390 * [backup-simplify]: Simplify -2.0 into -2.0 5.390 * [taylor]: Taking taylor expansion of (/ PI n) in k 5.390 * [taylor]: Taking taylor expansion of PI in k 5.390 * [backup-simplify]: Simplify PI into PI 5.391 * [taylor]: Taking taylor expansion of n in k 5.391 * [backup-simplify]: Simplify n into n 5.391 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 5.391 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 5.391 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 5.391 * [backup-simplify]: Simplify (+ 1 0) into 1 5.391 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 5.391 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 5.391 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 5.392 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 5.392 * [taylor]: Taking taylor expansion of (/ -1 k) in k 5.392 * [taylor]: Taking taylor expansion of -1 in k 5.392 * [backup-simplify]: Simplify -1 into -1 5.392 * [taylor]: Taking taylor expansion of k in k 5.392 * [backup-simplify]: Simplify 0 into 0 5.392 * [backup-simplify]: Simplify 1 into 1 5.392 * [backup-simplify]: Simplify (/ -1 1) into -1 5.392 * [backup-simplify]: Simplify (sqrt 0) into 0 5.393 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 5.393 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 5.393 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 5.393 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 5.393 * [taylor]: Taking taylor expansion of +nan.0 in n 5.393 * [backup-simplify]: Simplify +nan.0 into +nan.0 5.393 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 5.393 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 5.393 * [taylor]: Taking taylor expansion of 0.5 in n 5.394 * [backup-simplify]: Simplify 0.5 into 0.5 5.394 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 5.394 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 5.394 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.394 * [taylor]: Taking taylor expansion of k in n 5.394 * [backup-simplify]: Simplify k into k 5.394 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.394 * [taylor]: Taking taylor expansion of 1.0 in n 5.394 * [backup-simplify]: Simplify 1.0 into 1.0 5.394 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 5.394 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 5.394 * [taylor]: Taking taylor expansion of -2.0 in n 5.394 * [backup-simplify]: Simplify -2.0 into -2.0 5.394 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.394 * [taylor]: Taking taylor expansion of PI in n 5.394 * [backup-simplify]: Simplify PI into PI 5.394 * [taylor]: Taking taylor expansion of n in n 5.394 * [backup-simplify]: Simplify 0 into 0 5.394 * [backup-simplify]: Simplify 1 into 1 5.394 * [backup-simplify]: Simplify (/ PI 1) into PI 5.395 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 5.395 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 5.395 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 5.396 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.397 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 5.398 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 5.398 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 5.399 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 5.400 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 5.401 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 5.403 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 5.404 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 5.404 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 5.404 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 5.404 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 5.405 * [taylor]: Taking taylor expansion of +nan.0 in n 5.405 * [backup-simplify]: Simplify +nan.0 into +nan.0 5.405 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 5.405 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 5.405 * [taylor]: Taking taylor expansion of 0.5 in n 5.405 * [backup-simplify]: Simplify 0.5 into 0.5 5.405 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 5.405 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 5.405 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.405 * [taylor]: Taking taylor expansion of k in n 5.405 * [backup-simplify]: Simplify k into k 5.405 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.405 * [taylor]: Taking taylor expansion of 1.0 in n 5.405 * [backup-simplify]: Simplify 1.0 into 1.0 5.405 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 5.405 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 5.405 * [taylor]: Taking taylor expansion of -2.0 in n 5.405 * [backup-simplify]: Simplify -2.0 into -2.0 5.405 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.405 * [taylor]: Taking taylor expansion of PI in n 5.405 * [backup-simplify]: Simplify PI into PI 5.405 * [taylor]: Taking taylor expansion of n in n 5.405 * [backup-simplify]: Simplify 0 into 0 5.405 * [backup-simplify]: Simplify 1 into 1 5.406 * [backup-simplify]: Simplify (/ PI 1) into PI 5.406 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 5.407 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 5.407 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 5.409 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.410 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 5.411 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 5.413 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 5.414 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 5.416 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 5.417 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 5.418 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 5.419 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 5.420 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 5.421 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 5.421 * [backup-simplify]: Simplify (+ 0 0) into 0 5.422 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.424 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 5.425 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 5.427 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 5.429 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 5.429 * [backup-simplify]: Simplify 0 into 0 5.430 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.434 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 5.435 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 5.436 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 5.436 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 5.436 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 5.437 * [taylor]: Taking taylor expansion of +nan.0 in n 5.437 * [backup-simplify]: Simplify +nan.0 into +nan.0 5.437 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 5.437 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 5.437 * [taylor]: Taking taylor expansion of 0.5 in n 5.437 * [backup-simplify]: Simplify 0.5 into 0.5 5.437 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 5.437 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 5.437 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.437 * [taylor]: Taking taylor expansion of k in n 5.437 * [backup-simplify]: Simplify k into k 5.437 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.437 * [taylor]: Taking taylor expansion of 1.0 in n 5.437 * [backup-simplify]: Simplify 1.0 into 1.0 5.437 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 5.437 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 5.437 * [taylor]: Taking taylor expansion of -2.0 in n 5.437 * [backup-simplify]: Simplify -2.0 into -2.0 5.437 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.437 * [taylor]: Taking taylor expansion of PI in n 5.437 * [backup-simplify]: Simplify PI into PI 5.437 * [taylor]: Taking taylor expansion of n in n 5.437 * [backup-simplify]: Simplify 0 into 0 5.437 * [backup-simplify]: Simplify 1 into 1 5.438 * [backup-simplify]: Simplify (/ PI 1) into PI 5.438 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 5.439 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 5.439 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 5.440 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.441 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 5.441 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 5.442 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 5.443 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 5.444 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 5.445 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 5.447 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 5.448 * * * [progress]: simplifying candidates 5.450 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (expm1 (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log1p (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ (- (log 1.0) (log (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ (log (/ 1.0 (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) 1) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 5.455 * * [simplify]: Extracting # 0 : cost 0 5.455 * * [simplify]: Extracting # 1 : cost 0 5.456 * * [simplify]: Extracting # 2 : cost 0 5.456 * * [simplify]: Extracting # 3 : cost 0 5.457 * * [simplify]: Extracting # 4 : cost 0 5.457 * * [simplify]: Extracting # 5 : cost 0 5.458 * * [simplify]: Extracting # 6 : cost 0 5.458 * * [simplify]: Extracting # 7 : cost 0 5.459 * * [simplify]: Extracting # 8 : cost 0 5.459 * * [simplify]: Extracting # 9 : cost 0 5.460 * * [simplify]: Extracting # 10 : cost 0 5.461 * * [simplify]: Extracting # 11 : cost 0 5.461 * * [simplify]: Extracting # 12 : cost 0 5.462 * * [simplify]: Extracting # 13 : cost 0 5.462 * * [simplify]: Extracting # 14 : cost 0 5.463 * * [simplify]: Extracting # 15 : cost 0 5.463 * * [simplify]: Extracting # 16 : cost 0 5.464 * * [simplify]: Extracting # 17 : cost 0 5.465 * * [simplify]: Extracting # 18 : cost 0 5.465 * * [simplify]: Extracting # 19 : cost 0 5.466 * * [simplify]: Extracting # 20 : cost 0 5.466 * * [simplify]: Extracting # 21 : cost 0 5.472 * * [simplify]: Extracting # 22 : cost 0 5.473 * * [simplify]: Extracting # 23 : cost 0 5.474 * * [simplify]: Extracting # 24 : cost 0 5.475 * * [simplify]: Extracting # 25 : cost 0 5.476 * * [simplify]: Extracting # 26 : cost 0 5.477 * * [simplify]: Extracting # 27 : cost 0 5.478 * * [simplify]: Extracting # 28 : cost 0 5.479 * * [simplify]: Extracting # 29 : cost 0 5.480 * * [simplify]: Extracting # 30 : cost 0 5.482 * * [simplify]: Extracting # 31 : cost 0 5.483 * * [simplify]: Extracting # 32 : cost 0 5.484 * * [simplify]: iteration 0 : 369 enodes (cost 2880 ) 5.629 * * [simplify]: Extracting # 0 : cost 0 5.632 * * [simplify]: Extracting # 1 : cost 0 5.634 * * [simplify]: Extracting # 2 : cost 0 5.637 * * [simplify]: Extracting # 3 : cost 0 5.640 * * [simplify]: Extracting # 4 : cost 0 5.642 * * [simplify]: Extracting # 5 : cost 0 5.645 * * [simplify]: Extracting # 6 : cost 0 5.648 * * [simplify]: iteration 1 : 961 enodes (cost 2712 ) 6.216 * * [simplify]: Extracting # 0 : cost 0 6.221 * * [simplify]: Extracting # 1 : cost 0 6.226 * * [simplify]: Extracting # 2 : cost 0 6.230 * * [simplify]: Extracting # 3 : cost 0 6.238 * * [simplify]: Extracting # 4 : cost 0 6.246 * * [simplify]: Extracting # 5 : cost 0 6.254 * * [simplify]: iteration 2 : 3131 enodes (cost 2550 ) 7.638 * * [simplify]: Extracting # 0 : cost 0 7.646 * * [simplify]: Extracting # 1 : cost 0 7.655 * * [simplify]: Extracting # 2 : cost 0 7.669 * * [simplify]: Extracting # 3 : cost 0 7.693 * * [simplify]: Extracting # 4 : cost 0 7.705 * * [simplify]: iteration done: 5000 enodes (cost 2540 ) 7.707 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* 2.0 (* n PI)) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* n (* 2.0 PI)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (pow (* n (* 2.0 PI)) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* n (* 2.0 PI)) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* n (* 2.0 PI)) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (/ (pow 1.0 3) k) (sqrt k)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (/ (fabs (cbrt k)) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (log (* n (* 2.0 PI))) (log (* n (* 2.0 PI))) (log (* n (* 2.0 PI))) (exp (* (* 2.0 PI) n)) (pow (* 2.0 (* n PI)) 3) (pow (* 2.0 (* n PI)) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* 2.0 (* n PI)) 3) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* PI n) (expm1 (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log1p (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (/ (/ (pow 1.0 3) k) (sqrt k))) (pow (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (pow (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (fma (- 0.5) (* k (fma (log (* 2.0 PI)) (pow (* 2.0 (* n PI)) 0.5) (* (log n) (pow (* 2.0 (* n PI)) 0.5)))) (fma (* 0.125 (pow k 2)) (fma (pow (log (* 2.0 PI)) 2) (pow (* 2.0 (* n PI)) 0.5) (* (pow (* 2.0 (* n PI)) 0.5) (pow (log n) 2))) (fma 0.25 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* 2.0 (* n PI)) 0.5)) (pow (* 2.0 (* n PI)) 0.5)))) (pow (pow (* 2.0 (* n PI)) 0.5) (- 1.0 k)) (pow (exp (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))) 0.5) (- (- (fma k +nan.0 +nan.0) (* (* +nan.0 k) k))) (- (- (/ +nan.0 (pow k 2)) (- (/ +nan.0 k) (/ +nan.0 (pow k 3))))) (- (- (/ +nan.0 (pow k 2)) (- (/ +nan.0 k) +nan.0))) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (fma (* +nan.0 (* (pow k 2) (pow (log (* 2.0 PI)) 2))) (- (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (fma (* (pow k 2) (log (* 2.0 PI))) (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) +nan.0) (fma (- (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (log n))))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (fma (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5)) +nan.0 (fma +nan.0 (- (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (fma +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5)) (fma (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) +nan.0 (- (* +nan.0 (- (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))) (* (* +nan.0 (* k (log n))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))) (fma +nan.0 (- (/ (pow (pow (* 2.0 (* n PI)) 0.5) (- 1.0 k)) k) (/ (pow (pow (* 2.0 (* n PI)) 0.5) (- 1.0 k)) (pow k 2))) (- (/ +nan.0 (/ (pow k 3) (pow (pow (* 2.0 (* n PI)) 0.5) (- 1.0 k)))))) (fma (- +nan.0) (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k) (* +nan.0 (- (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))) 7.710 * * * [progress]: adding candidates to table 8.436 * * [progress]: iteration 2 / 4 8.436 * * * [progress]: picking best candidate 8.476 * * * * [pick]: Picked # 8.476 * * * [progress]: localizing error 8.511 * * * [progress]: generating rewritten candidates 8.511 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 8.556 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 8.602 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 8.609 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 8.653 * * * [progress]: generating series expansions 8.653 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 8.654 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 8.654 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 8.654 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 8.654 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 8.654 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 8.655 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 8.655 * [taylor]: Taking taylor expansion of 0.25 in k 8.655 * [backup-simplify]: Simplify 0.25 into 0.25 8.655 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.655 * [taylor]: Taking taylor expansion of 1.0 in k 8.655 * [backup-simplify]: Simplify 1.0 into 1.0 8.655 * [taylor]: Taking taylor expansion of k in k 8.655 * [backup-simplify]: Simplify 0 into 0 8.655 * [backup-simplify]: Simplify 1 into 1 8.655 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 8.655 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 8.655 * [taylor]: Taking taylor expansion of 2.0 in k 8.655 * [backup-simplify]: Simplify 2.0 into 2.0 8.655 * [taylor]: Taking taylor expansion of (* n PI) in k 8.655 * [taylor]: Taking taylor expansion of n in k 8.655 * [backup-simplify]: Simplify n into n 8.655 * [taylor]: Taking taylor expansion of PI in k 8.655 * [backup-simplify]: Simplify PI into PI 8.655 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.655 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 8.655 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 8.655 * [backup-simplify]: Simplify (- 0) into 0 8.656 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.656 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 8.656 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 8.656 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 8.656 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 8.656 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.656 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.656 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 8.656 * [taylor]: Taking taylor expansion of 0.25 in n 8.656 * [backup-simplify]: Simplify 0.25 into 0.25 8.656 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.656 * [taylor]: Taking taylor expansion of 1.0 in n 8.656 * [backup-simplify]: Simplify 1.0 into 1.0 8.656 * [taylor]: Taking taylor expansion of k in n 8.656 * [backup-simplify]: Simplify k into k 8.656 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.656 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.656 * [taylor]: Taking taylor expansion of 2.0 in n 8.657 * [backup-simplify]: Simplify 2.0 into 2.0 8.657 * [taylor]: Taking taylor expansion of (* n PI) in n 8.657 * [taylor]: Taking taylor expansion of n in n 8.657 * [backup-simplify]: Simplify 0 into 0 8.657 * [backup-simplify]: Simplify 1 into 1 8.657 * [taylor]: Taking taylor expansion of PI in n 8.657 * [backup-simplify]: Simplify PI into PI 8.657 * [backup-simplify]: Simplify (* 0 PI) into 0 8.657 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.658 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.659 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.660 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.660 * [backup-simplify]: Simplify (- k) into (- k) 8.660 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.660 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 8.661 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.662 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 8.663 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 8.663 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 8.663 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.663 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.663 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 8.663 * [taylor]: Taking taylor expansion of 0.25 in n 8.663 * [backup-simplify]: Simplify 0.25 into 0.25 8.663 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.663 * [taylor]: Taking taylor expansion of 1.0 in n 8.663 * [backup-simplify]: Simplify 1.0 into 1.0 8.663 * [taylor]: Taking taylor expansion of k in n 8.663 * [backup-simplify]: Simplify k into k 8.663 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.663 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.663 * [taylor]: Taking taylor expansion of 2.0 in n 8.663 * [backup-simplify]: Simplify 2.0 into 2.0 8.663 * [taylor]: Taking taylor expansion of (* n PI) in n 8.663 * [taylor]: Taking taylor expansion of n in n 8.663 * [backup-simplify]: Simplify 0 into 0 8.663 * [backup-simplify]: Simplify 1 into 1 8.663 * [taylor]: Taking taylor expansion of PI in n 8.663 * [backup-simplify]: Simplify PI into PI 8.663 * [backup-simplify]: Simplify (* 0 PI) into 0 8.664 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.665 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.666 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.666 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.666 * [backup-simplify]: Simplify (- k) into (- k) 8.666 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.666 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 8.667 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.668 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 8.669 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 8.669 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 8.669 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 8.669 * [taylor]: Taking taylor expansion of 0.25 in k 8.669 * [backup-simplify]: Simplify 0.25 into 0.25 8.669 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 8.669 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.669 * [taylor]: Taking taylor expansion of 1.0 in k 8.669 * [backup-simplify]: Simplify 1.0 into 1.0 8.669 * [taylor]: Taking taylor expansion of k in k 8.669 * [backup-simplify]: Simplify 0 into 0 8.669 * [backup-simplify]: Simplify 1 into 1 8.669 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 8.669 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.669 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.669 * [taylor]: Taking taylor expansion of 2.0 in k 8.669 * [backup-simplify]: Simplify 2.0 into 2.0 8.669 * [taylor]: Taking taylor expansion of PI in k 8.669 * [backup-simplify]: Simplify PI into PI 8.670 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.670 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.670 * [taylor]: Taking taylor expansion of (log n) in k 8.671 * [taylor]: Taking taylor expansion of n in k 8.671 * [backup-simplify]: Simplify n into n 8.671 * [backup-simplify]: Simplify (log n) into (log n) 8.671 * [backup-simplify]: Simplify (- 0) into 0 8.671 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.672 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 8.673 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 8.673 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 8.674 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 8.675 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 8.677 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.678 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 8.680 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.680 * [backup-simplify]: Simplify (- 0) into 0 8.681 * [backup-simplify]: Simplify (+ 0 0) into 0 8.681 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 8.683 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.684 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 8.686 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.686 * [taylor]: Taking taylor expansion of 0 in k 8.686 * [backup-simplify]: Simplify 0 into 0 8.686 * [backup-simplify]: Simplify 0 into 0 8.687 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.689 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.690 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 8.690 * [backup-simplify]: Simplify (+ 0 0) into 0 8.691 * [backup-simplify]: Simplify (- 1) into -1 8.691 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.693 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 8.695 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 8.699 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 8.702 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 8.703 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 8.704 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 8.707 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.707 * [backup-simplify]: Simplify (- 0) into 0 8.708 * [backup-simplify]: Simplify (+ 0 0) into 0 8.708 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 8.709 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.710 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.711 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.711 * [taylor]: Taking taylor expansion of 0 in k 8.711 * [backup-simplify]: Simplify 0 into 0 8.712 * [backup-simplify]: Simplify 0 into 0 8.712 * [backup-simplify]: Simplify 0 into 0 8.712 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.714 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.715 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 8.715 * [backup-simplify]: Simplify (+ 0 0) into 0 8.716 * [backup-simplify]: Simplify (- 0) into 0 8.716 * [backup-simplify]: Simplify (+ 0 0) into 0 8.717 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.719 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 8.721 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 8.725 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 8.731 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 8.732 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 8.732 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 8.732 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 8.732 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 8.732 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 8.732 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 8.732 * [taylor]: Taking taylor expansion of 0.25 in k 8.732 * [backup-simplify]: Simplify 0.25 into 0.25 8.732 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.732 * [taylor]: Taking taylor expansion of 1.0 in k 8.732 * [backup-simplify]: Simplify 1.0 into 1.0 8.732 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.732 * [taylor]: Taking taylor expansion of k in k 8.732 * [backup-simplify]: Simplify 0 into 0 8.732 * [backup-simplify]: Simplify 1 into 1 8.732 * [backup-simplify]: Simplify (/ 1 1) into 1 8.732 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 8.732 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 8.732 * [taylor]: Taking taylor expansion of 2.0 in k 8.732 * [backup-simplify]: Simplify 2.0 into 2.0 8.732 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.732 * [taylor]: Taking taylor expansion of PI in k 8.732 * [backup-simplify]: Simplify PI into PI 8.732 * [taylor]: Taking taylor expansion of n in k 8.732 * [backup-simplify]: Simplify n into n 8.732 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.732 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 8.733 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 8.733 * [backup-simplify]: Simplify (- 1) into -1 8.733 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.733 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 8.733 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 8.734 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 8.734 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 8.734 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.734 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.734 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 8.734 * [taylor]: Taking taylor expansion of 0.25 in n 8.734 * [backup-simplify]: Simplify 0.25 into 0.25 8.734 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.734 * [taylor]: Taking taylor expansion of 1.0 in n 8.734 * [backup-simplify]: Simplify 1.0 into 1.0 8.734 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.734 * [taylor]: Taking taylor expansion of k in n 8.734 * [backup-simplify]: Simplify k into k 8.734 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.734 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.734 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.734 * [taylor]: Taking taylor expansion of 2.0 in n 8.734 * [backup-simplify]: Simplify 2.0 into 2.0 8.734 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.734 * [taylor]: Taking taylor expansion of PI in n 8.734 * [backup-simplify]: Simplify PI into PI 8.734 * [taylor]: Taking taylor expansion of n in n 8.734 * [backup-simplify]: Simplify 0 into 0 8.734 * [backup-simplify]: Simplify 1 into 1 8.735 * [backup-simplify]: Simplify (/ PI 1) into PI 8.735 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.736 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.736 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.736 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.736 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 8.737 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.738 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 8.739 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.739 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 8.739 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.739 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.739 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 8.739 * [taylor]: Taking taylor expansion of 0.25 in n 8.739 * [backup-simplify]: Simplify 0.25 into 0.25 8.739 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.739 * [taylor]: Taking taylor expansion of 1.0 in n 8.739 * [backup-simplify]: Simplify 1.0 into 1.0 8.739 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.739 * [taylor]: Taking taylor expansion of k in n 8.739 * [backup-simplify]: Simplify k into k 8.739 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.739 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.740 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.740 * [taylor]: Taking taylor expansion of 2.0 in n 8.740 * [backup-simplify]: Simplify 2.0 into 2.0 8.740 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.740 * [taylor]: Taking taylor expansion of PI in n 8.740 * [backup-simplify]: Simplify PI into PI 8.740 * [taylor]: Taking taylor expansion of n in n 8.740 * [backup-simplify]: Simplify 0 into 0 8.740 * [backup-simplify]: Simplify 1 into 1 8.740 * [backup-simplify]: Simplify (/ PI 1) into PI 8.741 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.742 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.742 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.742 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.742 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 8.744 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.745 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 8.746 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.746 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 8.746 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 8.746 * [taylor]: Taking taylor expansion of 0.25 in k 8.746 * [backup-simplify]: Simplify 0.25 into 0.25 8.746 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 8.746 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 8.746 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.747 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.747 * [taylor]: Taking taylor expansion of 2.0 in k 8.747 * [backup-simplify]: Simplify 2.0 into 2.0 8.747 * [taylor]: Taking taylor expansion of PI in k 8.747 * [backup-simplify]: Simplify PI into PI 8.747 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.748 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.748 * [taylor]: Taking taylor expansion of (log n) in k 8.748 * [taylor]: Taking taylor expansion of n in k 8.748 * [backup-simplify]: Simplify n into n 8.748 * [backup-simplify]: Simplify (log n) into (log n) 8.748 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.748 * [taylor]: Taking taylor expansion of 1.0 in k 8.748 * [backup-simplify]: Simplify 1.0 into 1.0 8.748 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.748 * [taylor]: Taking taylor expansion of k in k 8.748 * [backup-simplify]: Simplify 0 into 0 8.749 * [backup-simplify]: Simplify 1 into 1 8.749 * [backup-simplify]: Simplify (/ 1 1) into 1 8.749 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.750 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 8.750 * [backup-simplify]: Simplify (- 1) into -1 8.751 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.752 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 8.753 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 8.754 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.756 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.757 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.758 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.759 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.760 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.760 * [backup-simplify]: Simplify (- 0) into 0 8.760 * [backup-simplify]: Simplify (+ 0 0) into 0 8.761 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 8.762 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.764 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 8.774 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.774 * [taylor]: Taking taylor expansion of 0 in k 8.774 * [backup-simplify]: Simplify 0 into 0 8.774 * [backup-simplify]: Simplify 0 into 0 8.774 * [backup-simplify]: Simplify 0 into 0 8.775 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.776 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.780 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.781 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.781 * [backup-simplify]: Simplify (- 0) into 0 8.781 * [backup-simplify]: Simplify (+ 0 0) into 0 8.782 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 8.784 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.786 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 8.790 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.790 * [taylor]: Taking taylor expansion of 0 in k 8.790 * [backup-simplify]: Simplify 0 into 0 8.790 * [backup-simplify]: Simplify 0 into 0 8.790 * [backup-simplify]: Simplify 0 into 0 8.790 * [backup-simplify]: Simplify 0 into 0 8.791 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.793 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.799 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 8.799 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.800 * [backup-simplify]: Simplify (- 0) into 0 8.800 * [backup-simplify]: Simplify (+ 0 0) into 0 8.802 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 8.803 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.805 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 8.808 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 8.808 * [taylor]: Taking taylor expansion of 0 in k 8.808 * [backup-simplify]: Simplify 0 into 0 8.808 * [backup-simplify]: Simplify 0 into 0 8.810 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 8.810 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 8.811 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 8.811 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 8.811 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 8.811 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 8.811 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 8.811 * [taylor]: Taking taylor expansion of 0.25 in k 8.811 * [backup-simplify]: Simplify 0.25 into 0.25 8.811 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.811 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.811 * [taylor]: Taking taylor expansion of k in k 8.811 * [backup-simplify]: Simplify 0 into 0 8.811 * [backup-simplify]: Simplify 1 into 1 8.811 * [backup-simplify]: Simplify (/ 1 1) into 1 8.811 * [taylor]: Taking taylor expansion of 1.0 in k 8.811 * [backup-simplify]: Simplify 1.0 into 1.0 8.811 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 8.811 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 8.811 * [taylor]: Taking taylor expansion of -2.0 in k 8.812 * [backup-simplify]: Simplify -2.0 into -2.0 8.812 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.812 * [taylor]: Taking taylor expansion of PI in k 8.812 * [backup-simplify]: Simplify PI into PI 8.812 * [taylor]: Taking taylor expansion of n in k 8.812 * [backup-simplify]: Simplify n into n 8.812 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.812 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 8.812 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 8.812 * [backup-simplify]: Simplify (+ 1 0) into 1 8.813 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 8.813 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 8.813 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 8.813 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 8.813 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.813 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.813 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 8.813 * [taylor]: Taking taylor expansion of 0.25 in n 8.813 * [backup-simplify]: Simplify 0.25 into 0.25 8.813 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.814 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.814 * [taylor]: Taking taylor expansion of k in n 8.814 * [backup-simplify]: Simplify k into k 8.814 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.814 * [taylor]: Taking taylor expansion of 1.0 in n 8.814 * [backup-simplify]: Simplify 1.0 into 1.0 8.814 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.814 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.814 * [taylor]: Taking taylor expansion of -2.0 in n 8.814 * [backup-simplify]: Simplify -2.0 into -2.0 8.814 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.814 * [taylor]: Taking taylor expansion of PI in n 8.814 * [backup-simplify]: Simplify PI into PI 8.814 * [taylor]: Taking taylor expansion of n in n 8.814 * [backup-simplify]: Simplify 0 into 0 8.814 * [backup-simplify]: Simplify 1 into 1 8.815 * [backup-simplify]: Simplify (/ PI 1) into PI 8.815 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.816 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.816 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.816 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 8.818 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.819 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 8.820 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.820 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 8.820 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.820 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.820 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 8.820 * [taylor]: Taking taylor expansion of 0.25 in n 8.820 * [backup-simplify]: Simplify 0.25 into 0.25 8.820 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.821 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.821 * [taylor]: Taking taylor expansion of k in n 8.821 * [backup-simplify]: Simplify k into k 8.821 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.821 * [taylor]: Taking taylor expansion of 1.0 in n 8.821 * [backup-simplify]: Simplify 1.0 into 1.0 8.821 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.821 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.821 * [taylor]: Taking taylor expansion of -2.0 in n 8.821 * [backup-simplify]: Simplify -2.0 into -2.0 8.821 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.821 * [taylor]: Taking taylor expansion of PI in n 8.821 * [backup-simplify]: Simplify PI into PI 8.821 * [taylor]: Taking taylor expansion of n in n 8.821 * [backup-simplify]: Simplify 0 into 0 8.821 * [backup-simplify]: Simplify 1 into 1 8.821 * [backup-simplify]: Simplify (/ PI 1) into PI 8.822 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.823 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.823 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.823 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 8.825 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.826 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 8.827 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.827 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 8.827 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 8.827 * [taylor]: Taking taylor expansion of 0.25 in k 8.827 * [backup-simplify]: Simplify 0.25 into 0.25 8.827 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 8.828 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.828 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.828 * [taylor]: Taking taylor expansion of k in k 8.828 * [backup-simplify]: Simplify 0 into 0 8.828 * [backup-simplify]: Simplify 1 into 1 8.828 * [backup-simplify]: Simplify (/ 1 1) into 1 8.828 * [taylor]: Taking taylor expansion of 1.0 in k 8.828 * [backup-simplify]: Simplify 1.0 into 1.0 8.828 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 8.828 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 8.828 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 8.828 * [taylor]: Taking taylor expansion of -2.0 in k 8.828 * [backup-simplify]: Simplify -2.0 into -2.0 8.828 * [taylor]: Taking taylor expansion of PI in k 8.828 * [backup-simplify]: Simplify PI into PI 8.829 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.830 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.830 * [taylor]: Taking taylor expansion of (log n) in k 8.830 * [taylor]: Taking taylor expansion of n in k 8.830 * [backup-simplify]: Simplify n into n 8.830 * [backup-simplify]: Simplify (log n) into (log n) 8.830 * [backup-simplify]: Simplify (+ 1 0) into 1 8.831 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.832 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 8.833 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 8.834 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 8.835 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.836 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.837 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.838 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 8.840 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 8.840 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.841 * [backup-simplify]: Simplify (+ 0 0) into 0 8.841 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 8.843 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.844 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 8.846 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.846 * [taylor]: Taking taylor expansion of 0 in k 8.846 * [backup-simplify]: Simplify 0 into 0 8.846 * [backup-simplify]: Simplify 0 into 0 8.847 * [backup-simplify]: Simplify 0 into 0 8.848 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.849 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.853 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 8.853 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.854 * [backup-simplify]: Simplify (+ 0 0) into 0 8.855 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 8.856 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.858 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 8.861 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.861 * [taylor]: Taking taylor expansion of 0 in k 8.861 * [backup-simplify]: Simplify 0 into 0 8.861 * [backup-simplify]: Simplify 0 into 0 8.861 * [backup-simplify]: Simplify 0 into 0 8.862 * [backup-simplify]: Simplify 0 into 0 8.863 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.864 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.871 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 8.871 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.871 * [backup-simplify]: Simplify (+ 0 0) into 0 8.873 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 8.875 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.877 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 8.880 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 8.880 * [taylor]: Taking taylor expansion of 0 in k 8.880 * [backup-simplify]: Simplify 0 into 0 8.880 * [backup-simplify]: Simplify 0 into 0 8.881 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 8.881 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 8.882 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 8.882 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 8.882 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 8.882 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 8.882 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 8.882 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 8.883 * [taylor]: Taking taylor expansion of 0.25 in k 8.883 * [backup-simplify]: Simplify 0.25 into 0.25 8.883 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.883 * [taylor]: Taking taylor expansion of 1.0 in k 8.883 * [backup-simplify]: Simplify 1.0 into 1.0 8.883 * [taylor]: Taking taylor expansion of k in k 8.883 * [backup-simplify]: Simplify 0 into 0 8.883 * [backup-simplify]: Simplify 1 into 1 8.883 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 8.883 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 8.883 * [taylor]: Taking taylor expansion of 2.0 in k 8.883 * [backup-simplify]: Simplify 2.0 into 2.0 8.883 * [taylor]: Taking taylor expansion of (* n PI) in k 8.883 * [taylor]: Taking taylor expansion of n in k 8.883 * [backup-simplify]: Simplify n into n 8.883 * [taylor]: Taking taylor expansion of PI in k 8.883 * [backup-simplify]: Simplify PI into PI 8.883 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.883 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 8.883 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 8.884 * [backup-simplify]: Simplify (- 0) into 0 8.884 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.885 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 8.885 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 8.885 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 8.885 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 8.885 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.885 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.885 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 8.885 * [taylor]: Taking taylor expansion of 0.25 in n 8.885 * [backup-simplify]: Simplify 0.25 into 0.25 8.885 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.885 * [taylor]: Taking taylor expansion of 1.0 in n 8.885 * [backup-simplify]: Simplify 1.0 into 1.0 8.885 * [taylor]: Taking taylor expansion of k in n 8.885 * [backup-simplify]: Simplify k into k 8.885 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.885 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.885 * [taylor]: Taking taylor expansion of 2.0 in n 8.886 * [backup-simplify]: Simplify 2.0 into 2.0 8.886 * [taylor]: Taking taylor expansion of (* n PI) in n 8.886 * [taylor]: Taking taylor expansion of n in n 8.886 * [backup-simplify]: Simplify 0 into 0 8.886 * [backup-simplify]: Simplify 1 into 1 8.886 * [taylor]: Taking taylor expansion of PI in n 8.886 * [backup-simplify]: Simplify PI into PI 8.886 * [backup-simplify]: Simplify (* 0 PI) into 0 8.887 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.888 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.890 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.891 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.891 * [backup-simplify]: Simplify (- k) into (- k) 8.891 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.891 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 8.892 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.894 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 8.895 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 8.895 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 8.895 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.895 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.895 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 8.895 * [taylor]: Taking taylor expansion of 0.25 in n 8.895 * [backup-simplify]: Simplify 0.25 into 0.25 8.895 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.895 * [taylor]: Taking taylor expansion of 1.0 in n 8.895 * [backup-simplify]: Simplify 1.0 into 1.0 8.895 * [taylor]: Taking taylor expansion of k in n 8.895 * [backup-simplify]: Simplify k into k 8.895 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.895 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.895 * [taylor]: Taking taylor expansion of 2.0 in n 8.895 * [backup-simplify]: Simplify 2.0 into 2.0 8.895 * [taylor]: Taking taylor expansion of (* n PI) in n 8.895 * [taylor]: Taking taylor expansion of n in n 8.895 * [backup-simplify]: Simplify 0 into 0 8.895 * [backup-simplify]: Simplify 1 into 1 8.895 * [taylor]: Taking taylor expansion of PI in n 8.895 * [backup-simplify]: Simplify PI into PI 8.896 * [backup-simplify]: Simplify (* 0 PI) into 0 8.896 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.898 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.900 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.901 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.901 * [backup-simplify]: Simplify (- k) into (- k) 8.901 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.901 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 8.903 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.904 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 8.905 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 8.905 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 8.905 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 8.905 * [taylor]: Taking taylor expansion of 0.25 in k 8.905 * [backup-simplify]: Simplify 0.25 into 0.25 8.905 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 8.905 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.905 * [taylor]: Taking taylor expansion of 1.0 in k 8.905 * [backup-simplify]: Simplify 1.0 into 1.0 8.905 * [taylor]: Taking taylor expansion of k in k 8.905 * [backup-simplify]: Simplify 0 into 0 8.905 * [backup-simplify]: Simplify 1 into 1 8.905 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 8.905 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.906 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.906 * [taylor]: Taking taylor expansion of 2.0 in k 8.906 * [backup-simplify]: Simplify 2.0 into 2.0 8.906 * [taylor]: Taking taylor expansion of PI in k 8.906 * [backup-simplify]: Simplify PI into PI 8.906 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.907 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.907 * [taylor]: Taking taylor expansion of (log n) in k 8.907 * [taylor]: Taking taylor expansion of n in k 8.907 * [backup-simplify]: Simplify n into n 8.907 * [backup-simplify]: Simplify (log n) into (log n) 8.908 * [backup-simplify]: Simplify (- 0) into 0 8.908 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.910 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 8.911 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 8.912 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 8.913 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 8.914 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 8.915 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.916 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 8.918 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.918 * [backup-simplify]: Simplify (- 0) into 0 8.919 * [backup-simplify]: Simplify (+ 0 0) into 0 8.919 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 8.921 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.922 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 8.924 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.924 * [taylor]: Taking taylor expansion of 0 in k 8.924 * [backup-simplify]: Simplify 0 into 0 8.924 * [backup-simplify]: Simplify 0 into 0 8.925 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.927 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.928 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 8.928 * [backup-simplify]: Simplify (+ 0 0) into 0 8.929 * [backup-simplify]: Simplify (- 1) into -1 8.929 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.939 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 8.942 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 8.945 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 8.948 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 8.950 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 8.951 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 8.955 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.956 * [backup-simplify]: Simplify (- 0) into 0 8.956 * [backup-simplify]: Simplify (+ 0 0) into 0 8.957 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 8.959 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.961 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.963 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.963 * [taylor]: Taking taylor expansion of 0 in k 8.963 * [backup-simplify]: Simplify 0 into 0 8.963 * [backup-simplify]: Simplify 0 into 0 8.963 * [backup-simplify]: Simplify 0 into 0 8.965 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.968 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.970 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 8.971 * [backup-simplify]: Simplify (+ 0 0) into 0 8.971 * [backup-simplify]: Simplify (- 0) into 0 8.971 * [backup-simplify]: Simplify (+ 0 0) into 0 8.973 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.975 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 8.978 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 8.981 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 8.987 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 8.988 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 8.988 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 8.988 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 8.988 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 8.988 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 8.988 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 8.988 * [taylor]: Taking taylor expansion of 0.25 in k 8.988 * [backup-simplify]: Simplify 0.25 into 0.25 8.988 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.988 * [taylor]: Taking taylor expansion of 1.0 in k 8.988 * [backup-simplify]: Simplify 1.0 into 1.0 8.988 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.988 * [taylor]: Taking taylor expansion of k in k 8.988 * [backup-simplify]: Simplify 0 into 0 8.988 * [backup-simplify]: Simplify 1 into 1 8.988 * [backup-simplify]: Simplify (/ 1 1) into 1 8.988 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 8.988 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 8.989 * [taylor]: Taking taylor expansion of 2.0 in k 8.989 * [backup-simplify]: Simplify 2.0 into 2.0 8.989 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.989 * [taylor]: Taking taylor expansion of PI in k 8.989 * [backup-simplify]: Simplify PI into PI 8.989 * [taylor]: Taking taylor expansion of n in k 8.989 * [backup-simplify]: Simplify n into n 8.989 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.989 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 8.989 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 8.989 * [backup-simplify]: Simplify (- 1) into -1 8.989 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.990 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 8.990 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 8.990 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 8.990 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 8.990 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.990 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.990 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 8.990 * [taylor]: Taking taylor expansion of 0.25 in n 8.990 * [backup-simplify]: Simplify 0.25 into 0.25 8.990 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.990 * [taylor]: Taking taylor expansion of 1.0 in n 8.990 * [backup-simplify]: Simplify 1.0 into 1.0 8.990 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.990 * [taylor]: Taking taylor expansion of k in n 8.990 * [backup-simplify]: Simplify k into k 8.990 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.990 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.990 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.990 * [taylor]: Taking taylor expansion of 2.0 in n 8.990 * [backup-simplify]: Simplify 2.0 into 2.0 8.990 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.990 * [taylor]: Taking taylor expansion of PI in n 8.990 * [backup-simplify]: Simplify PI into PI 8.990 * [taylor]: Taking taylor expansion of n in n 8.990 * [backup-simplify]: Simplify 0 into 0 8.990 * [backup-simplify]: Simplify 1 into 1 8.991 * [backup-simplify]: Simplify (/ PI 1) into PI 8.991 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.992 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.992 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.992 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.992 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 8.993 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.994 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 8.995 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.995 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 8.995 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.995 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.995 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 8.995 * [taylor]: Taking taylor expansion of 0.25 in n 8.995 * [backup-simplify]: Simplify 0.25 into 0.25 8.995 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.995 * [taylor]: Taking taylor expansion of 1.0 in n 8.995 * [backup-simplify]: Simplify 1.0 into 1.0 8.995 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.995 * [taylor]: Taking taylor expansion of k in n 8.995 * [backup-simplify]: Simplify k into k 8.995 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.995 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.995 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.995 * [taylor]: Taking taylor expansion of 2.0 in n 8.995 * [backup-simplify]: Simplify 2.0 into 2.0 8.995 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.995 * [taylor]: Taking taylor expansion of PI in n 8.995 * [backup-simplify]: Simplify PI into PI 8.995 * [taylor]: Taking taylor expansion of n in n 8.995 * [backup-simplify]: Simplify 0 into 0 8.995 * [backup-simplify]: Simplify 1 into 1 8.996 * [backup-simplify]: Simplify (/ PI 1) into PI 8.996 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.997 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.997 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.997 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.997 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 8.998 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.999 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 8.999 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 9.000 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 9.000 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 9.000 * [taylor]: Taking taylor expansion of 0.25 in k 9.000 * [backup-simplify]: Simplify 0.25 into 0.25 9.000 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 9.000 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 9.000 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 9.000 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 9.000 * [taylor]: Taking taylor expansion of 2.0 in k 9.000 * [backup-simplify]: Simplify 2.0 into 2.0 9.000 * [taylor]: Taking taylor expansion of PI in k 9.000 * [backup-simplify]: Simplify PI into PI 9.000 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.001 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.001 * [taylor]: Taking taylor expansion of (log n) in k 9.001 * [taylor]: Taking taylor expansion of n in k 9.001 * [backup-simplify]: Simplify n into n 9.001 * [backup-simplify]: Simplify (log n) into (log n) 9.001 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.001 * [taylor]: Taking taylor expansion of 1.0 in k 9.001 * [backup-simplify]: Simplify 1.0 into 1.0 9.001 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.001 * [taylor]: Taking taylor expansion of k in k 9.001 * [backup-simplify]: Simplify 0 into 0 9.001 * [backup-simplify]: Simplify 1 into 1 9.001 * [backup-simplify]: Simplify (/ 1 1) into 1 9.001 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.002 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 9.002 * [backup-simplify]: Simplify (- 1) into -1 9.003 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.003 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 9.004 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 9.005 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 9.006 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 9.007 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.008 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.010 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.010 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.010 * [backup-simplify]: Simplify (- 0) into 0 9.011 * [backup-simplify]: Simplify (+ 0 0) into 0 9.011 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 9.013 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.014 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 9.016 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.016 * [taylor]: Taking taylor expansion of 0 in k 9.016 * [backup-simplify]: Simplify 0 into 0 9.016 * [backup-simplify]: Simplify 0 into 0 9.016 * [backup-simplify]: Simplify 0 into 0 9.017 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.018 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.021 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 9.021 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.021 * [backup-simplify]: Simplify (- 0) into 0 9.021 * [backup-simplify]: Simplify (+ 0 0) into 0 9.022 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 9.023 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.024 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 9.026 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.026 * [taylor]: Taking taylor expansion of 0 in k 9.026 * [backup-simplify]: Simplify 0 into 0 9.026 * [backup-simplify]: Simplify 0 into 0 9.026 * [backup-simplify]: Simplify 0 into 0 9.026 * [backup-simplify]: Simplify 0 into 0 9.027 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.027 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.031 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 9.031 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.031 * [backup-simplify]: Simplify (- 0) into 0 9.032 * [backup-simplify]: Simplify (+ 0 0) into 0 9.032 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 9.033 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.035 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 9.036 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 9.036 * [taylor]: Taking taylor expansion of 0 in k 9.036 * [backup-simplify]: Simplify 0 into 0 9.036 * [backup-simplify]: Simplify 0 into 0 9.037 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 9.038 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 9.038 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 9.038 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 9.038 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 9.038 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 9.038 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 9.038 * [taylor]: Taking taylor expansion of 0.25 in k 9.038 * [backup-simplify]: Simplify 0.25 into 0.25 9.038 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.038 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.038 * [taylor]: Taking taylor expansion of k in k 9.038 * [backup-simplify]: Simplify 0 into 0 9.038 * [backup-simplify]: Simplify 1 into 1 9.038 * [backup-simplify]: Simplify (/ 1 1) into 1 9.038 * [taylor]: Taking taylor expansion of 1.0 in k 9.038 * [backup-simplify]: Simplify 1.0 into 1.0 9.038 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 9.038 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 9.038 * [taylor]: Taking taylor expansion of -2.0 in k 9.038 * [backup-simplify]: Simplify -2.0 into -2.0 9.039 * [taylor]: Taking taylor expansion of (/ PI n) in k 9.039 * [taylor]: Taking taylor expansion of PI in k 9.039 * [backup-simplify]: Simplify PI into PI 9.039 * [taylor]: Taking taylor expansion of n in k 9.039 * [backup-simplify]: Simplify n into n 9.039 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 9.039 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 9.039 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 9.039 * [backup-simplify]: Simplify (+ 1 0) into 1 9.039 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 9.039 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 9.040 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 9.040 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 9.040 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 9.040 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 9.040 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 9.040 * [taylor]: Taking taylor expansion of 0.25 in n 9.040 * [backup-simplify]: Simplify 0.25 into 0.25 9.040 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.040 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.040 * [taylor]: Taking taylor expansion of k in n 9.040 * [backup-simplify]: Simplify k into k 9.040 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.040 * [taylor]: Taking taylor expansion of 1.0 in n 9.040 * [backup-simplify]: Simplify 1.0 into 1.0 9.040 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 9.040 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.040 * [taylor]: Taking taylor expansion of -2.0 in n 9.040 * [backup-simplify]: Simplify -2.0 into -2.0 9.040 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.040 * [taylor]: Taking taylor expansion of PI in n 9.040 * [backup-simplify]: Simplify PI into PI 9.040 * [taylor]: Taking taylor expansion of n in n 9.040 * [backup-simplify]: Simplify 0 into 0 9.040 * [backup-simplify]: Simplify 1 into 1 9.040 * [backup-simplify]: Simplify (/ PI 1) into PI 9.041 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.041 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.041 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.042 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 9.042 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.043 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 9.044 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 9.044 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 9.044 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 9.044 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 9.044 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 9.044 * [taylor]: Taking taylor expansion of 0.25 in n 9.044 * [backup-simplify]: Simplify 0.25 into 0.25 9.044 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.044 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.044 * [taylor]: Taking taylor expansion of k in n 9.044 * [backup-simplify]: Simplify k into k 9.044 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.044 * [taylor]: Taking taylor expansion of 1.0 in n 9.044 * [backup-simplify]: Simplify 1.0 into 1.0 9.044 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 9.044 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.045 * [taylor]: Taking taylor expansion of -2.0 in n 9.045 * [backup-simplify]: Simplify -2.0 into -2.0 9.045 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.045 * [taylor]: Taking taylor expansion of PI in n 9.045 * [backup-simplify]: Simplify PI into PI 9.045 * [taylor]: Taking taylor expansion of n in n 9.045 * [backup-simplify]: Simplify 0 into 0 9.045 * [backup-simplify]: Simplify 1 into 1 9.045 * [backup-simplify]: Simplify (/ PI 1) into PI 9.045 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.046 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.046 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.046 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 9.047 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.048 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 9.049 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 9.049 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 9.049 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 9.049 * [taylor]: Taking taylor expansion of 0.25 in k 9.049 * [backup-simplify]: Simplify 0.25 into 0.25 9.049 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 9.049 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.049 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.049 * [taylor]: Taking taylor expansion of k in k 9.049 * [backup-simplify]: Simplify 0 into 0 9.049 * [backup-simplify]: Simplify 1 into 1 9.049 * [backup-simplify]: Simplify (/ 1 1) into 1 9.049 * [taylor]: Taking taylor expansion of 1.0 in k 9.049 * [backup-simplify]: Simplify 1.0 into 1.0 9.049 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 9.049 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 9.049 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 9.049 * [taylor]: Taking taylor expansion of -2.0 in k 9.050 * [backup-simplify]: Simplify -2.0 into -2.0 9.050 * [taylor]: Taking taylor expansion of PI in k 9.050 * [backup-simplify]: Simplify PI into PI 9.050 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.051 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.051 * [taylor]: Taking taylor expansion of (log n) in k 9.051 * [taylor]: Taking taylor expansion of n in k 9.051 * [backup-simplify]: Simplify n into n 9.051 * [backup-simplify]: Simplify (log n) into (log n) 9.051 * [backup-simplify]: Simplify (+ 1 0) into 1 9.051 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.052 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 9.052 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 9.059 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 9.060 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 9.061 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 9.062 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.062 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 9.064 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 9.064 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.064 * [backup-simplify]: Simplify (+ 0 0) into 0 9.064 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 9.065 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.066 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 9.067 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.067 * [taylor]: Taking taylor expansion of 0 in k 9.067 * [backup-simplify]: Simplify 0 into 0 9.067 * [backup-simplify]: Simplify 0 into 0 9.067 * [backup-simplify]: Simplify 0 into 0 9.068 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.069 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.072 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 9.072 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.073 * [backup-simplify]: Simplify (+ 0 0) into 0 9.074 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 9.075 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.077 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 9.079 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.079 * [taylor]: Taking taylor expansion of 0 in k 9.079 * [backup-simplify]: Simplify 0 into 0 9.079 * [backup-simplify]: Simplify 0 into 0 9.079 * [backup-simplify]: Simplify 0 into 0 9.080 * [backup-simplify]: Simplify 0 into 0 9.081 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.082 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.085 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 9.086 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.086 * [backup-simplify]: Simplify (+ 0 0) into 0 9.087 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 9.088 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.089 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 9.091 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 9.091 * [taylor]: Taking taylor expansion of 0 in k 9.091 * [backup-simplify]: Simplify 0 into 0 9.091 * [backup-simplify]: Simplify 0 into 0 9.092 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 9.092 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 9.092 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 9.092 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 9.092 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 9.092 * [taylor]: Taking taylor expansion of 1.0 in k 9.092 * [backup-simplify]: Simplify 1.0 into 1.0 9.092 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 9.092 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.092 * [taylor]: Taking taylor expansion of k in k 9.092 * [backup-simplify]: Simplify 0 into 0 9.092 * [backup-simplify]: Simplify 1 into 1 9.092 * [backup-simplify]: Simplify (/ 1 1) into 1 9.093 * [backup-simplify]: Simplify (sqrt 0) into 0 9.093 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.093 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 9.093 * [taylor]: Taking taylor expansion of 1.0 in k 9.093 * [backup-simplify]: Simplify 1.0 into 1.0 9.094 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 9.094 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.094 * [taylor]: Taking taylor expansion of k in k 9.094 * [backup-simplify]: Simplify 0 into 0 9.094 * [backup-simplify]: Simplify 1 into 1 9.094 * [backup-simplify]: Simplify (/ 1 1) into 1 9.094 * [backup-simplify]: Simplify (sqrt 0) into 0 9.095 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.095 * [backup-simplify]: Simplify (* 1.0 0) into 0 9.095 * [backup-simplify]: Simplify 0 into 0 9.096 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 9.096 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.097 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 9.099 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.100 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 9.100 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.101 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.103 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.104 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 9.105 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.106 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 9.106 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 9.106 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 9.106 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 9.106 * [taylor]: Taking taylor expansion of 1.0 in k 9.106 * [backup-simplify]: Simplify 1.0 into 1.0 9.106 * [taylor]: Taking taylor expansion of (sqrt k) in k 9.106 * [taylor]: Taking taylor expansion of k in k 9.106 * [backup-simplify]: Simplify 0 into 0 9.106 * [backup-simplify]: Simplify 1 into 1 9.106 * [backup-simplify]: Simplify (sqrt 0) into 0 9.107 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.107 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 9.107 * [taylor]: Taking taylor expansion of 1.0 in k 9.107 * [backup-simplify]: Simplify 1.0 into 1.0 9.107 * [taylor]: Taking taylor expansion of (sqrt k) in k 9.107 * [taylor]: Taking taylor expansion of k in k 9.107 * [backup-simplify]: Simplify 0 into 0 9.107 * [backup-simplify]: Simplify 1 into 1 9.107 * [backup-simplify]: Simplify (sqrt 0) into 0 9.108 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.108 * [backup-simplify]: Simplify (* 1.0 0) into 0 9.109 * [backup-simplify]: Simplify 0 into 0 9.109 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 9.110 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.112 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.113 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 9.113 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.117 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.119 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 9.119 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.120 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 9.120 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 9.120 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 9.120 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 9.120 * [taylor]: Taking taylor expansion of 1.0 in k 9.121 * [backup-simplify]: Simplify 1.0 into 1.0 9.121 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 9.121 * [taylor]: Taking taylor expansion of (/ -1 k) in k 9.121 * [taylor]: Taking taylor expansion of -1 in k 9.121 * [backup-simplify]: Simplify -1 into -1 9.121 * [taylor]: Taking taylor expansion of k in k 9.121 * [backup-simplify]: Simplify 0 into 0 9.121 * [backup-simplify]: Simplify 1 into 1 9.121 * [backup-simplify]: Simplify (/ -1 1) into -1 9.121 * [backup-simplify]: Simplify (sqrt 0) into 0 9.122 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 9.122 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 9.123 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 9.123 * [taylor]: Taking taylor expansion of 1.0 in k 9.123 * [backup-simplify]: Simplify 1.0 into 1.0 9.123 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 9.123 * [taylor]: Taking taylor expansion of (/ -1 k) in k 9.123 * [taylor]: Taking taylor expansion of -1 in k 9.123 * [backup-simplify]: Simplify -1 into -1 9.123 * [taylor]: Taking taylor expansion of k in k 9.123 * [backup-simplify]: Simplify 0 into 0 9.123 * [backup-simplify]: Simplify 1 into 1 9.123 * [backup-simplify]: Simplify (/ -1 1) into -1 9.123 * [backup-simplify]: Simplify (sqrt 0) into 0 9.124 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 9.125 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 9.125 * [backup-simplify]: Simplify +nan.0 into +nan.0 9.125 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 9.127 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.129 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 9.129 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.130 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.132 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.135 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 9.135 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.136 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 9.136 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 9.136 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 9.136 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 9.136 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.136 * [taylor]: Taking taylor expansion of 2.0 in n 9.136 * [backup-simplify]: Simplify 2.0 into 2.0 9.136 * [taylor]: Taking taylor expansion of (* n PI) in n 9.136 * [taylor]: Taking taylor expansion of n in n 9.136 * [backup-simplify]: Simplify 0 into 0 9.136 * [backup-simplify]: Simplify 1 into 1 9.136 * [taylor]: Taking taylor expansion of PI in n 9.136 * [backup-simplify]: Simplify PI into PI 9.136 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.136 * [taylor]: Taking taylor expansion of 2.0 in n 9.137 * [backup-simplify]: Simplify 2.0 into 2.0 9.137 * [taylor]: Taking taylor expansion of (* n PI) in n 9.137 * [taylor]: Taking taylor expansion of n in n 9.137 * [backup-simplify]: Simplify 0 into 0 9.137 * [backup-simplify]: Simplify 1 into 1 9.137 * [taylor]: Taking taylor expansion of PI in n 9.137 * [backup-simplify]: Simplify PI into PI 9.137 * [backup-simplify]: Simplify (* 0 PI) into 0 9.137 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.137 * [backup-simplify]: Simplify 0 into 0 9.138 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.139 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.140 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.140 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 9.141 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 9.141 * [backup-simplify]: Simplify 0 into 0 9.142 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 9.143 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 9.143 * [backup-simplify]: Simplify 0 into 0 9.144 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.146 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 9.146 * [backup-simplify]: Simplify 0 into 0 9.147 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 9.149 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 9.149 * [backup-simplify]: Simplify 0 into 0 9.151 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 9.153 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 9.153 * [backup-simplify]: Simplify 0 into 0 9.155 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 9.157 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 9.157 * [backup-simplify]: Simplify 0 into 0 9.158 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 9.158 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 9.158 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 9.158 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.158 * [taylor]: Taking taylor expansion of 2.0 in n 9.158 * [backup-simplify]: Simplify 2.0 into 2.0 9.158 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.159 * [taylor]: Taking taylor expansion of PI in n 9.159 * [backup-simplify]: Simplify PI into PI 9.159 * [taylor]: Taking taylor expansion of n in n 9.159 * [backup-simplify]: Simplify 0 into 0 9.159 * [backup-simplify]: Simplify 1 into 1 9.159 * [backup-simplify]: Simplify (/ PI 1) into PI 9.159 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.159 * [taylor]: Taking taylor expansion of 2.0 in n 9.159 * [backup-simplify]: Simplify 2.0 into 2.0 9.159 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.159 * [taylor]: Taking taylor expansion of PI in n 9.159 * [backup-simplify]: Simplify PI into PI 9.159 * [taylor]: Taking taylor expansion of n in n 9.159 * [backup-simplify]: Simplify 0 into 0 9.159 * [backup-simplify]: Simplify 1 into 1 9.160 * [backup-simplify]: Simplify (/ PI 1) into PI 9.160 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.161 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.162 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.163 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.163 * [backup-simplify]: Simplify 0 into 0 9.164 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.165 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.165 * [backup-simplify]: Simplify 0 into 0 9.166 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.177 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.177 * [backup-simplify]: Simplify 0 into 0 9.178 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.180 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.180 * [backup-simplify]: Simplify 0 into 0 9.181 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.183 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 9.183 * [backup-simplify]: Simplify 0 into 0 9.184 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.186 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 9.186 * [backup-simplify]: Simplify 0 into 0 9.186 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 9.187 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 9.187 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 9.187 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.187 * [taylor]: Taking taylor expansion of -2.0 in n 9.187 * [backup-simplify]: Simplify -2.0 into -2.0 9.187 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.187 * [taylor]: Taking taylor expansion of PI in n 9.187 * [backup-simplify]: Simplify PI into PI 9.187 * [taylor]: Taking taylor expansion of n in n 9.187 * [backup-simplify]: Simplify 0 into 0 9.187 * [backup-simplify]: Simplify 1 into 1 9.188 * [backup-simplify]: Simplify (/ PI 1) into PI 9.188 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.188 * [taylor]: Taking taylor expansion of -2.0 in n 9.188 * [backup-simplify]: Simplify -2.0 into -2.0 9.188 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.188 * [taylor]: Taking taylor expansion of PI in n 9.188 * [backup-simplify]: Simplify PI into PI 9.188 * [taylor]: Taking taylor expansion of n in n 9.188 * [backup-simplify]: Simplify 0 into 0 9.188 * [backup-simplify]: Simplify 1 into 1 9.188 * [backup-simplify]: Simplify (/ PI 1) into PI 9.189 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.189 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.190 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.191 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 9.191 * [backup-simplify]: Simplify 0 into 0 9.192 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.193 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.193 * [backup-simplify]: Simplify 0 into 0 9.194 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.196 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.196 * [backup-simplify]: Simplify 0 into 0 9.197 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.198 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.198 * [backup-simplify]: Simplify 0 into 0 9.199 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.201 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 9.201 * [backup-simplify]: Simplify 0 into 0 9.202 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.204 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 9.204 * [backup-simplify]: Simplify 0 into 0 9.205 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 9.205 * * * [progress]: simplifying candidates 9.211 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* 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k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 9.216 * * [simplify]: Extracting # 0 : cost 0 9.216 * * [simplify]: Extracting # 1 : cost 0 9.217 * * [simplify]: Extracting # 2 : cost 0 9.217 * * [simplify]: Extracting # 3 : cost 0 9.217 * * [simplify]: Extracting # 4 : cost 0 9.218 * * [simplify]: Extracting # 5 : cost 0 9.219 * * [simplify]: Extracting # 6 : cost 0 9.219 * * [simplify]: Extracting # 7 : cost 0 9.220 * * [simplify]: Extracting # 8 : cost 0 9.220 * * [simplify]: Extracting # 9 : cost 0 9.221 * * [simplify]: Extracting # 10 : cost 0 9.221 * * [simplify]: Extracting # 11 : cost 0 9.222 * * [simplify]: Extracting # 12 : cost 0 9.222 * * [simplify]: Extracting # 13 : cost 0 9.223 * * [simplify]: Extracting # 14 : cost 0 9.223 * * [simplify]: iteration 0 : 332 enodes (cost 3588 ) 9.377 * * [simplify]: Extracting # 0 : cost 0 9.378 * * [simplify]: Extracting # 1 : cost 0 9.380 * * [simplify]: Extracting # 2 : cost 0 9.381 * * [simplify]: Extracting # 3 : cost 0 9.387 * * [simplify]: Extracting # 4 : cost 0 9.389 * * [simplify]: Extracting # 5 : cost 0 9.390 * * [simplify]: Extracting # 6 : cost 0 9.391 * * [simplify]: Extracting # 7 : cost 0 9.392 * * [simplify]: iteration 1 : 854 enodes (cost 3308 ) 10.029 * * [simplify]: Extracting # 0 : cost 0 10.035 * * [simplify]: Extracting # 1 : cost 0 10.042 * * [simplify]: Extracting # 2 : cost 0 10.057 * * [simplify]: Extracting # 3 : cost 0 10.063 * * [simplify]: Extracting # 4 : cost 0 10.071 * * [simplify]: iteration 2 : 2490 enodes (cost 3202 ) 11.017 * * [simplify]: Extracting # 0 : cost 0 11.024 * * [simplify]: Extracting # 1 : cost 0 11.037 * * [simplify]: Extracting # 2 : cost 0 11.050 * * [simplify]: Extracting # 3 : cost 0 11.065 * * [simplify]: Extracting # 4 : cost 0 11.072 * * [simplify]: iteration done: 5002 enodes (cost 3197 ) 11.074 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (/ (- 1.0 k) 2.0) 1/2) (* (/ (- 1.0 k) 2.0) 1/2) (* (/ (- 1.0 k) 2.0) 1/2) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* PI n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* PI n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2))) (pow (* 2.0 (* PI n)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (sqrt 2))) (pow (* 2.0 (* PI n)) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* PI n) 2.0) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow (* 2.0 (* PI n)) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* PI n) 2.0) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* PI n) 2.0) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* PI n) 2.0) (- 1.0 k)) (* (* PI n) 2.0) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* 2.0 (* PI n)) (/ (/ (- 1.0 k) 2.0) 4)) (pow (* 2.0 (* PI n)) (/ (/ (- 1.0 k) 2.0) 4)) (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (/ (- 1.0 k) 2.0) 1/2) (* (/ (- 1.0 k) 2.0) 1/2) (* (/ (- 1.0 k) 2.0) 1/2) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* PI n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* PI n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2))) (pow (* 2.0 (* PI n)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (sqrt 2))) (pow (* 2.0 (* PI n)) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* PI n) 2.0) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow (* 2.0 (* PI n)) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* PI n) 2.0) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* PI n) 2.0) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* PI n) 2.0) (- 1.0 k)) (* (* PI n) 2.0) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* 2.0 (* PI n)) (/ (/ (- 1.0 k) 2.0) 4)) (pow (* 2.0 (* PI n)) (/ (/ (- 1.0 k) 2.0) 4)) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (pow 1.0 3) (* k (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* PI n) 2.0) (* (* PI n) 2.0) (log (* (* PI n) 2.0)) (log (* (* PI n) 2.0)) (log (* (* PI n) 2.0)) (exp (* (* 2.0 PI) n)) (pow (* 2.0 (* PI n)) 3) (pow (* 2.0 (* PI n)) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* 2.0 (* PI n)) 3) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* PI n) (fma (- 0.25) (* k (fma (pow (* 2.0 (* PI n)) 0.25) (log (* 2.0 PI)) (* (pow (* 2.0 (* PI n)) 0.25) (log n)))) (fma (* 0.03125 (pow k 2)) (* (pow (* 2.0 (* PI n)) 0.25) (pow (log (* 2.0 PI)) 2)) (fma (* 0.03125 (pow k 2)) (* (pow (log n) 2) (pow (* 2.0 (* PI n)) 0.25)) (fma (* 0.0625 (* (pow k 2) (log (* 2.0 PI)))) (* (pow (* 2.0 (* PI n)) 0.25) (log n)) (pow (* 2.0 (* PI n)) 0.25))))) (pow (pow (* 2.0 (* PI n)) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (fma (- 0.25) (* k (fma (pow (* 2.0 (* PI n)) 0.25) (log (* 2.0 PI)) (* (pow (* 2.0 (* PI n)) 0.25) (log n)))) (fma (* 0.03125 (pow k 2)) (* (pow (* 2.0 (* PI n)) 0.25) (pow (log (* 2.0 PI)) 2)) (fma (* 0.03125 (pow k 2)) (* (pow (log n) 2) (pow (* 2.0 (* PI n)) 0.25)) (fma (* 0.0625 (* (pow k 2) (log (* 2.0 PI)))) (* (pow (* 2.0 (* PI n)) 0.25) (log n)) (pow (* 2.0 (* PI n)) 0.25))))) (pow (pow (* 2.0 (* PI n)) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (fma (- k) +nan.0 (fma +nan.0 (pow k 2) (- +nan.0))) (+ (/ (- +nan.0) (pow k 2)) (- (/ +nan.0 k) (/ +nan.0 (pow k 3)))) (- (+ (- (/ +nan.0 (pow k 2)) (/ +nan.0 k)) +nan.0)) (* (* PI n) 2.0) (* (* PI n) 2.0) (* (* PI n) 2.0) 11.076 * * * [progress]: adding candidates to table 12.501 * * [progress]: iteration 3 / 4 12.501 * * * [progress]: picking best candidate 12.558 * * * * [pick]: Picked # 12.558 * * * [progress]: localizing error 12.617 * * * [progress]: generating rewritten candidates 12.617 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1) 12.650 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 12.705 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 12.718 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1 2) 12.751 * * * [progress]: generating series expansions 12.751 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1) 12.752 * [backup-simplify]: Simplify (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 12.752 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 12.752 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 12.752 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 12.752 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 12.752 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 12.752 * [taylor]: Taking taylor expansion of 0.5 in k 12.752 * [backup-simplify]: Simplify 0.5 into 0.5 12.752 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.752 * [taylor]: Taking taylor expansion of 1.0 in k 12.752 * [backup-simplify]: Simplify 1.0 into 1.0 12.752 * [taylor]: Taking taylor expansion of k in k 12.752 * [backup-simplify]: Simplify 0 into 0 12.752 * [backup-simplify]: Simplify 1 into 1 12.752 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 12.752 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 12.752 * [taylor]: Taking taylor expansion of 2.0 in k 12.752 * [backup-simplify]: Simplify 2.0 into 2.0 12.752 * [taylor]: Taking taylor expansion of (* n PI) in k 12.752 * [taylor]: Taking taylor expansion of n in k 12.752 * [backup-simplify]: Simplify n into n 12.752 * [taylor]: Taking taylor expansion of PI in k 12.752 * [backup-simplify]: Simplify PI into PI 12.752 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.752 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 12.752 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 12.753 * [backup-simplify]: Simplify (- 0) into 0 12.753 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.753 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 12.754 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 12.754 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 12.754 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 12.754 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.754 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.754 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 12.754 * [taylor]: Taking taylor expansion of 0.5 in n 12.754 * [backup-simplify]: Simplify 0.5 into 0.5 12.754 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.754 * [taylor]: Taking taylor expansion of 1.0 in n 12.754 * [backup-simplify]: Simplify 1.0 into 1.0 12.754 * [taylor]: Taking taylor expansion of k in n 12.754 * [backup-simplify]: Simplify k into k 12.754 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.754 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.754 * [taylor]: Taking taylor expansion of 2.0 in n 12.754 * [backup-simplify]: Simplify 2.0 into 2.0 12.754 * [taylor]: Taking taylor expansion of (* n PI) in n 12.754 * [taylor]: Taking taylor expansion of n in n 12.754 * [backup-simplify]: Simplify 0 into 0 12.754 * [backup-simplify]: Simplify 1 into 1 12.754 * [taylor]: Taking taylor expansion of PI in n 12.754 * [backup-simplify]: Simplify PI into PI 12.759 * [backup-simplify]: Simplify (* 0 PI) into 0 12.759 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.760 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.761 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.762 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.762 * [backup-simplify]: Simplify (- k) into (- k) 12.762 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.762 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 12.763 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.764 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.765 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.765 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 12.765 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.765 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.765 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 12.765 * [taylor]: Taking taylor expansion of 0.5 in n 12.765 * [backup-simplify]: Simplify 0.5 into 0.5 12.765 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.765 * [taylor]: Taking taylor expansion of 1.0 in n 12.765 * [backup-simplify]: Simplify 1.0 into 1.0 12.765 * [taylor]: Taking taylor expansion of k in n 12.765 * [backup-simplify]: Simplify k into k 12.765 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.765 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.765 * [taylor]: Taking taylor expansion of 2.0 in n 12.765 * [backup-simplify]: Simplify 2.0 into 2.0 12.765 * [taylor]: Taking taylor expansion of (* n PI) in n 12.765 * [taylor]: Taking taylor expansion of n in n 12.765 * [backup-simplify]: Simplify 0 into 0 12.765 * [backup-simplify]: Simplify 1 into 1 12.765 * [taylor]: Taking taylor expansion of PI in n 12.765 * [backup-simplify]: Simplify PI into PI 12.765 * [backup-simplify]: Simplify (* 0 PI) into 0 12.766 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.767 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.768 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.768 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.768 * [backup-simplify]: Simplify (- k) into (- k) 12.768 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.768 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 12.769 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.770 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.771 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.771 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 12.771 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 12.771 * [taylor]: Taking taylor expansion of 0.5 in k 12.771 * [backup-simplify]: Simplify 0.5 into 0.5 12.771 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 12.771 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.771 * [taylor]: Taking taylor expansion of 1.0 in k 12.771 * [backup-simplify]: Simplify 1.0 into 1.0 12.771 * [taylor]: Taking taylor expansion of k in k 12.771 * [backup-simplify]: Simplify 0 into 0 12.771 * [backup-simplify]: Simplify 1 into 1 12.771 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 12.771 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.771 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.771 * [taylor]: Taking taylor expansion of 2.0 in k 12.771 * [backup-simplify]: Simplify 2.0 into 2.0 12.771 * [taylor]: Taking taylor expansion of PI in k 12.771 * [backup-simplify]: Simplify PI into PI 12.772 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.772 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.772 * [taylor]: Taking taylor expansion of (log n) in k 12.772 * [taylor]: Taking taylor expansion of n in k 12.772 * [backup-simplify]: Simplify n into n 12.772 * [backup-simplify]: Simplify (log n) into (log n) 12.773 * [backup-simplify]: Simplify (- 0) into 0 12.773 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.774 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 12.774 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 12.775 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 12.776 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 12.776 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 12.777 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.778 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 12.780 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.780 * [backup-simplify]: Simplify (- 0) into 0 12.781 * [backup-simplify]: Simplify (+ 0 0) into 0 12.781 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 12.783 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.784 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 12.786 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.786 * [taylor]: Taking taylor expansion of 0 in k 12.786 * [backup-simplify]: Simplify 0 into 0 12.786 * [backup-simplify]: Simplify 0 into 0 12.787 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.788 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.789 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 12.790 * [backup-simplify]: Simplify (+ 0 0) into 0 12.790 * [backup-simplify]: Simplify (- 1) into -1 12.791 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.792 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 12.795 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 12.799 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 12.802 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 12.803 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.805 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 12.808 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.809 * [backup-simplify]: Simplify (- 0) into 0 12.809 * [backup-simplify]: Simplify (+ 0 0) into 0 12.811 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 12.812 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.814 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.817 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.817 * [taylor]: Taking taylor expansion of 0 in k 12.817 * [backup-simplify]: Simplify 0 into 0 12.817 * [backup-simplify]: Simplify 0 into 0 12.817 * [backup-simplify]: Simplify 0 into 0 12.818 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.822 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.824 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 12.824 * [backup-simplify]: Simplify (+ 0 0) into 0 12.825 * [backup-simplify]: Simplify (- 0) into 0 12.825 * [backup-simplify]: Simplify (+ 0 0) into 0 12.827 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.830 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 12.834 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 12.840 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 12.851 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 12.851 * [backup-simplify]: Simplify (pow (* 2.0 (* (/ 1 n) PI)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 12.851 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 12.851 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 12.852 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 12.852 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 12.852 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 12.852 * [taylor]: Taking taylor expansion of 0.5 in k 12.852 * [backup-simplify]: Simplify 0.5 into 0.5 12.852 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.852 * [taylor]: Taking taylor expansion of 1.0 in k 12.852 * [backup-simplify]: Simplify 1.0 into 1.0 12.852 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.852 * [taylor]: Taking taylor expansion of k in k 12.852 * [backup-simplify]: Simplify 0 into 0 12.852 * [backup-simplify]: Simplify 1 into 1 12.852 * [backup-simplify]: Simplify (/ 1 1) into 1 12.852 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 12.852 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 12.852 * [taylor]: Taking taylor expansion of 2.0 in k 12.852 * [backup-simplify]: Simplify 2.0 into 2.0 12.852 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.853 * [taylor]: Taking taylor expansion of PI in k 12.853 * [backup-simplify]: Simplify PI into PI 12.853 * [taylor]: Taking taylor expansion of n in k 12.853 * [backup-simplify]: Simplify n into n 12.853 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.853 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 12.853 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 12.854 * [backup-simplify]: Simplify (- 1) into -1 12.854 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.854 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 12.855 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 12.855 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 12.855 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 12.855 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.855 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.855 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 12.855 * [taylor]: Taking taylor expansion of 0.5 in n 12.855 * [backup-simplify]: Simplify 0.5 into 0.5 12.855 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.855 * [taylor]: Taking taylor expansion of 1.0 in n 12.855 * [backup-simplify]: Simplify 1.0 into 1.0 12.855 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.855 * [taylor]: Taking taylor expansion of k in n 12.855 * [backup-simplify]: Simplify k into k 12.855 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.855 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.855 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.855 * [taylor]: Taking taylor expansion of 2.0 in n 12.856 * [backup-simplify]: Simplify 2.0 into 2.0 12.856 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.856 * [taylor]: Taking taylor expansion of PI in n 12.856 * [backup-simplify]: Simplify PI into PI 12.856 * [taylor]: Taking taylor expansion of n in n 12.856 * [backup-simplify]: Simplify 0 into 0 12.856 * [backup-simplify]: Simplify 1 into 1 12.856 * [backup-simplify]: Simplify (/ PI 1) into PI 12.857 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.858 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.858 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.858 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.858 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 12.860 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.861 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 12.862 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.862 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 12.862 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.863 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.863 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 12.863 * [taylor]: Taking taylor expansion of 0.5 in n 12.863 * [backup-simplify]: Simplify 0.5 into 0.5 12.863 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.863 * [taylor]: Taking taylor expansion of 1.0 in n 12.863 * [backup-simplify]: Simplify 1.0 into 1.0 12.863 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.863 * [taylor]: Taking taylor expansion of k in n 12.863 * [backup-simplify]: Simplify k into k 12.863 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.863 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.863 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.863 * [taylor]: Taking taylor expansion of 2.0 in n 12.863 * [backup-simplify]: Simplify 2.0 into 2.0 12.863 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.863 * [taylor]: Taking taylor expansion of PI in n 12.863 * [backup-simplify]: Simplify PI into PI 12.863 * [taylor]: Taking taylor expansion of n in n 12.863 * [backup-simplify]: Simplify 0 into 0 12.863 * [backup-simplify]: Simplify 1 into 1 12.864 * [backup-simplify]: Simplify (/ PI 1) into PI 12.864 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.865 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.865 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.866 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.866 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 12.867 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.868 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 12.870 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.870 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 12.870 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 12.870 * [taylor]: Taking taylor expansion of 0.5 in k 12.870 * [backup-simplify]: Simplify 0.5 into 0.5 12.870 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 12.870 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 12.870 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.870 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.870 * [taylor]: Taking taylor expansion of 2.0 in k 12.870 * [backup-simplify]: Simplify 2.0 into 2.0 12.870 * [taylor]: Taking taylor expansion of PI in k 12.870 * [backup-simplify]: Simplify PI into PI 12.871 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.872 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.872 * [taylor]: Taking taylor expansion of (log n) in k 12.872 * [taylor]: Taking taylor expansion of n in k 12.872 * [backup-simplify]: Simplify n into n 12.872 * [backup-simplify]: Simplify (log n) into (log n) 12.872 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.872 * [taylor]: Taking taylor expansion of 1.0 in k 12.872 * [backup-simplify]: Simplify 1.0 into 1.0 12.872 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.872 * [taylor]: Taking taylor expansion of k in k 12.872 * [backup-simplify]: Simplify 0 into 0 12.872 * [backup-simplify]: Simplify 1 into 1 12.873 * [backup-simplify]: Simplify (/ 1 1) into 1 12.873 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.874 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 12.874 * [backup-simplify]: Simplify (- 1) into -1 12.875 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.876 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 12.877 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 12.878 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.879 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.880 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.881 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.883 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.883 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.883 * [backup-simplify]: Simplify (- 0) into 0 12.883 * [backup-simplify]: Simplify (+ 0 0) into 0 12.884 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 12.885 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.885 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 12.887 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.887 * [taylor]: Taking taylor expansion of 0 in k 12.887 * [backup-simplify]: Simplify 0 into 0 12.887 * [backup-simplify]: Simplify 0 into 0 12.887 * [backup-simplify]: Simplify 0 into 0 12.887 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.888 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.890 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.890 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.890 * [backup-simplify]: Simplify (- 0) into 0 12.891 * [backup-simplify]: Simplify (+ 0 0) into 0 12.891 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 12.892 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.893 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 12.900 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.900 * [taylor]: Taking taylor expansion of 0 in k 12.900 * [backup-simplify]: Simplify 0 into 0 12.900 * [backup-simplify]: Simplify 0 into 0 12.900 * [backup-simplify]: Simplify 0 into 0 12.900 * [backup-simplify]: Simplify 0 into 0 12.901 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.902 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.905 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 12.906 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.906 * [backup-simplify]: Simplify (- 0) into 0 12.906 * [backup-simplify]: Simplify (+ 0 0) into 0 12.907 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 12.908 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.909 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 12.911 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 12.911 * [taylor]: Taking taylor expansion of 0 in k 12.911 * [backup-simplify]: Simplify 0 into 0 12.911 * [backup-simplify]: Simplify 0 into 0 12.912 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 12.912 * [backup-simplify]: Simplify (pow (* 2.0 (* (/ 1 (- n)) PI)) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 12.912 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 12.912 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 12.912 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 12.912 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 12.912 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 12.912 * [taylor]: Taking taylor expansion of 0.5 in k 12.912 * [backup-simplify]: Simplify 0.5 into 0.5 12.912 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.912 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.912 * [taylor]: Taking taylor expansion of k in k 12.912 * [backup-simplify]: Simplify 0 into 0 12.912 * [backup-simplify]: Simplify 1 into 1 12.912 * [backup-simplify]: Simplify (/ 1 1) into 1 12.912 * [taylor]: Taking taylor expansion of 1.0 in k 12.912 * [backup-simplify]: Simplify 1.0 into 1.0 12.912 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 12.912 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 12.913 * [taylor]: Taking taylor expansion of -2.0 in k 12.913 * [backup-simplify]: Simplify -2.0 into -2.0 12.913 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.913 * [taylor]: Taking taylor expansion of PI in k 12.913 * [backup-simplify]: Simplify PI into PI 12.913 * [taylor]: Taking taylor expansion of n in k 12.913 * [backup-simplify]: Simplify n into n 12.913 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.913 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 12.913 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 12.913 * [backup-simplify]: Simplify (+ 1 0) into 1 12.913 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 12.913 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 12.914 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 12.914 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 12.914 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.914 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.914 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 12.914 * [taylor]: Taking taylor expansion of 0.5 in n 12.914 * [backup-simplify]: Simplify 0.5 into 0.5 12.914 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.914 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.914 * [taylor]: Taking taylor expansion of k in n 12.914 * [backup-simplify]: Simplify k into k 12.914 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.914 * [taylor]: Taking taylor expansion of 1.0 in n 12.914 * [backup-simplify]: Simplify 1.0 into 1.0 12.914 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.914 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.914 * [taylor]: Taking taylor expansion of -2.0 in n 12.914 * [backup-simplify]: Simplify -2.0 into -2.0 12.914 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.914 * [taylor]: Taking taylor expansion of PI in n 12.914 * [backup-simplify]: Simplify PI into PI 12.914 * [taylor]: Taking taylor expansion of n in n 12.914 * [backup-simplify]: Simplify 0 into 0 12.914 * [backup-simplify]: Simplify 1 into 1 12.915 * [backup-simplify]: Simplify (/ PI 1) into PI 12.915 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.916 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.916 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.916 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 12.917 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.918 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 12.918 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.918 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 12.918 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.918 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.918 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 12.918 * [taylor]: Taking taylor expansion of 0.5 in n 12.919 * [backup-simplify]: Simplify 0.5 into 0.5 12.919 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.919 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.919 * [taylor]: Taking taylor expansion of k in n 12.919 * [backup-simplify]: Simplify k into k 12.919 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.919 * [taylor]: Taking taylor expansion of 1.0 in n 12.919 * [backup-simplify]: Simplify 1.0 into 1.0 12.919 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.919 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.919 * [taylor]: Taking taylor expansion of -2.0 in n 12.919 * [backup-simplify]: Simplify -2.0 into -2.0 12.919 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.919 * [taylor]: Taking taylor expansion of PI in n 12.919 * [backup-simplify]: Simplify PI into PI 12.919 * [taylor]: Taking taylor expansion of n in n 12.919 * [backup-simplify]: Simplify 0 into 0 12.919 * [backup-simplify]: Simplify 1 into 1 12.919 * [backup-simplify]: Simplify (/ PI 1) into PI 12.920 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.920 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.920 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.920 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 12.921 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.922 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 12.923 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.923 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 12.923 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 12.923 * [taylor]: Taking taylor expansion of 0.5 in k 12.923 * [backup-simplify]: Simplify 0.5 into 0.5 12.923 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 12.923 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.923 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.923 * [taylor]: Taking taylor expansion of k in k 12.923 * [backup-simplify]: Simplify 0 into 0 12.923 * [backup-simplify]: Simplify 1 into 1 12.923 * [backup-simplify]: Simplify (/ 1 1) into 1 12.923 * [taylor]: Taking taylor expansion of 1.0 in k 12.923 * [backup-simplify]: Simplify 1.0 into 1.0 12.923 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 12.924 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 12.924 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 12.924 * [taylor]: Taking taylor expansion of -2.0 in k 12.924 * [backup-simplify]: Simplify -2.0 into -2.0 12.924 * [taylor]: Taking taylor expansion of PI in k 12.924 * [backup-simplify]: Simplify PI into PI 12.924 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.925 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.925 * [taylor]: Taking taylor expansion of (log n) in k 12.925 * [taylor]: Taking taylor expansion of n in k 12.925 * [backup-simplify]: Simplify n into n 12.925 * [backup-simplify]: Simplify (log n) into (log n) 12.925 * [backup-simplify]: Simplify (+ 1 0) into 1 12.925 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.926 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 12.926 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 12.927 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 12.928 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.929 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.929 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.930 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 12.932 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 12.932 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.932 * [backup-simplify]: Simplify (+ 0 0) into 0 12.933 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 12.934 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.936 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 12.938 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.938 * [taylor]: Taking taylor expansion of 0 in k 12.938 * [backup-simplify]: Simplify 0 into 0 12.938 * [backup-simplify]: Simplify 0 into 0 12.938 * [backup-simplify]: Simplify 0 into 0 12.939 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.940 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.944 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 12.944 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.944 * [backup-simplify]: Simplify (+ 0 0) into 0 12.945 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 12.947 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.948 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 12.951 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.951 * [taylor]: Taking taylor expansion of 0 in k 12.951 * [backup-simplify]: Simplify 0 into 0 12.951 * [backup-simplify]: Simplify 0 into 0 12.951 * [backup-simplify]: Simplify 0 into 0 12.951 * [backup-simplify]: Simplify 0 into 0 12.952 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.953 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.960 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 12.960 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.961 * [backup-simplify]: Simplify (+ 0 0) into 0 12.962 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 12.963 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.965 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 12.968 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 12.968 * [taylor]: Taking taylor expansion of 0 in k 12.969 * [backup-simplify]: Simplify 0 into 0 12.969 * [backup-simplify]: Simplify 0 into 0 12.970 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 12.970 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 12.971 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 12.971 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 12.971 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 12.971 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 12.971 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 12.971 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 12.971 * [taylor]: Taking taylor expansion of 0.25 in k 12.971 * [backup-simplify]: Simplify 0.25 into 0.25 12.971 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.971 * [taylor]: Taking taylor expansion of 1.0 in k 12.971 * [backup-simplify]: Simplify 1.0 into 1.0 12.971 * [taylor]: Taking taylor expansion of k in k 12.971 * [backup-simplify]: Simplify 0 into 0 12.971 * [backup-simplify]: Simplify 1 into 1 12.971 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 12.971 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 12.972 * [taylor]: Taking taylor expansion of 2.0 in k 12.972 * [backup-simplify]: Simplify 2.0 into 2.0 12.972 * [taylor]: Taking taylor expansion of (* n PI) in k 12.972 * [taylor]: Taking taylor expansion of n in k 12.972 * [backup-simplify]: Simplify n into n 12.972 * [taylor]: Taking taylor expansion of PI in k 12.972 * [backup-simplify]: Simplify PI into PI 12.972 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.972 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 12.972 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 12.972 * [backup-simplify]: Simplify (- 0) into 0 12.973 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.973 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 12.973 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 12.974 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 12.974 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 12.974 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.974 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.974 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 12.974 * [taylor]: Taking taylor expansion of 0.25 in n 12.974 * [backup-simplify]: Simplify 0.25 into 0.25 12.974 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.974 * [taylor]: Taking taylor expansion of 1.0 in n 12.974 * [backup-simplify]: Simplify 1.0 into 1.0 12.974 * [taylor]: Taking taylor expansion of k in n 12.974 * [backup-simplify]: Simplify k into k 12.974 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.974 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.974 * [taylor]: Taking taylor expansion of 2.0 in n 12.974 * [backup-simplify]: Simplify 2.0 into 2.0 12.974 * [taylor]: Taking taylor expansion of (* n PI) in n 12.974 * [taylor]: Taking taylor expansion of n in n 12.974 * [backup-simplify]: Simplify 0 into 0 12.974 * [backup-simplify]: Simplify 1 into 1 12.974 * [taylor]: Taking taylor expansion of PI in n 12.974 * [backup-simplify]: Simplify PI into PI 12.975 * [backup-simplify]: Simplify (* 0 PI) into 0 12.976 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.977 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.979 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.980 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.981 * [backup-simplify]: Simplify (- k) into (- k) 12.981 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.981 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 12.982 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.983 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.985 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.985 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 12.985 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.985 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.985 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 12.985 * [taylor]: Taking taylor expansion of 0.25 in n 12.985 * [backup-simplify]: Simplify 0.25 into 0.25 12.985 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.985 * [taylor]: Taking taylor expansion of 1.0 in n 12.985 * [backup-simplify]: Simplify 1.0 into 1.0 12.985 * [taylor]: Taking taylor expansion of k in n 12.985 * [backup-simplify]: Simplify k into k 12.985 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.985 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.985 * [taylor]: Taking taylor expansion of 2.0 in n 12.985 * [backup-simplify]: Simplify 2.0 into 2.0 12.985 * [taylor]: Taking taylor expansion of (* n PI) in n 12.985 * [taylor]: Taking taylor expansion of n in n 12.985 * [backup-simplify]: Simplify 0 into 0 12.985 * [backup-simplify]: Simplify 1 into 1 12.985 * [taylor]: Taking taylor expansion of PI in n 12.985 * [backup-simplify]: Simplify PI into PI 12.986 * [backup-simplify]: Simplify (* 0 PI) into 0 12.986 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.988 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.990 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.991 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.991 * [backup-simplify]: Simplify (- k) into (- k) 12.991 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.991 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 12.992 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.993 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.995 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.995 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 12.995 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 12.995 * [taylor]: Taking taylor expansion of 0.25 in k 12.995 * [backup-simplify]: Simplify 0.25 into 0.25 12.995 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 12.995 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.995 * [taylor]: Taking taylor expansion of 1.0 in k 12.995 * [backup-simplify]: Simplify 1.0 into 1.0 12.995 * [taylor]: Taking taylor expansion of k in k 12.995 * [backup-simplify]: Simplify 0 into 0 12.995 * [backup-simplify]: Simplify 1 into 1 12.995 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 12.995 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.995 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.995 * [taylor]: Taking taylor expansion of 2.0 in k 12.995 * [backup-simplify]: Simplify 2.0 into 2.0 12.995 * [taylor]: Taking taylor expansion of PI in k 12.995 * [backup-simplify]: Simplify PI into PI 12.996 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.997 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.997 * [taylor]: Taking taylor expansion of (log n) in k 12.997 * [taylor]: Taking taylor expansion of n in k 12.997 * [backup-simplify]: Simplify n into n 12.997 * [backup-simplify]: Simplify (log n) into (log n) 12.998 * [backup-simplify]: Simplify (- 0) into 0 12.998 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.999 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 13.000 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 13.001 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 13.002 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 13.004 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 13.005 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.006 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 13.008 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 13.008 * [backup-simplify]: Simplify (- 0) into 0 13.009 * [backup-simplify]: Simplify (+ 0 0) into 0 13.009 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 13.011 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.012 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 13.014 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.014 * [taylor]: Taking taylor expansion of 0 in k 13.014 * [backup-simplify]: Simplify 0 into 0 13.014 * [backup-simplify]: Simplify 0 into 0 13.015 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 13.016 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 13.017 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 13.018 * [backup-simplify]: Simplify (+ 0 0) into 0 13.018 * [backup-simplify]: Simplify (- 1) into -1 13.019 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.020 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 13.023 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 13.026 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 13.029 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 13.030 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 13.031 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 13.043 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 13.044 * [backup-simplify]: Simplify (- 0) into 0 13.045 * [backup-simplify]: Simplify (+ 0 0) into 0 13.046 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 13.047 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.049 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 13.052 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.052 * [taylor]: Taking taylor expansion of 0 in k 13.052 * [backup-simplify]: Simplify 0 into 0 13.052 * [backup-simplify]: Simplify 0 into 0 13.052 * [backup-simplify]: Simplify 0 into 0 13.054 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.058 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 13.061 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 13.061 * [backup-simplify]: Simplify (+ 0 0) into 0 13.062 * [backup-simplify]: Simplify (- 0) into 0 13.062 * [backup-simplify]: Simplify (+ 0 0) into 0 13.064 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 13.068 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 13.072 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 13.079 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 13.090 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 13.091 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 13.091 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 13.091 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 13.091 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 13.091 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 13.091 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 13.091 * [taylor]: Taking taylor expansion of 0.25 in k 13.091 * [backup-simplify]: Simplify 0.25 into 0.25 13.091 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.091 * [taylor]: Taking taylor expansion of 1.0 in k 13.091 * [backup-simplify]: Simplify 1.0 into 1.0 13.091 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.091 * [taylor]: Taking taylor expansion of k in k 13.091 * [backup-simplify]: Simplify 0 into 0 13.091 * [backup-simplify]: Simplify 1 into 1 13.092 * [backup-simplify]: Simplify (/ 1 1) into 1 13.092 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 13.092 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 13.092 * [taylor]: Taking taylor expansion of 2.0 in k 13.092 * [backup-simplify]: Simplify 2.0 into 2.0 13.092 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.092 * [taylor]: Taking taylor expansion of PI in k 13.092 * [backup-simplify]: Simplify PI into PI 13.092 * [taylor]: Taking taylor expansion of n in k 13.092 * [backup-simplify]: Simplify n into n 13.092 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.092 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 13.092 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 13.093 * [backup-simplify]: Simplify (- 1) into -1 13.093 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.094 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 13.094 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 13.094 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 13.094 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 13.094 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 13.094 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 13.094 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 13.094 * [taylor]: Taking taylor expansion of 0.25 in n 13.094 * [backup-simplify]: Simplify 0.25 into 0.25 13.094 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 13.095 * [taylor]: Taking taylor expansion of 1.0 in n 13.095 * [backup-simplify]: Simplify 1.0 into 1.0 13.095 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.095 * [taylor]: Taking taylor expansion of k in n 13.095 * [backup-simplify]: Simplify k into k 13.095 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.095 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 13.095 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.095 * [taylor]: Taking taylor expansion of 2.0 in n 13.095 * [backup-simplify]: Simplify 2.0 into 2.0 13.095 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.095 * [taylor]: Taking taylor expansion of PI in n 13.095 * [backup-simplify]: Simplify PI into PI 13.095 * [taylor]: Taking taylor expansion of n in n 13.095 * [backup-simplify]: Simplify 0 into 0 13.095 * [backup-simplify]: Simplify 1 into 1 13.096 * [backup-simplify]: Simplify (/ PI 1) into PI 13.096 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.097 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.098 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 13.098 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 13.098 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 13.099 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.101 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 13.102 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 13.102 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 13.102 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 13.102 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 13.102 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 13.102 * [taylor]: Taking taylor expansion of 0.25 in n 13.102 * [backup-simplify]: Simplify 0.25 into 0.25 13.102 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 13.102 * [taylor]: Taking taylor expansion of 1.0 in n 13.102 * [backup-simplify]: Simplify 1.0 into 1.0 13.103 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.103 * [taylor]: Taking taylor expansion of k in n 13.103 * [backup-simplify]: Simplify k into k 13.103 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.103 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 13.103 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.103 * [taylor]: Taking taylor expansion of 2.0 in n 13.103 * [backup-simplify]: Simplify 2.0 into 2.0 13.103 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.103 * [taylor]: Taking taylor expansion of PI in n 13.103 * [backup-simplify]: Simplify PI into PI 13.103 * [taylor]: Taking taylor expansion of n in n 13.103 * [backup-simplify]: Simplify 0 into 0 13.103 * [backup-simplify]: Simplify 1 into 1 13.104 * [backup-simplify]: Simplify (/ PI 1) into PI 13.104 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.105 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.105 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 13.105 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 13.106 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 13.108 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.111 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 13.113 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 13.113 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 13.113 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 13.113 * [taylor]: Taking taylor expansion of 0.25 in k 13.113 * [backup-simplify]: Simplify 0.25 into 0.25 13.113 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 13.113 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 13.113 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 13.113 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 13.113 * [taylor]: Taking taylor expansion of 2.0 in k 13.113 * [backup-simplify]: Simplify 2.0 into 2.0 13.113 * [taylor]: Taking taylor expansion of PI in k 13.113 * [backup-simplify]: Simplify PI into PI 13.114 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.114 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.114 * [taylor]: Taking taylor expansion of (log n) in k 13.114 * [taylor]: Taking taylor expansion of n in k 13.114 * [backup-simplify]: Simplify n into n 13.114 * [backup-simplify]: Simplify (log n) into (log n) 13.114 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.114 * [taylor]: Taking taylor expansion of 1.0 in k 13.114 * [backup-simplify]: Simplify 1.0 into 1.0 13.114 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.114 * [taylor]: Taking taylor expansion of k in k 13.114 * [backup-simplify]: Simplify 0 into 0 13.114 * [backup-simplify]: Simplify 1 into 1 13.115 * [backup-simplify]: Simplify (/ 1 1) into 1 13.115 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.116 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 13.116 * [backup-simplify]: Simplify (- 1) into -1 13.116 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.117 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 13.118 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 13.119 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 13.119 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 13.120 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.120 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 13.121 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 13.122 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.122 * [backup-simplify]: Simplify (- 0) into 0 13.122 * [backup-simplify]: Simplify (+ 0 0) into 0 13.122 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 13.123 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.124 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 13.125 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.126 * [taylor]: Taking taylor expansion of 0 in k 13.126 * [backup-simplify]: Simplify 0 into 0 13.126 * [backup-simplify]: Simplify 0 into 0 13.126 * [backup-simplify]: Simplify 0 into 0 13.126 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.127 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.129 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 13.129 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.129 * [backup-simplify]: Simplify (- 0) into 0 13.130 * [backup-simplify]: Simplify (+ 0 0) into 0 13.130 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 13.131 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.133 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 13.134 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.134 * [taylor]: Taking taylor expansion of 0 in k 13.134 * [backup-simplify]: Simplify 0 into 0 13.134 * [backup-simplify]: Simplify 0 into 0 13.134 * [backup-simplify]: Simplify 0 into 0 13.134 * [backup-simplify]: Simplify 0 into 0 13.135 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.136 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.139 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 13.139 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.140 * [backup-simplify]: Simplify (- 0) into 0 13.140 * [backup-simplify]: Simplify (+ 0 0) into 0 13.141 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 13.142 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.143 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 13.145 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.145 * [taylor]: Taking taylor expansion of 0 in k 13.145 * [backup-simplify]: Simplify 0 into 0 13.145 * [backup-simplify]: Simplify 0 into 0 13.146 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 13.146 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 13.146 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 13.146 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 13.146 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 13.146 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 13.146 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 13.146 * [taylor]: Taking taylor expansion of 0.25 in k 13.146 * [backup-simplify]: Simplify 0.25 into 0.25 13.146 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.147 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.147 * [taylor]: Taking taylor expansion of k in k 13.147 * [backup-simplify]: Simplify 0 into 0 13.147 * [backup-simplify]: Simplify 1 into 1 13.147 * [backup-simplify]: Simplify (/ 1 1) into 1 13.147 * [taylor]: Taking taylor expansion of 1.0 in k 13.147 * [backup-simplify]: Simplify 1.0 into 1.0 13.147 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 13.147 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 13.147 * [taylor]: Taking taylor expansion of -2.0 in k 13.147 * [backup-simplify]: Simplify -2.0 into -2.0 13.147 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.147 * [taylor]: Taking taylor expansion of PI in k 13.147 * [backup-simplify]: Simplify PI into PI 13.147 * [taylor]: Taking taylor expansion of n in k 13.147 * [backup-simplify]: Simplify n into n 13.147 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.147 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 13.147 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 13.148 * [backup-simplify]: Simplify (+ 1 0) into 1 13.148 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 13.148 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 13.148 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 13.148 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 13.148 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 13.148 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 13.148 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 13.148 * [taylor]: Taking taylor expansion of 0.25 in n 13.148 * [backup-simplify]: Simplify 0.25 into 0.25 13.148 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 13.148 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.148 * [taylor]: Taking taylor expansion of k in n 13.148 * [backup-simplify]: Simplify k into k 13.148 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.148 * [taylor]: Taking taylor expansion of 1.0 in n 13.148 * [backup-simplify]: Simplify 1.0 into 1.0 13.148 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 13.148 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.148 * [taylor]: Taking taylor expansion of -2.0 in n 13.148 * [backup-simplify]: Simplify -2.0 into -2.0 13.149 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.149 * [taylor]: Taking taylor expansion of PI in n 13.149 * [backup-simplify]: Simplify PI into PI 13.149 * [taylor]: Taking taylor expansion of n in n 13.149 * [backup-simplify]: Simplify 0 into 0 13.149 * [backup-simplify]: Simplify 1 into 1 13.149 * [backup-simplify]: Simplify (/ PI 1) into PI 13.149 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.150 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.150 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 13.150 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 13.151 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.152 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 13.153 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 13.153 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 13.153 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 13.153 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 13.153 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 13.153 * [taylor]: Taking taylor expansion of 0.25 in n 13.153 * [backup-simplify]: Simplify 0.25 into 0.25 13.153 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 13.153 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.153 * [taylor]: Taking taylor expansion of k in n 13.153 * [backup-simplify]: Simplify k into k 13.153 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.153 * [taylor]: Taking taylor expansion of 1.0 in n 13.153 * [backup-simplify]: Simplify 1.0 into 1.0 13.153 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 13.153 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.153 * [taylor]: Taking taylor expansion of -2.0 in n 13.153 * [backup-simplify]: Simplify -2.0 into -2.0 13.153 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.153 * [taylor]: Taking taylor expansion of PI in n 13.153 * [backup-simplify]: Simplify PI into PI 13.153 * [taylor]: Taking taylor expansion of n in n 13.153 * [backup-simplify]: Simplify 0 into 0 13.153 * [backup-simplify]: Simplify 1 into 1 13.154 * [backup-simplify]: Simplify (/ PI 1) into PI 13.154 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.155 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.155 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 13.155 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 13.156 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.157 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 13.158 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 13.158 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 13.158 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 13.158 * [taylor]: Taking taylor expansion of 0.25 in k 13.158 * [backup-simplify]: Simplify 0.25 into 0.25 13.158 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 13.158 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.158 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.158 * [taylor]: Taking taylor expansion of k in k 13.158 * [backup-simplify]: Simplify 0 into 0 13.158 * [backup-simplify]: Simplify 1 into 1 13.158 * [backup-simplify]: Simplify (/ 1 1) into 1 13.158 * [taylor]: Taking taylor expansion of 1.0 in k 13.158 * [backup-simplify]: Simplify 1.0 into 1.0 13.158 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 13.158 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 13.158 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 13.158 * [taylor]: Taking taylor expansion of -2.0 in k 13.158 * [backup-simplify]: Simplify -2.0 into -2.0 13.158 * [taylor]: Taking taylor expansion of PI in k 13.158 * [backup-simplify]: Simplify PI into PI 13.159 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.159 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.159 * [taylor]: Taking taylor expansion of (log n) in k 13.159 * [taylor]: Taking taylor expansion of n in k 13.159 * [backup-simplify]: Simplify n into n 13.159 * [backup-simplify]: Simplify (log n) into (log n) 13.160 * [backup-simplify]: Simplify (+ 1 0) into 1 13.160 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.161 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 13.161 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 13.162 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 13.163 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 13.164 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 13.164 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.165 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 13.166 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 13.166 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.166 * [backup-simplify]: Simplify (+ 0 0) into 0 13.167 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 13.169 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.170 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 13.172 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.172 * [taylor]: Taking taylor expansion of 0 in k 13.172 * [backup-simplify]: Simplify 0 into 0 13.172 * [backup-simplify]: Simplify 0 into 0 13.172 * [backup-simplify]: Simplify 0 into 0 13.173 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.174 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.186 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 13.186 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.187 * [backup-simplify]: Simplify (+ 0 0) into 0 13.188 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 13.190 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.191 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 13.194 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.194 * [taylor]: Taking taylor expansion of 0 in k 13.194 * [backup-simplify]: Simplify 0 into 0 13.194 * [backup-simplify]: Simplify 0 into 0 13.194 * [backup-simplify]: Simplify 0 into 0 13.194 * [backup-simplify]: Simplify 0 into 0 13.196 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.197 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.203 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 13.203 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.204 * [backup-simplify]: Simplify (+ 0 0) into 0 13.205 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 13.207 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.209 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 13.212 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.212 * [taylor]: Taking taylor expansion of 0 in k 13.212 * [backup-simplify]: Simplify 0 into 0 13.212 * [backup-simplify]: Simplify 0 into 0 13.214 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 13.214 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 13.214 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 13.214 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 13.214 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 13.214 * [taylor]: Taking taylor expansion of 1.0 in k 13.214 * [backup-simplify]: Simplify 1.0 into 1.0 13.214 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 13.214 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.214 * [taylor]: Taking taylor expansion of k in k 13.214 * [backup-simplify]: Simplify 0 into 0 13.214 * [backup-simplify]: Simplify 1 into 1 13.215 * [backup-simplify]: Simplify (/ 1 1) into 1 13.215 * [backup-simplify]: Simplify (sqrt 0) into 0 13.217 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.217 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 13.217 * [taylor]: Taking taylor expansion of 1.0 in k 13.217 * [backup-simplify]: Simplify 1.0 into 1.0 13.217 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 13.217 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.217 * [taylor]: Taking taylor expansion of k in k 13.217 * [backup-simplify]: Simplify 0 into 0 13.217 * [backup-simplify]: Simplify 1 into 1 13.218 * [backup-simplify]: Simplify (/ 1 1) into 1 13.218 * [backup-simplify]: Simplify (sqrt 0) into 0 13.219 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.220 * [backup-simplify]: Simplify (* 1.0 0) into 0 13.220 * [backup-simplify]: Simplify 0 into 0 13.221 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 13.222 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.223 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 13.226 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.228 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 13.228 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.229 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.234 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.236 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 13.237 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.238 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 13.238 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 13.238 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 13.238 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 13.238 * [taylor]: Taking taylor expansion of 1.0 in k 13.238 * [backup-simplify]: Simplify 1.0 into 1.0 13.238 * [taylor]: Taking taylor expansion of (sqrt k) in k 13.238 * [taylor]: Taking taylor expansion of k in k 13.239 * [backup-simplify]: Simplify 0 into 0 13.239 * [backup-simplify]: Simplify 1 into 1 13.239 * [backup-simplify]: Simplify (sqrt 0) into 0 13.241 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.241 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 13.241 * [taylor]: Taking taylor expansion of 1.0 in k 13.241 * [backup-simplify]: Simplify 1.0 into 1.0 13.241 * [taylor]: Taking taylor expansion of (sqrt k) in k 13.241 * [taylor]: Taking taylor expansion of k in k 13.241 * [backup-simplify]: Simplify 0 into 0 13.241 * [backup-simplify]: Simplify 1 into 1 13.241 * [backup-simplify]: Simplify (sqrt 0) into 0 13.243 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.243 * [backup-simplify]: Simplify (* 1.0 0) into 0 13.243 * [backup-simplify]: Simplify 0 into 0 13.245 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 13.245 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.248 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.250 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 13.251 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.255 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.257 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 13.258 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.260 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 13.260 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 13.260 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 13.260 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 13.260 * [taylor]: Taking taylor expansion of 1.0 in k 13.260 * [backup-simplify]: Simplify 1.0 into 1.0 13.260 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 13.260 * [taylor]: Taking taylor expansion of (/ -1 k) in k 13.260 * [taylor]: Taking taylor expansion of -1 in k 13.260 * [backup-simplify]: Simplify -1 into -1 13.260 * [taylor]: Taking taylor expansion of k in k 13.260 * [backup-simplify]: Simplify 0 into 0 13.260 * [backup-simplify]: Simplify 1 into 1 13.261 * [backup-simplify]: Simplify (/ -1 1) into -1 13.261 * [backup-simplify]: Simplify (sqrt 0) into 0 13.262 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 13.263 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 13.263 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 13.263 * [taylor]: Taking taylor expansion of 1.0 in k 13.263 * [backup-simplify]: Simplify 1.0 into 1.0 13.263 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 13.263 * [taylor]: Taking taylor expansion of (/ -1 k) in k 13.263 * [taylor]: Taking taylor expansion of -1 in k 13.263 * [backup-simplify]: Simplify -1 into -1 13.263 * [taylor]: Taking taylor expansion of k in k 13.263 * [backup-simplify]: Simplify 0 into 0 13.263 * [backup-simplify]: Simplify 1 into 1 13.263 * [backup-simplify]: Simplify (/ -1 1) into -1 13.263 * [backup-simplify]: Simplify (sqrt 0) into 0 13.264 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 13.265 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 13.265 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.265 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 13.267 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.269 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 13.269 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.270 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.272 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.275 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 13.275 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.276 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 13.276 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1 2) 13.276 * [backup-simplify]: Simplify (* n PI) into (* n PI) 13.276 * [approximate]: Taking taylor expansion of (* n PI) in (n) around 0 13.276 * [taylor]: Taking taylor expansion of (* n PI) in n 13.276 * [taylor]: Taking taylor expansion of n in n 13.276 * [backup-simplify]: Simplify 0 into 0 13.276 * [backup-simplify]: Simplify 1 into 1 13.276 * [taylor]: Taking taylor expansion of PI in n 13.276 * [backup-simplify]: Simplify PI into PI 13.276 * [taylor]: Taking taylor expansion of (* n PI) in n 13.276 * [taylor]: Taking taylor expansion of n in n 13.276 * [backup-simplify]: Simplify 0 into 0 13.276 * [backup-simplify]: Simplify 1 into 1 13.276 * [taylor]: Taking taylor expansion of PI in n 13.276 * [backup-simplify]: Simplify PI into PI 13.277 * [backup-simplify]: Simplify (* 0 PI) into 0 13.277 * [backup-simplify]: Simplify 0 into 0 13.278 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.278 * [backup-simplify]: Simplify PI into PI 13.279 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.279 * [backup-simplify]: Simplify 0 into 0 13.279 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 13.279 * [backup-simplify]: Simplify 0 into 0 13.280 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.280 * [backup-simplify]: Simplify 0 into 0 13.281 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.281 * [backup-simplify]: Simplify 0 into 0 13.282 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.282 * [backup-simplify]: Simplify 0 into 0 13.284 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 13.284 * [backup-simplify]: Simplify 0 into 0 13.284 * [backup-simplify]: Simplify (* PI n) into (* n PI) 13.284 * [backup-simplify]: Simplify (* (/ 1 n) PI) into (/ PI n) 13.284 * [approximate]: Taking taylor expansion of (/ PI n) in (n) around 0 13.284 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.284 * [taylor]: Taking taylor expansion of PI in n 13.284 * [backup-simplify]: Simplify PI into PI 13.284 * [taylor]: Taking taylor expansion of n in n 13.284 * [backup-simplify]: Simplify 0 into 0 13.284 * [backup-simplify]: Simplify 1 into 1 13.285 * [backup-simplify]: Simplify (/ PI 1) into PI 13.285 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.285 * [taylor]: Taking taylor expansion of PI in n 13.285 * [backup-simplify]: Simplify PI into PI 13.285 * [taylor]: Taking taylor expansion of n in n 13.285 * [backup-simplify]: Simplify 0 into 0 13.285 * [backup-simplify]: Simplify 1 into 1 13.286 * [backup-simplify]: Simplify (/ PI 1) into PI 13.286 * [backup-simplify]: Simplify PI into PI 13.288 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.288 * [backup-simplify]: Simplify 0 into 0 13.289 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.289 * [backup-simplify]: Simplify 0 into 0 13.290 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.290 * [backup-simplify]: Simplify 0 into 0 13.291 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.291 * [backup-simplify]: Simplify 0 into 0 13.291 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.292 * [backup-simplify]: Simplify 0 into 0 13.292 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.292 * [backup-simplify]: Simplify 0 into 0 13.292 * [backup-simplify]: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI) 13.292 * [backup-simplify]: Simplify (* (/ 1 (- n)) PI) into (* -1 (/ PI n)) 13.292 * [approximate]: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0 13.292 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 13.293 * [taylor]: Taking taylor expansion of -1 in n 13.293 * [backup-simplify]: Simplify -1 into -1 13.293 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.293 * [taylor]: Taking taylor expansion of PI in n 13.293 * [backup-simplify]: Simplify PI into PI 13.293 * [taylor]: Taking taylor expansion of n in n 13.293 * [backup-simplify]: Simplify 0 into 0 13.293 * [backup-simplify]: Simplify 1 into 1 13.293 * [backup-simplify]: Simplify (/ PI 1) into PI 13.293 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 13.293 * [taylor]: Taking taylor expansion of -1 in n 13.293 * [backup-simplify]: Simplify -1 into -1 13.293 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.293 * [taylor]: Taking taylor expansion of PI in n 13.293 * [backup-simplify]: Simplify PI into PI 13.293 * [taylor]: Taking taylor expansion of n in n 13.293 * [backup-simplify]: Simplify 0 into 0 13.293 * [backup-simplify]: Simplify 1 into 1 13.294 * [backup-simplify]: Simplify (/ PI 1) into PI 13.294 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 13.294 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 13.295 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.295 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0 13.295 * [backup-simplify]: Simplify 0 into 0 13.296 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.297 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 13.297 * [backup-simplify]: Simplify 0 into 0 13.297 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.298 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.298 * [backup-simplify]: Simplify 0 into 0 13.299 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.299 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.300 * [backup-simplify]: Simplify 0 into 0 13.300 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.301 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.301 * [backup-simplify]: Simplify 0 into 0 13.302 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.303 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.303 * [backup-simplify]: Simplify 0 into 0 13.303 * [backup-simplify]: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) 13.303 * * * [progress]: simplifying candidates 13.306 * [simplify]: Simplifying: (expm1 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (log1p (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (+ (log 2.0) (+ (log n) (log PI))) (/ (- 1.0 k) 2.0)) (* (+ (log 2.0) (log (* n PI))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* n PI)) (/ 1.0 2.0)) (pow (* 2.0 (* n PI)) (/ k 2.0)) (pow (* 2.0 (* n PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* 2.0 (* n PI)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) 1)) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ 1 1)) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ 1 1)) (pow (* 2.0 (* n PI)) 1) (pow (* 2.0 (* n PI)) (- 1.0 k)) (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)) (log (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (exp (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt 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(* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* n PI) (* n PI) (* n PI) 13.312 * * [simplify]: Extracting # 0 : cost 0 13.312 * * [simplify]: Extracting # 1 : cost 0 13.313 * * [simplify]: Extracting # 2 : cost 0 13.313 * * [simplify]: Extracting # 3 : cost 0 13.314 * * [simplify]: Extracting # 4 : cost 0 13.322 * * [simplify]: Extracting # 5 : cost 0 13.322 * * [simplify]: Extracting # 6 : cost 0 13.323 * * [simplify]: Extracting # 7 : cost 0 13.324 * * [simplify]: Extracting # 8 : cost 0 13.324 * * [simplify]: Extracting # 9 : cost 0 13.325 * * [simplify]: Extracting # 10 : cost 0 13.325 * * [simplify]: Extracting # 11 : cost 0 13.326 * * [simplify]: Extracting # 12 : cost 0 13.327 * * [simplify]: Extracting # 13 : cost 0 13.328 * * [simplify]: iteration 0 : 398 enodes (cost 2712 ) 13.499 * * [simplify]: Extracting # 0 : cost 0 13.502 * * [simplify]: Extracting # 1 : cost 0 13.505 * * [simplify]: Extracting # 2 : cost 0 13.508 * * [simplify]: Extracting # 3 : cost 0 13.519 * * [simplify]: Extracting # 4 : cost 0 13.522 * * [simplify]: Extracting # 5 : cost 0 13.525 * * [simplify]: Extracting # 6 : cost 0 13.527 * * [simplify]: iteration 1 : 1018 enodes (cost 2503 ) 14.148 * * [simplify]: Extracting # 0 : cost 0 14.151 * * [simplify]: Extracting # 1 : cost 0 14.156 * * [simplify]: Extracting # 2 : cost 0 14.160 * * [simplify]: Extracting # 3 : cost 0 14.164 * * [simplify]: Extracting # 4 : cost 0 14.168 * * [simplify]: iteration 2 : 2797 enodes (cost 2409 ) 15.253 * * [simplify]: Extracting # 0 : cost 0 15.260 * * [simplify]: Extracting # 1 : cost 0 15.267 * * [simplify]: Extracting # 2 : cost 0 15.273 * * [simplify]: Extracting # 3 : cost 0 15.280 * * [simplify]: Extracting # 4 : cost 0 15.293 * * [simplify]: iteration done: 5001 enodes (cost 2403 ) 15.294 * [simplify]: Simplified to: (expm1 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (log1p (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* n PI))) (/ (- 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2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2))) (pow (* n (* 2.0 PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (sqrt 2))) (pow (* n (* 2.0 PI)) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* PI (* 2.0 n)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow (* n (* 2.0 PI)) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* PI (* 2.0 n)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* PI (* 2.0 n)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* PI (* 2.0 n)) (- 1.0 k)) (* PI (* 2.0 n)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* n (* 2.0 PI)) (/ (/ (- 1.0 k) 2.0) 4)) (pow (* n (* 2.0 PI)) (/ (/ (- 1.0 k) 2.0) 4)) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (pow 1.0 3) (* (sqrt k) k)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* n PI)) (log1p (* n PI)) (* n PI) (log (* n PI)) (log (* n PI)) (exp (* n PI)) (pow (* n PI) 3) (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI)) (pow (* n PI) 3) (sqrt (* n PI)) (sqrt (* n PI)) (* (sqrt n) (sqrt PI)) (* (sqrt n) (sqrt PI)) (* n (* (cbrt PI) (cbrt PI))) (* n (sqrt PI)) n (* (cbrt n) PI) (* (sqrt n) PI) (* n PI) (- (fma (* 0.125 (pow k 2)) (fma (pow (* n (* 2.0 PI)) 0.5) (pow (log (* 2.0 PI)) 2) (* (pow (log n) 2) (pow (* n (* 2.0 PI)) 0.5))) (fma (* 0.25 (pow k 2)) (* (* (log (* 2.0 PI)) (log n)) (pow (* n (* 2.0 PI)) 0.5)) (pow (* n (* 2.0 PI)) 0.5))) (* (* 0.5 k) (fma (pow (* n (* 2.0 PI)) 0.5) (log n) (* (pow (* n (* 2.0 PI)) 0.5) (log (* 2.0 PI)))))) (pow (pow (* n (* 2.0 PI)) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (fma (* (* 0.03125 (pow k 2)) (pow (* n (* 2.0 PI)) 0.25)) (pow (log (* 2.0 PI)) 2) (fma (* (* (pow (* n (* 2.0 PI)) 0.25) (log n)) (* (pow k 2) (log (* 2.0 PI)))) 0.0625 (fma (pow k 2) (* (* (pow (log n) 2) (pow (* n (* 2.0 PI)) 0.25)) 0.03125) (pow (* n (* 2.0 PI)) 0.25)))) (* (* 0.25 k) (fma (pow (* n (* 2.0 PI)) 0.25) (log n) (* (log (* 2.0 PI)) (pow (* n (* 2.0 PI)) 0.25))))) (pow (pow (* n (* 2.0 PI)) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (fma (- k) +nan.0 (- (* +nan.0 (pow k 2)) +nan.0)) (+ (- (/ +nan.0 k) (/ +nan.0 (pow k 3))) (/ (- +nan.0) (pow k 2))) (+ (/ (- +nan.0) (pow k 2)) (- (/ +nan.0 k) +nan.0)) (* n PI) (* n PI) (* n PI) 15.296 * * * [progress]: adding candidates to table 16.555 * * [progress]: iteration 4 / 4 16.555 * * * [progress]: picking best candidate 16.613 * * * * [pick]: Picked # 16.613 * * * [progress]: localizing error 16.657 * * * [progress]: generating rewritten candidates 16.658 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1) 16.801 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 16.834 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1 2 2 1) 16.836 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1 2 1 2) 16.848 * * * [progress]: generating series expansions 16.848 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1) 16.849 * [backup-simplify]: Simplify (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 16.849 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 16.849 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 16.849 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 16.849 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 16.849 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 16.849 * [taylor]: Taking taylor expansion of 0.5 in k 16.849 * [backup-simplify]: Simplify 0.5 into 0.5 16.849 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 16.849 * [taylor]: Taking taylor expansion of 1.0 in k 16.849 * [backup-simplify]: Simplify 1.0 into 1.0 16.849 * [taylor]: Taking taylor expansion of k in k 16.849 * [backup-simplify]: Simplify 0 into 0 16.849 * [backup-simplify]: Simplify 1 into 1 16.849 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 16.849 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 16.849 * [taylor]: Taking taylor expansion of 2.0 in k 16.849 * [backup-simplify]: Simplify 2.0 into 2.0 16.849 * [taylor]: Taking taylor expansion of (* n PI) in k 16.849 * [taylor]: Taking taylor expansion of n in k 16.849 * [backup-simplify]: Simplify n into n 16.849 * [taylor]: Taking taylor expansion of PI in k 16.849 * [backup-simplify]: Simplify PI into PI 16.849 * [backup-simplify]: Simplify (* n PI) into (* n PI) 16.849 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 16.849 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 16.850 * [backup-simplify]: Simplify (- 0) into 0 16.850 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 16.851 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 16.851 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 16.851 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 16.851 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 16.851 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 16.851 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 16.851 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 16.851 * [taylor]: Taking taylor expansion of 0.5 in n 16.851 * [backup-simplify]: Simplify 0.5 into 0.5 16.851 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 16.851 * [taylor]: Taking taylor expansion of 1.0 in n 16.851 * [backup-simplify]: Simplify 1.0 into 1.0 16.851 * [taylor]: Taking taylor expansion of k in n 16.851 * [backup-simplify]: Simplify k into k 16.851 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 16.851 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 16.851 * [taylor]: Taking taylor expansion of 2.0 in n 16.851 * [backup-simplify]: Simplify 2.0 into 2.0 16.851 * [taylor]: Taking taylor expansion of (* n PI) in n 16.851 * [taylor]: Taking taylor expansion of n in n 16.851 * [backup-simplify]: Simplify 0 into 0 16.851 * [backup-simplify]: Simplify 1 into 1 16.851 * [taylor]: Taking taylor expansion of PI in n 16.851 * [backup-simplify]: Simplify PI into PI 16.852 * [backup-simplify]: Simplify (* 0 PI) into 0 16.852 * [backup-simplify]: Simplify (* 2.0 0) into 0 16.853 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.854 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 16.855 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.855 * [backup-simplify]: Simplify (- k) into (- k) 16.855 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 16.855 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 16.856 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 16.857 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 16.858 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 16.858 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 16.858 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 16.858 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 16.858 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 16.858 * [taylor]: Taking taylor expansion of 0.5 in n 16.858 * [backup-simplify]: Simplify 0.5 into 0.5 16.858 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 16.858 * [taylor]: Taking taylor expansion of 1.0 in n 16.858 * [backup-simplify]: Simplify 1.0 into 1.0 16.858 * [taylor]: Taking taylor expansion of k in n 16.858 * [backup-simplify]: Simplify k into k 16.858 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 16.858 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 16.858 * [taylor]: Taking taylor expansion of 2.0 in n 16.858 * [backup-simplify]: Simplify 2.0 into 2.0 16.858 * [taylor]: Taking taylor expansion of (* n PI) in n 16.858 * [taylor]: Taking taylor expansion of n in n 16.858 * [backup-simplify]: Simplify 0 into 0 16.858 * [backup-simplify]: Simplify 1 into 1 16.858 * [taylor]: Taking taylor expansion of PI in n 16.858 * [backup-simplify]: Simplify PI into PI 16.858 * [backup-simplify]: Simplify (* 0 PI) into 0 16.859 * [backup-simplify]: Simplify (* 2.0 0) into 0 16.859 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.860 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 16.861 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.861 * [backup-simplify]: Simplify (- k) into (- k) 16.861 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 16.861 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 16.862 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 16.863 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 16.864 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 16.864 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 16.864 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 16.864 * [taylor]: Taking taylor expansion of 0.5 in k 16.864 * [backup-simplify]: Simplify 0.5 into 0.5 16.864 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 16.864 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 16.864 * [taylor]: Taking taylor expansion of 1.0 in k 16.864 * [backup-simplify]: Simplify 1.0 into 1.0 16.864 * [taylor]: Taking taylor expansion of k in k 16.864 * [backup-simplify]: Simplify 0 into 0 16.864 * [backup-simplify]: Simplify 1 into 1 16.864 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 16.864 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 16.864 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 16.864 * [taylor]: Taking taylor expansion of 2.0 in k 16.864 * [backup-simplify]: Simplify 2.0 into 2.0 16.864 * [taylor]: Taking taylor expansion of PI in k 16.864 * [backup-simplify]: Simplify PI into PI 16.865 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 16.865 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.865 * [taylor]: Taking taylor expansion of (log n) in k 16.865 * [taylor]: Taking taylor expansion of n in k 16.865 * [backup-simplify]: Simplify n into n 16.866 * [backup-simplify]: Simplify (log n) into (log n) 16.866 * [backup-simplify]: Simplify (- 0) into 0 16.866 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 16.867 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 16.867 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 16.868 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 16.869 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 16.870 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 16.871 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 16.872 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 16.873 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 16.874 * [backup-simplify]: Simplify (- 0) into 0 16.874 * [backup-simplify]: Simplify (+ 0 0) into 0 16.875 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 16.876 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 16.877 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 16.880 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 16.880 * [taylor]: Taking taylor expansion of 0 in k 16.880 * [backup-simplify]: Simplify 0 into 0 16.880 * [backup-simplify]: Simplify 0 into 0 16.881 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 16.883 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 16.884 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 16.884 * [backup-simplify]: Simplify (+ 0 0) into 0 16.885 * [backup-simplify]: Simplify (- 1) into -1 16.885 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.886 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 16.889 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 16.892 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 16.904 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 16.905 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 16.907 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 16.910 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 16.911 * [backup-simplify]: Simplify (- 0) into 0 16.911 * [backup-simplify]: Simplify (+ 0 0) into 0 16.912 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 16.914 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 16.915 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 16.918 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 16.918 * [taylor]: Taking taylor expansion of 0 in k 16.918 * [backup-simplify]: Simplify 0 into 0 16.918 * [backup-simplify]: Simplify 0 into 0 16.918 * [backup-simplify]: Simplify 0 into 0 16.919 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 16.923 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 16.925 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 16.925 * [backup-simplify]: Simplify (+ 0 0) into 0 16.926 * [backup-simplify]: Simplify (- 0) into 0 16.926 * [backup-simplify]: Simplify (+ 0 0) into 0 16.928 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 16.931 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 16.935 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 16.939 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 16.946 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 16.946 * [backup-simplify]: Simplify (pow (* 2.0 (* (* (cbrt (/ 1 n)) (cbrt (/ 1 n))) (* (cbrt (/ 1 n)) PI))) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 16.946 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 16.946 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 16.946 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 16.946 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 16.946 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 16.946 * [taylor]: Taking taylor expansion of 0.5 in k 16.946 * [backup-simplify]: Simplify 0.5 into 0.5 16.946 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 16.946 * [taylor]: Taking taylor expansion of 1.0 in k 16.946 * [backup-simplify]: Simplify 1.0 into 1.0 16.946 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.946 * [taylor]: Taking taylor expansion of k in k 16.946 * [backup-simplify]: Simplify 0 into 0 16.946 * [backup-simplify]: Simplify 1 into 1 16.947 * [backup-simplify]: Simplify (/ 1 1) into 1 16.947 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 16.947 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 16.947 * [taylor]: Taking taylor expansion of 2.0 in k 16.947 * [backup-simplify]: Simplify 2.0 into 2.0 16.947 * [taylor]: Taking taylor expansion of (/ PI n) in k 16.947 * [taylor]: Taking taylor expansion of PI in k 16.947 * [backup-simplify]: Simplify PI into PI 16.947 * [taylor]: Taking taylor expansion of n in k 16.947 * [backup-simplify]: Simplify n into n 16.947 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 16.947 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 16.947 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 16.947 * [backup-simplify]: Simplify (- 1) into -1 16.948 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.948 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 16.948 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 16.948 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 16.948 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 16.948 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 16.948 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 16.948 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 16.948 * [taylor]: Taking taylor expansion of 0.5 in n 16.948 * [backup-simplify]: Simplify 0.5 into 0.5 16.948 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 16.948 * [taylor]: Taking taylor expansion of 1.0 in n 16.948 * [backup-simplify]: Simplify 1.0 into 1.0 16.948 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.948 * [taylor]: Taking taylor expansion of k in n 16.948 * [backup-simplify]: Simplify k into k 16.948 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.948 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 16.949 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 16.949 * [taylor]: Taking taylor expansion of 2.0 in n 16.949 * [backup-simplify]: Simplify 2.0 into 2.0 16.949 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.949 * [taylor]: Taking taylor expansion of PI in n 16.949 * [backup-simplify]: Simplify PI into PI 16.949 * [taylor]: Taking taylor expansion of n in n 16.949 * [backup-simplify]: Simplify 0 into 0 16.949 * [backup-simplify]: Simplify 1 into 1 16.949 * [backup-simplify]: Simplify (/ PI 1) into PI 16.949 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 16.950 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.950 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 16.950 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 16.950 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 16.951 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.952 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 16.953 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 16.953 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 16.953 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 16.953 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 16.953 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 16.953 * [taylor]: Taking taylor expansion of 0.5 in n 16.953 * [backup-simplify]: Simplify 0.5 into 0.5 16.953 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 16.953 * [taylor]: Taking taylor expansion of 1.0 in n 16.953 * [backup-simplify]: Simplify 1.0 into 1.0 16.953 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.953 * [taylor]: Taking taylor expansion of k in n 16.953 * [backup-simplify]: Simplify k into k 16.953 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.953 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 16.953 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 16.953 * [taylor]: Taking taylor expansion of 2.0 in n 16.953 * [backup-simplify]: Simplify 2.0 into 2.0 16.953 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.953 * [taylor]: Taking taylor expansion of PI in n 16.953 * [backup-simplify]: Simplify PI into PI 16.953 * [taylor]: Taking taylor expansion of n in n 16.953 * [backup-simplify]: Simplify 0 into 0 16.953 * [backup-simplify]: Simplify 1 into 1 16.954 * [backup-simplify]: Simplify (/ PI 1) into PI 16.954 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 16.955 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.955 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 16.955 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 16.955 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 16.956 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.957 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 16.957 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 16.957 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 16.957 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 16.958 * [taylor]: Taking taylor expansion of 0.5 in k 16.958 * [backup-simplify]: Simplify 0.5 into 0.5 16.958 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 16.958 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 16.958 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 16.958 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 16.958 * [taylor]: Taking taylor expansion of 2.0 in k 16.958 * [backup-simplify]: Simplify 2.0 into 2.0 16.958 * [taylor]: Taking taylor expansion of PI in k 16.958 * [backup-simplify]: Simplify PI into PI 16.958 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 16.959 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.959 * [taylor]: Taking taylor expansion of (log n) in k 16.960 * [taylor]: Taking taylor expansion of n in k 16.960 * [backup-simplify]: Simplify n into n 16.960 * [backup-simplify]: Simplify (log n) into (log n) 16.960 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 16.960 * [taylor]: Taking taylor expansion of 1.0 in k 16.960 * [backup-simplify]: Simplify 1.0 into 1.0 16.960 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.960 * [taylor]: Taking taylor expansion of k in k 16.960 * [backup-simplify]: Simplify 0 into 0 16.960 * [backup-simplify]: Simplify 1 into 1 16.960 * [backup-simplify]: Simplify (/ 1 1) into 1 16.960 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 16.962 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 16.962 * [backup-simplify]: Simplify (- 1) into -1 16.963 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.964 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 16.965 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 16.966 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 16.967 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 16.968 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 16.969 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 16.971 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 16.971 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 16.971 * [backup-simplify]: Simplify (- 0) into 0 16.972 * [backup-simplify]: Simplify (+ 0 0) into 0 16.972 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 16.974 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.975 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 16.977 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 16.977 * [taylor]: Taking taylor expansion of 0 in k 16.977 * [backup-simplify]: Simplify 0 into 0 16.977 * [backup-simplify]: Simplify 0 into 0 16.977 * [backup-simplify]: Simplify 0 into 0 16.978 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.979 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 16.983 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 16.983 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.983 * [backup-simplify]: Simplify (- 0) into 0 16.983 * [backup-simplify]: Simplify (+ 0 0) into 0 16.984 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 16.985 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.986 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 16.988 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 16.988 * [taylor]: Taking taylor expansion of 0 in k 16.988 * [backup-simplify]: Simplify 0 into 0 16.988 * [backup-simplify]: Simplify 0 into 0 16.988 * [backup-simplify]: Simplify 0 into 0 16.988 * [backup-simplify]: Simplify 0 into 0 16.988 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.989 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 16.992 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 16.993 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.993 * [backup-simplify]: Simplify (- 0) into 0 16.993 * [backup-simplify]: Simplify (+ 0 0) into 0 16.994 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 16.995 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.996 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 16.998 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 16.998 * [taylor]: Taking taylor expansion of 0 in k 16.998 * [backup-simplify]: Simplify 0 into 0 16.998 * [backup-simplify]: Simplify 0 into 0 16.999 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 17.000 * [backup-simplify]: Simplify (pow (* 2.0 (* (* (cbrt (/ 1 (- n))) (cbrt (/ 1 (- n)))) (* (cbrt (/ 1 (- n))) PI))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) 17.000 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 17.000 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 17.000 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in k 17.000 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in k 17.000 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 17.000 * [taylor]: Taking taylor expansion of 0.5 in k 17.000 * [backup-simplify]: Simplify 0.5 into 0.5 17.000 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 17.000 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.000 * [taylor]: Taking taylor expansion of k in k 17.000 * [backup-simplify]: Simplify 0 into 0 17.000 * [backup-simplify]: Simplify 1 into 1 17.000 * [backup-simplify]: Simplify (/ 1 1) into 1 17.000 * [taylor]: Taking taylor expansion of 1.0 in k 17.000 * [backup-simplify]: Simplify 1.0 into 1.0 17.000 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in k 17.000 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in k 17.000 * [taylor]: Taking taylor expansion of 2.0 in k 17.000 * [backup-simplify]: Simplify 2.0 into 2.0 17.000 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in k 17.000 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in k 17.000 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in k 17.000 * [taylor]: Taking taylor expansion of (cbrt -1) in k 17.000 * [taylor]: Taking taylor expansion of -1 in k 17.000 * [backup-simplify]: Simplify -1 into -1 17.001 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 17.001 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 17.001 * [taylor]: Taking taylor expansion of PI in k 17.001 * [backup-simplify]: Simplify PI into PI 17.001 * [taylor]: Taking taylor expansion of n in k 17.001 * [backup-simplify]: Simplify n into n 17.002 * [backup-simplify]: Simplify (* (cbrt -1) (cbrt -1)) into (pow (cbrt -1) 2) 17.004 * [backup-simplify]: Simplify (* (cbrt -1) (pow (cbrt -1) 2)) into (pow (cbrt -1) 3) 17.005 * [backup-simplify]: Simplify (* (pow (cbrt -1) 3) PI) into (* -1 PI) 17.005 * [backup-simplify]: Simplify (/ (* -1 PI) n) into (* -1 (/ PI n)) 17.005 * [backup-simplify]: Simplify (* 2.0 (* -1 (/ PI n))) into (* -2.0 (/ PI n)) 17.005 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 17.006 * [backup-simplify]: Simplify (+ 1 0) into 1 17.006 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 17.006 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 17.007 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 17.007 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 17.007 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in n 17.007 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in n 17.007 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 17.007 * [taylor]: Taking taylor expansion of 0.5 in n 17.007 * [backup-simplify]: Simplify 0.5 into 0.5 17.007 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 17.007 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.007 * [taylor]: Taking taylor expansion of k in n 17.008 * [backup-simplify]: Simplify k into k 17.008 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.008 * [taylor]: Taking taylor expansion of 1.0 in n 17.008 * [backup-simplify]: Simplify 1.0 into 1.0 17.008 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in n 17.008 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in n 17.008 * [taylor]: Taking taylor expansion of 2.0 in n 17.008 * [backup-simplify]: Simplify 2.0 into 2.0 17.008 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in n 17.008 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in n 17.008 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in n 17.008 * [taylor]: Taking taylor expansion of (cbrt -1) in n 17.008 * [taylor]: Taking taylor expansion of -1 in n 17.008 * [backup-simplify]: Simplify -1 into -1 17.008 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 17.009 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 17.009 * [taylor]: Taking taylor expansion of PI in n 17.009 * [backup-simplify]: Simplify PI into PI 17.009 * [taylor]: Taking taylor expansion of n in n 17.009 * [backup-simplify]: Simplify 0 into 0 17.009 * [backup-simplify]: Simplify 1 into 1 17.009 * [backup-simplify]: Simplify (* (cbrt -1) (cbrt -1)) into (pow (cbrt -1) 2) 17.011 * [backup-simplify]: Simplify (* (cbrt -1) (pow (cbrt -1) 2)) into (pow (cbrt -1) 3) 17.012 * [backup-simplify]: Simplify (* (pow (cbrt -1) 3) PI) into (* -1 PI) 17.013 * [backup-simplify]: Simplify (/ (* -1 PI) 1) into (* -1 PI) 17.014 * [backup-simplify]: Simplify (* 2.0 (* -1 PI)) into (* -2.0 PI) 17.014 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 17.014 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 17.015 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 17.016 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.016 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 17.017 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 17.017 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 17.017 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in n 17.017 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in n 17.017 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 17.017 * [taylor]: Taking taylor expansion of 0.5 in n 17.017 * [backup-simplify]: Simplify 0.5 into 0.5 17.017 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 17.017 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.017 * [taylor]: Taking taylor expansion of k in n 17.017 * [backup-simplify]: Simplify k into k 17.017 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.017 * [taylor]: Taking taylor expansion of 1.0 in n 17.017 * [backup-simplify]: Simplify 1.0 into 1.0 17.017 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in n 17.017 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in n 17.018 * [taylor]: Taking taylor expansion of 2.0 in n 17.018 * [backup-simplify]: Simplify 2.0 into 2.0 17.018 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in n 17.018 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in n 17.018 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in n 17.018 * [taylor]: Taking taylor expansion of (cbrt -1) in n 17.018 * [taylor]: Taking taylor expansion of -1 in n 17.018 * [backup-simplify]: Simplify -1 into -1 17.018 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 17.018 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 17.018 * [taylor]: Taking taylor expansion of PI in n 17.018 * [backup-simplify]: Simplify PI into PI 17.018 * [taylor]: Taking taylor expansion of n in n 17.018 * [backup-simplify]: Simplify 0 into 0 17.018 * [backup-simplify]: Simplify 1 into 1 17.025 * [backup-simplify]: Simplify (* (cbrt -1) (cbrt -1)) into (pow (cbrt -1) 2) 17.027 * [backup-simplify]: Simplify (* (cbrt -1) (pow (cbrt -1) 2)) into (pow (cbrt -1) 3) 17.029 * [backup-simplify]: Simplify (* (pow (cbrt -1) 3) PI) into (* -1 PI) 17.031 * [backup-simplify]: Simplify (/ (* -1 PI) 1) into (* -1 PI) 17.032 * [backup-simplify]: Simplify (* 2.0 (* -1 PI)) into (* -2.0 PI) 17.033 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 17.033 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 17.033 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 17.035 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.036 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 17.037 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 17.038 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 17.038 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 17.038 * [taylor]: Taking taylor expansion of 0.5 in k 17.038 * [backup-simplify]: Simplify 0.5 into 0.5 17.038 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 17.038 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 17.038 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.038 * [taylor]: Taking taylor expansion of k in k 17.038 * [backup-simplify]: Simplify 0 into 0 17.038 * [backup-simplify]: Simplify 1 into 1 17.038 * [backup-simplify]: Simplify (/ 1 1) into 1 17.038 * [taylor]: Taking taylor expansion of 1.0 in k 17.038 * [backup-simplify]: Simplify 1.0 into 1.0 17.038 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 17.039 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 17.039 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 17.039 * [taylor]: Taking taylor expansion of -2.0 in k 17.039 * [backup-simplify]: Simplify -2.0 into -2.0 17.039 * [taylor]: Taking taylor expansion of PI in k 17.039 * [backup-simplify]: Simplify PI into PI 17.039 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 17.040 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 17.040 * [taylor]: Taking taylor expansion of (log n) in k 17.040 * [taylor]: Taking taylor expansion of n in k 17.040 * [backup-simplify]: Simplify n into n 17.040 * [backup-simplify]: Simplify (log n) into (log n) 17.041 * [backup-simplify]: Simplify (+ 1 0) into 1 17.041 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 17.042 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 17.043 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 17.045 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 17.046 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 17.047 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 17.048 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (cbrt -1))) into 0 17.049 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (pow (cbrt -1) 2))) into 0 17.050 * [backup-simplify]: Simplify (+ (* (pow (cbrt -1) 3) 0) (* 0 PI)) into 0 17.052 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (* -1 PI) (/ 0 1)))) into 0 17.053 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* -1 PI))) into 0 17.055 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 17.055 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 17.055 * [backup-simplify]: Simplify (+ 0 0) into 0 17.056 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 17.057 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.059 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 17.061 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 17.061 * [taylor]: Taking taylor expansion of 0 in k 17.061 * [backup-simplify]: Simplify 0 into 0 17.061 * [backup-simplify]: Simplify 0 into 0 17.061 * [backup-simplify]: Simplify 0 into 0 17.063 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 17.064 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (cbrt -1)))) into 0 17.065 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (pow (cbrt -1) 2)))) into 0 17.067 * [backup-simplify]: Simplify (+ (* (pow (cbrt -1) 3) 0) (+ (* 0 0) (* 0 PI))) into 0 17.068 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (* -1 PI) (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.069 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* -1 PI)))) into 0 17.073 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 17.073 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.074 * [backup-simplify]: Simplify (+ 0 0) into 0 17.075 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 17.076 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.077 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 17.080 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.080 * [taylor]: Taking taylor expansion of 0 in k 17.080 * [backup-simplify]: Simplify 0 into 0 17.080 * [backup-simplify]: Simplify 0 into 0 17.080 * [backup-simplify]: Simplify 0 into 0 17.080 * [backup-simplify]: Simplify 0 into 0 17.082 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 17.083 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (cbrt -1))))) into 0 17.085 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (cbrt -1) 2))))) into 0 17.086 * [backup-simplify]: Simplify (+ (* (pow (cbrt -1) 3) 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 17.088 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (* -1 PI) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.089 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* -1 PI))))) into 0 17.096 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 17.096 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.097 * [backup-simplify]: Simplify (+ 0 0) into 0 17.098 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 17.099 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.101 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 17.104 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.104 * [taylor]: Taking taylor expansion of 0 in k 17.104 * [backup-simplify]: Simplify 0 into 0 17.105 * [backup-simplify]: Simplify 0 into 0 17.106 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 17.106 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 17.107 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 17.107 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 17.107 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 17.107 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 17.107 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 17.107 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 17.107 * [taylor]: Taking taylor expansion of 0.25 in k 17.107 * [backup-simplify]: Simplify 0.25 into 0.25 17.107 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 17.107 * [taylor]: Taking taylor expansion of 1.0 in k 17.107 * [backup-simplify]: Simplify 1.0 into 1.0 17.107 * [taylor]: Taking taylor expansion of k in k 17.107 * [backup-simplify]: Simplify 0 into 0 17.107 * [backup-simplify]: Simplify 1 into 1 17.107 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 17.107 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 17.107 * [taylor]: Taking taylor expansion of 2.0 in k 17.107 * [backup-simplify]: Simplify 2.0 into 2.0 17.107 * [taylor]: Taking taylor expansion of (* n PI) in k 17.107 * [taylor]: Taking taylor expansion of n in k 17.107 * [backup-simplify]: Simplify n into n 17.107 * [taylor]: Taking taylor expansion of PI in k 17.107 * [backup-simplify]: Simplify PI into PI 17.107 * [backup-simplify]: Simplify (* n PI) into (* n PI) 17.107 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 17.107 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 17.107 * [backup-simplify]: Simplify (- 0) into 0 17.108 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 17.108 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 17.108 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 17.108 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 17.108 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 17.108 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 17.108 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 17.108 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 17.108 * [taylor]: Taking taylor expansion of 0.25 in n 17.108 * [backup-simplify]: Simplify 0.25 into 0.25 17.108 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 17.108 * [taylor]: Taking taylor expansion of 1.0 in n 17.108 * [backup-simplify]: Simplify 1.0 into 1.0 17.108 * [taylor]: Taking taylor expansion of k in n 17.108 * [backup-simplify]: Simplify k into k 17.109 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 17.109 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 17.109 * [taylor]: Taking taylor expansion of 2.0 in n 17.109 * [backup-simplify]: Simplify 2.0 into 2.0 17.109 * [taylor]: Taking taylor expansion of (* n PI) in n 17.109 * [taylor]: Taking taylor expansion of n in n 17.109 * [backup-simplify]: Simplify 0 into 0 17.109 * [backup-simplify]: Simplify 1 into 1 17.109 * [taylor]: Taking taylor expansion of PI in n 17.109 * [backup-simplify]: Simplify PI into PI 17.109 * [backup-simplify]: Simplify (* 0 PI) into 0 17.109 * [backup-simplify]: Simplify (* 2.0 0) into 0 17.110 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.111 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 17.112 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.112 * [backup-simplify]: Simplify (- k) into (- k) 17.112 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 17.112 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 17.113 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 17.114 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 17.114 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 17.114 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 17.114 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 17.115 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 17.115 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 17.115 * [taylor]: Taking taylor expansion of 0.25 in n 17.115 * [backup-simplify]: Simplify 0.25 into 0.25 17.115 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 17.115 * [taylor]: Taking taylor expansion of 1.0 in n 17.115 * [backup-simplify]: Simplify 1.0 into 1.0 17.115 * [taylor]: Taking taylor expansion of k in n 17.115 * [backup-simplify]: Simplify k into k 17.115 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 17.115 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 17.115 * [taylor]: Taking taylor expansion of 2.0 in n 17.115 * [backup-simplify]: Simplify 2.0 into 2.0 17.115 * [taylor]: Taking taylor expansion of (* n PI) in n 17.115 * [taylor]: Taking taylor expansion of n in n 17.115 * [backup-simplify]: Simplify 0 into 0 17.115 * [backup-simplify]: Simplify 1 into 1 17.115 * [taylor]: Taking taylor expansion of PI in n 17.115 * [backup-simplify]: Simplify PI into PI 17.115 * [backup-simplify]: Simplify (* 0 PI) into 0 17.115 * [backup-simplify]: Simplify (* 2.0 0) into 0 17.117 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.117 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 17.118 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.118 * [backup-simplify]: Simplify (- k) into (- k) 17.118 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 17.118 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 17.119 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 17.120 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 17.121 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 17.121 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 17.121 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 17.121 * [taylor]: Taking taylor expansion of 0.25 in k 17.121 * [backup-simplify]: Simplify 0.25 into 0.25 17.121 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 17.121 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 17.121 * [taylor]: Taking taylor expansion of 1.0 in k 17.121 * [backup-simplify]: Simplify 1.0 into 1.0 17.121 * [taylor]: Taking taylor expansion of k in k 17.121 * [backup-simplify]: Simplify 0 into 0 17.121 * [backup-simplify]: Simplify 1 into 1 17.121 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 17.121 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 17.121 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 17.121 * [taylor]: Taking taylor expansion of 2.0 in k 17.121 * [backup-simplify]: Simplify 2.0 into 2.0 17.121 * [taylor]: Taking taylor expansion of PI in k 17.121 * [backup-simplify]: Simplify PI into PI 17.121 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.122 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.122 * [taylor]: Taking taylor expansion of (log n) in k 17.122 * [taylor]: Taking taylor expansion of n in k 17.122 * [backup-simplify]: Simplify n into n 17.122 * [backup-simplify]: Simplify (log n) into (log n) 17.123 * [backup-simplify]: Simplify (- 0) into 0 17.123 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 17.124 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 17.124 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 17.125 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 17.126 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 17.127 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 17.127 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 17.128 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 17.129 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 17.129 * [backup-simplify]: Simplify (- 0) into 0 17.129 * [backup-simplify]: Simplify (+ 0 0) into 0 17.130 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 17.131 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 17.131 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 17.133 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 17.133 * [taylor]: Taking taylor expansion of 0 in k 17.133 * [backup-simplify]: Simplify 0 into 0 17.133 * [backup-simplify]: Simplify 0 into 0 17.133 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 17.134 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 17.135 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 17.135 * [backup-simplify]: Simplify (+ 0 0) into 0 17.135 * [backup-simplify]: Simplify (- 1) into -1 17.136 * [backup-simplify]: Simplify (+ 0 -1) into -1 17.137 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 17.138 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 17.140 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 17.142 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 17.143 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 17.144 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 17.145 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 17.146 * [backup-simplify]: Simplify (- 0) into 0 17.146 * [backup-simplify]: Simplify (+ 0 0) into 0 17.147 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 17.147 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 17.148 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 17.159 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.159 * [taylor]: Taking taylor expansion of 0 in k 17.159 * [backup-simplify]: Simplify 0 into 0 17.159 * [backup-simplify]: Simplify 0 into 0 17.159 * [backup-simplify]: Simplify 0 into 0 17.160 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 17.164 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 17.166 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 17.166 * [backup-simplify]: Simplify (+ 0 0) into 0 17.167 * [backup-simplify]: Simplify (- 0) into 0 17.167 * [backup-simplify]: Simplify (+ 0 0) into 0 17.169 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 17.172 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 17.176 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 17.182 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 17.193 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 17.194 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 17.194 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 17.194 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 17.194 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 17.194 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 17.194 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 17.194 * [taylor]: Taking taylor expansion of 0.25 in k 17.194 * [backup-simplify]: Simplify 0.25 into 0.25 17.194 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 17.194 * [taylor]: Taking taylor expansion of 1.0 in k 17.194 * [backup-simplify]: Simplify 1.0 into 1.0 17.194 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.194 * [taylor]: Taking taylor expansion of k in k 17.194 * [backup-simplify]: Simplify 0 into 0 17.194 * [backup-simplify]: Simplify 1 into 1 17.195 * [backup-simplify]: Simplify (/ 1 1) into 1 17.195 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 17.195 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 17.195 * [taylor]: Taking taylor expansion of 2.0 in k 17.195 * [backup-simplify]: Simplify 2.0 into 2.0 17.195 * [taylor]: Taking taylor expansion of (/ PI n) in k 17.195 * [taylor]: Taking taylor expansion of PI in k 17.195 * [backup-simplify]: Simplify PI into PI 17.195 * [taylor]: Taking taylor expansion of n in k 17.195 * [backup-simplify]: Simplify n into n 17.195 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 17.195 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 17.195 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 17.195 * [backup-simplify]: Simplify (- 1) into -1 17.196 * [backup-simplify]: Simplify (+ 0 -1) into -1 17.196 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 17.197 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 17.197 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 17.197 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 17.197 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 17.197 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 17.197 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 17.197 * [taylor]: Taking taylor expansion of 0.25 in n 17.197 * [backup-simplify]: Simplify 0.25 into 0.25 17.197 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 17.197 * [taylor]: Taking taylor expansion of 1.0 in n 17.197 * [backup-simplify]: Simplify 1.0 into 1.0 17.197 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.197 * [taylor]: Taking taylor expansion of k in n 17.197 * [backup-simplify]: Simplify k into k 17.197 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.197 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 17.197 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 17.197 * [taylor]: Taking taylor expansion of 2.0 in n 17.197 * [backup-simplify]: Simplify 2.0 into 2.0 17.197 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.197 * [taylor]: Taking taylor expansion of PI in n 17.197 * [backup-simplify]: Simplify PI into PI 17.197 * [taylor]: Taking taylor expansion of n in n 17.197 * [backup-simplify]: Simplify 0 into 0 17.198 * [backup-simplify]: Simplify 1 into 1 17.198 * [backup-simplify]: Simplify (/ PI 1) into PI 17.199 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.200 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.200 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 17.200 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 17.200 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 17.201 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.203 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 17.204 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 17.204 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 17.204 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 17.204 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 17.204 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 17.204 * [taylor]: Taking taylor expansion of 0.25 in n 17.204 * [backup-simplify]: Simplify 0.25 into 0.25 17.204 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 17.204 * [taylor]: Taking taylor expansion of 1.0 in n 17.204 * [backup-simplify]: Simplify 1.0 into 1.0 17.204 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.204 * [taylor]: Taking taylor expansion of k in n 17.204 * [backup-simplify]: Simplify k into k 17.204 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.204 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 17.204 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 17.204 * [taylor]: Taking taylor expansion of 2.0 in n 17.204 * [backup-simplify]: Simplify 2.0 into 2.0 17.205 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.205 * [taylor]: Taking taylor expansion of PI in n 17.205 * [backup-simplify]: Simplify PI into PI 17.205 * [taylor]: Taking taylor expansion of n in n 17.205 * [backup-simplify]: Simplify 0 into 0 17.205 * [backup-simplify]: Simplify 1 into 1 17.205 * [backup-simplify]: Simplify (/ PI 1) into PI 17.206 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.207 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.207 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 17.207 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 17.207 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 17.209 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.210 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 17.211 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 17.211 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 17.211 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 17.211 * [taylor]: Taking taylor expansion of 0.25 in k 17.211 * [backup-simplify]: Simplify 0.25 into 0.25 17.211 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 17.211 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 17.211 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 17.211 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 17.212 * [taylor]: Taking taylor expansion of 2.0 in k 17.212 * [backup-simplify]: Simplify 2.0 into 2.0 17.212 * [taylor]: Taking taylor expansion of PI in k 17.212 * [backup-simplify]: Simplify PI into PI 17.212 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.213 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.213 * [taylor]: Taking taylor expansion of (log n) in k 17.213 * [taylor]: Taking taylor expansion of n in k 17.213 * [backup-simplify]: Simplify n into n 17.213 * [backup-simplify]: Simplify (log n) into (log n) 17.213 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 17.213 * [taylor]: Taking taylor expansion of 1.0 in k 17.213 * [backup-simplify]: Simplify 1.0 into 1.0 17.213 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.213 * [taylor]: Taking taylor expansion of k in k 17.213 * [backup-simplify]: Simplify 0 into 0 17.213 * [backup-simplify]: Simplify 1 into 1 17.214 * [backup-simplify]: Simplify (/ 1 1) into 1 17.214 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 17.215 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 17.215 * [backup-simplify]: Simplify (- 1) into -1 17.216 * [backup-simplify]: Simplify (+ 0 -1) into -1 17.217 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 17.218 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 17.219 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 17.221 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 17.222 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.223 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 17.225 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 17.225 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 17.226 * [backup-simplify]: Simplify (- 0) into 0 17.226 * [backup-simplify]: Simplify (+ 0 0) into 0 17.227 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 17.228 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.230 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 17.232 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 17.232 * [taylor]: Taking taylor expansion of 0 in k 17.232 * [backup-simplify]: Simplify 0 into 0 17.232 * [backup-simplify]: Simplify 0 into 0 17.232 * [backup-simplify]: Simplify 0 into 0 17.233 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.234 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 17.238 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 17.238 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.239 * [backup-simplify]: Simplify (- 0) into 0 17.239 * [backup-simplify]: Simplify (+ 0 0) into 0 17.240 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 17.241 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.243 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 17.246 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.246 * [taylor]: Taking taylor expansion of 0 in k 17.246 * [backup-simplify]: Simplify 0 into 0 17.246 * [backup-simplify]: Simplify 0 into 0 17.246 * [backup-simplify]: Simplify 0 into 0 17.246 * [backup-simplify]: Simplify 0 into 0 17.247 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.248 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 17.254 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 17.255 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.255 * [backup-simplify]: Simplify (- 0) into 0 17.256 * [backup-simplify]: Simplify (+ 0 0) into 0 17.257 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 17.258 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.260 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 17.263 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.263 * [taylor]: Taking taylor expansion of 0 in k 17.263 * [backup-simplify]: Simplify 0 into 0 17.263 * [backup-simplify]: Simplify 0 into 0 17.265 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 17.265 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 17.265 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 17.266 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 17.266 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 17.266 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 17.266 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 17.266 * [taylor]: Taking taylor expansion of 0.25 in k 17.266 * [backup-simplify]: Simplify 0.25 into 0.25 17.266 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 17.266 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.266 * [taylor]: Taking taylor expansion of k in k 17.266 * [backup-simplify]: Simplify 0 into 0 17.266 * [backup-simplify]: Simplify 1 into 1 17.266 * [backup-simplify]: Simplify (/ 1 1) into 1 17.266 * [taylor]: Taking taylor expansion of 1.0 in k 17.266 * [backup-simplify]: Simplify 1.0 into 1.0 17.266 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 17.266 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 17.266 * [taylor]: Taking taylor expansion of -2.0 in k 17.266 * [backup-simplify]: Simplify -2.0 into -2.0 17.266 * [taylor]: Taking taylor expansion of (/ PI n) in k 17.267 * [taylor]: Taking taylor expansion of PI in k 17.267 * [backup-simplify]: Simplify PI into PI 17.267 * [taylor]: Taking taylor expansion of n in k 17.267 * [backup-simplify]: Simplify n into n 17.267 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 17.267 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 17.267 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 17.267 * [backup-simplify]: Simplify (+ 1 0) into 1 17.268 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 17.268 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 17.268 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 17.268 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 17.268 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 17.268 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 17.268 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 17.268 * [taylor]: Taking taylor expansion of 0.25 in n 17.268 * [backup-simplify]: Simplify 0.25 into 0.25 17.268 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 17.269 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.269 * [taylor]: Taking taylor expansion of k in n 17.269 * [backup-simplify]: Simplify k into k 17.269 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.269 * [taylor]: Taking taylor expansion of 1.0 in n 17.269 * [backup-simplify]: Simplify 1.0 into 1.0 17.269 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 17.269 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 17.269 * [taylor]: Taking taylor expansion of -2.0 in n 17.269 * [backup-simplify]: Simplify -2.0 into -2.0 17.269 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.269 * [taylor]: Taking taylor expansion of PI in n 17.269 * [backup-simplify]: Simplify PI into PI 17.269 * [taylor]: Taking taylor expansion of n in n 17.269 * [backup-simplify]: Simplify 0 into 0 17.269 * [backup-simplify]: Simplify 1 into 1 17.270 * [backup-simplify]: Simplify (/ PI 1) into PI 17.270 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 17.271 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 17.271 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 17.271 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 17.273 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.274 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 17.275 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 17.275 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 17.275 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 17.275 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 17.275 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 17.275 * [taylor]: Taking taylor expansion of 0.25 in n 17.275 * [backup-simplify]: Simplify 0.25 into 0.25 17.275 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 17.276 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.276 * [taylor]: Taking taylor expansion of k in n 17.276 * [backup-simplify]: Simplify k into k 17.276 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.276 * [taylor]: Taking taylor expansion of 1.0 in n 17.276 * [backup-simplify]: Simplify 1.0 into 1.0 17.276 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 17.276 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 17.276 * [taylor]: Taking taylor expansion of -2.0 in n 17.276 * [backup-simplify]: Simplify -2.0 into -2.0 17.276 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.276 * [taylor]: Taking taylor expansion of PI in n 17.276 * [backup-simplify]: Simplify PI into PI 17.276 * [taylor]: Taking taylor expansion of n in n 17.276 * [backup-simplify]: Simplify 0 into 0 17.276 * [backup-simplify]: Simplify 1 into 1 17.277 * [backup-simplify]: Simplify (/ PI 1) into PI 17.277 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 17.278 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 17.278 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 17.278 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 17.280 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.281 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 17.282 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 17.283 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 17.283 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 17.283 * [taylor]: Taking taylor expansion of 0.25 in k 17.283 * [backup-simplify]: Simplify 0.25 into 0.25 17.283 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 17.283 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 17.283 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.283 * [taylor]: Taking taylor expansion of k in k 17.283 * [backup-simplify]: Simplify 0 into 0 17.283 * [backup-simplify]: Simplify 1 into 1 17.284 * [backup-simplify]: Simplify (/ 1 1) into 1 17.284 * [taylor]: Taking taylor expansion of 1.0 in k 17.284 * [backup-simplify]: Simplify 1.0 into 1.0 17.284 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 17.284 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 17.284 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 17.284 * [taylor]: Taking taylor expansion of -2.0 in k 17.284 * [backup-simplify]: Simplify -2.0 into -2.0 17.284 * [taylor]: Taking taylor expansion of PI in k 17.284 * [backup-simplify]: Simplify PI into PI 17.284 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 17.285 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 17.285 * [taylor]: Taking taylor expansion of (log n) in k 17.285 * [taylor]: Taking taylor expansion of n in k 17.285 * [backup-simplify]: Simplify n into n 17.286 * [backup-simplify]: Simplify (log n) into (log n) 17.286 * [backup-simplify]: Simplify (+ 1 0) into 1 17.286 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 17.287 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 17.288 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 17.289 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 17.290 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 17.292 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 17.293 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.293 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 17.295 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 17.295 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 17.296 * [backup-simplify]: Simplify (+ 0 0) into 0 17.296 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 17.298 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.299 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 17.301 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 17.301 * [taylor]: Taking taylor expansion of 0 in k 17.301 * [backup-simplify]: Simplify 0 into 0 17.301 * [backup-simplify]: Simplify 0 into 0 17.301 * [backup-simplify]: Simplify 0 into 0 17.302 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.303 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 17.306 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 17.307 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.307 * [backup-simplify]: Simplify (+ 0 0) into 0 17.308 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 17.318 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.319 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 17.322 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.322 * [taylor]: Taking taylor expansion of 0 in k 17.322 * [backup-simplify]: Simplify 0 into 0 17.322 * [backup-simplify]: Simplify 0 into 0 17.322 * [backup-simplify]: Simplify 0 into 0 17.322 * [backup-simplify]: Simplify 0 into 0 17.324 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.326 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 17.332 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 17.333 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.333 * [backup-simplify]: Simplify (+ 0 0) into 0 17.335 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 17.336 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.338 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 17.341 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.341 * [taylor]: Taking taylor expansion of 0 in k 17.341 * [backup-simplify]: Simplify 0 into 0 17.341 * [backup-simplify]: Simplify 0 into 0 17.342 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 17.343 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1 2 2 1) 17.343 * [backup-simplify]: Simplify (cbrt n) into (pow n 1/3) 17.343 * [approximate]: Taking taylor expansion of (pow n 1/3) in (n) around 0 17.343 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 17.343 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 17.343 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 17.343 * [taylor]: Taking taylor expansion of 1/3 in n 17.343 * [backup-simplify]: Simplify 1/3 into 1/3 17.343 * [taylor]: Taking taylor expansion of (log n) in n 17.343 * [taylor]: Taking taylor expansion of n in n 17.343 * [backup-simplify]: Simplify 0 into 0 17.343 * [backup-simplify]: Simplify 1 into 1 17.343 * [backup-simplify]: Simplify (log 1) into 0 17.344 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.344 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 17.344 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 17.344 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 17.344 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 17.344 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 17.344 * [taylor]: Taking taylor expansion of 1/3 in n 17.344 * [backup-simplify]: Simplify 1/3 into 1/3 17.344 * [taylor]: Taking taylor expansion of (log n) in n 17.344 * [taylor]: Taking taylor expansion of n in n 17.344 * [backup-simplify]: Simplify 0 into 0 17.344 * [backup-simplify]: Simplify 1 into 1 17.345 * [backup-simplify]: Simplify (log 1) into 0 17.345 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.345 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 17.345 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 17.346 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 17.347 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 17.347 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.348 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (log n))) into 0 17.349 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 17.349 * [backup-simplify]: Simplify 0 into 0 17.352 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 17.352 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.353 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (log n)))) into 0 17.354 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.354 * [backup-simplify]: Simplify 0 into 0 17.360 * [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 17.360 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.361 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0 17.363 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.363 * [backup-simplify]: Simplify 0 into 0 17.374 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 17.375 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.376 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))) into 0 17.379 * [backup-simplify]: Simplify (* (exp (* 1/3 (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 17.379 * [backup-simplify]: Simplify 0 into 0 17.398 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 17.399 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.401 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))))) into 0 17.405 * [backup-simplify]: Simplify (* (exp (* 1/3 (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 17.405 * [backup-simplify]: Simplify 0 into 0 17.438 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 17.438 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.441 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))))) into 0 17.447 * [backup-simplify]: Simplify (* (exp (* 1/3 (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 17.447 * [backup-simplify]: Simplify 0 into 0 17.447 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 17.447 * [backup-simplify]: Simplify (cbrt (/ 1 n)) into (pow (/ 1 n) 1/3) 17.447 * [approximate]: Taking taylor expansion of (pow (/ 1 n) 1/3) in (n) around 0 17.447 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 17.447 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 17.447 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 17.448 * [taylor]: Taking taylor expansion of 1/3 in n 17.448 * [backup-simplify]: Simplify 1/3 into 1/3 17.448 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 17.448 * [taylor]: Taking taylor expansion of (/ 1 n) in n 17.448 * [taylor]: Taking taylor expansion of n in n 17.448 * [backup-simplify]: Simplify 0 into 0 17.448 * [backup-simplify]: Simplify 1 into 1 17.448 * [backup-simplify]: Simplify (/ 1 1) into 1 17.449 * [backup-simplify]: Simplify (log 1) into 0 17.449 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.449 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 17.449 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 17.449 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 17.449 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 17.449 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 17.449 * [taylor]: Taking taylor expansion of 1/3 in n 17.449 * [backup-simplify]: Simplify 1/3 into 1/3 17.449 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 17.449 * [taylor]: Taking taylor expansion of (/ 1 n) in n 17.449 * [taylor]: Taking taylor expansion of n in n 17.449 * [backup-simplify]: Simplify 0 into 0 17.449 * [backup-simplify]: Simplify 1 into 1 17.450 * [backup-simplify]: Simplify (/ 1 1) into 1 17.450 * [backup-simplify]: Simplify (log 1) into 0 17.451 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.451 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 17.451 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 17.451 * [backup-simplify]: Simplify (pow n -1/3) into (pow n -1/3) 17.452 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 17.453 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 17.454 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.455 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 17.456 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 17.456 * [backup-simplify]: Simplify 0 into 0 17.457 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.459 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 17.460 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.461 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 17.462 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.462 * [backup-simplify]: Simplify 0 into 0 17.463 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.468 * [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 17.469 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.470 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 17.472 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.472 * [backup-simplify]: Simplify 0 into 0 17.473 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.494 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 17.495 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.497 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 17.500 * [backup-simplify]: Simplify (* (exp (* -1/3 (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 17.500 * [backup-simplify]: Simplify 0 into 0 17.501 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.519 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 17.520 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.522 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 17.526 * [backup-simplify]: Simplify (* (exp (* -1/3 (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 17.526 * [backup-simplify]: Simplify 0 into 0 17.527 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.561 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 17.561 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.564 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 17.570 * [backup-simplify]: Simplify (* (exp (* -1/3 (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 17.570 * [backup-simplify]: Simplify 0 into 0 17.570 * [backup-simplify]: Simplify (pow (/ 1 n) -1/3) into (pow (/ 1 n) -1/3) 17.570 * [backup-simplify]: Simplify (cbrt (/ 1 (- n))) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 17.570 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in (n) around 0 17.570 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 17.570 * [taylor]: Taking taylor expansion of (cbrt -1) in n 17.570 * [taylor]: Taking taylor expansion of -1 in n 17.570 * [backup-simplify]: Simplify -1 into -1 17.571 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 17.572 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 17.572 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 17.572 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 17.572 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 17.572 * [taylor]: Taking taylor expansion of 1/3 in n 17.572 * [backup-simplify]: Simplify 1/3 into 1/3 17.572 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 17.572 * [taylor]: Taking taylor expansion of (/ 1 n) in n 17.572 * [taylor]: Taking taylor expansion of n in n 17.572 * [backup-simplify]: Simplify 0 into 0 17.572 * [backup-simplify]: Simplify 1 into 1 17.572 * [backup-simplify]: Simplify (/ 1 1) into 1 17.573 * [backup-simplify]: Simplify (log 1) into 0 17.573 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.573 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 17.574 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 17.574 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 17.574 * [taylor]: Taking taylor expansion of (cbrt -1) in n 17.574 * [taylor]: Taking taylor expansion of -1 in n 17.574 * [backup-simplify]: Simplify -1 into -1 17.574 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 17.575 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 17.575 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 17.575 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 17.575 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 17.575 * [taylor]: Taking taylor expansion of 1/3 in n 17.575 * [backup-simplify]: Simplify 1/3 into 1/3 17.575 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 17.575 * [taylor]: Taking taylor expansion of (/ 1 n) in n 17.575 * [taylor]: Taking taylor expansion of n in n 17.576 * [backup-simplify]: Simplify 0 into 0 17.576 * [backup-simplify]: Simplify 1 into 1 17.576 * [backup-simplify]: Simplify (/ 1 1) into 1 17.576 * [backup-simplify]: Simplify (log 1) into 0 17.577 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.577 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 17.577 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 17.578 * [backup-simplify]: Simplify (* (cbrt -1) (pow n -1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 17.578 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 n) 1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 17.579 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 17.581 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 17.581 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.582 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 17.582 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 17.583 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (pow n -1/3))) into 0 17.583 * [backup-simplify]: Simplify 0 into 0 17.584 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.587 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 17.588 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.588 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 17.590 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.591 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 17.592 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (pow n -1/3)))) into 0 17.592 * [backup-simplify]: Simplify 0 into 0 17.593 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.599 * [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 17.599 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.600 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 17.602 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.603 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 17.605 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))) into 0 17.605 * [backup-simplify]: Simplify 0 into 0 17.606 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.617 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 17.618 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.620 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 17.623 * [backup-simplify]: Simplify (* (exp (* -1/3 (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 17.625 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 17.627 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))) into 0 17.627 * [backup-simplify]: Simplify 0 into 0 17.628 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.649 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 17.650 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.651 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 17.654 * [backup-simplify]: Simplify (* (exp (* -1/3 (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 17.654 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 17.656 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))))) into 0 17.656 * [backup-simplify]: Simplify 0 into 0 17.657 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.681 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 17.682 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.684 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 17.690 * [backup-simplify]: Simplify (* (exp (* -1/3 (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 17.692 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 17.695 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))))) into 0 17.695 * [backup-simplify]: Simplify 0 into 0 17.695 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 (/ 1 (- n))) 1/3)) into (* (pow (* -1 n) 1/3) (cbrt -1)) 17.696 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1 2 1 2) 17.696 * [backup-simplify]: Simplify (cbrt n) into (pow n 1/3) 17.696 * [approximate]: Taking taylor expansion of (pow n 1/3) in (n) around 0 17.696 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 17.696 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 17.696 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 17.696 * [taylor]: Taking taylor expansion of 1/3 in n 17.696 * [backup-simplify]: Simplify 1/3 into 1/3 17.696 * [taylor]: Taking taylor expansion of (log n) in n 17.696 * [taylor]: Taking taylor expansion of n in n 17.696 * [backup-simplify]: Simplify 0 into 0 17.696 * [backup-simplify]: Simplify 1 into 1 17.696 * [backup-simplify]: Simplify (log 1) into 0 17.697 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.697 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 17.697 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 17.697 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 17.697 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 17.697 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 17.697 * [taylor]: Taking taylor expansion of 1/3 in n 17.697 * [backup-simplify]: Simplify 1/3 into 1/3 17.697 * [taylor]: Taking taylor expansion of (log n) in n 17.697 * [taylor]: Taking taylor expansion of n in n 17.697 * [backup-simplify]: Simplify 0 into 0 17.697 * [backup-simplify]: Simplify 1 into 1 17.698 * [backup-simplify]: Simplify (log 1) into 0 17.698 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.698 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 17.698 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 17.699 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 17.700 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 17.701 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.701 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (log n))) into 0 17.702 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 17.702 * [backup-simplify]: Simplify 0 into 0 17.705 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 17.706 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.706 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (log n)))) into 0 17.708 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.708 * [backup-simplify]: Simplify 0 into 0 17.713 * [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 17.714 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.715 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0 17.717 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.717 * [backup-simplify]: Simplify 0 into 0 17.728 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 17.728 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.730 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))) into 0 17.733 * [backup-simplify]: Simplify (* (exp (* 1/3 (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 17.733 * [backup-simplify]: Simplify 0 into 0 17.752 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 17.753 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.755 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))))) into 0 17.759 * [backup-simplify]: Simplify (* (exp (* 1/3 (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 17.759 * [backup-simplify]: Simplify 0 into 0 17.790 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 17.791 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.793 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))))) into 0 17.800 * [backup-simplify]: Simplify (* (exp (* 1/3 (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 17.800 * [backup-simplify]: Simplify 0 into 0 17.800 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 17.800 * [backup-simplify]: Simplify (cbrt (/ 1 n)) into (pow (/ 1 n) 1/3) 17.800 * [approximate]: Taking taylor expansion of (pow (/ 1 n) 1/3) in (n) around 0 17.800 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 17.800 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 17.800 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 17.800 * [taylor]: Taking taylor expansion of 1/3 in n 17.800 * [backup-simplify]: Simplify 1/3 into 1/3 17.800 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 17.800 * [taylor]: Taking taylor expansion of (/ 1 n) in n 17.800 * [taylor]: Taking taylor expansion of n in n 17.800 * [backup-simplify]: Simplify 0 into 0 17.800 * [backup-simplify]: Simplify 1 into 1 17.801 * [backup-simplify]: Simplify (/ 1 1) into 1 17.801 * [backup-simplify]: Simplify (log 1) into 0 17.802 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.802 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 17.802 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 17.802 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 17.802 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 17.802 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 17.802 * [taylor]: Taking taylor expansion of 1/3 in n 17.802 * [backup-simplify]: Simplify 1/3 into 1/3 17.802 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 17.802 * [taylor]: Taking taylor expansion of (/ 1 n) in n 17.802 * [taylor]: Taking taylor expansion of n in n 17.802 * [backup-simplify]: Simplify 0 into 0 17.802 * [backup-simplify]: Simplify 1 into 1 17.803 * [backup-simplify]: Simplify (/ 1 1) into 1 17.803 * [backup-simplify]: Simplify (log 1) into 0 17.804 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.804 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 17.804 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 17.804 * [backup-simplify]: Simplify (pow n -1/3) into (pow n -1/3) 17.805 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 17.806 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 17.807 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.807 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 17.808 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 17.808 * [backup-simplify]: Simplify 0 into 0 17.808 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.810 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 17.810 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.811 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 17.812 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.812 * [backup-simplify]: Simplify 0 into 0 17.812 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.815 * [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 17.816 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.816 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 17.817 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.817 * [backup-simplify]: Simplify 0 into 0 17.818 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.824 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 17.825 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.826 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 17.827 * [backup-simplify]: Simplify (* (exp (* -1/3 (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 17.827 * [backup-simplify]: Simplify 0 into 0 17.828 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.840 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 17.841 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.843 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 17.847 * [backup-simplify]: Simplify (* (exp (* -1/3 (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 17.847 * [backup-simplify]: Simplify 0 into 0 17.849 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.882 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 17.883 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.885 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 17.891 * [backup-simplify]: Simplify (* (exp (* -1/3 (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 17.891 * [backup-simplify]: Simplify 0 into 0 17.891 * [backup-simplify]: Simplify (pow (/ 1 n) -1/3) into (pow (/ 1 n) -1/3) 17.892 * [backup-simplify]: Simplify (cbrt (/ 1 (- n))) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 17.892 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in (n) around 0 17.892 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 17.892 * [taylor]: Taking taylor expansion of (cbrt -1) in n 17.892 * [taylor]: Taking taylor expansion of -1 in n 17.892 * [backup-simplify]: Simplify -1 into -1 17.892 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 17.893 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 17.893 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 17.893 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 17.893 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 17.893 * [taylor]: Taking taylor expansion of 1/3 in n 17.893 * [backup-simplify]: Simplify 1/3 into 1/3 17.893 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 17.893 * [taylor]: Taking taylor expansion of (/ 1 n) in n 17.893 * [taylor]: Taking taylor expansion of n in n 17.893 * [backup-simplify]: Simplify 0 into 0 17.893 * [backup-simplify]: Simplify 1 into 1 17.894 * [backup-simplify]: Simplify (/ 1 1) into 1 17.894 * [backup-simplify]: Simplify (log 1) into 0 17.895 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.895 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 17.895 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 17.895 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 17.895 * [taylor]: Taking taylor expansion of (cbrt -1) in n 17.895 * [taylor]: Taking taylor expansion of -1 in n 17.895 * [backup-simplify]: Simplify -1 into -1 17.895 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 17.896 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 17.896 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 17.896 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 17.896 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 17.896 * [taylor]: Taking taylor expansion of 1/3 in n 17.896 * [backup-simplify]: Simplify 1/3 into 1/3 17.896 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 17.896 * [taylor]: Taking taylor expansion of (/ 1 n) in n 17.896 * [taylor]: Taking taylor expansion of n in n 17.896 * [backup-simplify]: Simplify 0 into 0 17.897 * [backup-simplify]: Simplify 1 into 1 17.897 * [backup-simplify]: Simplify (/ 1 1) into 1 17.898 * [backup-simplify]: Simplify (log 1) into 0 17.898 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.898 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 17.898 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 17.899 * [backup-simplify]: Simplify (* (cbrt -1) (pow n -1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 17.900 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 n) 1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 17.900 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 17.902 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 17.902 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.903 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 17.904 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 17.905 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (pow n -1/3))) into 0 17.905 * [backup-simplify]: Simplify 0 into 0 17.906 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.909 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 17.909 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.910 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 17.912 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.913 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 17.914 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (pow n -1/3)))) into 0 17.914 * [backup-simplify]: Simplify 0 into 0 17.916 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.922 * [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 17.923 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.924 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 17.926 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.927 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 17.929 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))) into 0 17.929 * [backup-simplify]: Simplify 0 into 0 17.930 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.949 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 17.949 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.951 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 17.952 * [backup-simplify]: Simplify (* (exp (* -1/3 (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 17.953 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 17.954 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))) into 0 17.955 * [backup-simplify]: Simplify 0 into 0 17.955 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.965 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 17.965 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.967 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 17.969 * [backup-simplify]: Simplify (* (exp (* -1/3 (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 17.970 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 17.972 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))))) into 0 17.972 * [backup-simplify]: Simplify 0 into 0 17.972 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 18.005 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 18.006 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 18.008 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 18.012 * [backup-simplify]: Simplify (* (exp (* -1/3 (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 18.013 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 18.015 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))))) into 0 18.015 * [backup-simplify]: Simplify 0 into 0 18.015 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 (/ 1 (- n))) 1/3)) into (* (pow (* -1 n) 1/3) (cbrt -1)) 18.015 * * * [progress]: simplifying candidates 18.018 * [simplify]: Simplifying: (expm1 (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (log1p (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (* (+ (log 2.0) (+ (+ (log (cbrt n)) (log (cbrt n))) (+ (log (cbrt n)) (log PI)))) (/ (- 1.0 k) 2.0)) (* (+ (log 2.0) (+ (+ (log (cbrt n)) (log (cbrt n))) (log (* (cbrt n) PI)))) (/ (- 1.0 k) 2.0)) (* (+ (log 2.0) (+ (log (* (cbrt n) (cbrt n))) (+ (log (cbrt n)) (log PI)))) (/ (- 1.0 k) 2.0)) (* (+ (log 2.0) (+ (log (* (cbrt n) (cbrt n))) (log (* (cbrt n) PI)))) (/ (- 1.0 k) 2.0)) (* (+ (log 2.0) (log (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI)))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI)))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI)))) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ 1.0 2.0)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ k 2.0)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (sqrt (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (sqrt (- 1.0 k)) 1)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ 1 (sqrt 2.0))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ 1 1)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ 1 (sqrt 2.0))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ 1 1)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) 1) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (- 1.0 k)) (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI)) (/ (- 1.0 k) 2.0)) (log (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (exp (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (* (* (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (expm1 (cbrt n)) (log1p (cbrt n)) (log (cbrt n)) (exp (cbrt n)) (cbrt (* (cbrt n) (cbrt n))) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) (cbrt 1) (cbrt n) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) (* (* (cbrt n) (cbrt n)) (cbrt n)) (sqrt (cbrt n)) (sqrt (cbrt n)) (expm1 (cbrt n)) (log1p (cbrt n)) (log (cbrt n)) (exp (cbrt n)) (cbrt (* (cbrt n) (cbrt n))) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) (cbrt 1) (cbrt n) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) (* (* (cbrt n) (cbrt n)) (cbrt n)) (sqrt (cbrt n)) (sqrt (cbrt n)) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow n 1/3) (pow (/ 1 n) -1/3) (* (pow (* -1 n) 1/3) (cbrt -1)) (pow n 1/3) (pow (/ 1 n) -1/3) (* (pow (* -1 n) 1/3) (cbrt -1)) 18.022 * * [simplify]: Extracting # 0 : cost 0 18.022 * * [simplify]: Extracting # 1 : cost 0 18.023 * * [simplify]: Extracting # 2 : cost 0 18.023 * * [simplify]: Extracting # 3 : cost 0 18.024 * * [simplify]: Extracting # 4 : cost 0 18.024 * * [simplify]: Extracting # 5 : cost 0 18.025 * * [simplify]: Extracting # 6 : cost 0 18.025 * * [simplify]: Extracting # 7 : cost 0 18.026 * * [simplify]: Extracting # 8 : cost 0 18.026 * * [simplify]: Extracting # 9 : cost 0 18.027 * * [simplify]: Extracting # 10 : cost 0 18.027 * * [simplify]: Extracting # 11 : cost 0 18.028 * * [simplify]: Extracting # 12 : cost 0 18.029 * * [simplify]: iteration 0 : 323 enodes (cost 2686 ) 18.167 * * [simplify]: Extracting # 0 : cost 0 18.170 * * [simplify]: Extracting # 1 : cost 0 18.173 * * [simplify]: Extracting # 2 : cost 0 18.183 * * [simplify]: Extracting # 3 : cost 0 18.185 * * [simplify]: Extracting # 4 : cost 0 18.188 * * [simplify]: Extracting # 5 : cost 0 18.190 * * [simplify]: Extracting # 6 : cost 0 18.193 * * [simplify]: iteration 1 : 860 enodes (cost 2492 ) 18.742 * * [simplify]: Extracting # 0 : cost 0 18.745 * * [simplify]: Extracting # 1 : cost 0 18.749 * * [simplify]: Extracting # 2 : cost 0 18.752 * * [simplify]: Extracting # 3 : cost 0 18.756 * * [simplify]: Extracting # 4 : cost 0 18.759 * * [simplify]: Extracting # 5 : cost 0 18.763 * * [simplify]: iteration 2 : 2533 enodes (cost 2247 ) 19.866 * * [simplify]: Extracting # 0 : cost 0 19.880 * * [simplify]: Extracting # 1 : cost 0 19.904 * * [simplify]: Extracting # 2 : cost 0 19.919 * * [simplify]: Extracting # 3 : cost 0 19.931 * * [simplify]: Extracting # 4 : cost 0 19.941 * * [simplify]: iteration done: 5001 enodes (cost 2113 ) 19.942 * [simplify]: Simplified to: (expm1 (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* n 2.0) PI) (/ 1.0 2.0)) (pow (* (* n 2.0) PI) (/ k 2.0)) (pow (* (* n 2.0) PI) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* n 2.0) PI) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* n 2.0) PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* n 2.0) PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* n 2.0) PI) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (sqrt (- 1.0 k))) (pow (* n (* 2.0 PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n (* 2.0 PI)) (/ 1 (sqrt 2.0))) (* (* n 2.0) PI) (pow (* (* n 2.0) PI) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* n 2.0) PI) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* n 2.0) PI) (+ (sqrt 1.0) (sqrt k))) (pow (* n (* 2.0 PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n (* 2.0 PI)) (/ 1 (sqrt 2.0))) (* (* n 2.0) PI) (* (* n 2.0) PI) (pow (* (* n 2.0) PI) (- 1.0 k)) (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* PI n) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (exp (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))) (pow (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))) (pow (* (* n 2.0) PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* n 2.0) PI) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (- 1.0 k) 2.0) 1/2) (* (/ (- 1.0 k) 2.0) 1/2) (* (/ (- 1.0 k) 2.0) 1/2) (pow (* (* n 2.0) PI) (/ (/ 1.0 2.0) 2)) (pow (* (* n 2.0) PI) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* n 2.0) PI) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* n 2.0) PI) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* n 2.0) PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* n 2.0) PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2))) (pow (* (* n 2.0) PI) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (sqrt 2))) (pow (* n (* 2.0 PI)) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* n 2.0) PI) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* n 2.0) PI) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* n 2.0) PI) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow (* (* n 2.0) PI) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* n 2.0) PI) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* n 2.0) PI) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* n 2.0) PI) (- 1.0 k)) (* (* n 2.0) PI) (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow (* (* n 2.0) PI) (/ (/ (- 1.0 k) 2.0) 2)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* n 2.0) PI) (/ (/ (- 1.0 k) 2.0) 4)) (pow (* (* n 2.0) PI) (/ (/ (- 1.0 k) 2.0) 4)) (expm1 (cbrt n)) (log1p (cbrt n)) (log (cbrt n)) (exp (cbrt n)) (cbrt (pow n 2/3)) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) 1 (cbrt n) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) n (sqrt (cbrt n)) (sqrt (cbrt n)) (expm1 (cbrt n)) (log1p (cbrt n)) (log (cbrt n)) (exp (cbrt n)) (cbrt (pow n 2/3)) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) 1 (cbrt n) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) n (sqrt (cbrt n)) (sqrt (cbrt n)) (fma (* 0.125 (pow k 2)) (fma (pow (log (* 2.0 PI)) 2) (pow (* n (* 2.0 PI)) 0.5) (* (pow (* n (* 2.0 PI)) 0.5) (pow (log n) 2))) (- (fma (* 0.25 (pow k 2)) (* (log n) (* (pow (* n (* 2.0 PI)) 0.5) (log (* 2.0 PI)))) (pow (* n (* 2.0 PI)) 0.5)) (* (* 0.5 k) (fma (pow (* n (* 2.0 PI)) 0.5) (log (* 2.0 PI)) (* (pow (* n (* 2.0 PI)) 0.5) (log n)))))) (pow (pow (* n (* 2.0 PI)) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (fma (* (pow (log (* 2.0 PI)) 2) (pow (* n (* 2.0 PI)) 0.25)) (* 0.03125 (pow k 2)) (- (fma (pow k 2) (* (* (pow (log n) 2) (pow (* n (* 2.0 PI)) 0.25)) 0.03125) (fma (* (* (log (* 2.0 PI)) (* (pow (* n (* 2.0 PI)) 0.25) (log n))) (pow k 2)) 0.0625 (pow (* n (* 2.0 PI)) 0.25))) (* 0.25 (* k (fma (log (* 2.0 PI)) (pow (* n (* 2.0 PI)) 0.25) (* (pow (* n (* 2.0 PI)) 0.25) (log n))))))) (pow (pow (* n (* 2.0 PI)) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (cbrt n) (pow (/ 1 n) -1/3) (* (cbrt (- n)) (cbrt -1)) (cbrt n) (pow (/ 1 n) -1/3) (* (cbrt (- n)) (cbrt -1)) 19.944 * * * [progress]: adding candidates to table 21.008 * [progress]: [Phase 3 of 3] Extracting. 21.008 * * [regime]: Finding splitpoints for: (# # # # # # #) 21.011 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 21.011 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # #) 21.070 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # #) 21.089 * * * * [regimes]: Trying to branch on n from (# # # # # # #) 21.134 * * * * [regimes]: Trying to branch on k from (# # # # # # #) 21.182 * * * [regime]: Found split indices: #