11.182 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.081 * * * [progress]: [2/2] Setting up program. 0.084 * [progress]: [Phase 2 of 3] Improving. 0.084 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.084 * [simplify]: Sending expressions to egg_math: (* (/ h0 (sqrt h1)) (pow (* (* h2 h3) h4) (/ (- h0 h1) h2))) 0.086 * * [simplify]: iteration 0 : 29 enodes (cost 8 ) 0.087 * * [simplify]: iteration 1 : 59 enodes (cost 8 ) 0.089 * * [simplify]: iteration 2 : 119 enodes (cost 8 ) 0.092 * * [simplify]: iteration 3 : 325 enodes (cost 8 ) 0.097 * * [simplify]: iteration 4 : 1034 enodes (cost 8 ) 0.120 * * [simplify]: iteration 5 : 5001 enodes (cost 8 ) 0.121 * * [progress]: iteration 1 / 4 0.121 * * * [progress]: picking best candidate 0.123 * * * * [pick]: Picked # 0.123 * * * [progress]: localizing error 0.136 * * * [progress]: generating rewritten candidates 0.136 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.159 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 0.175 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 0.181 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 0.226 * * * [progress]: generating series expansions 0.226 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.227 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 0.227 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 0.227 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.227 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.227 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.227 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.227 * [taylor]: Taking taylor expansion of 0.5 in k 0.227 * [backup-simplify]: Simplify 0.5 into 0.5 0.227 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.227 * [taylor]: Taking taylor expansion of 1.0 in k 0.227 * [backup-simplify]: Simplify 1.0 into 1.0 0.227 * [taylor]: Taking taylor expansion of k in k 0.227 * [backup-simplify]: Simplify 0 into 0 0.227 * [backup-simplify]: Simplify 1 into 1 0.227 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.227 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.227 * [taylor]: Taking taylor expansion of 2.0 in k 0.227 * [backup-simplify]: Simplify 2.0 into 2.0 0.227 * [taylor]: Taking taylor expansion of (* n PI) in k 0.227 * [taylor]: Taking taylor expansion of n in k 0.227 * [backup-simplify]: Simplify n into n 0.227 * [taylor]: Taking taylor expansion of PI in k 0.227 * [backup-simplify]: Simplify PI into PI 0.227 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.227 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.227 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.228 * [backup-simplify]: Simplify (- 0) into 0 0.228 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.228 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.228 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.228 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.228 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.228 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.228 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.228 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.228 * [taylor]: Taking taylor expansion of 0.5 in n 0.228 * [backup-simplify]: Simplify 0.5 into 0.5 0.228 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.228 * [taylor]: Taking taylor expansion of 1.0 in n 0.228 * [backup-simplify]: Simplify 1.0 into 1.0 0.229 * [taylor]: Taking taylor expansion of k in n 0.229 * [backup-simplify]: Simplify k into k 0.229 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.229 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.229 * [taylor]: Taking taylor expansion of 2.0 in n 0.229 * [backup-simplify]: Simplify 2.0 into 2.0 0.229 * [taylor]: Taking taylor expansion of (* n PI) in n 0.229 * [taylor]: Taking taylor expansion of n in n 0.229 * [backup-simplify]: Simplify 0 into 0 0.229 * [backup-simplify]: Simplify 1 into 1 0.229 * [taylor]: Taking taylor expansion of PI in n 0.229 * [backup-simplify]: Simplify PI into PI 0.229 * [backup-simplify]: Simplify (* 0 PI) into 0 0.229 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.230 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.231 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.232 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.232 * [backup-simplify]: Simplify (- k) into (- k) 0.232 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.232 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.233 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.233 * [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)))) 0.234 * [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))))) 0.234 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.234 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.234 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.234 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.234 * [taylor]: Taking taylor expansion of 0.5 in n 0.234 * [backup-simplify]: Simplify 0.5 into 0.5 0.234 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.234 * [taylor]: Taking taylor expansion of 1.0 in n 0.234 * [backup-simplify]: Simplify 1.0 into 1.0 0.234 * [taylor]: Taking taylor expansion of k in n 0.234 * [backup-simplify]: Simplify k into k 0.234 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.234 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.234 * [taylor]: Taking taylor expansion of 2.0 in n 0.234 * [backup-simplify]: Simplify 2.0 into 2.0 0.234 * [taylor]: Taking taylor expansion of (* n PI) in n 0.234 * [taylor]: Taking taylor expansion of n in n 0.234 * [backup-simplify]: Simplify 0 into 0 0.234 * [backup-simplify]: Simplify 1 into 1 0.234 * [taylor]: Taking taylor expansion of PI in n 0.234 * [backup-simplify]: Simplify PI into PI 0.235 * [backup-simplify]: Simplify (* 0 PI) into 0 0.235 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.236 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.237 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.237 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.237 * [backup-simplify]: Simplify (- k) into (- k) 0.237 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.237 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.238 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.239 * [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)))) 0.240 * [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))))) 0.240 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 0.240 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 0.240 * [taylor]: Taking taylor expansion of 0.5 in k 0.240 * [backup-simplify]: Simplify 0.5 into 0.5 0.240 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 0.240 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.240 * [taylor]: Taking taylor expansion of 1.0 in k 0.240 * [backup-simplify]: Simplify 1.0 into 1.0 0.240 * [taylor]: Taking taylor expansion of k in k 0.240 * [backup-simplify]: Simplify 0 into 0 0.240 * [backup-simplify]: Simplify 1 into 1 0.240 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 0.240 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.240 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.240 * [taylor]: Taking taylor expansion of 2.0 in k 0.240 * [backup-simplify]: Simplify 2.0 into 2.0 0.240 * [taylor]: Taking taylor expansion of PI in k 0.240 * [backup-simplify]: Simplify PI into PI 0.240 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.241 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.241 * [taylor]: Taking taylor expansion of (log n) in k 0.241 * [taylor]: Taking taylor expansion of n in k 0.241 * [backup-simplify]: Simplify n into n 0.241 * [backup-simplify]: Simplify (log n) into (log n) 0.241 * [backup-simplify]: Simplify (- 0) into 0 0.242 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.242 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 0.243 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 0.244 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 0.244 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0.245 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0.246 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 0.246 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 0.247 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.248 * [backup-simplify]: Simplify (- 0) into 0 0.248 * [backup-simplify]: Simplify (+ 0 0) into 0 0.248 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 0.249 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.250 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 0.251 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.251 * [taylor]: Taking taylor expansion of 0 in k 0.251 * [backup-simplify]: Simplify 0 into 0 0.251 * [backup-simplify]: Simplify 0 into 0 0.251 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.252 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.253 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 0.253 * [backup-simplify]: Simplify (+ 0 0) into 0 0.253 * [backup-simplify]: Simplify (- 1) into -1 0.253 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.254 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 0.256 * [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)))) 0.257 * [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)))))) 0.259 * [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)))))) 0.260 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 0.261 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 0.262 * [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 0.263 * [backup-simplify]: Simplify (- 0) into 0 0.263 * [backup-simplify]: Simplify (+ 0 0) into 0 0.263 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 0.264 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.265 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 0.266 * [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 0.266 * [taylor]: Taking taylor expansion of 0 in k 0.266 * [backup-simplify]: Simplify 0 into 0 0.266 * [backup-simplify]: Simplify 0 into 0 0.267 * [backup-simplify]: Simplify 0 into 0 0.267 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.269 * [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 0.270 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 0.270 * [backup-simplify]: Simplify (+ 0 0) into 0 0.271 * [backup-simplify]: Simplify (- 0) into 0 0.271 * [backup-simplify]: Simplify (+ 0 0) into 0 0.273 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 0.274 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 0.276 * [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)))))) 0.279 * [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)))))) 0.285 * [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)))))) 0.286 * [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)))) 0.286 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 0.286 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.286 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.286 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.286 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.286 * [taylor]: Taking taylor expansion of 0.5 in k 0.286 * [backup-simplify]: Simplify 0.5 into 0.5 0.286 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.286 * [taylor]: Taking taylor expansion of 1.0 in k 0.286 * [backup-simplify]: Simplify 1.0 into 1.0 0.286 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.286 * [taylor]: Taking taylor expansion of k in k 0.286 * [backup-simplify]: Simplify 0 into 0 0.286 * [backup-simplify]: Simplify 1 into 1 0.286 * [backup-simplify]: Simplify (/ 1 1) into 1 0.286 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.286 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.286 * [taylor]: Taking taylor expansion of 2.0 in k 0.286 * [backup-simplify]: Simplify 2.0 into 2.0 0.286 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.286 * [taylor]: Taking taylor expansion of PI in k 0.286 * [backup-simplify]: Simplify PI into PI 0.286 * [taylor]: Taking taylor expansion of n in k 0.286 * [backup-simplify]: Simplify n into n 0.286 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.287 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.287 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.287 * [backup-simplify]: Simplify (- 1) into -1 0.287 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.291 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.291 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.291 * [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))))) 0.291 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.291 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.291 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.291 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.291 * [taylor]: Taking taylor expansion of 0.5 in n 0.291 * [backup-simplify]: Simplify 0.5 into 0.5 0.291 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.291 * [taylor]: Taking taylor expansion of 1.0 in n 0.291 * [backup-simplify]: Simplify 1.0 into 1.0 0.291 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.291 * [taylor]: Taking taylor expansion of k in n 0.291 * [backup-simplify]: Simplify k into k 0.291 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.291 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.291 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.291 * [taylor]: Taking taylor expansion of 2.0 in n 0.291 * [backup-simplify]: Simplify 2.0 into 2.0 0.291 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.291 * [taylor]: Taking taylor expansion of PI in n 0.291 * [backup-simplify]: Simplify PI into PI 0.291 * [taylor]: Taking taylor expansion of n in n 0.291 * [backup-simplify]: Simplify 0 into 0 0.291 * [backup-simplify]: Simplify 1 into 1 0.292 * [backup-simplify]: Simplify (/ PI 1) into PI 0.292 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.293 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.293 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.293 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.293 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.294 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.295 * [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)))) 0.296 * [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))))) 0.296 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.296 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.296 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.296 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.296 * [taylor]: Taking taylor expansion of 0.5 in n 0.296 * [backup-simplify]: Simplify 0.5 into 0.5 0.296 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.296 * [taylor]: Taking taylor expansion of 1.0 in n 0.296 * [backup-simplify]: Simplify 1.0 into 1.0 0.296 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.296 * [taylor]: Taking taylor expansion of k in n 0.296 * [backup-simplify]: Simplify k into k 0.296 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.296 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.296 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.296 * [taylor]: Taking taylor expansion of 2.0 in n 0.296 * [backup-simplify]: Simplify 2.0 into 2.0 0.296 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.296 * [taylor]: Taking taylor expansion of PI in n 0.296 * [backup-simplify]: Simplify PI into PI 0.296 * [taylor]: Taking taylor expansion of n in n 0.296 * [backup-simplify]: Simplify 0 into 0 0.296 * [backup-simplify]: Simplify 1 into 1 0.296 * [backup-simplify]: Simplify (/ PI 1) into PI 0.297 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.297 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.297 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.297 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.297 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.298 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.299 * [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)))) 0.300 * [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))))) 0.300 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 0.300 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 0.300 * [taylor]: Taking taylor expansion of 0.5 in k 0.300 * [backup-simplify]: Simplify 0.5 into 0.5 0.300 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 0.300 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 0.300 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.300 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.300 * [taylor]: Taking taylor expansion of 2.0 in k 0.300 * [backup-simplify]: Simplify 2.0 into 2.0 0.300 * [taylor]: Taking taylor expansion of PI in k 0.300 * [backup-simplify]: Simplify PI into PI 0.300 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.301 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.301 * [taylor]: Taking taylor expansion of (log n) in k 0.301 * [taylor]: Taking taylor expansion of n in k 0.301 * [backup-simplify]: Simplify n into n 0.301 * [backup-simplify]: Simplify (log n) into (log n) 0.301 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.301 * [taylor]: Taking taylor expansion of 1.0 in k 0.301 * [backup-simplify]: Simplify 1.0 into 1.0 0.301 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.301 * [taylor]: Taking taylor expansion of k in k 0.301 * [backup-simplify]: Simplify 0 into 0 0.301 * [backup-simplify]: Simplify 1 into 1 0.301 * [backup-simplify]: Simplify (/ 1 1) into 1 0.301 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 0.302 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 0.302 * [backup-simplify]: Simplify (- 1) into -1 0.302 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.303 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 0.304 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 0.304 * [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))))) 0.305 * [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))))) 0.306 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.306 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.307 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.307 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.308 * [backup-simplify]: Simplify (- 0) into 0 0.308 * [backup-simplify]: Simplify (+ 0 0) into 0 0.308 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 0.309 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.310 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 0.311 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.311 * [taylor]: Taking taylor expansion of 0 in k 0.311 * [backup-simplify]: Simplify 0 into 0 0.311 * [backup-simplify]: Simplify 0 into 0 0.311 * [backup-simplify]: Simplify 0 into 0 0.312 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.312 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.314 * [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 0.314 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.314 * [backup-simplify]: Simplify (- 0) into 0 0.315 * [backup-simplify]: Simplify (+ 0 0) into 0 0.315 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 0.316 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.317 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 0.318 * [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 0.318 * [taylor]: Taking taylor expansion of 0 in k 0.318 * [backup-simplify]: Simplify 0 into 0 0.318 * [backup-simplify]: Simplify 0 into 0 0.318 * [backup-simplify]: Simplify 0 into 0 0.318 * [backup-simplify]: Simplify 0 into 0 0.319 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.320 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.323 * [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 0.323 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.323 * [backup-simplify]: Simplify (- 0) into 0 0.323 * [backup-simplify]: Simplify (+ 0 0) into 0 0.324 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 0.325 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.326 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 0.328 * [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 0.328 * [taylor]: Taking taylor expansion of 0 in k 0.328 * [backup-simplify]: Simplify 0 into 0 0.328 * [backup-simplify]: Simplify 0 into 0 0.328 * [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)))) 0.329 * [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))) 0.329 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 0.329 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.329 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.329 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.329 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.329 * [taylor]: Taking taylor expansion of 0.5 in k 0.329 * [backup-simplify]: Simplify 0.5 into 0.5 0.329 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.329 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.329 * [taylor]: Taking taylor expansion of k in k 0.329 * [backup-simplify]: Simplify 0 into 0 0.329 * [backup-simplify]: Simplify 1 into 1 0.329 * [backup-simplify]: Simplify (/ 1 1) into 1 0.329 * [taylor]: Taking taylor expansion of 1.0 in k 0.329 * [backup-simplify]: Simplify 1.0 into 1.0 0.329 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.329 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.329 * [taylor]: Taking taylor expansion of -2.0 in k 0.329 * [backup-simplify]: Simplify -2.0 into -2.0 0.329 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.330 * [taylor]: Taking taylor expansion of PI in k 0.330 * [backup-simplify]: Simplify PI into PI 0.330 * [taylor]: Taking taylor expansion of n in k 0.330 * [backup-simplify]: Simplify n into n 0.330 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.330 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.330 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.330 * [backup-simplify]: Simplify (+ 1 0) into 1 0.330 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.330 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.330 * [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)))))) 0.330 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.330 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.331 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.331 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.331 * [taylor]: Taking taylor expansion of 0.5 in n 0.331 * [backup-simplify]: Simplify 0.5 into 0.5 0.331 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.331 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.331 * [taylor]: Taking taylor expansion of k in n 0.331 * [backup-simplify]: Simplify k into k 0.331 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.331 * [taylor]: Taking taylor expansion of 1.0 in n 0.331 * [backup-simplify]: Simplify 1.0 into 1.0 0.331 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.331 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.331 * [taylor]: Taking taylor expansion of -2.0 in n 0.331 * [backup-simplify]: Simplify -2.0 into -2.0 0.331 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.331 * [taylor]: Taking taylor expansion of PI in n 0.331 * [backup-simplify]: Simplify PI into PI 0.331 * [taylor]: Taking taylor expansion of n in n 0.331 * [backup-simplify]: Simplify 0 into 0 0.331 * [backup-simplify]: Simplify 1 into 1 0.331 * [backup-simplify]: Simplify (/ PI 1) into PI 0.331 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.332 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.332 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.332 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.333 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.334 * [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)))) 0.334 * [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))))) 0.334 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.335 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.335 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.335 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.335 * [taylor]: Taking taylor expansion of 0.5 in n 0.335 * [backup-simplify]: Simplify 0.5 into 0.5 0.335 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.335 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.335 * [taylor]: Taking taylor expansion of k in n 0.335 * [backup-simplify]: Simplify k into k 0.335 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.335 * [taylor]: Taking taylor expansion of 1.0 in n 0.335 * [backup-simplify]: Simplify 1.0 into 1.0 0.335 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.335 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.335 * [taylor]: Taking taylor expansion of -2.0 in n 0.335 * [backup-simplify]: Simplify -2.0 into -2.0 0.335 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.335 * [taylor]: Taking taylor expansion of PI in n 0.335 * [backup-simplify]: Simplify PI into PI 0.335 * [taylor]: Taking taylor expansion of n in n 0.335 * [backup-simplify]: Simplify 0 into 0 0.335 * [backup-simplify]: Simplify 1 into 1 0.335 * [backup-simplify]: Simplify (/ PI 1) into PI 0.335 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.336 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.336 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.336 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.337 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.338 * [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)))) 0.338 * [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))))) 0.339 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 0.339 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 0.339 * [taylor]: Taking taylor expansion of 0.5 in k 0.339 * [backup-simplify]: Simplify 0.5 into 0.5 0.339 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 0.339 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.339 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.339 * [taylor]: Taking taylor expansion of k in k 0.339 * [backup-simplify]: Simplify 0 into 0 0.339 * [backup-simplify]: Simplify 1 into 1 0.339 * [backup-simplify]: Simplify (/ 1 1) into 1 0.339 * [taylor]: Taking taylor expansion of 1.0 in k 0.339 * [backup-simplify]: Simplify 1.0 into 1.0 0.339 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 0.339 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 0.339 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 0.339 * [taylor]: Taking taylor expansion of -2.0 in k 0.339 * [backup-simplify]: Simplify -2.0 into -2.0 0.339 * [taylor]: Taking taylor expansion of PI in k 0.339 * [backup-simplify]: Simplify PI into PI 0.339 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.340 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.340 * [taylor]: Taking taylor expansion of (log n) in k 0.340 * [taylor]: Taking taylor expansion of n in k 0.340 * [backup-simplify]: Simplify n into n 0.340 * [backup-simplify]: Simplify (log n) into (log n) 0.340 * [backup-simplify]: Simplify (+ 1 0) into 1 0.340 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 0.341 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 0.342 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 0.342 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 0.343 * [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))))) 0.344 * [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))))) 0.344 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.345 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.346 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 0.346 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.346 * [backup-simplify]: Simplify (+ 0 0) into 0 0.346 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 0.347 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.348 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 0.349 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.349 * [taylor]: Taking taylor expansion of 0 in k 0.349 * [backup-simplify]: Simplify 0 into 0 0.349 * [backup-simplify]: Simplify 0 into 0 0.349 * [backup-simplify]: Simplify 0 into 0 0.350 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.350 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.352 * [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 0.352 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.352 * [backup-simplify]: Simplify (+ 0 0) into 0 0.353 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 0.354 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.355 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 0.356 * [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 0.356 * [taylor]: Taking taylor expansion of 0 in k 0.356 * [backup-simplify]: Simplify 0 into 0 0.356 * [backup-simplify]: Simplify 0 into 0 0.356 * [backup-simplify]: Simplify 0 into 0 0.356 * [backup-simplify]: Simplify 0 into 0 0.357 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.357 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.360 * [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 0.360 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.361 * [backup-simplify]: Simplify (+ 0 0) into 0 0.361 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 0.362 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.363 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 0.365 * [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 0.365 * [taylor]: Taking taylor expansion of 0 in k 0.365 * [backup-simplify]: Simplify 0 into 0 0.365 * [backup-simplify]: Simplify 0 into 0 0.366 * [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)))))) 0.366 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 0.366 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 0.366 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 0.366 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.366 * [taylor]: Taking taylor expansion of 2.0 in n 0.366 * [backup-simplify]: Simplify 2.0 into 2.0 0.366 * [taylor]: Taking taylor expansion of (* n PI) in n 0.366 * [taylor]: Taking taylor expansion of n in n 0.366 * [backup-simplify]: Simplify 0 into 0 0.366 * [backup-simplify]: Simplify 1 into 1 0.366 * [taylor]: Taking taylor expansion of PI in n 0.366 * [backup-simplify]: Simplify PI into PI 0.366 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.366 * [taylor]: Taking taylor expansion of 2.0 in n 0.366 * [backup-simplify]: Simplify 2.0 into 2.0 0.366 * [taylor]: Taking taylor expansion of (* n PI) in n 0.366 * [taylor]: Taking taylor expansion of n in n 0.366 * [backup-simplify]: Simplify 0 into 0 0.366 * [backup-simplify]: Simplify 1 into 1 0.366 * [taylor]: Taking taylor expansion of PI in n 0.366 * [backup-simplify]: Simplify PI into PI 0.367 * [backup-simplify]: Simplify (* 0 PI) into 0 0.367 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.367 * [backup-simplify]: Simplify 0 into 0 0.368 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.369 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.369 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.370 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 0.370 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 0.370 * [backup-simplify]: Simplify 0 into 0 0.371 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 0.372 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 0.372 * [backup-simplify]: Simplify 0 into 0 0.373 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.373 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 0.373 * [backup-simplify]: Simplify 0 into 0 0.374 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.375 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 0.375 * [backup-simplify]: Simplify 0 into 0 0.376 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.377 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 0.377 * [backup-simplify]: Simplify 0 into 0 0.378 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 0.379 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 0.379 * [backup-simplify]: Simplify 0 into 0 0.379 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 0.380 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 0.380 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 0.380 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.380 * [taylor]: Taking taylor expansion of 2.0 in n 0.380 * [backup-simplify]: Simplify 2.0 into 2.0 0.380 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.380 * [taylor]: Taking taylor expansion of PI in n 0.380 * [backup-simplify]: Simplify PI into PI 0.380 * [taylor]: Taking taylor expansion of n in n 0.380 * [backup-simplify]: Simplify 0 into 0 0.380 * [backup-simplify]: Simplify 1 into 1 0.380 * [backup-simplify]: Simplify (/ PI 1) into PI 0.380 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.380 * [taylor]: Taking taylor expansion of 2.0 in n 0.380 * [backup-simplify]: Simplify 2.0 into 2.0 0.380 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.380 * [taylor]: Taking taylor expansion of PI in n 0.380 * [backup-simplify]: Simplify PI into PI 0.380 * [taylor]: Taking taylor expansion of n in n 0.380 * [backup-simplify]: Simplify 0 into 0 0.380 * [backup-simplify]: Simplify 1 into 1 0.380 * [backup-simplify]: Simplify (/ PI 1) into PI 0.381 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.381 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.385 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.385 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.385 * [backup-simplify]: Simplify 0 into 0 0.386 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.386 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.386 * [backup-simplify]: Simplify 0 into 0 0.387 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.387 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.388 * [backup-simplify]: Simplify 0 into 0 0.388 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.389 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.389 * [backup-simplify]: Simplify 0 into 0 0.389 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.390 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.390 * [backup-simplify]: Simplify 0 into 0 0.391 * [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 0.392 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.392 * [backup-simplify]: Simplify 0 into 0 0.392 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 0.393 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 0.393 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 0.393 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.393 * [taylor]: Taking taylor expansion of -2.0 in n 0.393 * [backup-simplify]: Simplify -2.0 into -2.0 0.393 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.393 * [taylor]: Taking taylor expansion of PI in n 0.393 * [backup-simplify]: Simplify PI into PI 0.393 * [taylor]: Taking taylor expansion of n in n 0.393 * [backup-simplify]: Simplify 0 into 0 0.393 * [backup-simplify]: Simplify 1 into 1 0.393 * [backup-simplify]: Simplify (/ PI 1) into PI 0.393 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.393 * [taylor]: Taking taylor expansion of -2.0 in n 0.393 * [backup-simplify]: Simplify -2.0 into -2.0 0.393 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.393 * [taylor]: Taking taylor expansion of PI in n 0.393 * [backup-simplify]: Simplify PI into PI 0.393 * [taylor]: Taking taylor expansion of n in n 0.393 * [backup-simplify]: Simplify 0 into 0 0.393 * [backup-simplify]: Simplify 1 into 1 0.394 * [backup-simplify]: Simplify (/ PI 1) into PI 0.394 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.394 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.395 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.395 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.395 * [backup-simplify]: Simplify 0 into 0 0.396 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.396 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.396 * [backup-simplify]: Simplify 0 into 0 0.397 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.398 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.398 * [backup-simplify]: Simplify 0 into 0 0.398 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.399 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.399 * [backup-simplify]: Simplify 0 into 0 0.399 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.400 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.400 * [backup-simplify]: Simplify 0 into 0 0.401 * [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 0.402 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.402 * [backup-simplify]: Simplify 0 into 0 0.402 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 0.402 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 0.402 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 0.402 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 0.402 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.402 * [taylor]: Taking taylor expansion of 1.0 in k 0.402 * [backup-simplify]: Simplify 1.0 into 1.0 0.402 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.402 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.402 * [taylor]: Taking taylor expansion of k in k 0.402 * [backup-simplify]: Simplify 0 into 0 0.402 * [backup-simplify]: Simplify 1 into 1 0.403 * [backup-simplify]: Simplify (/ 1 1) into 1 0.403 * [backup-simplify]: Simplify (sqrt 0) into 0 0.404 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.404 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.404 * [taylor]: Taking taylor expansion of 1.0 in k 0.404 * [backup-simplify]: Simplify 1.0 into 1.0 0.404 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.404 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.404 * [taylor]: Taking taylor expansion of k in k 0.404 * [backup-simplify]: Simplify 0 into 0 0.404 * [backup-simplify]: Simplify 1 into 1 0.404 * [backup-simplify]: Simplify (/ 1 1) into 1 0.404 * [backup-simplify]: Simplify (sqrt 0) into 0 0.405 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.405 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.405 * [backup-simplify]: Simplify 0 into 0 0.406 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 0.406 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.407 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 0.408 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.410 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 0.410 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.410 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.412 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.414 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 0.414 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.415 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 0.415 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 0.415 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 0.415 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.415 * [taylor]: Taking taylor expansion of 1.0 in k 0.415 * [backup-simplify]: Simplify 1.0 into 1.0 0.415 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.415 * [taylor]: Taking taylor expansion of k in k 0.415 * [backup-simplify]: Simplify 0 into 0 0.415 * [backup-simplify]: Simplify 1 into 1 0.415 * [backup-simplify]: Simplify (sqrt 0) into 0 0.416 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.416 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.416 * [taylor]: Taking taylor expansion of 1.0 in k 0.416 * [backup-simplify]: Simplify 1.0 into 1.0 0.416 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.416 * [taylor]: Taking taylor expansion of k in k 0.416 * [backup-simplify]: Simplify 0 into 0 0.416 * [backup-simplify]: Simplify 1 into 1 0.416 * [backup-simplify]: Simplify (sqrt 0) into 0 0.417 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.417 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.417 * [backup-simplify]: Simplify 0 into 0 0.418 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 0.418 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.420 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.421 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 0.421 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.424 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.425 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 0.425 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.426 * [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)))))))) 0.426 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 0.426 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 0.426 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.426 * [taylor]: Taking taylor expansion of 1.0 in k 0.426 * [backup-simplify]: Simplify 1.0 into 1.0 0.426 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.426 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.426 * [taylor]: Taking taylor expansion of -1 in k 0.426 * [backup-simplify]: Simplify -1 into -1 0.426 * [taylor]: Taking taylor expansion of k in k 0.426 * [backup-simplify]: Simplify 0 into 0 0.426 * [backup-simplify]: Simplify 1 into 1 0.427 * [backup-simplify]: Simplify (/ -1 1) into -1 0.427 * [backup-simplify]: Simplify (sqrt 0) into 0 0.428 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.428 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 0.428 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.428 * [taylor]: Taking taylor expansion of 1.0 in k 0.428 * [backup-simplify]: Simplify 1.0 into 1.0 0.428 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.428 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.428 * [taylor]: Taking taylor expansion of -1 in k 0.428 * [backup-simplify]: Simplify -1 into -1 0.428 * [taylor]: Taking taylor expansion of k in k 0.428 * [backup-simplify]: Simplify 0 into 0 0.428 * [backup-simplify]: Simplify 1 into 1 0.428 * [backup-simplify]: Simplify (/ -1 1) into -1 0.428 * [backup-simplify]: Simplify (sqrt 0) into 0 0.429 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.429 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 0.429 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.430 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 0.432 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.433 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 0.433 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.434 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.436 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.439 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 0.439 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.439 * [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))))) 0.440 * * * * [progress]: [ 4 / 4 ] generating series at (2) 0.440 * [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))))) 0.440 * [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 0.440 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 0.440 * [taylor]: Taking taylor expansion of 1.0 in n 0.440 * [backup-simplify]: Simplify 1.0 into 1.0 0.440 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 0.440 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 0.440 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.440 * [taylor]: Taking taylor expansion of k in n 0.440 * [backup-simplify]: Simplify k into k 0.440 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.440 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 0.440 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.440 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 0.440 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.440 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.440 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.440 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.440 * [taylor]: Taking taylor expansion of 0.5 in n 0.441 * [backup-simplify]: Simplify 0.5 into 0.5 0.441 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.441 * [taylor]: Taking taylor expansion of 1.0 in n 0.441 * [backup-simplify]: Simplify 1.0 into 1.0 0.441 * [taylor]: Taking taylor expansion of k in n 0.441 * [backup-simplify]: Simplify k into k 0.441 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.441 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.441 * [taylor]: Taking taylor expansion of 2.0 in n 0.441 * [backup-simplify]: Simplify 2.0 into 2.0 0.441 * [taylor]: Taking taylor expansion of (* n PI) in n 0.441 * [taylor]: Taking taylor expansion of n in n 0.441 * [backup-simplify]: Simplify 0 into 0 0.441 * [backup-simplify]: Simplify 1 into 1 0.441 * [taylor]: Taking taylor expansion of PI in n 0.441 * [backup-simplify]: Simplify PI into PI 0.441 * [backup-simplify]: Simplify (* 0 PI) into 0 0.441 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.442 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.443 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.444 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.444 * [backup-simplify]: Simplify (- k) into (- k) 0.444 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.444 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.445 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.445 * [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)))) 0.446 * [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))))) 0.446 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.446 * [taylor]: Taking taylor expansion of 1.0 in k 0.446 * [backup-simplify]: Simplify 1.0 into 1.0 0.446 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.446 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.446 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.446 * [taylor]: Taking taylor expansion of k in k 0.446 * [backup-simplify]: Simplify 0 into 0 0.446 * [backup-simplify]: Simplify 1 into 1 0.446 * [backup-simplify]: Simplify (/ 1 1) into 1 0.447 * [backup-simplify]: Simplify (sqrt 0) into 0 0.447 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.447 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.447 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.447 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.447 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.447 * [taylor]: Taking taylor expansion of 0.5 in k 0.448 * [backup-simplify]: Simplify 0.5 into 0.5 0.448 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.448 * [taylor]: Taking taylor expansion of 1.0 in k 0.448 * [backup-simplify]: Simplify 1.0 into 1.0 0.448 * [taylor]: Taking taylor expansion of k in k 0.448 * [backup-simplify]: Simplify 0 into 0 0.448 * [backup-simplify]: Simplify 1 into 1 0.448 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.448 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.448 * [taylor]: Taking taylor expansion of 2.0 in k 0.448 * [backup-simplify]: Simplify 2.0 into 2.0 0.448 * [taylor]: Taking taylor expansion of (* n PI) in k 0.448 * [taylor]: Taking taylor expansion of n in k 0.448 * [backup-simplify]: Simplify n into n 0.448 * [taylor]: Taking taylor expansion of PI in k 0.448 * [backup-simplify]: Simplify PI into PI 0.448 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.448 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.448 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.448 * [backup-simplify]: Simplify (- 0) into 0 0.448 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.449 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.449 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.449 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.449 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.449 * [taylor]: Taking taylor expansion of 1.0 in k 0.449 * [backup-simplify]: Simplify 1.0 into 1.0 0.449 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.449 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.449 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.449 * [taylor]: Taking taylor expansion of k in k 0.449 * [backup-simplify]: Simplify 0 into 0 0.449 * [backup-simplify]: Simplify 1 into 1 0.449 * [backup-simplify]: Simplify (/ 1 1) into 1 0.449 * [backup-simplify]: Simplify (sqrt 0) into 0 0.450 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.450 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.450 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.450 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.450 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.450 * [taylor]: Taking taylor expansion of 0.5 in k 0.450 * [backup-simplify]: Simplify 0.5 into 0.5 0.450 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.450 * [taylor]: Taking taylor expansion of 1.0 in k 0.450 * [backup-simplify]: Simplify 1.0 into 1.0 0.450 * [taylor]: Taking taylor expansion of k in k 0.450 * [backup-simplify]: Simplify 0 into 0 0.450 * [backup-simplify]: Simplify 1 into 1 0.450 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.450 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.450 * [taylor]: Taking taylor expansion of 2.0 in k 0.450 * [backup-simplify]: Simplify 2.0 into 2.0 0.450 * [taylor]: Taking taylor expansion of (* n PI) in k 0.450 * [taylor]: Taking taylor expansion of n in k 0.450 * [backup-simplify]: Simplify n into n 0.450 * [taylor]: Taking taylor expansion of PI in k 0.450 * [backup-simplify]: Simplify PI into PI 0.451 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.451 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.451 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.451 * [backup-simplify]: Simplify (- 0) into 0 0.451 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.451 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.451 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.451 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.452 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 0.452 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.452 * [taylor]: Taking taylor expansion of 0 in n 0.452 * [backup-simplify]: Simplify 0 into 0 0.452 * [backup-simplify]: Simplify 0 into 0 0.452 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 0.453 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 0.453 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 0.453 * [backup-simplify]: Simplify (- 1) into -1 0.454 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.455 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 0.455 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 0.455 * [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))) 0.456 * [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))) 0.457 * [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))) 0.457 * [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 0.457 * [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 0.457 * [taylor]: Taking taylor expansion of +nan.0 in n 0.457 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.458 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.458 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.458 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.458 * [taylor]: Taking taylor expansion of 0.5 in n 0.458 * [backup-simplify]: Simplify 0.5 into 0.5 0.458 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.458 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.458 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.458 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.458 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.458 * [taylor]: Taking taylor expansion of 1.0 in n 0.458 * [backup-simplify]: Simplify 1.0 into 1.0 0.458 * [taylor]: Taking taylor expansion of (log PI) in n 0.458 * [taylor]: Taking taylor expansion of PI in n 0.458 * [backup-simplify]: Simplify PI into PI 0.458 * [backup-simplify]: Simplify (log PI) into (log PI) 0.459 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.460 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.460 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.460 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.460 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.460 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.460 * [taylor]: Taking taylor expansion of 1.0 in n 0.460 * [backup-simplify]: Simplify 1.0 into 1.0 0.460 * [taylor]: Taking taylor expansion of (log n) in n 0.460 * [taylor]: Taking taylor expansion of n in n 0.460 * [backup-simplify]: Simplify 0 into 0 0.460 * [backup-simplify]: Simplify 1 into 1 0.460 * [backup-simplify]: Simplify (log 1) into 0 0.460 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.460 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.460 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.460 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.460 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.460 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.460 * [taylor]: Taking taylor expansion of 1.0 in n 0.460 * [backup-simplify]: Simplify 1.0 into 1.0 0.460 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.460 * [taylor]: Taking taylor expansion of 2.0 in n 0.460 * [backup-simplify]: Simplify 2.0 into 2.0 0.461 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.461 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.462 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.463 * [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) 0.463 * [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) 0.464 * [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)) 0.465 * [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))) 0.466 * [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) 0.466 * [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)) 0.467 * [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))) 0.468 * [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))) 0.468 * [backup-simplify]: Simplify 0 into 0 0.469 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 0.469 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 0.470 * [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 0.470 * [backup-simplify]: Simplify (- 0) into 0 0.471 * [backup-simplify]: Simplify (+ 0 0) into 0 0.471 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 0.472 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 0.473 * [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))) 0.473 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 0.478 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.480 * [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)))))))) 0.483 * [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)))))))) 0.483 * [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 0.483 * [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 0.483 * [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 0.483 * [taylor]: Taking taylor expansion of +nan.0 in n 0.483 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.483 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.483 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.483 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.484 * [taylor]: Taking taylor expansion of 0.5 in n 0.484 * [backup-simplify]: Simplify 0.5 into 0.5 0.484 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.484 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.484 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.484 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.484 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.484 * [taylor]: Taking taylor expansion of 1.0 in n 0.484 * [backup-simplify]: Simplify 1.0 into 1.0 0.484 * [taylor]: Taking taylor expansion of (log PI) in n 0.484 * [taylor]: Taking taylor expansion of PI in n 0.484 * [backup-simplify]: Simplify PI into PI 0.484 * [backup-simplify]: Simplify (log PI) into (log PI) 0.485 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.485 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.485 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.486 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.486 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.486 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.486 * [taylor]: Taking taylor expansion of 1.0 in n 0.486 * [backup-simplify]: Simplify 1.0 into 1.0 0.486 * [taylor]: Taking taylor expansion of (log n) in n 0.486 * [taylor]: Taking taylor expansion of n in n 0.486 * [backup-simplify]: Simplify 0 into 0 0.486 * [backup-simplify]: Simplify 1 into 1 0.486 * [backup-simplify]: Simplify (log 1) into 0 0.486 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.486 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.486 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.486 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.486 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.486 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.486 * [taylor]: Taking taylor expansion of 1.0 in n 0.486 * [backup-simplify]: Simplify 1.0 into 1.0 0.486 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.486 * [taylor]: Taking taylor expansion of 2.0 in n 0.486 * [backup-simplify]: Simplify 2.0 into 2.0 0.487 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.487 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.488 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.488 * [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) 0.489 * [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) 0.490 * [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)) 0.491 * [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))) 0.492 * [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) 0.492 * [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 0.492 * [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 0.492 * [taylor]: Taking taylor expansion of +nan.0 in n 0.492 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.492 * [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 0.492 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.492 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.492 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.492 * [taylor]: Taking taylor expansion of 0.5 in n 0.492 * [backup-simplify]: Simplify 0.5 into 0.5 0.492 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.492 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.492 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.492 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.492 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.492 * [taylor]: Taking taylor expansion of 1.0 in n 0.492 * [backup-simplify]: Simplify 1.0 into 1.0 0.492 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.492 * [taylor]: Taking taylor expansion of 2.0 in n 0.492 * [backup-simplify]: Simplify 2.0 into 2.0 0.492 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.493 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.494 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.494 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.494 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.494 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.494 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.494 * [taylor]: Taking taylor expansion of 1.0 in n 0.494 * [backup-simplify]: Simplify 1.0 into 1.0 0.494 * [taylor]: Taking taylor expansion of (log PI) in n 0.494 * [taylor]: Taking taylor expansion of PI in n 0.494 * [backup-simplify]: Simplify PI into PI 0.494 * [backup-simplify]: Simplify (log PI) into (log PI) 0.495 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.495 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.495 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.496 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.496 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.496 * [taylor]: Taking taylor expansion of 1.0 in n 0.496 * [backup-simplify]: Simplify 1.0 into 1.0 0.496 * [taylor]: Taking taylor expansion of (log n) in n 0.496 * [taylor]: Taking taylor expansion of n in n 0.496 * [backup-simplify]: Simplify 0 into 0 0.496 * [backup-simplify]: Simplify 1 into 1 0.496 * [backup-simplify]: Simplify (log 1) into 0 0.496 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.496 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.496 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.497 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.497 * [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) 0.498 * [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)) 0.499 * [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))) 0.500 * [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) 0.500 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.500 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.500 * [taylor]: Taking taylor expansion of 2.0 in n 0.500 * [backup-simplify]: Simplify 2.0 into 2.0 0.500 * [taylor]: Taking taylor expansion of (* n PI) in n 0.500 * [taylor]: Taking taylor expansion of n in n 0.500 * [backup-simplify]: Simplify 0 into 0 0.500 * [backup-simplify]: Simplify 1 into 1 0.500 * [taylor]: Taking taylor expansion of PI in n 0.500 * [backup-simplify]: Simplify PI into PI 0.500 * [backup-simplify]: Simplify (* 0 PI) into 0 0.501 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.501 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.502 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.503 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.504 * [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)) 0.505 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.506 * [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)) 0.508 * [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))) 0.509 * [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)))))) 0.513 * [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)))))))) 0.517 * [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)))))))) 0.520 * [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)))))))) 0.521 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 0.522 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 0.523 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 0.523 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 0.524 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.524 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 0.524 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 0.525 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 0.526 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 0.526 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 0.527 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 0.528 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 0.529 * [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 0.530 * [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 0.532 * [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 0.533 * [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 0.533 * [backup-simplify]: Simplify (- 0) into 0 0.533 * [backup-simplify]: Simplify 0 into 0 0.533 * [backup-simplify]: Simplify 0 into 0 0.533 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.534 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 0.536 * [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 0.536 * [backup-simplify]: Simplify (- 0) into 0 0.536 * [backup-simplify]: Simplify (+ 0 0) into 0 0.537 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 0.538 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 0.539 * [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))) 0.539 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.542 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.545 * [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)))))))) 0.551 * [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)))))))) 0.551 * [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 0.551 * [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 0.551 * [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 0.551 * [taylor]: Taking taylor expansion of +nan.0 in n 0.551 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.551 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 0.551 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 0.551 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 0.551 * [taylor]: Taking taylor expansion of 0.5 in n 0.551 * [backup-simplify]: Simplify 0.5 into 0.5 0.551 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 0.551 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 0.551 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.551 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.551 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.551 * [taylor]: Taking taylor expansion of 1.0 in n 0.551 * [backup-simplify]: Simplify 1.0 into 1.0 0.551 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.551 * [taylor]: Taking taylor expansion of 2.0 in n 0.551 * [backup-simplify]: Simplify 2.0 into 2.0 0.552 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.552 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.553 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.553 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 0.553 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.553 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.553 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.553 * [taylor]: Taking taylor expansion of 1.0 in n 0.553 * [backup-simplify]: Simplify 1.0 into 1.0 0.553 * [taylor]: Taking taylor expansion of (log n) in n 0.553 * [taylor]: Taking taylor expansion of n in n 0.553 * [backup-simplify]: Simplify 0 into 0 0.553 * [backup-simplify]: Simplify 1 into 1 0.553 * [backup-simplify]: Simplify (log 1) into 0 0.554 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.554 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.554 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.554 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.554 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.554 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.554 * [taylor]: Taking taylor expansion of 1.0 in n 0.554 * [backup-simplify]: Simplify 1.0 into 1.0 0.554 * [taylor]: Taking taylor expansion of (log PI) in n 0.554 * [taylor]: Taking taylor expansion of PI in n 0.554 * [backup-simplify]: Simplify PI into PI 0.554 * [backup-simplify]: Simplify (log PI) into (log PI) 0.555 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.556 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.556 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.557 * [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) 0.557 * [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)) 0.558 * [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))) 0.559 * [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) 0.559 * [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 0.559 * [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 0.559 * [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 0.559 * [taylor]: Taking taylor expansion of +nan.0 in n 0.559 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.559 * [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 0.559 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.559 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.559 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.559 * [taylor]: Taking taylor expansion of 0.5 in n 0.559 * [backup-simplify]: Simplify 0.5 into 0.5 0.559 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.559 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.559 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.559 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.560 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.560 * [taylor]: Taking taylor expansion of 1.0 in n 0.560 * [backup-simplify]: Simplify 1.0 into 1.0 0.560 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.560 * [taylor]: Taking taylor expansion of 2.0 in n 0.560 * [backup-simplify]: Simplify 2.0 into 2.0 0.560 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.560 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.561 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.561 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.561 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.561 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.561 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.561 * [taylor]: Taking taylor expansion of 1.0 in n 0.561 * [backup-simplify]: Simplify 1.0 into 1.0 0.561 * [taylor]: Taking taylor expansion of (log PI) in n 0.561 * [taylor]: Taking taylor expansion of PI in n 0.561 * [backup-simplify]: Simplify PI into PI 0.562 * [backup-simplify]: Simplify (log PI) into (log PI) 0.562 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.563 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.563 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.563 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.563 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.563 * [taylor]: Taking taylor expansion of 1.0 in n 0.563 * [backup-simplify]: Simplify 1.0 into 1.0 0.563 * [taylor]: Taking taylor expansion of (log n) in n 0.563 * [taylor]: Taking taylor expansion of n in n 0.563 * [backup-simplify]: Simplify 0 into 0 0.563 * [backup-simplify]: Simplify 1 into 1 0.564 * [backup-simplify]: Simplify (log 1) into 0 0.564 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.564 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.564 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.564 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.565 * [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) 0.566 * [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)) 0.567 * [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))) 0.568 * [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) 0.568 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.568 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.568 * [taylor]: Taking taylor expansion of 2.0 in n 0.568 * [backup-simplify]: Simplify 2.0 into 2.0 0.568 * [taylor]: Taking taylor expansion of (* n PI) in n 0.568 * [taylor]: Taking taylor expansion of n in n 0.568 * [backup-simplify]: Simplify 0 into 0 0.568 * [backup-simplify]: Simplify 1 into 1 0.568 * [taylor]: Taking taylor expansion of PI in n 0.568 * [backup-simplify]: Simplify PI into PI 0.568 * [backup-simplify]: Simplify (* 0 PI) into 0 0.568 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.569 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.570 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.571 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.571 * [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 0.571 * [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 0.571 * [taylor]: Taking taylor expansion of +nan.0 in n 0.571 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.571 * [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 0.571 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.571 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.571 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.571 * [taylor]: Taking taylor expansion of 0.5 in n 0.571 * [backup-simplify]: Simplify 0.5 into 0.5 0.571 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.571 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.571 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.571 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.571 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.571 * [taylor]: Taking taylor expansion of 1.0 in n 0.571 * [backup-simplify]: Simplify 1.0 into 1.0 0.571 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.571 * [taylor]: Taking taylor expansion of 2.0 in n 0.571 * [backup-simplify]: Simplify 2.0 into 2.0 0.571 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.572 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.576 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.576 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.577 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.577 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.577 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.577 * [taylor]: Taking taylor expansion of 1.0 in n 0.577 * [backup-simplify]: Simplify 1.0 into 1.0 0.577 * [taylor]: Taking taylor expansion of (log PI) in n 0.577 * [taylor]: Taking taylor expansion of PI in n 0.577 * [backup-simplify]: Simplify PI into PI 0.577 * [backup-simplify]: Simplify (log PI) into (log PI) 0.577 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.578 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.578 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.578 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.578 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.579 * [taylor]: Taking taylor expansion of 1.0 in n 0.579 * [backup-simplify]: Simplify 1.0 into 1.0 0.579 * [taylor]: Taking taylor expansion of (log n) in n 0.579 * [taylor]: Taking taylor expansion of n in n 0.579 * [backup-simplify]: Simplify 0 into 0 0.579 * [backup-simplify]: Simplify 1 into 1 0.579 * [backup-simplify]: Simplify (log 1) into 0 0.579 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.579 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.579 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.580 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.580 * [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) 0.581 * [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)) 0.582 * [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))) 0.583 * [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) 0.583 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 0.583 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.583 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.583 * [taylor]: Taking taylor expansion of 2.0 in n 0.583 * [backup-simplify]: Simplify 2.0 into 2.0 0.583 * [taylor]: Taking taylor expansion of (* n PI) in n 0.583 * [taylor]: Taking taylor expansion of n in n 0.583 * [backup-simplify]: Simplify 0 into 0 0.583 * [backup-simplify]: Simplify 1 into 1 0.583 * [taylor]: Taking taylor expansion of PI in n 0.583 * [backup-simplify]: Simplify PI into PI 0.583 * [backup-simplify]: Simplify (* 0 PI) into 0 0.583 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.585 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.585 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.586 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.587 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.588 * [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)) 0.589 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.590 * [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)) 0.592 * [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))) 0.592 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.593 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.595 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 0.596 * [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)) 0.598 * [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))) 0.599 * [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)))))))) 0.606 * [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)))))))))))) 0.614 * [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)))))))))))) 0.622 * [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)))))))))))))) 0.632 * [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)))))))))))))) 0.641 * [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)))))))))))))) 0.656 * [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)))))))))))))))))))))) 0.656 * [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)))))) 0.656 * [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 0.656 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 0.656 * [taylor]: Taking taylor expansion of 1.0 in n 0.656 * [backup-simplify]: Simplify 1.0 into 1.0 0.656 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 0.656 * [taylor]: Taking taylor expansion of (sqrt k) in n 0.656 * [taylor]: Taking taylor expansion of k in n 0.656 * [backup-simplify]: Simplify k into k 0.656 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 0.657 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 0.657 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.657 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.657 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.657 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.657 * [taylor]: Taking taylor expansion of 0.5 in n 0.657 * [backup-simplify]: Simplify 0.5 into 0.5 0.657 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.657 * [taylor]: Taking taylor expansion of 1.0 in n 0.657 * [backup-simplify]: Simplify 1.0 into 1.0 0.657 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.657 * [taylor]: Taking taylor expansion of k in n 0.657 * [backup-simplify]: Simplify k into k 0.657 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.657 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.657 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.657 * [taylor]: Taking taylor expansion of 2.0 in n 0.657 * [backup-simplify]: Simplify 2.0 into 2.0 0.657 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.657 * [taylor]: Taking taylor expansion of PI in n 0.657 * [backup-simplify]: Simplify PI into PI 0.657 * [taylor]: Taking taylor expansion of n in n 0.657 * [backup-simplify]: Simplify 0 into 0 0.657 * [backup-simplify]: Simplify 1 into 1 0.657 * [backup-simplify]: Simplify (/ PI 1) into PI 0.658 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.658 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.658 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.658 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.658 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.659 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.660 * [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)))) 0.661 * [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))))) 0.661 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.661 * [taylor]: Taking taylor expansion of 1.0 in k 0.661 * [backup-simplify]: Simplify 1.0 into 1.0 0.661 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.661 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.661 * [taylor]: Taking taylor expansion of k in k 0.661 * [backup-simplify]: Simplify 0 into 0 0.661 * [backup-simplify]: Simplify 1 into 1 0.661 * [backup-simplify]: Simplify (sqrt 0) into 0 0.662 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.662 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.662 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.662 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.662 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.662 * [taylor]: Taking taylor expansion of 0.5 in k 0.662 * [backup-simplify]: Simplify 0.5 into 0.5 0.662 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.662 * [taylor]: Taking taylor expansion of 1.0 in k 0.662 * [backup-simplify]: Simplify 1.0 into 1.0 0.662 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.662 * [taylor]: Taking taylor expansion of k in k 0.662 * [backup-simplify]: Simplify 0 into 0 0.662 * [backup-simplify]: Simplify 1 into 1 0.662 * [backup-simplify]: Simplify (/ 1 1) into 1 0.662 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.662 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.662 * [taylor]: Taking taylor expansion of 2.0 in k 0.662 * [backup-simplify]: Simplify 2.0 into 2.0 0.662 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.662 * [taylor]: Taking taylor expansion of PI in k 0.662 * [backup-simplify]: Simplify PI into PI 0.662 * [taylor]: Taking taylor expansion of n in k 0.662 * [backup-simplify]: Simplify n into n 0.662 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.663 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.663 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.666 * [backup-simplify]: Simplify (- 1) into -1 0.666 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.666 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.667 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.667 * [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))))) 0.667 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.667 * [taylor]: Taking taylor expansion of 1.0 in k 0.667 * [backup-simplify]: Simplify 1.0 into 1.0 0.667 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.667 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.667 * [taylor]: Taking taylor expansion of k in k 0.667 * [backup-simplify]: Simplify 0 into 0 0.667 * [backup-simplify]: Simplify 1 into 1 0.667 * [backup-simplify]: Simplify (sqrt 0) into 0 0.668 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.668 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.668 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.668 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.668 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.668 * [taylor]: Taking taylor expansion of 0.5 in k 0.668 * [backup-simplify]: Simplify 0.5 into 0.5 0.668 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.668 * [taylor]: Taking taylor expansion of 1.0 in k 0.668 * [backup-simplify]: Simplify 1.0 into 1.0 0.668 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.668 * [taylor]: Taking taylor expansion of k in k 0.668 * [backup-simplify]: Simplify 0 into 0 0.668 * [backup-simplify]: Simplify 1 into 1 0.668 * [backup-simplify]: Simplify (/ 1 1) into 1 0.668 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.668 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.668 * [taylor]: Taking taylor expansion of 2.0 in k 0.668 * [backup-simplify]: Simplify 2.0 into 2.0 0.668 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.668 * [taylor]: Taking taylor expansion of PI in k 0.668 * [backup-simplify]: Simplify PI into PI 0.668 * [taylor]: Taking taylor expansion of n in k 0.668 * [backup-simplify]: Simplify n into n 0.669 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.669 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.669 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.669 * [backup-simplify]: Simplify (- 1) into -1 0.669 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.669 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.669 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.670 * [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))))) 0.670 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 0.670 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.670 * [taylor]: Taking taylor expansion of 0 in n 0.670 * [backup-simplify]: Simplify 0 into 0 0.670 * [backup-simplify]: Simplify 0 into 0 0.671 * [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))))))) 0.671 * [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))))))) 0.671 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.671 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.671 * [taylor]: Taking taylor expansion of +nan.0 in n 0.671 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.671 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.671 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.671 * [taylor]: Taking taylor expansion of 0.5 in n 0.671 * [backup-simplify]: Simplify 0.5 into 0.5 0.671 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.671 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.671 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.671 * [taylor]: Taking taylor expansion of 2.0 in n 0.671 * [backup-simplify]: Simplify 2.0 into 2.0 0.671 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.671 * [taylor]: Taking taylor expansion of PI in n 0.671 * [backup-simplify]: Simplify PI into PI 0.671 * [taylor]: Taking taylor expansion of n in n 0.671 * [backup-simplify]: Simplify 0 into 0 0.671 * [backup-simplify]: Simplify 1 into 1 0.672 * [backup-simplify]: Simplify (/ PI 1) into PI 0.672 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.672 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.672 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.673 * [taylor]: Taking taylor expansion of 1.0 in n 0.673 * [backup-simplify]: Simplify 1.0 into 1.0 0.673 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.673 * [taylor]: Taking taylor expansion of k in n 0.673 * [backup-simplify]: Simplify k into k 0.673 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.673 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.674 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.674 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.674 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.675 * [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)))) 0.676 * [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))))) 0.676 * [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)))))) 0.677 * [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))))))) 0.678 * [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))))))) 0.678 * [backup-simplify]: Simplify 0 into 0 0.680 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.680 * [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))))))) 0.681 * [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))))))) 0.681 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.681 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.681 * [taylor]: Taking taylor expansion of +nan.0 in n 0.681 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.681 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.681 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.681 * [taylor]: Taking taylor expansion of 0.5 in n 0.681 * [backup-simplify]: Simplify 0.5 into 0.5 0.681 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.681 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.681 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.681 * [taylor]: Taking taylor expansion of 2.0 in n 0.681 * [backup-simplify]: Simplify 2.0 into 2.0 0.681 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.681 * [taylor]: Taking taylor expansion of PI in n 0.681 * [backup-simplify]: Simplify PI into PI 0.681 * [taylor]: Taking taylor expansion of n in n 0.681 * [backup-simplify]: Simplify 0 into 0 0.681 * [backup-simplify]: Simplify 1 into 1 0.681 * [backup-simplify]: Simplify (/ PI 1) into PI 0.682 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.682 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.682 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.682 * [taylor]: Taking taylor expansion of 1.0 in n 0.682 * [backup-simplify]: Simplify 1.0 into 1.0 0.682 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.683 * [taylor]: Taking taylor expansion of k in n 0.683 * [backup-simplify]: Simplify k into k 0.683 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.684 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.684 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.684 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.684 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.685 * [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)))) 0.686 * [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))))) 0.687 * [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)))))) 0.687 * [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))))))) 0.688 * [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))))))) 0.689 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.689 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.689 * [backup-simplify]: Simplify (- 0) into 0 0.690 * [backup-simplify]: Simplify (+ 0 0) into 0 0.690 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.691 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.692 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.693 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 0.694 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 0.695 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.696 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 0.696 * [backup-simplify]: Simplify (- 0) into 0 0.696 * [backup-simplify]: Simplify 0 into 0 0.696 * [backup-simplify]: Simplify 0 into 0 0.698 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.699 * [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))))))) 0.700 * [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))))))) 0.700 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.700 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.700 * [taylor]: Taking taylor expansion of +nan.0 in n 0.700 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.700 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.700 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.700 * [taylor]: Taking taylor expansion of 0.5 in n 0.700 * [backup-simplify]: Simplify 0.5 into 0.5 0.700 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.700 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.700 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.700 * [taylor]: Taking taylor expansion of 2.0 in n 0.700 * [backup-simplify]: Simplify 2.0 into 2.0 0.700 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.700 * [taylor]: Taking taylor expansion of PI in n 0.700 * [backup-simplify]: Simplify PI into PI 0.700 * [taylor]: Taking taylor expansion of n in n 0.700 * [backup-simplify]: Simplify 0 into 0 0.700 * [backup-simplify]: Simplify 1 into 1 0.700 * [backup-simplify]: Simplify (/ PI 1) into PI 0.701 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.701 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.701 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.701 * [taylor]: Taking taylor expansion of 1.0 in n 0.701 * [backup-simplify]: Simplify 1.0 into 1.0 0.701 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.701 * [taylor]: Taking taylor expansion of k in n 0.702 * [backup-simplify]: Simplify k into k 0.702 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.702 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.702 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.703 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.703 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 0.704 * [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)))) 0.705 * [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))))) 0.705 * [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)))))) 0.706 * [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))))))) 0.707 * [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))))))) 0.710 * [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)))))))) 0.710 * [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)))) 0.710 * [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 0.710 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 0.710 * [taylor]: Taking taylor expansion of 1.0 in n 0.710 * [backup-simplify]: Simplify 1.0 into 1.0 0.710 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 0.710 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.710 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.710 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.710 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.710 * [taylor]: Taking taylor expansion of 0.5 in n 0.710 * [backup-simplify]: Simplify 0.5 into 0.5 0.710 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.710 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.710 * [taylor]: Taking taylor expansion of k in n 0.710 * [backup-simplify]: Simplify k into k 0.710 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.710 * [taylor]: Taking taylor expansion of 1.0 in n 0.710 * [backup-simplify]: Simplify 1.0 into 1.0 0.710 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.711 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.711 * [taylor]: Taking taylor expansion of -2.0 in n 0.711 * [backup-simplify]: Simplify -2.0 into -2.0 0.711 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.711 * [taylor]: Taking taylor expansion of PI in n 0.711 * [backup-simplify]: Simplify PI into PI 0.711 * [taylor]: Taking taylor expansion of n in n 0.711 * [backup-simplify]: Simplify 0 into 0 0.711 * [backup-simplify]: Simplify 1 into 1 0.711 * [backup-simplify]: Simplify (/ PI 1) into PI 0.711 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.712 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.712 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.712 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.713 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.714 * [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)))) 0.714 * [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))))) 0.714 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 0.714 * [taylor]: Taking taylor expansion of (/ -1 k) in n 0.714 * [taylor]: Taking taylor expansion of -1 in n 0.714 * [backup-simplify]: Simplify -1 into -1 0.714 * [taylor]: Taking taylor expansion of k in n 0.714 * [backup-simplify]: Simplify k into k 0.714 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 0.714 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 0.715 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 0.715 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 0.715 * [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))) 0.715 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.715 * [taylor]: Taking taylor expansion of 1.0 in k 0.715 * [backup-simplify]: Simplify 1.0 into 1.0 0.715 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.715 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.716 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.716 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.716 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.716 * [taylor]: Taking taylor expansion of 0.5 in k 0.716 * [backup-simplify]: Simplify 0.5 into 0.5 0.716 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.716 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.716 * [taylor]: Taking taylor expansion of k in k 0.716 * [backup-simplify]: Simplify 0 into 0 0.716 * [backup-simplify]: Simplify 1 into 1 0.716 * [backup-simplify]: Simplify (/ 1 1) into 1 0.716 * [taylor]: Taking taylor expansion of 1.0 in k 0.716 * [backup-simplify]: Simplify 1.0 into 1.0 0.716 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.716 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.716 * [taylor]: Taking taylor expansion of -2.0 in k 0.716 * [backup-simplify]: Simplify -2.0 into -2.0 0.716 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.716 * [taylor]: Taking taylor expansion of PI in k 0.716 * [backup-simplify]: Simplify PI into PI 0.716 * [taylor]: Taking taylor expansion of n in k 0.716 * [backup-simplify]: Simplify n into n 0.716 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.716 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.716 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.716 * [backup-simplify]: Simplify (+ 1 0) into 1 0.717 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.717 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.717 * [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)))))) 0.717 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.717 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.717 * [taylor]: Taking taylor expansion of -1 in k 0.717 * [backup-simplify]: Simplify -1 into -1 0.717 * [taylor]: Taking taylor expansion of k in k 0.717 * [backup-simplify]: Simplify 0 into 0 0.717 * [backup-simplify]: Simplify 1 into 1 0.717 * [backup-simplify]: Simplify (/ -1 1) into -1 0.718 * [backup-simplify]: Simplify (sqrt 0) into 0 0.718 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.718 * [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))))))) 0.718 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.719 * [taylor]: Taking taylor expansion of 1.0 in k 0.719 * [backup-simplify]: Simplify 1.0 into 1.0 0.719 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.719 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.719 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.719 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.719 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.719 * [taylor]: Taking taylor expansion of 0.5 in k 0.719 * [backup-simplify]: Simplify 0.5 into 0.5 0.719 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.719 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.719 * [taylor]: Taking taylor expansion of k in k 0.719 * [backup-simplify]: Simplify 0 into 0 0.719 * [backup-simplify]: Simplify 1 into 1 0.719 * [backup-simplify]: Simplify (/ 1 1) into 1 0.719 * [taylor]: Taking taylor expansion of 1.0 in k 0.719 * [backup-simplify]: Simplify 1.0 into 1.0 0.719 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.719 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.719 * [taylor]: Taking taylor expansion of -2.0 in k 0.719 * [backup-simplify]: Simplify -2.0 into -2.0 0.719 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.719 * [taylor]: Taking taylor expansion of PI in k 0.719 * [backup-simplify]: Simplify PI into PI 0.719 * [taylor]: Taking taylor expansion of n in k 0.719 * [backup-simplify]: Simplify n into n 0.719 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.719 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.719 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.720 * [backup-simplify]: Simplify (+ 1 0) into 1 0.720 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.720 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.720 * [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)))))) 0.720 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.720 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.720 * [taylor]: Taking taylor expansion of -1 in k 0.720 * [backup-simplify]: Simplify -1 into -1 0.720 * [taylor]: Taking taylor expansion of k in k 0.720 * [backup-simplify]: Simplify 0 into 0 0.720 * [backup-simplify]: Simplify 1 into 1 0.720 * [backup-simplify]: Simplify (/ -1 1) into -1 0.721 * [backup-simplify]: Simplify (sqrt 0) into 0 0.721 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.722 * [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))))))) 0.722 * [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))))))) 0.722 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.722 * [taylor]: Taking taylor expansion of +nan.0 in n 0.722 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.722 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.722 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.722 * [taylor]: Taking taylor expansion of 0.5 in n 0.722 * [backup-simplify]: Simplify 0.5 into 0.5 0.722 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.722 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.722 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.722 * [taylor]: Taking taylor expansion of k in n 0.722 * [backup-simplify]: Simplify k into k 0.722 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.722 * [taylor]: Taking taylor expansion of 1.0 in n 0.722 * [backup-simplify]: Simplify 1.0 into 1.0 0.722 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.722 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.722 * [taylor]: Taking taylor expansion of -2.0 in n 0.722 * [backup-simplify]: Simplify -2.0 into -2.0 0.722 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.722 * [taylor]: Taking taylor expansion of PI in n 0.722 * [backup-simplify]: Simplify PI into PI 0.722 * [taylor]: Taking taylor expansion of n in n 0.722 * [backup-simplify]: Simplify 0 into 0 0.722 * [backup-simplify]: Simplify 1 into 1 0.722 * [backup-simplify]: Simplify (/ PI 1) into PI 0.723 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.723 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.723 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.724 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.725 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.726 * [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)))) 0.726 * [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))))) 0.727 * [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)))))) 0.728 * [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)))))) 0.728 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 0.730 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.731 * [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)))))))) 0.731 * [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)))))))) 0.731 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.731 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.731 * [taylor]: Taking taylor expansion of +nan.0 in n 0.731 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.731 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.731 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.731 * [taylor]: Taking taylor expansion of 0.5 in n 0.731 * [backup-simplify]: Simplify 0.5 into 0.5 0.731 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.731 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.731 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.731 * [taylor]: Taking taylor expansion of k in n 0.731 * [backup-simplify]: Simplify k into k 0.731 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.731 * [taylor]: Taking taylor expansion of 1.0 in n 0.731 * [backup-simplify]: Simplify 1.0 into 1.0 0.731 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.731 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.731 * [taylor]: Taking taylor expansion of -2.0 in n 0.731 * [backup-simplify]: Simplify -2.0 into -2.0 0.731 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.731 * [taylor]: Taking taylor expansion of PI in n 0.732 * [backup-simplify]: Simplify PI into PI 0.732 * [taylor]: Taking taylor expansion of n in n 0.732 * [backup-simplify]: Simplify 0 into 0 0.732 * [backup-simplify]: Simplify 1 into 1 0.732 * [backup-simplify]: Simplify (/ PI 1) into PI 0.732 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.733 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.733 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.734 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.735 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.735 * [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)))) 0.736 * [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))))) 0.737 * [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)))))) 0.737 * [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))))))) 0.738 * [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))))))) 0.739 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.739 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.740 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 0.740 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.740 * [backup-simplify]: Simplify (+ 0 0) into 0 0.741 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.742 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 0.743 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 0.744 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.745 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 0.745 * [backup-simplify]: Simplify 0 into 0 0.746 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.748 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.749 * [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)))))))) 0.750 * [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)))))))) 0.750 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.750 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.750 * [taylor]: Taking taylor expansion of +nan.0 in n 0.750 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.750 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.750 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.750 * [taylor]: Taking taylor expansion of 0.5 in n 0.750 * [backup-simplify]: Simplify 0.5 into 0.5 0.750 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.750 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.750 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.750 * [taylor]: Taking taylor expansion of k in n 0.750 * [backup-simplify]: Simplify k into k 0.750 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.750 * [taylor]: Taking taylor expansion of 1.0 in n 0.750 * [backup-simplify]: Simplify 1.0 into 1.0 0.750 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.750 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.750 * [taylor]: Taking taylor expansion of -2.0 in n 0.750 * [backup-simplify]: Simplify -2.0 into -2.0 0.750 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.750 * [taylor]: Taking taylor expansion of PI in n 0.750 * [backup-simplify]: Simplify PI into PI 0.750 * [taylor]: Taking taylor expansion of n in n 0.750 * [backup-simplify]: Simplify 0 into 0 0.750 * [backup-simplify]: Simplify 1 into 1 0.751 * [backup-simplify]: Simplify (/ PI 1) into PI 0.751 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.752 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.752 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.752 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.753 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 0.754 * [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)))) 0.755 * [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))))) 0.755 * [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)))))) 0.756 * [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))))))) 0.757 * [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))))))) 0.760 * [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)))))))))))) 0.760 * * * [progress]: simplifying candidates 0.765 * [simplify]: Simplifying: (* (+ (+ (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)) (* (* 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) (- (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 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(log (sqrt h4))) (* (+ (+ (log h0) (log h1)) (log h2)) (/ (- h3 h4) h0))) (+ (- (log h3) (log (sqrt h4))) (* (+ (log (* h0 h1)) (log h2)) (/ (- h3 h4) h0))) (+ (- (log h3) (log (sqrt h4))) (* (log (* (* h0 h1) h2)) (/ (- h3 h4) h0))) (+ (- (log h3) (log (sqrt h4))) (* (log (* (* h0 h1) h2)) (/ (- h3 h4) h0))) (+ (- (log h3) (log (sqrt h4))) (log (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (+ (log (/ h3 (sqrt h4))) (* (+ (+ (log h0) (log h1)) (log h2)) (/ (- h3 h4) h0))) (+ (log (/ h3 (sqrt h4))) (* (+ (log (* h0 h1)) (log h2)) (/ (- h3 h4) h0))) (+ (log (/ h3 (sqrt h4))) (* (log (* (* h0 h1) h2)) (/ (- h3 h4) h0))) (+ (log (/ h3 (sqrt h4))) (* (log (* (* h0 h1) h2)) (/ (- h3 h4) h0))) (+ (log (/ h3 (sqrt h4))) (log (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (log (* (/ h3 (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (exp (* (/ h3 (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (* (/ (* (* h3 h3) h3) (* (* (sqrt h4) (sqrt h4)) (sqrt h4))) (* (* (pow (* (* h0 h1) h2) (/ (- h3 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h4))) (sqrt (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (* (sqrt (/ h3 (sqrt h4))) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (sqrt (/ h3 (sqrt h4))) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (/ (sqrt h3) (sqrt (sqrt h4))) (sqrt (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (* (/ (sqrt h3) (sqrt (sqrt h4))) (sqrt (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (* (/ (sqrt h3) (sqrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (/ (sqrt h3) (sqrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (/ (sqrt h3) (sqrt (sqrt h4))) (sqrt (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (* (/ (sqrt h3) (sqrt (sqrt h4))) (sqrt (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (* (/ (sqrt h3) (sqrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (/ (sqrt h3) (sqrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (/ h3 (sqrt h4)) (pow (* h0 h1) (/ (- h3 h4) h0))) (* (/ h3 (sqrt h4)) (* (cbrt (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (cbrt (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))))) (* (/ h3 (sqrt h4)) (sqrt (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)))) (* (/ h3 (sqrt h4)) 1) (* (/ h3 (sqrt h4)) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (cbrt (/ h3 (sqrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (sqrt (/ h3 (sqrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ (cbrt h3) (cbrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ (cbrt h3) (sqrt (cbrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ (cbrt h3) (sqrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ (cbrt h3) (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ (cbrt h3) (sqrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ (cbrt h3) (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ (sqrt h3) (cbrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ (sqrt h3) (sqrt (cbrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ (sqrt h3) (sqrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ (sqrt h3) (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ (sqrt h3) (sqrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ (sqrt h3) (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ h3 (cbrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ h3 (sqrt (cbrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ h3 (sqrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ h3 (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ h3 (sqrt (sqrt h4))) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ h3 (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ h3 (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ 1 (sqrt h4)) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (* (/ h3 (sqrt h4)) (pow (* (* h0 h1) h2) (/ h3 h0))) (* h3 (pow (* (* h0 h1) h2) (/ (- h3 h4) h0))) (- (+ (* h5 (* (pow h4 2) (* (pow (log (* h0 h1)) 2) (exp (* h6 (+ (log (* h0 h1)) (log h2))))))) (+ (* h5 (* (pow h4 2) (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (pow (log h2) 2)))) (+ (* h7 (* (pow h4 2) (* (log (* h0 h1)) (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (log h2))))) (exp (* h6 (+ (log (* h0 h1)) (log h2))))))) (+ (* h6 (* h4 (* (log (* h0 h1)) (exp (* h6 (+ (log (* h0 h1)) (log h2))))))) (* h6 (* h4 (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (log h2)))))) (exp (* h6 (* (- (log (* h0 h1)) (log (/ 1 h2))) (- h3 h4)))) (exp (* h6 (* (- h3 h4) (- (log (* h8 h1)) (log (/ -1 h2)))))) (* h0 (* h2 h1)) (* h0 (* h2 h1)) (* h0 (* h2 h1)) (- (+ (* h9 h4) (- (+ (* h9 (pow h4 2)) (- h9))))) (- (+ (* h9 (/ 1 (pow h4 2))) (- (+ (* h9 (/ 1 h4)) (- (* h9 (/ 1 (pow h4 3)))))))) (- (+ (* h9 (/ 1 (pow h4 2))) (- (+ (* h9 (/ 1 h4)) (- h9))))) (- (+ (* h9 (* (* (pow h4 2) (pow (log (* h0 h1)) 2)) (pow (* (pow h0 h3) (* (pow h2 h3) (pow h1 h3))) h6))) (- (+ (* h9 (* (* (pow h4 2) (log (* h0 h1))) (pow (* (pow h1 h3) (* (pow h2 h3) (pow h0 h3))) h6))) (- (+ (* h9 (* (* (pow h4 2) (* (log (* h0 h1)) (log h2))) (pow (* (pow h1 h3) (* (pow h0 h3) (pow h2 h3))) h6))) (- (+ (* h9 (* (* (pow h4 2) (log h2)) (pow (* (pow h0 h3) (* (pow h1 h3) (pow h2 h3))) h6))) (- (+ (* h9 (* (* h4 (log (* h0 h1))) (pow (* (pow h0 h3) (* (pow h2 h3) (pow h1 h3))) h6))) (- (+ (* h9 (* (* (pow h4 2) (pow (log h2) 2)) (pow (* (pow h0 h3) (* (pow h1 h3) (pow h2 h3))) h6))) (- (+ (* h9 (* (* h4 (log h2)) (pow (* (pow h0 h3) (* (pow h1 h3) (pow h2 h3))) h6))) (- (+ (* h9 (pow (* (pow h0 h3) (* (pow h2 h3) (pow h1 h3))) h6)) (- (+ (* h9 (* (pow h4 2) (pow (* (pow h1 h3) (* (pow h2 h3) (pow h0 h3))) h6))) (- (* h9 (* h4 (pow (* (pow h0 h3) (* (pow h2 h3) (pow h1 h3))) h6)))))))))))))))))))))) (- (+ (* h9 (/ (exp (* h6 (* (- (log (* h0 h1)) (log (/ 1 h2))) (- h3 h4)))) (pow h4 3))) (- (+ (* h9 (/ (exp (* h6 (* (- (log (* h0 h1)) (log (/ 1 h2))) (- h3 h4)))) h4)) (- (* h9 (/ (exp (* h6 (* (- (log (* h0 h1)) (log (/ 1 h2))) (- h3 h4)))) (pow h4 2)))))))) (- (+ (* h9 (/ (exp (* h6 (* (- h3 h4) (- (log (* h8 h1)) (log (/ -1 h2)))))) h4)) (- (+ (* h9 (/ (exp (* h6 (* (- h3 h4) (- (log (* h8 h1)) (log (/ -1 h2)))))) (pow h4 2))) (- (* h9 (exp (* h6 (* (- h3 h4) (- (log (* h8 h1)) (log (/ -1 h2)))))))))))) 0.775 * * [simplify]: iteration 0 : 950 enodes (cost 1461 ) 0.791 * * [simplify]: iteration 1 : 3924 enodes (cost 1358 ) 0.852 * * [simplify]: iteration 2 : 5002 enodes (cost 1344 ) 0.858 * * * [progress]: adding candidates to table 1.244 * * [progress]: iteration 2 / 4 1.244 * * * [progress]: picking best candidate 1.265 * * * * [pick]: Picked # 1.265 * * * [progress]: localizing error 1.281 * * * [progress]: generating rewritten candidates 1.281 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 1.309 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 1.333 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2 1) 1.350 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1) 1.379 * * * [progress]: generating series expansions 1.379 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 1.380 * [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))) 1.380 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 1.380 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 1.380 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.380 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.380 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 1.380 * [taylor]: Taking taylor expansion of 0.25 in k 1.380 * [backup-simplify]: Simplify 0.25 into 0.25 1.380 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.380 * [taylor]: Taking taylor expansion of 1.0 in k 1.380 * [backup-simplify]: Simplify 1.0 into 1.0 1.380 * [taylor]: Taking taylor expansion of k in k 1.380 * [backup-simplify]: Simplify 0 into 0 1.380 * [backup-simplify]: Simplify 1 into 1 1.380 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.380 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.380 * [taylor]: Taking taylor expansion of 2.0 in k 1.380 * [backup-simplify]: Simplify 2.0 into 2.0 1.380 * [taylor]: Taking taylor expansion of (* n PI) in k 1.380 * [taylor]: Taking taylor expansion of n in k 1.380 * [backup-simplify]: Simplify n into n 1.380 * [taylor]: Taking taylor expansion of PI in k 1.380 * [backup-simplify]: Simplify PI into PI 1.380 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.380 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.380 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.381 * [backup-simplify]: Simplify (- 0) into 0 1.381 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.381 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 1.381 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 1.381 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 1.381 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 1.381 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.381 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.381 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 1.381 * [taylor]: Taking taylor expansion of 0.25 in n 1.382 * [backup-simplify]: Simplify 0.25 into 0.25 1.382 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.382 * [taylor]: Taking taylor expansion of 1.0 in n 1.382 * [backup-simplify]: Simplify 1.0 into 1.0 1.382 * [taylor]: Taking taylor expansion of k in n 1.382 * [backup-simplify]: Simplify k into k 1.382 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.382 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.382 * [taylor]: Taking taylor expansion of 2.0 in n 1.382 * [backup-simplify]: Simplify 2.0 into 2.0 1.382 * [taylor]: Taking taylor expansion of (* n PI) in n 1.382 * [taylor]: Taking taylor expansion of n in n 1.382 * [backup-simplify]: Simplify 0 into 0 1.382 * [backup-simplify]: Simplify 1 into 1 1.382 * [taylor]: Taking taylor expansion of PI in n 1.382 * [backup-simplify]: Simplify PI into PI 1.382 * [backup-simplify]: Simplify (* 0 PI) into 0 1.382 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.383 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.384 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.385 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.385 * [backup-simplify]: Simplify (- k) into (- k) 1.385 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.385 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 1.386 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.386 * [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)))) 1.387 * [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))))) 1.387 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 1.387 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.387 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.387 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 1.387 * [taylor]: Taking taylor expansion of 0.25 in n 1.387 * [backup-simplify]: Simplify 0.25 into 0.25 1.387 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.387 * [taylor]: Taking taylor expansion of 1.0 in n 1.387 * [backup-simplify]: Simplify 1.0 into 1.0 1.387 * [taylor]: Taking taylor expansion of k in n 1.387 * [backup-simplify]: Simplify k into k 1.387 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.387 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.387 * [taylor]: Taking taylor expansion of 2.0 in n 1.387 * [backup-simplify]: Simplify 2.0 into 2.0 1.387 * [taylor]: Taking taylor expansion of (* n PI) in n 1.387 * [taylor]: Taking taylor expansion of n in n 1.387 * [backup-simplify]: Simplify 0 into 0 1.387 * [backup-simplify]: Simplify 1 into 1 1.387 * [taylor]: Taking taylor expansion of PI in n 1.387 * [backup-simplify]: Simplify PI into PI 1.388 * [backup-simplify]: Simplify (* 0 PI) into 0 1.388 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.389 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.390 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.390 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.390 * [backup-simplify]: Simplify (- k) into (- k) 1.390 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.390 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 1.391 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.392 * [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)))) 1.393 * [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))))) 1.393 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.393 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.393 * [taylor]: Taking taylor expansion of 0.25 in k 1.393 * [backup-simplify]: Simplify 0.25 into 0.25 1.393 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.393 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.393 * [taylor]: Taking taylor expansion of 1.0 in k 1.393 * [backup-simplify]: Simplify 1.0 into 1.0 1.393 * [taylor]: Taking taylor expansion of k in k 1.393 * [backup-simplify]: Simplify 0 into 0 1.393 * [backup-simplify]: Simplify 1 into 1 1.393 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.393 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.393 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.393 * [taylor]: Taking taylor expansion of 2.0 in k 1.393 * [backup-simplify]: Simplify 2.0 into 2.0 1.393 * [taylor]: Taking taylor expansion of PI in k 1.393 * [backup-simplify]: Simplify PI into PI 1.393 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.394 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.394 * [taylor]: Taking taylor expansion of (log n) in k 1.394 * [taylor]: Taking taylor expansion of n in k 1.394 * [backup-simplify]: Simplify n into n 1.394 * [backup-simplify]: Simplify (log n) into (log n) 1.394 * [backup-simplify]: Simplify (- 0) into 0 1.395 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.395 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 1.396 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 1.396 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 1.397 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 1.398 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 1.398 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.399 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.400 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.400 * [backup-simplify]: Simplify (- 0) into 0 1.400 * [backup-simplify]: Simplify (+ 0 0) into 0 1.401 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 1.401 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.402 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.403 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.403 * [taylor]: Taking taylor expansion of 0 in k 1.403 * [backup-simplify]: Simplify 0 into 0 1.403 * [backup-simplify]: Simplify 0 into 0 1.404 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.405 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.405 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.406 * [backup-simplify]: Simplify (+ 0 0) into 0 1.406 * [backup-simplify]: Simplify (- 1) into -1 1.406 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.407 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.408 * [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)))) 1.410 * [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)))))) 1.412 * [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)))))) 1.413 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.413 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.415 * [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 1.415 * [backup-simplify]: Simplify (- 0) into 0 1.416 * [backup-simplify]: Simplify (+ 0 0) into 0 1.416 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 1.417 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.418 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.419 * [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 1.419 * [taylor]: Taking taylor expansion of 0 in k 1.419 * [backup-simplify]: Simplify 0 into 0 1.419 * [backup-simplify]: Simplify 0 into 0 1.419 * [backup-simplify]: Simplify 0 into 0 1.420 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.421 * [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 1.422 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.423 * [backup-simplify]: Simplify (+ 0 0) into 0 1.423 * [backup-simplify]: Simplify (- 0) into 0 1.423 * [backup-simplify]: Simplify (+ 0 0) into 0 1.424 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.426 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.428 * [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))))) 1.431 * [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))))) 1.442 * [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)))))) 1.443 * [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)))) 1.443 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 1.443 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 1.443 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.443 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.443 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 1.443 * [taylor]: Taking taylor expansion of 0.25 in k 1.443 * [backup-simplify]: Simplify 0.25 into 0.25 1.443 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.443 * [taylor]: Taking taylor expansion of 1.0 in k 1.443 * [backup-simplify]: Simplify 1.0 into 1.0 1.443 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.443 * [taylor]: Taking taylor expansion of k in k 1.443 * [backup-simplify]: Simplify 0 into 0 1.443 * [backup-simplify]: Simplify 1 into 1 1.444 * [backup-simplify]: Simplify (/ 1 1) into 1 1.444 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.444 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.444 * [taylor]: Taking taylor expansion of 2.0 in k 1.444 * [backup-simplify]: Simplify 2.0 into 2.0 1.444 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.444 * [taylor]: Taking taylor expansion of PI in k 1.444 * [backup-simplify]: Simplify PI into PI 1.444 * [taylor]: Taking taylor expansion of n in k 1.444 * [backup-simplify]: Simplify n into n 1.444 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.444 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.444 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.444 * [backup-simplify]: Simplify (- 1) into -1 1.444 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.445 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 1.445 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 1.445 * [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))))) 1.445 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 1.445 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.445 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.445 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 1.445 * [taylor]: Taking taylor expansion of 0.25 in n 1.445 * [backup-simplify]: Simplify 0.25 into 0.25 1.445 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.445 * [taylor]: Taking taylor expansion of 1.0 in n 1.445 * [backup-simplify]: Simplify 1.0 into 1.0 1.445 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.445 * [taylor]: Taking taylor expansion of k in n 1.445 * [backup-simplify]: Simplify k into k 1.445 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.445 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.445 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.445 * [taylor]: Taking taylor expansion of 2.0 in n 1.445 * [backup-simplify]: Simplify 2.0 into 2.0 1.445 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.445 * [taylor]: Taking taylor expansion of PI in n 1.445 * [backup-simplify]: Simplify PI into PI 1.445 * [taylor]: Taking taylor expansion of n in n 1.445 * [backup-simplify]: Simplify 0 into 0 1.445 * [backup-simplify]: Simplify 1 into 1 1.445 * [backup-simplify]: Simplify (/ PI 1) into PI 1.446 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.446 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.446 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.446 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.447 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 1.447 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.448 * [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)))) 1.449 * [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))))) 1.449 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 1.449 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.449 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.449 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 1.449 * [taylor]: Taking taylor expansion of 0.25 in n 1.449 * [backup-simplify]: Simplify 0.25 into 0.25 1.449 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.449 * [taylor]: Taking taylor expansion of 1.0 in n 1.449 * [backup-simplify]: Simplify 1.0 into 1.0 1.449 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.449 * [taylor]: Taking taylor expansion of k in n 1.449 * [backup-simplify]: Simplify k into k 1.449 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.449 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.449 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.449 * [taylor]: Taking taylor expansion of 2.0 in n 1.449 * [backup-simplify]: Simplify 2.0 into 2.0 1.449 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.449 * [taylor]: Taking taylor expansion of PI in n 1.449 * [backup-simplify]: Simplify PI into PI 1.449 * [taylor]: Taking taylor expansion of n in n 1.449 * [backup-simplify]: Simplify 0 into 0 1.449 * [backup-simplify]: Simplify 1 into 1 1.449 * [backup-simplify]: Simplify (/ PI 1) into PI 1.450 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.450 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.450 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.450 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.451 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 1.451 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.452 * [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)))) 1.453 * [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))))) 1.453 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.453 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.453 * [taylor]: Taking taylor expansion of 0.25 in k 1.453 * [backup-simplify]: Simplify 0.25 into 0.25 1.453 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.453 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.453 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.453 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.453 * [taylor]: Taking taylor expansion of 2.0 in k 1.453 * [backup-simplify]: Simplify 2.0 into 2.0 1.453 * [taylor]: Taking taylor expansion of PI in k 1.453 * [backup-simplify]: Simplify PI into PI 1.453 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.454 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.454 * [taylor]: Taking taylor expansion of (log n) in k 1.454 * [taylor]: Taking taylor expansion of n in k 1.454 * [backup-simplify]: Simplify n into n 1.454 * [backup-simplify]: Simplify (log n) into (log n) 1.454 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.454 * [taylor]: Taking taylor expansion of 1.0 in k 1.454 * [backup-simplify]: Simplify 1.0 into 1.0 1.454 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.454 * [taylor]: Taking taylor expansion of k in k 1.454 * [backup-simplify]: Simplify 0 into 0 1.454 * [backup-simplify]: Simplify 1 into 1 1.454 * [backup-simplify]: Simplify (/ 1 1) into 1 1.454 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.455 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 1.455 * [backup-simplify]: Simplify (- 1) into -1 1.456 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.456 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 1.457 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 1.458 * [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))))) 1.458 * [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))))) 1.459 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.460 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.460 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.461 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.461 * [backup-simplify]: Simplify (- 0) into 0 1.461 * [backup-simplify]: Simplify (+ 0 0) into 0 1.461 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 1.462 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.463 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 1.464 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.464 * [taylor]: Taking taylor expansion of 0 in k 1.464 * [backup-simplify]: Simplify 0 into 0 1.464 * [backup-simplify]: Simplify 0 into 0 1.464 * [backup-simplify]: Simplify 0 into 0 1.465 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.465 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.467 * [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 1.467 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.467 * [backup-simplify]: Simplify (- 0) into 0 1.467 * [backup-simplify]: Simplify (+ 0 0) into 0 1.468 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 1.469 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.470 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 1.471 * [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 1.471 * [taylor]: Taking taylor expansion of 0 in k 1.471 * [backup-simplify]: Simplify 0 into 0 1.471 * [backup-simplify]: Simplify 0 into 0 1.471 * [backup-simplify]: Simplify 0 into 0 1.471 * [backup-simplify]: Simplify 0 into 0 1.472 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.472 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.475 * [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 1.475 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.476 * [backup-simplify]: Simplify (- 0) into 0 1.476 * [backup-simplify]: Simplify (+ 0 0) into 0 1.477 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 1.477 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.479 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 1.480 * [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 1.480 * [taylor]: Taking taylor expansion of 0 in k 1.480 * [backup-simplify]: Simplify 0 into 0 1.480 * [backup-simplify]: Simplify 0 into 0 1.481 * [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)))) 1.482 * [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))) 1.482 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 1.482 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 1.482 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.482 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.482 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 1.482 * [taylor]: Taking taylor expansion of 0.25 in k 1.482 * [backup-simplify]: Simplify 0.25 into 0.25 1.482 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.482 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.482 * [taylor]: Taking taylor expansion of k in k 1.482 * [backup-simplify]: Simplify 0 into 0 1.482 * [backup-simplify]: Simplify 1 into 1 1.482 * [backup-simplify]: Simplify (/ 1 1) into 1 1.482 * [taylor]: Taking taylor expansion of 1.0 in k 1.482 * [backup-simplify]: Simplify 1.0 into 1.0 1.482 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.482 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.482 * [taylor]: Taking taylor expansion of -2.0 in k 1.482 * [backup-simplify]: Simplify -2.0 into -2.0 1.482 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.482 * [taylor]: Taking taylor expansion of PI in k 1.482 * [backup-simplify]: Simplify PI into PI 1.482 * [taylor]: Taking taylor expansion of n in k 1.482 * [backup-simplify]: Simplify n into n 1.482 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.482 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.482 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.483 * [backup-simplify]: Simplify (+ 1 0) into 1 1.483 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 1.483 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 1.483 * [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)))))) 1.483 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 1.483 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.483 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.483 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 1.483 * [taylor]: Taking taylor expansion of 0.25 in n 1.483 * [backup-simplify]: Simplify 0.25 into 0.25 1.483 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.483 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.483 * [taylor]: Taking taylor expansion of k in n 1.483 * [backup-simplify]: Simplify k into k 1.483 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.483 * [taylor]: Taking taylor expansion of 1.0 in n 1.483 * [backup-simplify]: Simplify 1.0 into 1.0 1.483 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.483 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.483 * [taylor]: Taking taylor expansion of -2.0 in n 1.483 * [backup-simplify]: Simplify -2.0 into -2.0 1.483 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.483 * [taylor]: Taking taylor expansion of PI in n 1.483 * [backup-simplify]: Simplify PI into PI 1.483 * [taylor]: Taking taylor expansion of n in n 1.483 * [backup-simplify]: Simplify 0 into 0 1.483 * [backup-simplify]: Simplify 1 into 1 1.484 * [backup-simplify]: Simplify (/ PI 1) into PI 1.484 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.485 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.485 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.485 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 1.486 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.486 * [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)))) 1.487 * [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))))) 1.487 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 1.487 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.487 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.487 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 1.487 * [taylor]: Taking taylor expansion of 0.25 in n 1.487 * [backup-simplify]: Simplify 0.25 into 0.25 1.487 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.487 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.487 * [taylor]: Taking taylor expansion of k in n 1.487 * [backup-simplify]: Simplify k into k 1.487 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.487 * [taylor]: Taking taylor expansion of 1.0 in n 1.487 * [backup-simplify]: Simplify 1.0 into 1.0 1.487 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.487 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.487 * [taylor]: Taking taylor expansion of -2.0 in n 1.487 * [backup-simplify]: Simplify -2.0 into -2.0 1.487 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.487 * [taylor]: Taking taylor expansion of PI in n 1.487 * [backup-simplify]: Simplify PI into PI 1.487 * [taylor]: Taking taylor expansion of n in n 1.487 * [backup-simplify]: Simplify 0 into 0 1.488 * [backup-simplify]: Simplify 1 into 1 1.488 * [backup-simplify]: Simplify (/ PI 1) into PI 1.488 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.489 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.489 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.489 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 1.490 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.490 * [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)))) 1.491 * [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))))) 1.491 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.491 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.491 * [taylor]: Taking taylor expansion of 0.25 in k 1.491 * [backup-simplify]: Simplify 0.25 into 0.25 1.491 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.491 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.491 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.491 * [taylor]: Taking taylor expansion of k in k 1.491 * [backup-simplify]: Simplify 0 into 0 1.491 * [backup-simplify]: Simplify 1 into 1 1.492 * [backup-simplify]: Simplify (/ 1 1) into 1 1.492 * [taylor]: Taking taylor expansion of 1.0 in k 1.492 * [backup-simplify]: Simplify 1.0 into 1.0 1.492 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.492 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.492 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.492 * [taylor]: Taking taylor expansion of -2.0 in k 1.492 * [backup-simplify]: Simplify -2.0 into -2.0 1.492 * [taylor]: Taking taylor expansion of PI in k 1.492 * [backup-simplify]: Simplify PI into PI 1.492 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.493 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.493 * [taylor]: Taking taylor expansion of (log n) in k 1.493 * [taylor]: Taking taylor expansion of n in k 1.493 * [backup-simplify]: Simplify n into n 1.493 * [backup-simplify]: Simplify (log n) into (log n) 1.493 * [backup-simplify]: Simplify (+ 1 0) into 1 1.493 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.494 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 1.494 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 1.495 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 1.496 * [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))))) 1.497 * [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))))) 1.497 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.497 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.498 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.499 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.499 * [backup-simplify]: Simplify (+ 0 0) into 0 1.499 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 1.500 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.501 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.502 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.502 * [taylor]: Taking taylor expansion of 0 in k 1.502 * [backup-simplify]: Simplify 0 into 0 1.502 * [backup-simplify]: Simplify 0 into 0 1.502 * [backup-simplify]: Simplify 0 into 0 1.503 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.503 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.505 * [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 1.505 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.505 * [backup-simplify]: Simplify (+ 0 0) into 0 1.506 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 1.507 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.508 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 1.509 * [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 1.509 * [taylor]: Taking taylor expansion of 0 in k 1.509 * [backup-simplify]: Simplify 0 into 0 1.509 * [backup-simplify]: Simplify 0 into 0 1.509 * [backup-simplify]: Simplify 0 into 0 1.509 * [backup-simplify]: Simplify 0 into 0 1.510 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.510 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.513 * [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 1.513 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.514 * [backup-simplify]: Simplify (+ 0 0) into 0 1.514 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 1.515 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.516 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 1.518 * [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 1.518 * [taylor]: Taking taylor expansion of 0 in k 1.518 * [backup-simplify]: Simplify 0 into 0 1.518 * [backup-simplify]: Simplify 0 into 0 1.519 * [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)))))) 1.519 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 1.519 * [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))) 1.519 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 1.519 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 1.519 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.519 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.519 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 1.519 * [taylor]: Taking taylor expansion of 0.25 in k 1.520 * [backup-simplify]: Simplify 0.25 into 0.25 1.520 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.520 * [taylor]: Taking taylor expansion of 1.0 in k 1.520 * [backup-simplify]: Simplify 1.0 into 1.0 1.520 * [taylor]: Taking taylor expansion of k in k 1.520 * [backup-simplify]: Simplify 0 into 0 1.520 * [backup-simplify]: Simplify 1 into 1 1.520 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.520 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.520 * [taylor]: Taking taylor expansion of 2.0 in k 1.520 * [backup-simplify]: Simplify 2.0 into 2.0 1.520 * [taylor]: Taking taylor expansion of (* n PI) in k 1.520 * [taylor]: Taking taylor expansion of n in k 1.520 * [backup-simplify]: Simplify n into n 1.520 * [taylor]: Taking taylor expansion of PI in k 1.520 * [backup-simplify]: Simplify PI into PI 1.520 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.520 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.520 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.520 * [backup-simplify]: Simplify (- 0) into 0 1.520 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.521 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 1.521 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 1.521 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 1.521 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 1.521 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.521 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.521 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 1.521 * [taylor]: Taking taylor expansion of 0.25 in n 1.521 * [backup-simplify]: Simplify 0.25 into 0.25 1.521 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.521 * [taylor]: Taking taylor expansion of 1.0 in n 1.521 * [backup-simplify]: Simplify 1.0 into 1.0 1.521 * [taylor]: Taking taylor expansion of k in n 1.521 * [backup-simplify]: Simplify k into k 1.521 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.521 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.521 * [taylor]: Taking taylor expansion of 2.0 in n 1.521 * [backup-simplify]: Simplify 2.0 into 2.0 1.521 * [taylor]: Taking taylor expansion of (* n PI) in n 1.521 * [taylor]: Taking taylor expansion of n in n 1.521 * [backup-simplify]: Simplify 0 into 0 1.521 * [backup-simplify]: Simplify 1 into 1 1.521 * [taylor]: Taking taylor expansion of PI in n 1.521 * [backup-simplify]: Simplify PI into PI 1.522 * [backup-simplify]: Simplify (* 0 PI) into 0 1.522 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.523 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.524 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.524 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.524 * [backup-simplify]: Simplify (- k) into (- k) 1.524 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.524 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 1.525 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.526 * [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)))) 1.527 * [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))))) 1.527 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 1.527 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.527 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.527 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 1.527 * [taylor]: Taking taylor expansion of 0.25 in n 1.527 * [backup-simplify]: Simplify 0.25 into 0.25 1.527 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.527 * [taylor]: Taking taylor expansion of 1.0 in n 1.527 * [backup-simplify]: Simplify 1.0 into 1.0 1.527 * [taylor]: Taking taylor expansion of k in n 1.527 * [backup-simplify]: Simplify k into k 1.527 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.527 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.527 * [taylor]: Taking taylor expansion of 2.0 in n 1.527 * [backup-simplify]: Simplify 2.0 into 2.0 1.527 * [taylor]: Taking taylor expansion of (* n PI) in n 1.527 * [taylor]: Taking taylor expansion of n in n 1.527 * [backup-simplify]: Simplify 0 into 0 1.527 * [backup-simplify]: Simplify 1 into 1 1.527 * [taylor]: Taking taylor expansion of PI in n 1.527 * [backup-simplify]: Simplify PI into PI 1.528 * [backup-simplify]: Simplify (* 0 PI) into 0 1.528 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.529 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.530 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.531 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.531 * [backup-simplify]: Simplify (- k) into (- k) 1.531 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.531 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 1.532 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.537 * [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)))) 1.538 * [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))))) 1.538 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.538 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.538 * [taylor]: Taking taylor expansion of 0.25 in k 1.538 * [backup-simplify]: Simplify 0.25 into 0.25 1.538 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.538 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.538 * [taylor]: Taking taylor expansion of 1.0 in k 1.538 * [backup-simplify]: Simplify 1.0 into 1.0 1.538 * [taylor]: Taking taylor expansion of k in k 1.538 * [backup-simplify]: Simplify 0 into 0 1.538 * [backup-simplify]: Simplify 1 into 1 1.538 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.538 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.538 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.538 * [taylor]: Taking taylor expansion of 2.0 in k 1.539 * [backup-simplify]: Simplify 2.0 into 2.0 1.539 * [taylor]: Taking taylor expansion of PI in k 1.539 * [backup-simplify]: Simplify PI into PI 1.539 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.539 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.539 * [taylor]: Taking taylor expansion of (log n) in k 1.539 * [taylor]: Taking taylor expansion of n in k 1.540 * [backup-simplify]: Simplify n into n 1.540 * [backup-simplify]: Simplify (log n) into (log n) 1.540 * [backup-simplify]: Simplify (- 0) into 0 1.540 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.541 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 1.541 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 1.542 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 1.543 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 1.543 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 1.544 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.544 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.545 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.546 * [backup-simplify]: Simplify (- 0) into 0 1.546 * [backup-simplify]: Simplify (+ 0 0) into 0 1.546 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 1.547 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.548 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.549 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.549 * [taylor]: Taking taylor expansion of 0 in k 1.549 * [backup-simplify]: Simplify 0 into 0 1.549 * [backup-simplify]: Simplify 0 into 0 1.549 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.550 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.551 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.551 * [backup-simplify]: Simplify (+ 0 0) into 0 1.551 * [backup-simplify]: Simplify (- 1) into -1 1.551 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.552 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.553 * [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)))) 1.555 * [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)))))) 1.558 * [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)))))) 1.558 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.559 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.561 * [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 1.561 * [backup-simplify]: Simplify (- 0) into 0 1.561 * [backup-simplify]: Simplify (+ 0 0) into 0 1.561 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 1.562 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.563 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.565 * [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 1.565 * [taylor]: Taking taylor expansion of 0 in k 1.565 * [backup-simplify]: Simplify 0 into 0 1.565 * [backup-simplify]: Simplify 0 into 0 1.565 * [backup-simplify]: Simplify 0 into 0 1.565 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.567 * [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 1.568 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.568 * [backup-simplify]: Simplify (+ 0 0) into 0 1.568 * [backup-simplify]: Simplify (- 0) into 0 1.569 * [backup-simplify]: Simplify (+ 0 0) into 0 1.570 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.571 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.574 * [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))))) 1.577 * [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))))) 1.582 * [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)))))) 1.583 * [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)))) 1.583 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 1.583 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 1.583 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.583 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.583 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 1.583 * [taylor]: Taking taylor expansion of 0.25 in k 1.583 * [backup-simplify]: Simplify 0.25 into 0.25 1.583 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.583 * [taylor]: Taking taylor expansion of 1.0 in k 1.583 * [backup-simplify]: Simplify 1.0 into 1.0 1.583 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.583 * [taylor]: Taking taylor expansion of k in k 1.583 * [backup-simplify]: Simplify 0 into 0 1.583 * [backup-simplify]: Simplify 1 into 1 1.583 * [backup-simplify]: Simplify (/ 1 1) into 1 1.583 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.583 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.583 * [taylor]: Taking taylor expansion of 2.0 in k 1.583 * [backup-simplify]: Simplify 2.0 into 2.0 1.583 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.583 * [taylor]: Taking taylor expansion of PI in k 1.584 * [backup-simplify]: Simplify PI into PI 1.584 * [taylor]: Taking taylor expansion of n in k 1.584 * [backup-simplify]: Simplify n into n 1.584 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.584 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.584 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.584 * [backup-simplify]: Simplify (- 1) into -1 1.584 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.584 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 1.584 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 1.585 * [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))))) 1.585 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 1.585 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.585 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.585 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 1.585 * [taylor]: Taking taylor expansion of 0.25 in n 1.585 * [backup-simplify]: Simplify 0.25 into 0.25 1.585 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.585 * [taylor]: Taking taylor expansion of 1.0 in n 1.585 * [backup-simplify]: Simplify 1.0 into 1.0 1.585 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.585 * [taylor]: Taking taylor expansion of k in n 1.585 * [backup-simplify]: Simplify k into k 1.585 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.585 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.585 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.585 * [taylor]: Taking taylor expansion of 2.0 in n 1.585 * [backup-simplify]: Simplify 2.0 into 2.0 1.585 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.585 * [taylor]: Taking taylor expansion of PI in n 1.585 * [backup-simplify]: Simplify PI into PI 1.585 * [taylor]: Taking taylor expansion of n in n 1.585 * [backup-simplify]: Simplify 0 into 0 1.585 * [backup-simplify]: Simplify 1 into 1 1.585 * [backup-simplify]: Simplify (/ PI 1) into PI 1.586 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.586 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.586 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.586 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.586 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 1.587 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.588 * [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)))) 1.589 * [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))))) 1.589 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 1.589 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.589 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.589 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 1.589 * [taylor]: Taking taylor expansion of 0.25 in n 1.589 * [backup-simplify]: Simplify 0.25 into 0.25 1.589 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.589 * [taylor]: Taking taylor expansion of 1.0 in n 1.589 * [backup-simplify]: Simplify 1.0 into 1.0 1.589 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.589 * [taylor]: Taking taylor expansion of k in n 1.589 * [backup-simplify]: Simplify k into k 1.589 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.589 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.589 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.589 * [taylor]: Taking taylor expansion of 2.0 in n 1.589 * [backup-simplify]: Simplify 2.0 into 2.0 1.589 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.589 * [taylor]: Taking taylor expansion of PI in n 1.589 * [backup-simplify]: Simplify PI into PI 1.589 * [taylor]: Taking taylor expansion of n in n 1.589 * [backup-simplify]: Simplify 0 into 0 1.589 * [backup-simplify]: Simplify 1 into 1 1.589 * [backup-simplify]: Simplify (/ PI 1) into PI 1.590 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.590 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.590 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.590 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.590 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 1.591 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.592 * [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)))) 1.593 * [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))))) 1.593 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.593 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.593 * [taylor]: Taking taylor expansion of 0.25 in k 1.593 * [backup-simplify]: Simplify 0.25 into 0.25 1.593 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.593 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.593 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.593 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.593 * [taylor]: Taking taylor expansion of 2.0 in k 1.593 * [backup-simplify]: Simplify 2.0 into 2.0 1.593 * [taylor]: Taking taylor expansion of PI in k 1.593 * [backup-simplify]: Simplify PI into PI 1.593 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.594 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.594 * [taylor]: Taking taylor expansion of (log n) in k 1.594 * [taylor]: Taking taylor expansion of n in k 1.594 * [backup-simplify]: Simplify n into n 1.594 * [backup-simplify]: Simplify (log n) into (log n) 1.594 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.594 * [taylor]: Taking taylor expansion of 1.0 in k 1.594 * [backup-simplify]: Simplify 1.0 into 1.0 1.594 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.594 * [taylor]: Taking taylor expansion of k in k 1.594 * [backup-simplify]: Simplify 0 into 0 1.594 * [backup-simplify]: Simplify 1 into 1 1.594 * [backup-simplify]: Simplify (/ 1 1) into 1 1.594 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.595 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 1.595 * [backup-simplify]: Simplify (- 1) into -1 1.595 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.596 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 1.597 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 1.597 * [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))))) 1.598 * [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))))) 1.599 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.599 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.600 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.600 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.600 * [backup-simplify]: Simplify (- 0) into 0 1.601 * [backup-simplify]: Simplify (+ 0 0) into 0 1.601 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 1.602 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.602 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 1.603 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.604 * [taylor]: Taking taylor expansion of 0 in k 1.604 * [backup-simplify]: Simplify 0 into 0 1.604 * [backup-simplify]: Simplify 0 into 0 1.604 * [backup-simplify]: Simplify 0 into 0 1.604 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.605 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.606 * [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 1.606 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.607 * [backup-simplify]: Simplify (- 0) into 0 1.607 * [backup-simplify]: Simplify (+ 0 0) into 0 1.608 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 1.608 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.609 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 1.611 * [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 1.611 * [taylor]: Taking taylor expansion of 0 in k 1.611 * [backup-simplify]: Simplify 0 into 0 1.611 * [backup-simplify]: Simplify 0 into 0 1.611 * [backup-simplify]: Simplify 0 into 0 1.611 * [backup-simplify]: Simplify 0 into 0 1.612 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.612 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.615 * [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 1.615 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.616 * [backup-simplify]: Simplify (- 0) into 0 1.616 * [backup-simplify]: Simplify (+ 0 0) into 0 1.617 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 1.617 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.619 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 1.620 * [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 1.620 * [taylor]: Taking taylor expansion of 0 in k 1.621 * [backup-simplify]: Simplify 0 into 0 1.621 * [backup-simplify]: Simplify 0 into 0 1.621 * [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)))) 1.622 * [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))) 1.622 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 1.622 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 1.622 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.622 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.622 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 1.622 * [taylor]: Taking taylor expansion of 0.25 in k 1.622 * [backup-simplify]: Simplify 0.25 into 0.25 1.622 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.622 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.622 * [taylor]: Taking taylor expansion of k in k 1.622 * [backup-simplify]: Simplify 0 into 0 1.622 * [backup-simplify]: Simplify 1 into 1 1.622 * [backup-simplify]: Simplify (/ 1 1) into 1 1.622 * [taylor]: Taking taylor expansion of 1.0 in k 1.622 * [backup-simplify]: Simplify 1.0 into 1.0 1.622 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.622 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.622 * [taylor]: Taking taylor expansion of -2.0 in k 1.622 * [backup-simplify]: Simplify -2.0 into -2.0 1.622 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.622 * [taylor]: Taking taylor expansion of PI in k 1.622 * [backup-simplify]: Simplify PI into PI 1.622 * [taylor]: Taking taylor expansion of n in k 1.622 * [backup-simplify]: Simplify n into n 1.622 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.622 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.623 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.623 * [backup-simplify]: Simplify (+ 1 0) into 1 1.623 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 1.623 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 1.623 * [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)))))) 1.623 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 1.623 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.623 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.623 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 1.623 * [taylor]: Taking taylor expansion of 0.25 in n 1.623 * [backup-simplify]: Simplify 0.25 into 0.25 1.623 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.623 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.623 * [taylor]: Taking taylor expansion of k in n 1.623 * [backup-simplify]: Simplify k into k 1.623 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.624 * [taylor]: Taking taylor expansion of 1.0 in n 1.624 * [backup-simplify]: Simplify 1.0 into 1.0 1.624 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.624 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.624 * [taylor]: Taking taylor expansion of -2.0 in n 1.624 * [backup-simplify]: Simplify -2.0 into -2.0 1.624 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.624 * [taylor]: Taking taylor expansion of PI in n 1.624 * [backup-simplify]: Simplify PI into PI 1.624 * [taylor]: Taking taylor expansion of n in n 1.624 * [backup-simplify]: Simplify 0 into 0 1.624 * [backup-simplify]: Simplify 1 into 1 1.624 * [backup-simplify]: Simplify (/ PI 1) into PI 1.624 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.625 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.625 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.625 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 1.626 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.627 * [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)))) 1.632 * [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))))) 1.632 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 1.632 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.632 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.633 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 1.633 * [taylor]: Taking taylor expansion of 0.25 in n 1.633 * [backup-simplify]: Simplify 0.25 into 0.25 1.633 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.633 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.633 * [taylor]: Taking taylor expansion of k in n 1.633 * [backup-simplify]: Simplify k into k 1.633 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.633 * [taylor]: Taking taylor expansion of 1.0 in n 1.633 * [backup-simplify]: Simplify 1.0 into 1.0 1.633 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.633 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.633 * [taylor]: Taking taylor expansion of -2.0 in n 1.633 * [backup-simplify]: Simplify -2.0 into -2.0 1.633 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.633 * [taylor]: Taking taylor expansion of PI in n 1.633 * [backup-simplify]: Simplify PI into PI 1.633 * [taylor]: Taking taylor expansion of n in n 1.633 * [backup-simplify]: Simplify 0 into 0 1.633 * [backup-simplify]: Simplify 1 into 1 1.633 * [backup-simplify]: Simplify (/ PI 1) into PI 1.633 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.634 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.634 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.634 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 1.635 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.636 * [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)))) 1.636 * [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))))) 1.637 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.637 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.637 * [taylor]: Taking taylor expansion of 0.25 in k 1.637 * [backup-simplify]: Simplify 0.25 into 0.25 1.637 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.637 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.637 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.637 * [taylor]: Taking taylor expansion of k in k 1.637 * [backup-simplify]: Simplify 0 into 0 1.637 * [backup-simplify]: Simplify 1 into 1 1.637 * [backup-simplify]: Simplify (/ 1 1) into 1 1.637 * [taylor]: Taking taylor expansion of 1.0 in k 1.637 * [backup-simplify]: Simplify 1.0 into 1.0 1.637 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.637 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.637 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.637 * [taylor]: Taking taylor expansion of -2.0 in k 1.637 * [backup-simplify]: Simplify -2.0 into -2.0 1.637 * [taylor]: Taking taylor expansion of PI in k 1.637 * [backup-simplify]: Simplify PI into PI 1.637 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.638 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.638 * [taylor]: Taking taylor expansion of (log n) in k 1.638 * [taylor]: Taking taylor expansion of n in k 1.638 * [backup-simplify]: Simplify n into n 1.638 * [backup-simplify]: Simplify (log n) into (log n) 1.638 * [backup-simplify]: Simplify (+ 1 0) into 1 1.638 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.639 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 1.640 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 1.640 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 1.641 * [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))))) 1.642 * [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))))) 1.642 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.643 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.644 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.644 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.644 * [backup-simplify]: Simplify (+ 0 0) into 0 1.644 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 1.645 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.646 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.647 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.647 * [taylor]: Taking taylor expansion of 0 in k 1.647 * [backup-simplify]: Simplify 0 into 0 1.647 * [backup-simplify]: Simplify 0 into 0 1.647 * [backup-simplify]: Simplify 0 into 0 1.648 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.648 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.650 * [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 1.650 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.650 * [backup-simplify]: Simplify (+ 0 0) into 0 1.651 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 1.652 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.652 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 1.654 * [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 1.654 * [taylor]: Taking taylor expansion of 0 in k 1.654 * [backup-simplify]: Simplify 0 into 0 1.654 * [backup-simplify]: Simplify 0 into 0 1.654 * [backup-simplify]: Simplify 0 into 0 1.654 * [backup-simplify]: Simplify 0 into 0 1.655 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.655 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.658 * [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 1.658 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.659 * [backup-simplify]: Simplify (+ 0 0) into 0 1.659 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 1.660 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.661 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 1.663 * [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 1.663 * [taylor]: Taking taylor expansion of 0 in k 1.663 * [backup-simplify]: Simplify 0 into 0 1.663 * [backup-simplify]: Simplify 0 into 0 1.664 * [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)))))) 1.664 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2 1) 1.664 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.664 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.664 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.664 * [taylor]: Taking taylor expansion of 2.0 in n 1.664 * [backup-simplify]: Simplify 2.0 into 2.0 1.664 * [taylor]: Taking taylor expansion of (* n PI) in n 1.664 * [taylor]: Taking taylor expansion of n in n 1.664 * [backup-simplify]: Simplify 0 into 0 1.664 * [backup-simplify]: Simplify 1 into 1 1.664 * [taylor]: Taking taylor expansion of PI in n 1.664 * [backup-simplify]: Simplify PI into PI 1.664 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.664 * [taylor]: Taking taylor expansion of 2.0 in n 1.664 * [backup-simplify]: Simplify 2.0 into 2.0 1.664 * [taylor]: Taking taylor expansion of (* n PI) in n 1.664 * [taylor]: Taking taylor expansion of n in n 1.664 * [backup-simplify]: Simplify 0 into 0 1.664 * [backup-simplify]: Simplify 1 into 1 1.664 * [taylor]: Taking taylor expansion of PI in n 1.664 * [backup-simplify]: Simplify PI into PI 1.665 * [backup-simplify]: Simplify (* 0 PI) into 0 1.665 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.665 * [backup-simplify]: Simplify 0 into 0 1.666 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.667 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.667 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.668 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.668 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.668 * [backup-simplify]: Simplify 0 into 0 1.669 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.669 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.669 * [backup-simplify]: Simplify 0 into 0 1.670 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.671 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1.671 * [backup-simplify]: Simplify 0 into 0 1.672 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.672 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1.672 * [backup-simplify]: Simplify 0 into 0 1.673 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.674 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1.674 * [backup-simplify]: Simplify 0 into 0 1.675 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1.676 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1.676 * [backup-simplify]: Simplify 0 into 0 1.676 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.677 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 1.677 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.677 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.677 * [taylor]: Taking taylor expansion of 2.0 in n 1.677 * [backup-simplify]: Simplify 2.0 into 2.0 1.677 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.677 * [taylor]: Taking taylor expansion of PI in n 1.677 * [backup-simplify]: Simplify PI into PI 1.677 * [taylor]: Taking taylor expansion of n in n 1.677 * [backup-simplify]: Simplify 0 into 0 1.677 * [backup-simplify]: Simplify 1 into 1 1.677 * [backup-simplify]: Simplify (/ PI 1) into PI 1.677 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.677 * [taylor]: Taking taylor expansion of 2.0 in n 1.677 * [backup-simplify]: Simplify 2.0 into 2.0 1.677 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.677 * [taylor]: Taking taylor expansion of PI in n 1.677 * [backup-simplify]: Simplify PI into PI 1.677 * [taylor]: Taking taylor expansion of n in n 1.677 * [backup-simplify]: Simplify 0 into 0 1.677 * [backup-simplify]: Simplify 1 into 1 1.678 * [backup-simplify]: Simplify (/ PI 1) into PI 1.678 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.678 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.679 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.679 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.679 * [backup-simplify]: Simplify 0 into 0 1.680 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.680 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.680 * [backup-simplify]: Simplify 0 into 0 1.681 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.682 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.682 * [backup-simplify]: Simplify 0 into 0 1.682 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.683 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.683 * [backup-simplify]: Simplify 0 into 0 1.684 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.684 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.684 * [backup-simplify]: Simplify 0 into 0 1.685 * [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 1.686 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.686 * [backup-simplify]: Simplify 0 into 0 1.686 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 1.687 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 1.687 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.687 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.687 * [taylor]: Taking taylor expansion of -2.0 in n 1.687 * [backup-simplify]: Simplify -2.0 into -2.0 1.687 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.687 * [taylor]: Taking taylor expansion of PI in n 1.687 * [backup-simplify]: Simplify PI into PI 1.687 * [taylor]: Taking taylor expansion of n in n 1.687 * [backup-simplify]: Simplify 0 into 0 1.687 * [backup-simplify]: Simplify 1 into 1 1.687 * [backup-simplify]: Simplify (/ PI 1) into PI 1.687 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.687 * [taylor]: Taking taylor expansion of -2.0 in n 1.687 * [backup-simplify]: Simplify -2.0 into -2.0 1.687 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.687 * [taylor]: Taking taylor expansion of PI in n 1.687 * [backup-simplify]: Simplify PI into PI 1.687 * [taylor]: Taking taylor expansion of n in n 1.687 * [backup-simplify]: Simplify 0 into 0 1.687 * [backup-simplify]: Simplify 1 into 1 1.687 * [backup-simplify]: Simplify (/ PI 1) into PI 1.688 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.688 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.689 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.689 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.689 * [backup-simplify]: Simplify 0 into 0 1.690 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.690 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.690 * [backup-simplify]: Simplify 0 into 0 1.691 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.691 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.691 * [backup-simplify]: Simplify 0 into 0 1.692 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.693 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.693 * [backup-simplify]: Simplify 0 into 0 1.693 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.694 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.694 * [backup-simplify]: Simplify 0 into 0 1.695 * [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 1.695 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.696 * [backup-simplify]: Simplify 0 into 0 1.696 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 1.696 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1) 1.696 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.696 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.696 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.696 * [taylor]: Taking taylor expansion of 2.0 in n 1.696 * [backup-simplify]: Simplify 2.0 into 2.0 1.696 * [taylor]: Taking taylor expansion of (* n PI) in n 1.696 * [taylor]: Taking taylor expansion of n in n 1.696 * [backup-simplify]: Simplify 0 into 0 1.696 * [backup-simplify]: Simplify 1 into 1 1.696 * [taylor]: Taking taylor expansion of PI in n 1.696 * [backup-simplify]: Simplify PI into PI 1.696 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.696 * [taylor]: Taking taylor expansion of 2.0 in n 1.696 * [backup-simplify]: Simplify 2.0 into 2.0 1.696 * [taylor]: Taking taylor expansion of (* n PI) in n 1.696 * [taylor]: Taking taylor expansion of n in n 1.697 * [backup-simplify]: Simplify 0 into 0 1.697 * [backup-simplify]: Simplify 1 into 1 1.697 * [taylor]: Taking taylor expansion of PI in n 1.697 * [backup-simplify]: Simplify PI into PI 1.697 * [backup-simplify]: Simplify (* 0 PI) into 0 1.697 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.697 * [backup-simplify]: Simplify 0 into 0 1.698 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.699 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.699 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.700 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.700 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.700 * [backup-simplify]: Simplify 0 into 0 1.701 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.702 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.702 * [backup-simplify]: Simplify 0 into 0 1.702 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.703 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1.703 * [backup-simplify]: Simplify 0 into 0 1.704 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.704 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1.705 * [backup-simplify]: Simplify 0 into 0 1.705 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.706 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1.706 * [backup-simplify]: Simplify 0 into 0 1.707 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1.708 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1.708 * [backup-simplify]: Simplify 0 into 0 1.709 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.709 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 1.709 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.709 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.709 * [taylor]: Taking taylor expansion of 2.0 in n 1.709 * [backup-simplify]: Simplify 2.0 into 2.0 1.709 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.709 * [taylor]: Taking taylor expansion of PI in n 1.709 * [backup-simplify]: Simplify PI into PI 1.709 * [taylor]: Taking taylor expansion of n in n 1.709 * [backup-simplify]: Simplify 0 into 0 1.709 * [backup-simplify]: Simplify 1 into 1 1.709 * [backup-simplify]: Simplify (/ PI 1) into PI 1.710 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.710 * [taylor]: Taking taylor expansion of 2.0 in n 1.710 * [backup-simplify]: Simplify 2.0 into 2.0 1.710 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.710 * [taylor]: Taking taylor expansion of PI in n 1.710 * [backup-simplify]: Simplify PI into PI 1.710 * [taylor]: Taking taylor expansion of n in n 1.710 * [backup-simplify]: Simplify 0 into 0 1.710 * [backup-simplify]: Simplify 1 into 1 1.710 * [backup-simplify]: Simplify (/ PI 1) into PI 1.710 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.711 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.711 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.711 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.711 * [backup-simplify]: Simplify 0 into 0 1.712 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.713 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.713 * [backup-simplify]: Simplify 0 into 0 1.713 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.714 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.714 * [backup-simplify]: Simplify 0 into 0 1.714 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.715 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.715 * [backup-simplify]: Simplify 0 into 0 1.716 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.716 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.716 * [backup-simplify]: Simplify 0 into 0 1.717 * [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 1.724 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.724 * [backup-simplify]: Simplify 0 into 0 1.724 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 1.725 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 1.725 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.725 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.725 * [taylor]: Taking taylor expansion of -2.0 in n 1.725 * [backup-simplify]: Simplify -2.0 into -2.0 1.725 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.725 * [taylor]: Taking taylor expansion of PI in n 1.725 * [backup-simplify]: Simplify PI into PI 1.725 * [taylor]: Taking taylor expansion of n in n 1.725 * [backup-simplify]: Simplify 0 into 0 1.725 * [backup-simplify]: Simplify 1 into 1 1.725 * [backup-simplify]: Simplify (/ PI 1) into PI 1.725 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.725 * [taylor]: Taking taylor expansion of -2.0 in n 1.725 * [backup-simplify]: Simplify -2.0 into -2.0 1.725 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.725 * [taylor]: Taking taylor expansion of PI in n 1.725 * [backup-simplify]: Simplify PI into PI 1.725 * [taylor]: Taking taylor expansion of n in n 1.725 * [backup-simplify]: Simplify 0 into 0 1.725 * [backup-simplify]: Simplify 1 into 1 1.726 * [backup-simplify]: Simplify (/ PI 1) into PI 1.726 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.726 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.727 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.727 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.727 * [backup-simplify]: Simplify 0 into 0 1.728 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.729 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.729 * [backup-simplify]: Simplify 0 into 0 1.729 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.730 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.730 * [backup-simplify]: Simplify 0 into 0 1.731 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.731 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.731 * [backup-simplify]: Simplify 0 into 0 1.732 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.733 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.733 * [backup-simplify]: Simplify 0 into 0 1.733 * [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 1.734 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.734 * [backup-simplify]: Simplify 0 into 0 1.734 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 1.735 * * * [progress]: simplifying candidates 1.737 * [simplify]: Simplifying: (* (+ (+ (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)) (* (+ (+ (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)) 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(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 (* 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(/ (/ (- h3 h4) h0) 2)) (pow h2 (/ (/ (- h3 h4) h0) 2)) (log (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (exp (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (cbrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (cbrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2)))) (cbrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (* (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2)) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (sqrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (sqrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (pow (* (* h0 h1) h2) (/ (/ (/ (- h3 h4) h0) 2) 2)) (pow (* (* h0 h1) h2) (/ (/ (/ (- h3 h4) h0) 2) 2)) (* (+ (+ (log h0) (log h1)) (log h2)) (/ (/ (- h3 h4) h0) 2)) (* (+ (log (* h0 h1)) (log h2)) (/ (/ (- h3 h4) h0) 2)) (* (log (* (* h0 h1) h2)) (/ (/ (- h3 h4) h0) 2)) (* (log (* (* h0 h1) h2)) (/ (/ (- h3 h4) h0) 2)) (* 1 (/ (/ (- h3 h4) h0) 2)) (* 1 (/ (/ (- h3 h4) h0) 2)) (* 1 (/ (/ (- h3 h4) h0) 2)) (pow (* (* h0 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(* (cbrt (- h3 h4)) (cbrt (- h3 h4))) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (* (cbrt (- h3 h4)) (cbrt (- h3 h4))) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (* (cbrt (- h3 h4)) (cbrt (- h3 h4))) (sqrt h0)) 1)) (pow (* (* h0 h1) h2) (/ (/ (* (cbrt (- h3 h4)) (cbrt (- h3 h4))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (* (cbrt (- h3 h4)) (cbrt (- h3 h4))) 1) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (* (cbrt (- h3 h4)) (cbrt (- h3 h4))) 1) 1)) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) (sqrt h0)) 1)) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) 1) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) 1) 1)) (pow (* (* h0 h1) h2) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ 1 (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h1) h2) (/ (/ 1 (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ 1 (sqrt h0)) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ 1 (sqrt h0)) 1)) (pow (* (* h0 h1) h2) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ 1 1) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ 1 1) 1)) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) (sqrt h0)) 1)) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) 1) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) 1) 1)) (pow (* (* h0 h1) h2) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ 1 (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h1) h2) (/ (/ 1 (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ 1 (sqrt h0)) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ 1 (sqrt h0)) 1)) (pow (* (* h0 h1) h2) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ 1 1) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ 1 1) 1)) (pow (* (* h0 h1) h2) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ 1 (sqrt 2))) (pow (* (* h0 h1) h2) (/ 1 1)) (pow (* (* h0 h1) h2) (/ (- h3 h4) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (- h3 h4) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (- h3 h4) 1)) (pow (* (* h0 h1) h2) 1) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)) (pow (* h0 h1) (/ (/ (- h3 h4) h0) 2)) (pow h2 (/ (/ (- h3 h4) h0) 2)) (log (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (exp (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (cbrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (cbrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2)))) (cbrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (* (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2)) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (sqrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (sqrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (pow (* (* h0 h1) h2) (/ (/ (/ (- h3 h4) h0) 2) 2)) (pow (* (* h0 h1) h2) (/ (/ (/ (- h3 h4) h0) 2) 2)) (* (* h0 h1) h2) (* (* h0 h1) h2) (+ (+ (log h0) (log h1)) (log h2)) (+ (log (* h0 h1)) (log h2)) (log (* (* h0 h1) h2)) (exp (* (* h0 h1) h2)) (* (* (* (* h0 h0) h0) (* (* h1 h1) h1)) (* (* h2 h2) h2)) (* (* (* (* h0 h1) (* h0 h1)) (* h0 h1)) (* (* h2 h2) h2)) (* (cbrt (* (* h0 h1) h2)) (cbrt (* (* h0 h1) h2))) (cbrt (* (* h0 h1) h2)) (* (* (* (* h0 h1) h2) (* (* h0 h1) h2)) (* (* h0 h1) h2)) (sqrt (* (* h0 h1) h2)) (sqrt (* (* h0 h1) h2)) (* (* h0 h1) (* (cbrt h2) (cbrt h2))) (* (* h0 h1) (sqrt h2)) (* (* h0 h1) 1) (* h1 h2) (* (* h0 h1) h2) (* (* h0 h1) h2) (+ (+ (log h0) (log h1)) (log h2)) (+ (log (* h0 h1)) (log h2)) (log (* (* h0 h1) h2)) (exp (* (* h0 h1) h2)) (* (* (* (* h0 h0) h0) (* (* h1 h1) h1)) (* (* h2 h2) h2)) (* (* (* (* h0 h1) (* h0 h1)) (* h0 h1)) (* (* h2 h2) h2)) (* (cbrt (* (* h0 h1) h2)) (cbrt (* (* h0 h1) h2))) (cbrt (* (* h0 h1) h2)) (* (* (* (* h0 h1) h2) (* (* h0 h1) h2)) (* (* h0 h1) h2)) (sqrt (* (* h0 h1) h2)) (sqrt (* (* h0 h1) h2)) (* (* h0 h1) (* (cbrt h2) (cbrt h2))) (* (* h0 h1) (sqrt h2)) (* (* h0 h1) 1) (* h1 h2) (- (+ (* h5 (* (pow h4 2) (* (pow (log (* h0 h1)) 2) (exp (* h6 (+ (log (* h0 h1)) (log h2))))))) (+ (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (+ (* h7 (* (pow h4 2) (* (log (* h0 h1)) (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (log h2))))) (* h5 (* (pow h4 2) (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (pow (log h2) 2))))))) (+ (* h6 (* h4 (* (log (* h0 h1)) (exp (* h6 (+ (log (* h0 h1)) (log h2))))))) (* h6 (* h4 (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (log h2)))))) (exp (* h6 (* (- (log (* h0 h1)) (log (/ 1 h2))) (- h3 h4)))) (exp (* h6 (* (- h3 h4) (- (log (* h8 h1)) (log (/ -1 h2)))))) (- (+ (* h5 (* (pow h4 2) (* (pow (log (* h0 h1)) 2) (exp (* h6 (+ (log (* h0 h1)) (log h2))))))) (+ (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (+ (* h7 (* (pow h4 2) (* (log (* h0 h1)) (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (log h2))))) (* h5 (* (pow h4 2) (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (pow (log h2) 2))))))) (+ (* h6 (* h4 (* (log (* h0 h1)) (exp (* h6 (+ (log (* h0 h1)) (log h2))))))) (* h6 (* h4 (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (log h2)))))) (exp (* h6 (* (- (log (* h0 h1)) (log (/ 1 h2))) (- h3 h4)))) (exp (* h6 (* (- h3 h4) (- (log (* h8 h1)) (log (/ -1 h2)))))) (* h0 (* h2 h1)) (* h0 (* h2 h1)) (* h0 (* h2 h1)) (* h0 (* h2 h1)) (* h0 (* h2 h1)) (* h0 (* h2 h1)) 1.746 * * [simplify]: iteration 0 : 696 enodes (cost 1678 ) 1.757 * * [simplify]: iteration 1 : 2767 enodes (cost 1618 ) 1.798 * * [simplify]: iteration 2 : 5001 enodes (cost 1608 ) 1.805 * * * [progress]: adding candidates to table 2.448 * * [progress]: iteration 3 / 4 2.448 * * * [progress]: picking best candidate 2.470 * * * * [pick]: Picked # 2.470 * * * [progress]: localizing error 2.485 * * * [progress]: generating rewritten candidates 2.485 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 2.513 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 2.537 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 2.543 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 2.574 * * * [progress]: generating series expansions 2.574 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 2.575 * [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))) 2.575 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 2.575 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 2.575 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.575 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.575 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 2.575 * [taylor]: Taking taylor expansion of 0.25 in k 2.575 * [backup-simplify]: Simplify 0.25 into 0.25 2.575 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.575 * [taylor]: Taking taylor expansion of 1.0 in k 2.575 * [backup-simplify]: Simplify 1.0 into 1.0 2.575 * [taylor]: Taking taylor expansion of k in k 2.575 * [backup-simplify]: Simplify 0 into 0 2.575 * [backup-simplify]: Simplify 1 into 1 2.575 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.575 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.575 * [taylor]: Taking taylor expansion of 2.0 in k 2.575 * [backup-simplify]: Simplify 2.0 into 2.0 2.575 * [taylor]: Taking taylor expansion of (* n PI) in k 2.575 * [taylor]: Taking taylor expansion of n in k 2.575 * [backup-simplify]: Simplify n into n 2.575 * [taylor]: Taking taylor expansion of PI in k 2.575 * [backup-simplify]: Simplify PI into PI 2.575 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.575 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.575 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.576 * [backup-simplify]: Simplify (- 0) into 0 2.576 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.576 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 2.576 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 2.576 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 2.576 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.576 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.576 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.576 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.576 * [taylor]: Taking taylor expansion of 0.25 in n 2.576 * [backup-simplify]: Simplify 0.25 into 0.25 2.576 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.576 * [taylor]: Taking taylor expansion of 1.0 in n 2.576 * [backup-simplify]: Simplify 1.0 into 1.0 2.576 * [taylor]: Taking taylor expansion of k in n 2.576 * [backup-simplify]: Simplify k into k 2.576 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.577 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.577 * [taylor]: Taking taylor expansion of 2.0 in n 2.577 * [backup-simplify]: Simplify 2.0 into 2.0 2.577 * [taylor]: Taking taylor expansion of (* n PI) in n 2.577 * [taylor]: Taking taylor expansion of n in n 2.577 * [backup-simplify]: Simplify 0 into 0 2.577 * [backup-simplify]: Simplify 1 into 1 2.577 * [taylor]: Taking taylor expansion of PI in n 2.577 * [backup-simplify]: Simplify PI into PI 2.577 * [backup-simplify]: Simplify (* 0 PI) into 0 2.577 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.578 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.579 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.580 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.580 * [backup-simplify]: Simplify (- k) into (- k) 2.580 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.580 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.581 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.581 * [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)))) 2.582 * [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))))) 2.582 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.582 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.582 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.582 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.582 * [taylor]: Taking taylor expansion of 0.25 in n 2.582 * [backup-simplify]: Simplify 0.25 into 0.25 2.582 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.582 * [taylor]: Taking taylor expansion of 1.0 in n 2.582 * [backup-simplify]: Simplify 1.0 into 1.0 2.582 * [taylor]: Taking taylor expansion of k in n 2.582 * [backup-simplify]: Simplify k into k 2.582 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.582 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.582 * [taylor]: Taking taylor expansion of 2.0 in n 2.582 * [backup-simplify]: Simplify 2.0 into 2.0 2.582 * [taylor]: Taking taylor expansion of (* n PI) in n 2.582 * [taylor]: Taking taylor expansion of n in n 2.582 * [backup-simplify]: Simplify 0 into 0 2.582 * [backup-simplify]: Simplify 1 into 1 2.582 * [taylor]: Taking taylor expansion of PI in n 2.582 * [backup-simplify]: Simplify PI into PI 2.583 * [backup-simplify]: Simplify (* 0 PI) into 0 2.583 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.584 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.585 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.585 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.585 * [backup-simplify]: Simplify (- k) into (- k) 2.585 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.585 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.586 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.587 * [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)))) 2.587 * [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))))) 2.588 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.588 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.588 * [taylor]: Taking taylor expansion of 0.25 in k 2.588 * [backup-simplify]: Simplify 0.25 into 0.25 2.588 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.588 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.588 * [taylor]: Taking taylor expansion of 1.0 in k 2.588 * [backup-simplify]: Simplify 1.0 into 1.0 2.588 * [taylor]: Taking taylor expansion of k in k 2.588 * [backup-simplify]: Simplify 0 into 0 2.588 * [backup-simplify]: Simplify 1 into 1 2.588 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.588 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.588 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.588 * [taylor]: Taking taylor expansion of 2.0 in k 2.588 * [backup-simplify]: Simplify 2.0 into 2.0 2.588 * [taylor]: Taking taylor expansion of PI in k 2.588 * [backup-simplify]: Simplify PI into PI 2.588 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.589 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.589 * [taylor]: Taking taylor expansion of (log n) in k 2.589 * [taylor]: Taking taylor expansion of n in k 2.589 * [backup-simplify]: Simplify n into n 2.589 * [backup-simplify]: Simplify (log n) into (log n) 2.589 * [backup-simplify]: Simplify (- 0) into 0 2.589 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.590 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.591 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.591 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 2.592 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.593 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.593 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.594 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.595 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.595 * [backup-simplify]: Simplify (- 0) into 0 2.595 * [backup-simplify]: Simplify (+ 0 0) into 0 2.595 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 2.596 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.597 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.598 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.598 * [taylor]: Taking taylor expansion of 0 in k 2.598 * [backup-simplify]: Simplify 0 into 0 2.598 * [backup-simplify]: Simplify 0 into 0 2.599 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.599 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.600 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.600 * [backup-simplify]: Simplify (+ 0 0) into 0 2.600 * [backup-simplify]: Simplify (- 1) into -1 2.601 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.602 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.603 * [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)))) 2.605 * [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)))))) 2.607 * [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)))))) 2.607 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.608 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.610 * [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 2.610 * [backup-simplify]: Simplify (- 0) into 0 2.610 * [backup-simplify]: Simplify (+ 0 0) into 0 2.611 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.612 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.612 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.614 * [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 2.614 * [taylor]: Taking taylor expansion of 0 in k 2.614 * [backup-simplify]: Simplify 0 into 0 2.614 * [backup-simplify]: Simplify 0 into 0 2.614 * [backup-simplify]: Simplify 0 into 0 2.614 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.616 * [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 2.617 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.617 * [backup-simplify]: Simplify (+ 0 0) into 0 2.618 * [backup-simplify]: Simplify (- 0) into 0 2.618 * [backup-simplify]: Simplify (+ 0 0) into 0 2.619 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.620 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.623 * [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))))) 2.626 * [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))))) 2.631 * [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)))))) 2.632 * [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)))) 2.632 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 2.632 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 2.632 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.632 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.632 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 2.632 * [taylor]: Taking taylor expansion of 0.25 in k 2.632 * [backup-simplify]: Simplify 0.25 into 0.25 2.632 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.632 * [taylor]: Taking taylor expansion of 1.0 in k 2.632 * [backup-simplify]: Simplify 1.0 into 1.0 2.632 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.632 * [taylor]: Taking taylor expansion of k in k 2.632 * [backup-simplify]: Simplify 0 into 0 2.632 * [backup-simplify]: Simplify 1 into 1 2.632 * [backup-simplify]: Simplify (/ 1 1) into 1 2.632 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.632 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.633 * [taylor]: Taking taylor expansion of 2.0 in k 2.633 * [backup-simplify]: Simplify 2.0 into 2.0 2.633 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.633 * [taylor]: Taking taylor expansion of PI in k 2.633 * [backup-simplify]: Simplify PI into PI 2.633 * [taylor]: Taking taylor expansion of n in k 2.633 * [backup-simplify]: Simplify n into n 2.633 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.633 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.633 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.633 * [backup-simplify]: Simplify (- 1) into -1 2.633 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.633 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 2.634 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 2.634 * [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))))) 2.634 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.634 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.634 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.634 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.634 * [taylor]: Taking taylor expansion of 0.25 in n 2.634 * [backup-simplify]: Simplify 0.25 into 0.25 2.634 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.634 * [taylor]: Taking taylor expansion of 1.0 in n 2.634 * [backup-simplify]: Simplify 1.0 into 1.0 2.634 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.634 * [taylor]: Taking taylor expansion of k in n 2.634 * [backup-simplify]: Simplify k into k 2.634 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.634 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.634 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.634 * [taylor]: Taking taylor expansion of 2.0 in n 2.634 * [backup-simplify]: Simplify 2.0 into 2.0 2.634 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.634 * [taylor]: Taking taylor expansion of PI in n 2.634 * [backup-simplify]: Simplify PI into PI 2.634 * [taylor]: Taking taylor expansion of n in n 2.634 * [backup-simplify]: Simplify 0 into 0 2.634 * [backup-simplify]: Simplify 1 into 1 2.634 * [backup-simplify]: Simplify (/ PI 1) into PI 2.635 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.635 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.635 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.635 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.635 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.636 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.637 * [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)))) 2.638 * [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))))) 2.638 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.638 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.638 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.638 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.638 * [taylor]: Taking taylor expansion of 0.25 in n 2.638 * [backup-simplify]: Simplify 0.25 into 0.25 2.638 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.638 * [taylor]: Taking taylor expansion of 1.0 in n 2.638 * [backup-simplify]: Simplify 1.0 into 1.0 2.638 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.638 * [taylor]: Taking taylor expansion of k in n 2.638 * [backup-simplify]: Simplify k into k 2.638 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.638 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.638 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.638 * [taylor]: Taking taylor expansion of 2.0 in n 2.638 * [backup-simplify]: Simplify 2.0 into 2.0 2.638 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.638 * [taylor]: Taking taylor expansion of PI in n 2.638 * [backup-simplify]: Simplify PI into PI 2.638 * [taylor]: Taking taylor expansion of n in n 2.638 * [backup-simplify]: Simplify 0 into 0 2.638 * [backup-simplify]: Simplify 1 into 1 2.638 * [backup-simplify]: Simplify (/ PI 1) into PI 2.639 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.639 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.639 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.639 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.639 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.640 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.641 * [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)))) 2.642 * [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))))) 2.642 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.642 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.642 * [taylor]: Taking taylor expansion of 0.25 in k 2.642 * [backup-simplify]: Simplify 0.25 into 0.25 2.642 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.642 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.642 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.642 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.642 * [taylor]: Taking taylor expansion of 2.0 in k 2.642 * [backup-simplify]: Simplify 2.0 into 2.0 2.642 * [taylor]: Taking taylor expansion of PI in k 2.642 * [backup-simplify]: Simplify PI into PI 2.642 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.643 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.643 * [taylor]: Taking taylor expansion of (log n) in k 2.643 * [taylor]: Taking taylor expansion of n in k 2.643 * [backup-simplify]: Simplify n into n 2.643 * [backup-simplify]: Simplify (log n) into (log n) 2.643 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.643 * [taylor]: Taking taylor expansion of 1.0 in k 2.643 * [backup-simplify]: Simplify 1.0 into 1.0 2.643 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.643 * [taylor]: Taking taylor expansion of k in k 2.643 * [backup-simplify]: Simplify 0 into 0 2.643 * [backup-simplify]: Simplify 1 into 1 2.643 * [backup-simplify]: Simplify (/ 1 1) into 1 2.643 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.644 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.644 * [backup-simplify]: Simplify (- 1) into -1 2.644 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.645 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.646 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 2.647 * [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))))) 2.647 * [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))))) 2.648 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.648 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.649 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.649 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.650 * [backup-simplify]: Simplify (- 0) into 0 2.650 * [backup-simplify]: Simplify (+ 0 0) into 0 2.650 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.651 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.652 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.653 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.653 * [taylor]: Taking taylor expansion of 0 in k 2.653 * [backup-simplify]: Simplify 0 into 0 2.653 * [backup-simplify]: Simplify 0 into 0 2.653 * [backup-simplify]: Simplify 0 into 0 2.654 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.655 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.662 * [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 2.662 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.663 * [backup-simplify]: Simplify (- 0) into 0 2.663 * [backup-simplify]: Simplify (+ 0 0) into 0 2.663 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.664 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.665 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.666 * [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 2.666 * [taylor]: Taking taylor expansion of 0 in k 2.666 * [backup-simplify]: Simplify 0 into 0 2.666 * [backup-simplify]: Simplify 0 into 0 2.666 * [backup-simplify]: Simplify 0 into 0 2.667 * [backup-simplify]: Simplify 0 into 0 2.667 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.668 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.671 * [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 2.671 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.671 * [backup-simplify]: Simplify (- 0) into 0 2.671 * [backup-simplify]: Simplify (+ 0 0) into 0 2.672 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.673 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.674 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.675 * [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 2.675 * [taylor]: Taking taylor expansion of 0 in k 2.675 * [backup-simplify]: Simplify 0 into 0 2.675 * [backup-simplify]: Simplify 0 into 0 2.676 * [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)))) 2.677 * [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))) 2.677 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 2.677 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 2.677 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.677 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.677 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 2.677 * [taylor]: Taking taylor expansion of 0.25 in k 2.677 * [backup-simplify]: Simplify 0.25 into 0.25 2.677 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.677 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.677 * [taylor]: Taking taylor expansion of k in k 2.677 * [backup-simplify]: Simplify 0 into 0 2.677 * [backup-simplify]: Simplify 1 into 1 2.677 * [backup-simplify]: Simplify (/ 1 1) into 1 2.677 * [taylor]: Taking taylor expansion of 1.0 in k 2.677 * [backup-simplify]: Simplify 1.0 into 1.0 2.677 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.677 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.677 * [taylor]: Taking taylor expansion of -2.0 in k 2.677 * [backup-simplify]: Simplify -2.0 into -2.0 2.677 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.677 * [taylor]: Taking taylor expansion of PI in k 2.677 * [backup-simplify]: Simplify PI into PI 2.677 * [taylor]: Taking taylor expansion of n in k 2.677 * [backup-simplify]: Simplify n into n 2.677 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.677 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.677 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.678 * [backup-simplify]: Simplify (+ 1 0) into 1 2.678 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 2.678 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 2.678 * [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)))))) 2.678 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.678 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.678 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.678 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.678 * [taylor]: Taking taylor expansion of 0.25 in n 2.678 * [backup-simplify]: Simplify 0.25 into 0.25 2.678 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.678 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.678 * [taylor]: Taking taylor expansion of k in n 2.678 * [backup-simplify]: Simplify k into k 2.678 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.678 * [taylor]: Taking taylor expansion of 1.0 in n 2.678 * [backup-simplify]: Simplify 1.0 into 1.0 2.678 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.678 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.678 * [taylor]: Taking taylor expansion of -2.0 in n 2.678 * [backup-simplify]: Simplify -2.0 into -2.0 2.678 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.679 * [taylor]: Taking taylor expansion of PI in n 2.679 * [backup-simplify]: Simplify PI into PI 2.679 * [taylor]: Taking taylor expansion of n in n 2.679 * [backup-simplify]: Simplify 0 into 0 2.679 * [backup-simplify]: Simplify 1 into 1 2.679 * [backup-simplify]: Simplify (/ PI 1) into PI 2.679 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.680 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.680 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.680 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.681 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.681 * [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)))) 2.682 * [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))))) 2.682 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.682 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.682 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.682 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.682 * [taylor]: Taking taylor expansion of 0.25 in n 2.682 * [backup-simplify]: Simplify 0.25 into 0.25 2.682 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.682 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.682 * [taylor]: Taking taylor expansion of k in n 2.682 * [backup-simplify]: Simplify k into k 2.682 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.682 * [taylor]: Taking taylor expansion of 1.0 in n 2.682 * [backup-simplify]: Simplify 1.0 into 1.0 2.682 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.682 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.682 * [taylor]: Taking taylor expansion of -2.0 in n 2.682 * [backup-simplify]: Simplify -2.0 into -2.0 2.682 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.682 * [taylor]: Taking taylor expansion of PI in n 2.682 * [backup-simplify]: Simplify PI into PI 2.682 * [taylor]: Taking taylor expansion of n in n 2.683 * [backup-simplify]: Simplify 0 into 0 2.683 * [backup-simplify]: Simplify 1 into 1 2.683 * [backup-simplify]: Simplify (/ PI 1) into PI 2.683 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.684 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.684 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.684 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.685 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.685 * [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)))) 2.686 * [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))))) 2.686 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.686 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.686 * [taylor]: Taking taylor expansion of 0.25 in k 2.686 * [backup-simplify]: Simplify 0.25 into 0.25 2.686 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.686 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.686 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.686 * [taylor]: Taking taylor expansion of k in k 2.686 * [backup-simplify]: Simplify 0 into 0 2.686 * [backup-simplify]: Simplify 1 into 1 2.687 * [backup-simplify]: Simplify (/ 1 1) into 1 2.687 * [taylor]: Taking taylor expansion of 1.0 in k 2.687 * [backup-simplify]: Simplify 1.0 into 1.0 2.687 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.687 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.687 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.687 * [taylor]: Taking taylor expansion of -2.0 in k 2.687 * [backup-simplify]: Simplify -2.0 into -2.0 2.687 * [taylor]: Taking taylor expansion of PI in k 2.687 * [backup-simplify]: Simplify PI into PI 2.687 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.688 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.688 * [taylor]: Taking taylor expansion of (log n) in k 2.688 * [taylor]: Taking taylor expansion of n in k 2.688 * [backup-simplify]: Simplify n into n 2.688 * [backup-simplify]: Simplify (log n) into (log n) 2.688 * [backup-simplify]: Simplify (+ 1 0) into 1 2.688 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.689 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.689 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.690 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 2.691 * [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))))) 2.691 * [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))))) 2.692 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.692 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.693 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.693 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.694 * [backup-simplify]: Simplify (+ 0 0) into 0 2.694 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.695 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.695 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.696 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.697 * [taylor]: Taking taylor expansion of 0 in k 2.697 * [backup-simplify]: Simplify 0 into 0 2.697 * [backup-simplify]: Simplify 0 into 0 2.697 * [backup-simplify]: Simplify 0 into 0 2.697 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.698 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.699 * [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 2.699 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.700 * [backup-simplify]: Simplify (+ 0 0) into 0 2.700 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.701 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.702 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.704 * [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 2.704 * [taylor]: Taking taylor expansion of 0 in k 2.704 * [backup-simplify]: Simplify 0 into 0 2.704 * [backup-simplify]: Simplify 0 into 0 2.704 * [backup-simplify]: Simplify 0 into 0 2.704 * [backup-simplify]: Simplify 0 into 0 2.704 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.705 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.708 * [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 2.708 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.708 * [backup-simplify]: Simplify (+ 0 0) into 0 2.709 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.710 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.711 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.712 * [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 2.712 * [taylor]: Taking taylor expansion of 0 in k 2.712 * [backup-simplify]: Simplify 0 into 0 2.712 * [backup-simplify]: Simplify 0 into 0 2.713 * [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)))))) 2.713 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 2.714 * [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))) 2.714 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 2.714 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 2.714 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.714 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.714 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 2.714 * [taylor]: Taking taylor expansion of 0.25 in k 2.714 * [backup-simplify]: Simplify 0.25 into 0.25 2.714 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.714 * [taylor]: Taking taylor expansion of 1.0 in k 2.714 * [backup-simplify]: Simplify 1.0 into 1.0 2.714 * [taylor]: Taking taylor expansion of k in k 2.714 * [backup-simplify]: Simplify 0 into 0 2.714 * [backup-simplify]: Simplify 1 into 1 2.714 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.714 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.714 * [taylor]: Taking taylor expansion of 2.0 in k 2.714 * [backup-simplify]: Simplify 2.0 into 2.0 2.714 * [taylor]: Taking taylor expansion of (* n PI) in k 2.714 * [taylor]: Taking taylor expansion of n in k 2.714 * [backup-simplify]: Simplify n into n 2.714 * [taylor]: Taking taylor expansion of PI in k 2.714 * [backup-simplify]: Simplify PI into PI 2.714 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.714 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.714 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.714 * [backup-simplify]: Simplify (- 0) into 0 2.715 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.715 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 2.715 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 2.715 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 2.715 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.715 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.715 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.715 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.715 * [taylor]: Taking taylor expansion of 0.25 in n 2.715 * [backup-simplify]: Simplify 0.25 into 0.25 2.715 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.715 * [taylor]: Taking taylor expansion of 1.0 in n 2.715 * [backup-simplify]: Simplify 1.0 into 1.0 2.715 * [taylor]: Taking taylor expansion of k in n 2.715 * [backup-simplify]: Simplify k into k 2.715 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.715 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.715 * [taylor]: Taking taylor expansion of 2.0 in n 2.715 * [backup-simplify]: Simplify 2.0 into 2.0 2.715 * [taylor]: Taking taylor expansion of (* n PI) in n 2.715 * [taylor]: Taking taylor expansion of n in n 2.715 * [backup-simplify]: Simplify 0 into 0 2.715 * [backup-simplify]: Simplify 1 into 1 2.715 * [taylor]: Taking taylor expansion of PI in n 2.715 * [backup-simplify]: Simplify PI into PI 2.716 * [backup-simplify]: Simplify (* 0 PI) into 0 2.716 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.717 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.718 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.718 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.718 * [backup-simplify]: Simplify (- k) into (- k) 2.718 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.718 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.719 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.720 * [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)))) 2.721 * [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))))) 2.721 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.721 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.721 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.721 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.721 * [taylor]: Taking taylor expansion of 0.25 in n 2.721 * [backup-simplify]: Simplify 0.25 into 0.25 2.721 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.721 * [taylor]: Taking taylor expansion of 1.0 in n 2.721 * [backup-simplify]: Simplify 1.0 into 1.0 2.721 * [taylor]: Taking taylor expansion of k in n 2.721 * [backup-simplify]: Simplify k into k 2.721 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.721 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.721 * [taylor]: Taking taylor expansion of 2.0 in n 2.721 * [backup-simplify]: Simplify 2.0 into 2.0 2.721 * [taylor]: Taking taylor expansion of (* n PI) in n 2.721 * [taylor]: Taking taylor expansion of n in n 2.721 * [backup-simplify]: Simplify 0 into 0 2.721 * [backup-simplify]: Simplify 1 into 1 2.721 * [taylor]: Taking taylor expansion of PI in n 2.721 * [backup-simplify]: Simplify PI into PI 2.721 * [backup-simplify]: Simplify (* 0 PI) into 0 2.721 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.722 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.723 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.724 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.724 * [backup-simplify]: Simplify (- k) into (- k) 2.724 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.724 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.725 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.725 * [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)))) 2.726 * [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))))) 2.726 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.726 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.726 * [taylor]: Taking taylor expansion of 0.25 in k 2.726 * [backup-simplify]: Simplify 0.25 into 0.25 2.726 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.726 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.726 * [taylor]: Taking taylor expansion of 1.0 in k 2.726 * [backup-simplify]: Simplify 1.0 into 1.0 2.726 * [taylor]: Taking taylor expansion of k in k 2.726 * [backup-simplify]: Simplify 0 into 0 2.726 * [backup-simplify]: Simplify 1 into 1 2.726 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.726 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.726 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.726 * [taylor]: Taking taylor expansion of 2.0 in k 2.726 * [backup-simplify]: Simplify 2.0 into 2.0 2.726 * [taylor]: Taking taylor expansion of PI in k 2.726 * [backup-simplify]: Simplify PI into PI 2.727 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.727 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.727 * [taylor]: Taking taylor expansion of (log n) in k 2.727 * [taylor]: Taking taylor expansion of n in k 2.727 * [backup-simplify]: Simplify n into n 2.727 * [backup-simplify]: Simplify (log n) into (log n) 2.728 * [backup-simplify]: Simplify (- 0) into 0 2.728 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.728 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.729 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.730 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 2.730 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.731 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.732 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.732 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.733 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.733 * [backup-simplify]: Simplify (- 0) into 0 2.734 * [backup-simplify]: Simplify (+ 0 0) into 0 2.734 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 2.735 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.735 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.736 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.736 * [taylor]: Taking taylor expansion of 0 in k 2.736 * [backup-simplify]: Simplify 0 into 0 2.737 * [backup-simplify]: Simplify 0 into 0 2.737 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.738 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.738 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.739 * [backup-simplify]: Simplify (+ 0 0) into 0 2.739 * [backup-simplify]: Simplify (- 1) into -1 2.739 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.740 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.741 * [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)))) 2.743 * [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)))))) 2.745 * [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)))))) 2.745 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.746 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.748 * [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 2.748 * [backup-simplify]: Simplify (- 0) into 0 2.748 * [backup-simplify]: Simplify (+ 0 0) into 0 2.749 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.755 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.756 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.758 * [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 2.758 * [taylor]: Taking taylor expansion of 0 in k 2.758 * [backup-simplify]: Simplify 0 into 0 2.758 * [backup-simplify]: Simplify 0 into 0 2.758 * [backup-simplify]: Simplify 0 into 0 2.758 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.760 * [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 2.761 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.761 * [backup-simplify]: Simplify (+ 0 0) into 0 2.762 * [backup-simplify]: Simplify (- 0) into 0 2.762 * [backup-simplify]: Simplify (+ 0 0) into 0 2.763 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.764 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.767 * [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))))) 2.770 * [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))))) 2.775 * [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)))))) 2.776 * [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)))) 2.776 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 2.776 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 2.776 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.776 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.776 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 2.776 * [taylor]: Taking taylor expansion of 0.25 in k 2.776 * [backup-simplify]: Simplify 0.25 into 0.25 2.776 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.776 * [taylor]: Taking taylor expansion of 1.0 in k 2.776 * [backup-simplify]: Simplify 1.0 into 1.0 2.776 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.776 * [taylor]: Taking taylor expansion of k in k 2.776 * [backup-simplify]: Simplify 0 into 0 2.776 * [backup-simplify]: Simplify 1 into 1 2.776 * [backup-simplify]: Simplify (/ 1 1) into 1 2.776 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.776 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.776 * [taylor]: Taking taylor expansion of 2.0 in k 2.777 * [backup-simplify]: Simplify 2.0 into 2.0 2.777 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.777 * [taylor]: Taking taylor expansion of PI in k 2.777 * [backup-simplify]: Simplify PI into PI 2.777 * [taylor]: Taking taylor expansion of n in k 2.777 * [backup-simplify]: Simplify n into n 2.777 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.777 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.777 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.777 * [backup-simplify]: Simplify (- 1) into -1 2.777 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.777 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 2.778 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 2.778 * [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))))) 2.778 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.778 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.778 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.778 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.778 * [taylor]: Taking taylor expansion of 0.25 in n 2.778 * [backup-simplify]: Simplify 0.25 into 0.25 2.778 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.778 * [taylor]: Taking taylor expansion of 1.0 in n 2.778 * [backup-simplify]: Simplify 1.0 into 1.0 2.778 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.778 * [taylor]: Taking taylor expansion of k in n 2.778 * [backup-simplify]: Simplify k into k 2.778 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.778 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.778 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.778 * [taylor]: Taking taylor expansion of 2.0 in n 2.778 * [backup-simplify]: Simplify 2.0 into 2.0 2.778 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.778 * [taylor]: Taking taylor expansion of PI in n 2.778 * [backup-simplify]: Simplify PI into PI 2.778 * [taylor]: Taking taylor expansion of n in n 2.778 * [backup-simplify]: Simplify 0 into 0 2.778 * [backup-simplify]: Simplify 1 into 1 2.778 * [backup-simplify]: Simplify (/ PI 1) into PI 2.779 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.779 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.779 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.779 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.779 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.780 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.781 * [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)))) 2.782 * [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))))) 2.782 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.782 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.782 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.782 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.782 * [taylor]: Taking taylor expansion of 0.25 in n 2.782 * [backup-simplify]: Simplify 0.25 into 0.25 2.782 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.782 * [taylor]: Taking taylor expansion of 1.0 in n 2.782 * [backup-simplify]: Simplify 1.0 into 1.0 2.782 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.782 * [taylor]: Taking taylor expansion of k in n 2.782 * [backup-simplify]: Simplify k into k 2.782 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.782 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.782 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.782 * [taylor]: Taking taylor expansion of 2.0 in n 2.782 * [backup-simplify]: Simplify 2.0 into 2.0 2.782 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.782 * [taylor]: Taking taylor expansion of PI in n 2.782 * [backup-simplify]: Simplify PI into PI 2.782 * [taylor]: Taking taylor expansion of n in n 2.782 * [backup-simplify]: Simplify 0 into 0 2.782 * [backup-simplify]: Simplify 1 into 1 2.782 * [backup-simplify]: Simplify (/ PI 1) into PI 2.783 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.783 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.783 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.783 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.783 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.784 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.785 * [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)))) 2.786 * [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))))) 2.786 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.786 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.786 * [taylor]: Taking taylor expansion of 0.25 in k 2.786 * [backup-simplify]: Simplify 0.25 into 0.25 2.786 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.786 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.786 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.786 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.786 * [taylor]: Taking taylor expansion of 2.0 in k 2.786 * [backup-simplify]: Simplify 2.0 into 2.0 2.786 * [taylor]: Taking taylor expansion of PI in k 2.786 * [backup-simplify]: Simplify PI into PI 2.786 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.787 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.787 * [taylor]: Taking taylor expansion of (log n) in k 2.787 * [taylor]: Taking taylor expansion of n in k 2.787 * [backup-simplify]: Simplify n into n 2.787 * [backup-simplify]: Simplify (log n) into (log n) 2.787 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.787 * [taylor]: Taking taylor expansion of 1.0 in k 2.787 * [backup-simplify]: Simplify 1.0 into 1.0 2.787 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.787 * [taylor]: Taking taylor expansion of k in k 2.787 * [backup-simplify]: Simplify 0 into 0 2.787 * [backup-simplify]: Simplify 1 into 1 2.787 * [backup-simplify]: Simplify (/ 1 1) into 1 2.787 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.788 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.788 * [backup-simplify]: Simplify (- 1) into -1 2.788 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.789 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.790 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 2.790 * [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))))) 2.791 * [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))))) 2.792 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.792 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.793 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.793 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.793 * [backup-simplify]: Simplify (- 0) into 0 2.794 * [backup-simplify]: Simplify (+ 0 0) into 0 2.794 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.795 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.795 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.797 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.797 * [taylor]: Taking taylor expansion of 0 in k 2.797 * [backup-simplify]: Simplify 0 into 0 2.797 * [backup-simplify]: Simplify 0 into 0 2.797 * [backup-simplify]: Simplify 0 into 0 2.797 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.798 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.799 * [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 2.800 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.800 * [backup-simplify]: Simplify (- 0) into 0 2.800 * [backup-simplify]: Simplify (+ 0 0) into 0 2.801 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.801 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.802 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.804 * [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 2.804 * [taylor]: Taking taylor expansion of 0 in k 2.804 * [backup-simplify]: Simplify 0 into 0 2.804 * [backup-simplify]: Simplify 0 into 0 2.804 * [backup-simplify]: Simplify 0 into 0 2.804 * [backup-simplify]: Simplify 0 into 0 2.804 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.805 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.808 * [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 2.808 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.808 * [backup-simplify]: Simplify (- 0) into 0 2.808 * [backup-simplify]: Simplify (+ 0 0) into 0 2.809 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.810 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.811 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.813 * [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 2.813 * [taylor]: Taking taylor expansion of 0 in k 2.813 * [backup-simplify]: Simplify 0 into 0 2.813 * [backup-simplify]: Simplify 0 into 0 2.813 * [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)))) 2.814 * [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))) 2.814 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 2.814 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 2.814 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.814 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.814 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 2.814 * [taylor]: Taking taylor expansion of 0.25 in k 2.814 * [backup-simplify]: Simplify 0.25 into 0.25 2.814 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.814 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.814 * [taylor]: Taking taylor expansion of k in k 2.814 * [backup-simplify]: Simplify 0 into 0 2.814 * [backup-simplify]: Simplify 1 into 1 2.814 * [backup-simplify]: Simplify (/ 1 1) into 1 2.815 * [taylor]: Taking taylor expansion of 1.0 in k 2.815 * [backup-simplify]: Simplify 1.0 into 1.0 2.815 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.815 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.815 * [taylor]: Taking taylor expansion of -2.0 in k 2.815 * [backup-simplify]: Simplify -2.0 into -2.0 2.815 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.815 * [taylor]: Taking taylor expansion of PI in k 2.815 * [backup-simplify]: Simplify PI into PI 2.815 * [taylor]: Taking taylor expansion of n in k 2.815 * [backup-simplify]: Simplify n into n 2.815 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.815 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.815 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.815 * [backup-simplify]: Simplify (+ 1 0) into 1 2.815 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 2.815 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 2.816 * [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)))))) 2.816 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.816 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.816 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.816 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.816 * [taylor]: Taking taylor expansion of 0.25 in n 2.816 * [backup-simplify]: Simplify 0.25 into 0.25 2.816 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.816 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.816 * [taylor]: Taking taylor expansion of k in n 2.816 * [backup-simplify]: Simplify k into k 2.816 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.816 * [taylor]: Taking taylor expansion of 1.0 in n 2.816 * [backup-simplify]: Simplify 1.0 into 1.0 2.816 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.816 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.816 * [taylor]: Taking taylor expansion of -2.0 in n 2.816 * [backup-simplify]: Simplify -2.0 into -2.0 2.816 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.816 * [taylor]: Taking taylor expansion of PI in n 2.816 * [backup-simplify]: Simplify PI into PI 2.816 * [taylor]: Taking taylor expansion of n in n 2.816 * [backup-simplify]: Simplify 0 into 0 2.816 * [backup-simplify]: Simplify 1 into 1 2.816 * [backup-simplify]: Simplify (/ PI 1) into PI 2.817 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.817 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.817 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.817 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.818 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.819 * [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)))) 2.820 * [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))))) 2.820 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.820 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.820 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.820 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.820 * [taylor]: Taking taylor expansion of 0.25 in n 2.820 * [backup-simplify]: Simplify 0.25 into 0.25 2.820 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.820 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.820 * [taylor]: Taking taylor expansion of k in n 2.820 * [backup-simplify]: Simplify k into k 2.820 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.820 * [taylor]: Taking taylor expansion of 1.0 in n 2.820 * [backup-simplify]: Simplify 1.0 into 1.0 2.820 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.820 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.820 * [taylor]: Taking taylor expansion of -2.0 in n 2.820 * [backup-simplify]: Simplify -2.0 into -2.0 2.820 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.820 * [taylor]: Taking taylor expansion of PI in n 2.820 * [backup-simplify]: Simplify PI into PI 2.820 * [taylor]: Taking taylor expansion of n in n 2.820 * [backup-simplify]: Simplify 0 into 0 2.820 * [backup-simplify]: Simplify 1 into 1 2.820 * [backup-simplify]: Simplify (/ PI 1) into PI 2.821 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.821 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.822 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.822 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.822 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.823 * [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)))) 2.824 * [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))))) 2.824 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.824 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.824 * [taylor]: Taking taylor expansion of 0.25 in k 2.824 * [backup-simplify]: Simplify 0.25 into 0.25 2.824 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.824 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.824 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.824 * [taylor]: Taking taylor expansion of k in k 2.824 * [backup-simplify]: Simplify 0 into 0 2.824 * [backup-simplify]: Simplify 1 into 1 2.824 * [backup-simplify]: Simplify (/ 1 1) into 1 2.824 * [taylor]: Taking taylor expansion of 1.0 in k 2.824 * [backup-simplify]: Simplify 1.0 into 1.0 2.824 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.824 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.824 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.824 * [taylor]: Taking taylor expansion of -2.0 in k 2.825 * [backup-simplify]: Simplify -2.0 into -2.0 2.825 * [taylor]: Taking taylor expansion of PI in k 2.825 * [backup-simplify]: Simplify PI into PI 2.825 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.825 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.825 * [taylor]: Taking taylor expansion of (log n) in k 2.825 * [taylor]: Taking taylor expansion of n in k 2.826 * [backup-simplify]: Simplify n into n 2.826 * [backup-simplify]: Simplify (log n) into (log n) 2.826 * [backup-simplify]: Simplify (+ 1 0) into 1 2.826 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.826 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.827 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.828 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 2.828 * [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))))) 2.829 * [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))))) 2.830 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.830 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.831 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.831 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.832 * [backup-simplify]: Simplify (+ 0 0) into 0 2.832 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.833 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.834 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.835 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.835 * [taylor]: Taking taylor expansion of 0 in k 2.835 * [backup-simplify]: Simplify 0 into 0 2.835 * [backup-simplify]: Simplify 0 into 0 2.835 * [backup-simplify]: Simplify 0 into 0 2.836 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.836 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.838 * [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 2.838 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.838 * [backup-simplify]: Simplify (+ 0 0) into 0 2.839 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.840 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.840 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.842 * [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 2.842 * [taylor]: Taking taylor expansion of 0 in k 2.842 * [backup-simplify]: Simplify 0 into 0 2.842 * [backup-simplify]: Simplify 0 into 0 2.842 * [backup-simplify]: Simplify 0 into 0 2.842 * [backup-simplify]: Simplify 0 into 0 2.843 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.843 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.851 * [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 2.852 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.852 * [backup-simplify]: Simplify (+ 0 0) into 0 2.853 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.853 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.855 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.856 * [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 2.856 * [taylor]: Taking taylor expansion of 0 in k 2.856 * [backup-simplify]: Simplify 0 into 0 2.856 * [backup-simplify]: Simplify 0 into 0 2.857 * [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)))))) 2.857 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 2.857 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 2.857 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 2.857 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 2.857 * [taylor]: Taking taylor expansion of 1.0 in k 2.857 * [backup-simplify]: Simplify 1.0 into 1.0 2.857 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.857 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.857 * [taylor]: Taking taylor expansion of k in k 2.857 * [backup-simplify]: Simplify 0 into 0 2.857 * [backup-simplify]: Simplify 1 into 1 2.858 * [backup-simplify]: Simplify (/ 1 1) into 1 2.858 * [backup-simplify]: Simplify (sqrt 0) into 0 2.859 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.859 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 2.859 * [taylor]: Taking taylor expansion of 1.0 in k 2.859 * [backup-simplify]: Simplify 1.0 into 1.0 2.859 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.859 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.859 * [taylor]: Taking taylor expansion of k in k 2.859 * [backup-simplify]: Simplify 0 into 0 2.859 * [backup-simplify]: Simplify 1 into 1 2.859 * [backup-simplify]: Simplify (/ 1 1) into 1 2.859 * [backup-simplify]: Simplify (sqrt 0) into 0 2.860 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.860 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.860 * [backup-simplify]: Simplify 0 into 0 2.861 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 2.861 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.862 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.864 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.865 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 2.865 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.866 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.868 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.869 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 2.869 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.870 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 2.870 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 2.870 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 2.870 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 2.870 * [taylor]: Taking taylor expansion of 1.0 in k 2.870 * [backup-simplify]: Simplify 1.0 into 1.0 2.870 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.870 * [taylor]: Taking taylor expansion of k in k 2.870 * [backup-simplify]: Simplify 0 into 0 2.870 * [backup-simplify]: Simplify 1 into 1 2.870 * [backup-simplify]: Simplify (sqrt 0) into 0 2.871 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.871 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 2.871 * [taylor]: Taking taylor expansion of 1.0 in k 2.871 * [backup-simplify]: Simplify 1.0 into 1.0 2.871 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.871 * [taylor]: Taking taylor expansion of k in k 2.871 * [backup-simplify]: Simplify 0 into 0 2.871 * [backup-simplify]: Simplify 1 into 1 2.871 * [backup-simplify]: Simplify (sqrt 0) into 0 2.872 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.872 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.872 * [backup-simplify]: Simplify 0 into 0 2.873 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 2.873 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.875 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.876 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 2.876 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.878 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.880 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 2.880 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.881 * [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)))))))) 2.881 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 2.881 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 2.881 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 2.881 * [taylor]: Taking taylor expansion of 1.0 in k 2.881 * [backup-simplify]: Simplify 1.0 into 1.0 2.881 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.881 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.881 * [taylor]: Taking taylor expansion of -1 in k 2.881 * [backup-simplify]: Simplify -1 into -1 2.881 * [taylor]: Taking taylor expansion of k in k 2.881 * [backup-simplify]: Simplify 0 into 0 2.881 * [backup-simplify]: Simplify 1 into 1 2.881 * [backup-simplify]: Simplify (/ -1 1) into -1 2.882 * [backup-simplify]: Simplify (sqrt 0) into 0 2.882 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.883 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 2.883 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 2.883 * [taylor]: Taking taylor expansion of 1.0 in k 2.883 * [backup-simplify]: Simplify 1.0 into 1.0 2.883 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.883 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.883 * [taylor]: Taking taylor expansion of -1 in k 2.883 * [backup-simplify]: Simplify -1 into -1 2.883 * [taylor]: Taking taylor expansion of k in k 2.883 * [backup-simplify]: Simplify 0 into 0 2.883 * [backup-simplify]: Simplify 1 into 1 2.883 * [backup-simplify]: Simplify (/ -1 1) into -1 2.883 * [backup-simplify]: Simplify (sqrt 0) into 0 2.884 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.884 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 2.884 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.885 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.886 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.888 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 2.888 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.888 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.891 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.893 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 2.893 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.894 * [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))))) 2.894 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 2.894 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.894 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 2.894 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.894 * [taylor]: Taking taylor expansion of 2.0 in n 2.894 * [backup-simplify]: Simplify 2.0 into 2.0 2.894 * [taylor]: Taking taylor expansion of (* n PI) in n 2.894 * [taylor]: Taking taylor expansion of n in n 2.894 * [backup-simplify]: Simplify 0 into 0 2.894 * [backup-simplify]: Simplify 1 into 1 2.894 * [taylor]: Taking taylor expansion of PI in n 2.894 * [backup-simplify]: Simplify PI into PI 2.894 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.894 * [taylor]: Taking taylor expansion of 2.0 in n 2.894 * [backup-simplify]: Simplify 2.0 into 2.0 2.894 * [taylor]: Taking taylor expansion of (* n PI) in n 2.894 * [taylor]: Taking taylor expansion of n in n 2.894 * [backup-simplify]: Simplify 0 into 0 2.894 * [backup-simplify]: Simplify 1 into 1 2.894 * [taylor]: Taking taylor expansion of PI in n 2.894 * [backup-simplify]: Simplify PI into PI 2.895 * [backup-simplify]: Simplify (* 0 PI) into 0 2.895 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.895 * [backup-simplify]: Simplify 0 into 0 2.896 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.897 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.897 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.898 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.898 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.898 * [backup-simplify]: Simplify 0 into 0 2.899 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.899 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.899 * [backup-simplify]: Simplify 0 into 0 2.900 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.901 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.901 * [backup-simplify]: Simplify 0 into 0 2.902 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.902 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 2.902 * [backup-simplify]: Simplify 0 into 0 2.903 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.904 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 2.904 * [backup-simplify]: Simplify 0 into 0 2.905 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.906 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.906 * [backup-simplify]: Simplify 0 into 0 2.906 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.907 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 2.907 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 2.907 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.907 * [taylor]: Taking taylor expansion of 2.0 in n 2.907 * [backup-simplify]: Simplify 2.0 into 2.0 2.907 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.907 * [taylor]: Taking taylor expansion of PI in n 2.907 * [backup-simplify]: Simplify PI into PI 2.907 * [taylor]: Taking taylor expansion of n in n 2.907 * [backup-simplify]: Simplify 0 into 0 2.907 * [backup-simplify]: Simplify 1 into 1 2.907 * [backup-simplify]: Simplify (/ PI 1) into PI 2.907 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.907 * [taylor]: Taking taylor expansion of 2.0 in n 2.907 * [backup-simplify]: Simplify 2.0 into 2.0 2.907 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.907 * [taylor]: Taking taylor expansion of PI in n 2.907 * [backup-simplify]: Simplify PI into PI 2.907 * [taylor]: Taking taylor expansion of n in n 2.907 * [backup-simplify]: Simplify 0 into 0 2.907 * [backup-simplify]: Simplify 1 into 1 2.908 * [backup-simplify]: Simplify (/ PI 1) into PI 2.908 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.908 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.909 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.909 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.909 * [backup-simplify]: Simplify 0 into 0 2.910 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.910 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.910 * [backup-simplify]: Simplify 0 into 0 2.911 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.911 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.911 * [backup-simplify]: Simplify 0 into 0 2.912 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.913 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.913 * [backup-simplify]: Simplify 0 into 0 2.913 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.914 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.914 * [backup-simplify]: Simplify 0 into 0 2.915 * [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 2.916 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.916 * [backup-simplify]: Simplify 0 into 0 2.916 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 2.916 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 2.917 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 2.917 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.917 * [taylor]: Taking taylor expansion of -2.0 in n 2.917 * [backup-simplify]: Simplify -2.0 into -2.0 2.917 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.917 * [taylor]: Taking taylor expansion of PI in n 2.917 * [backup-simplify]: Simplify PI into PI 2.917 * [taylor]: Taking taylor expansion of n in n 2.917 * [backup-simplify]: Simplify 0 into 0 2.917 * [backup-simplify]: Simplify 1 into 1 2.917 * [backup-simplify]: Simplify (/ PI 1) into PI 2.917 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.917 * [taylor]: Taking taylor expansion of -2.0 in n 2.917 * [backup-simplify]: Simplify -2.0 into -2.0 2.917 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.917 * [taylor]: Taking taylor expansion of PI in n 2.917 * [backup-simplify]: Simplify PI into PI 2.917 * [taylor]: Taking taylor expansion of n in n 2.917 * [backup-simplify]: Simplify 0 into 0 2.917 * [backup-simplify]: Simplify 1 into 1 2.917 * [backup-simplify]: Simplify (/ PI 1) into PI 2.918 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.918 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.919 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.919 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.919 * [backup-simplify]: Simplify 0 into 0 2.920 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.920 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.920 * [backup-simplify]: Simplify 0 into 0 2.921 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.921 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.921 * [backup-simplify]: Simplify 0 into 0 2.922 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.923 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.923 * [backup-simplify]: Simplify 0 into 0 2.923 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.924 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.924 * [backup-simplify]: Simplify 0 into 0 2.925 * [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 2.925 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.925 * [backup-simplify]: Simplify 0 into 0 2.926 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 2.926 * * * [progress]: simplifying candidates 2.929 * [simplify]: Simplifying: (* (+ (+ (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 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(cbrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2)))) (cbrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (* (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2)) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (sqrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (sqrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (pow (* (* h0 h1) h2) (/ (/ (/ (- h3 h4) h0) 2) 2)) (pow (* (* h0 h1) h2) (/ (/ (/ (- h3 h4) h0) 2) 2)) (* (+ (+ (log h0) (log h1)) (log h2)) (/ (/ (- h3 h4) h0) 2)) (* (+ (log (* h0 h1)) (log h2)) (/ (/ (- h3 h4) h0) 2)) (* (log (* (* h0 h1) h2)) (/ (/ (- h3 h4) h0) 2)) (* (log (* (* h0 h1) h2)) (/ (/ (- h3 h4) h0) 2)) (* 1 (/ (/ (- h3 h4) h0) 2)) (* 1 (/ (/ (- h3 h4) h0) 2)) (* 1 (/ (/ (- h3 h4) h0) 2)) (pow (* (* h0 h1) h2) (/ (/ h3 h0) 2)) (pow (* (* h0 h1) h2) (/ (/ h4 h0) 2)) (pow (* (* h0 h1) h2) (* (cbrt (/ (/ (- h3 h4) h0) 2)) (cbrt (/ (/ (- h3 h4) h0) 2)))) (pow (* (* h0 h1) h2) (sqrt (/ (/ (- h3 h4) h0) 2))) (pow (* (* h0 h1) h2) (/ (* (cbrt (/ (- h3 h4) h0)) (cbrt (/ (- h3 h4) h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (* (cbrt (/ (- h3 h4) h0)) (cbrt (/ (- h3 h4) h0))) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (* (cbrt (/ (- h3 h4) h0)) (cbrt (/ (- h3 h4) h0))) 1)) (pow (* (* h0 h1) h2) (/ (sqrt (/ (- h3 h4) h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (sqrt (/ (- h3 h4) h0)) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (sqrt (/ (- h3 h4) h0)) 1)) (pow (* (* h0 h1) h2) (/ (/ (* (cbrt (- h3 h4)) (cbrt (- h3 h4))) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (* (cbrt (- h3 h4)) (cbrt (- h3 h4))) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (* (cbrt (- h3 h4)) (cbrt (- h3 h4))) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h1) h2) (/ (/ (* (cbrt (- h3 h4)) (cbrt (- h3 h4))) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (* (cbrt (- h3 h4)) (cbrt (- h3 h4))) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (* (cbrt (- h3 h4)) (cbrt (- h3 h4))) (sqrt h0)) 1)) (pow (* (* h0 h1) h2) (/ (/ (* (cbrt (- h3 h4)) (cbrt (- h3 h4))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (* (cbrt (- h3 h4)) (cbrt (- h3 h4))) 1) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (* (cbrt (- h3 h4)) (cbrt (- h3 h4))) 1) 1)) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) (sqrt h0)) 1)) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) 1) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (sqrt (- h3 h4)) 1) 1)) (pow (* (* h0 h1) h2) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ 1 (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h1) h2) (/ (/ 1 (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ 1 (sqrt h0)) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ 1 (sqrt h0)) 1)) (pow (* (* h0 h1) h2) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ 1 1) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ 1 1) 1)) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) (sqrt h0)) 1)) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) 1) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ (+ (sqrt h3) (sqrt h4)) 1) 1)) (pow (* (* h0 h1) h2) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ 1 (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h1) h2) (/ (/ 1 (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ 1 (sqrt h0)) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ 1 (sqrt h0)) 1)) (pow (* (* h0 h1) h2) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (/ 1 1) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (/ 1 1) 1)) (pow (* (* h0 h1) h2) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ 1 (sqrt 2))) (pow (* (* h0 h1) h2) (/ 1 1)) (pow (* (* h0 h1) h2) (/ (- h3 h4) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h1) h2) (/ (- h3 h4) (sqrt 2))) (pow (* (* h0 h1) h2) (/ (- h3 h4) 1)) (pow (* (* h0 h1) h2) 1) (pow (* (* h0 h1) h2) (/ (- h3 h4) h0)) (pow (* h0 h1) (/ (/ (- h3 h4) h0) 2)) (pow h2 (/ (/ (- h3 h4) h0) 2)) (log (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (exp (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (cbrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (cbrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2)))) (cbrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (* (* (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2)) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (sqrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (sqrt (pow (* (* h0 h1) h2) (/ (/ (- h3 h4) h0) 2))) (pow (* (* h0 h1) h2) (/ (/ (/ (- h3 h4) h0) 2) 2)) (pow (* (* h0 h1) h2) (/ (/ (/ (- h3 h4) h0) 2) 2)) (- (log h3) (log (sqrt h4))) (log (/ h3 (sqrt h4))) (exp (/ h3 (sqrt h4))) (/ (* (* h3 h3) h3) (* (* (sqrt h4) (sqrt h4)) (sqrt h4))) (* (cbrt (/ h3 (sqrt h4))) (cbrt (/ h3 (sqrt h4)))) (cbrt (/ h3 (sqrt h4))) (* (* (/ h3 (sqrt h4)) (/ h3 (sqrt h4))) (/ h3 (sqrt h4))) (sqrt (/ h3 (sqrt h4))) (sqrt (/ h3 (sqrt h4))) (- h3) (- (sqrt h4)) (/ (* (cbrt h3) (cbrt h3)) (* (cbrt (sqrt h4)) (cbrt (sqrt h4)))) (/ (cbrt h3) (cbrt (sqrt h4))) (/ (* (cbrt h3) (cbrt h3)) (sqrt (* (cbrt h4) (cbrt h4)))) (/ (cbrt h3) (sqrt (cbrt h4))) (/ (* (cbrt h3) (cbrt h3)) (sqrt (sqrt h4))) (/ (cbrt h3) (sqrt (sqrt h4))) (/ (* (cbrt h3) (cbrt h3)) (sqrt 1)) (/ (cbrt h3) (sqrt h4)) (/ (* (cbrt h3) (cbrt h3)) (sqrt (sqrt h4))) (/ (cbrt h3) (sqrt (sqrt h4))) (/ (* (cbrt h3) (cbrt h3)) 1) (/ (cbrt h3) (sqrt h4)) (/ (sqrt h3) (* (cbrt (sqrt h4)) (cbrt (sqrt h4)))) (/ (sqrt h3) (cbrt (sqrt h4))) (/ (sqrt h3) (sqrt (* (cbrt h4) (cbrt h4)))) (/ (sqrt h3) (sqrt (cbrt h4))) (/ (sqrt h3) (sqrt (sqrt h4))) (/ (sqrt h3) (sqrt (sqrt h4))) (/ (sqrt h3) (sqrt 1)) (/ (sqrt h3) (sqrt h4)) (/ (sqrt h3) (sqrt (sqrt h4))) (/ (sqrt h3) (sqrt (sqrt h4))) (/ (sqrt h3) 1) (/ (sqrt h3) (sqrt h4)) (/ 1 (* (cbrt (sqrt h4)) (cbrt (sqrt h4)))) (/ h3 (cbrt (sqrt h4))) (/ 1 (sqrt (* (cbrt h4) (cbrt h4)))) (/ h3 (sqrt (cbrt h4))) (/ 1 (sqrt (sqrt h4))) (/ h3 (sqrt (sqrt h4))) (/ 1 (sqrt 1)) (/ h3 (sqrt h4)) (/ 1 (sqrt (sqrt h4))) (/ h3 (sqrt (sqrt h4))) (/ 1 1) (/ h3 (sqrt h4)) (/ 1 (sqrt h4)) (/ (sqrt h4) h3) (/ h3 (* (cbrt (sqrt h4)) (cbrt (sqrt h4)))) (/ h3 (sqrt (* (cbrt h4) (cbrt h4)))) (/ h3 (sqrt (sqrt h4))) (/ h3 (sqrt 1)) (/ h3 (sqrt (sqrt h4))) (/ h3 1) (/ (sqrt h4) (cbrt h3)) (/ (sqrt h4) (sqrt h3)) (/ (sqrt h4) h3) (* (* h0 h1) h2) (* (* h0 h1) h2) (+ (+ (log h0) (log h1)) (log h2)) (+ (log (* h0 h1)) (log h2)) (log (* (* h0 h1) h2)) (exp (* (* h0 h1) h2)) (* (* (* (* h0 h0) h0) (* (* h1 h1) h1)) (* (* h2 h2) h2)) (* (* (* (* h0 h1) (* h0 h1)) (* h0 h1)) (* (* h2 h2) h2)) (* (cbrt (* (* h0 h1) h2)) (cbrt (* (* h0 h1) h2))) (cbrt (* (* h0 h1) h2)) (* (* (* (* h0 h1) h2) (* (* h0 h1) h2)) (* (* h0 h1) h2)) (sqrt (* (* h0 h1) h2)) (sqrt (* (* h0 h1) h2)) (* (* h0 h1) (* (cbrt h2) (cbrt h2))) (* (* h0 h1) (sqrt h2)) (* (* h0 h1) 1) (* h1 h2) (- (+ (* h5 (* (pow h4 2) (* (pow (log (* h0 h1)) 2) (exp (* h6 (+ (log (* h0 h1)) (log h2))))))) (+ (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (+ (* h7 (* (pow h4 2) (* (log (* h0 h1)) (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (log h2))))) (* h5 (* (pow h4 2) (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (pow (log h2) 2))))))) (+ (* h6 (* h4 (* (log (* h0 h1)) (exp (* h6 (+ (log (* h0 h1)) (log h2))))))) (* h6 (* h4 (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (log h2)))))) (exp (* h6 (* (- (log (* h0 h1)) (log (/ 1 h2))) (- h3 h4)))) (exp (* h6 (* (- h3 h4) (- (log (* h8 h1)) (log (/ -1 h2)))))) (- (+ (* h5 (* (pow h4 2) (* (pow (log (* h0 h1)) 2) (exp (* h6 (+ (log (* h0 h1)) (log h2))))))) (+ (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (+ (* h7 (* (pow h4 2) (* (log (* h0 h1)) (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (log h2))))) (* h5 (* (pow h4 2) (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (pow (log h2) 2))))))) (+ (* h6 (* h4 (* (log (* h0 h1)) (exp (* h6 (+ (log (* h0 h1)) (log h2))))))) (* h6 (* h4 (* (exp (* h6 (+ (log (* h0 h1)) (log h2)))) (log h2)))))) (exp (* h6 (* (- (log (* h0 h1)) (log (/ 1 h2))) (- h3 h4)))) (exp (* h6 (* (- h3 h4) (- (log (* h8 h1)) (log (/ -1 h2)))))) (- (+ (* h9 h4) (- (+ (* h9 (pow h4 2)) (- h9))))) (- (+ (* h9 (/ 1 (pow h4 2))) (- (+ (* h9 (/ 1 h4)) (- (* h9 (/ 1 (pow h4 3)))))))) (- (+ (* h9 (/ 1 (pow h4 2))) (- (+ (* h9 (/ 1 h4)) (- h9))))) (* h0 (* h2 h1)) (* h0 (* h2 h1)) (* h0 (* h2 h1)) 2.945 * * [simplify]: iteration 0 : 859 enodes (cost 1848 ) 2.958 * * [simplify]: iteration 1 : 3384 enodes (cost 1776 ) 3.006 * * [simplify]: iteration 2 : 5001 enodes (cost 1766 ) 3.014 * * * [progress]: adding candidates to table 3.716 * * [progress]: iteration 4 / 4 3.716 * * * [progress]: picking best candidate 3.736 * * * * [pick]: Picked # 3.736 * * * [progress]: localizing error 3.756 * * * [progress]: generating rewritten candidates 3.757 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 3.784 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2 2) 3.820 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 2 1) 3.858 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 3.915 * * * [progress]: generating series expansions 3.915 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 3.916 * [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))) 3.916 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 3.916 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 3.916 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.916 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.916 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 3.916 * [taylor]: Taking taylor expansion of 0.25 in k 3.916 * [backup-simplify]: Simplify 0.25 into 0.25 3.916 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.916 * [taylor]: Taking taylor expansion of 1.0 in k 3.916 * [backup-simplify]: Simplify 1.0 into 1.0 3.916 * [taylor]: Taking taylor expansion of k in k 3.916 * [backup-simplify]: Simplify 0 into 0 3.916 * [backup-simplify]: Simplify 1 into 1 3.916 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.916 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.916 * [taylor]: Taking taylor expansion of 2.0 in k 3.916 * [backup-simplify]: Simplify 2.0 into 2.0 3.916 * [taylor]: Taking taylor expansion of (* n PI) in k 3.916 * [taylor]: Taking taylor expansion of n in k 3.916 * [backup-simplify]: Simplify n into n 3.916 * [taylor]: Taking taylor expansion of PI in k 3.916 * [backup-simplify]: Simplify PI into PI 3.916 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.916 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.916 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.917 * [backup-simplify]: Simplify (- 0) into 0 3.917 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.917 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 3.917 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 3.917 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 3.917 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 3.917 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.918 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.918 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 3.918 * [taylor]: Taking taylor expansion of 0.25 in n 3.918 * [backup-simplify]: Simplify 0.25 into 0.25 3.918 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.918 * [taylor]: Taking taylor expansion of 1.0 in n 3.918 * [backup-simplify]: Simplify 1.0 into 1.0 3.918 * [taylor]: Taking taylor expansion of k in n 3.918 * [backup-simplify]: Simplify k into k 3.918 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.918 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.918 * [taylor]: Taking taylor expansion of 2.0 in n 3.918 * [backup-simplify]: Simplify 2.0 into 2.0 3.918 * [taylor]: Taking taylor expansion of (* n PI) in n 3.918 * [taylor]: Taking taylor expansion of n in n 3.918 * [backup-simplify]: Simplify 0 into 0 3.918 * [backup-simplify]: Simplify 1 into 1 3.918 * [taylor]: Taking taylor expansion of PI in n 3.918 * [backup-simplify]: Simplify PI into PI 3.918 * [backup-simplify]: Simplify (* 0 PI) into 0 3.918 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.919 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.920 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.921 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.921 * [backup-simplify]: Simplify (- k) into (- k) 3.921 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.921 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 3.922 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.922 * [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)))) 3.923 * [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))))) 3.923 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 3.923 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.923 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.923 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 3.923 * [taylor]: Taking taylor expansion of 0.25 in n 3.923 * [backup-simplify]: Simplify 0.25 into 0.25 3.923 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.923 * [taylor]: Taking taylor expansion of 1.0 in n 3.923 * [backup-simplify]: Simplify 1.0 into 1.0 3.923 * [taylor]: Taking taylor expansion of k in n 3.923 * [backup-simplify]: Simplify k into k 3.923 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.923 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.923 * [taylor]: Taking taylor expansion of 2.0 in n 3.923 * [backup-simplify]: Simplify 2.0 into 2.0 3.923 * [taylor]: Taking taylor expansion of (* n PI) in n 3.923 * [taylor]: Taking taylor expansion of n in n 3.923 * [backup-simplify]: Simplify 0 into 0 3.923 * [backup-simplify]: Simplify 1 into 1 3.923 * [taylor]: Taking taylor expansion of PI in n 3.923 * [backup-simplify]: Simplify PI into PI 3.924 * [backup-simplify]: Simplify (* 0 PI) into 0 3.924 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.925 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.926 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.926 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.926 * [backup-simplify]: Simplify (- k) into (- k) 3.926 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.926 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 3.927 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.928 * [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)))) 3.929 * [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))))) 3.929 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 3.929 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 3.929 * [taylor]: Taking taylor expansion of 0.25 in k 3.929 * [backup-simplify]: Simplify 0.25 into 0.25 3.929 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 3.929 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.929 * [taylor]: Taking taylor expansion of 1.0 in k 3.929 * [backup-simplify]: Simplify 1.0 into 1.0 3.929 * [taylor]: Taking taylor expansion of k in k 3.929 * [backup-simplify]: Simplify 0 into 0 3.929 * [backup-simplify]: Simplify 1 into 1 3.929 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 3.929 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.929 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.929 * [taylor]: Taking taylor expansion of 2.0 in k 3.929 * [backup-simplify]: Simplify 2.0 into 2.0 3.929 * [taylor]: Taking taylor expansion of PI in k 3.929 * [backup-simplify]: Simplify PI into PI 3.929 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.930 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.930 * [taylor]: Taking taylor expansion of (log n) in k 3.930 * [taylor]: Taking taylor expansion of n in k 3.930 * [backup-simplify]: Simplify n into n 3.930 * [backup-simplify]: Simplify (log n) into (log n) 3.930 * [backup-simplify]: Simplify (- 0) into 0 3.930 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.931 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 3.932 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 3.932 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 3.933 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 3.934 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 3.934 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.935 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 3.936 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.936 * [backup-simplify]: Simplify (- 0) into 0 3.936 * [backup-simplify]: Simplify (+ 0 0) into 0 3.937 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 3.937 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.938 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 3.939 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.939 * [taylor]: Taking taylor expansion of 0 in k 3.939 * [backup-simplify]: Simplify 0 into 0 3.939 * [backup-simplify]: Simplify 0 into 0 3.940 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.941 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.941 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 3.942 * [backup-simplify]: Simplify (+ 0 0) into 0 3.942 * [backup-simplify]: Simplify (- 1) into -1 3.942 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.943 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 3.944 * [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)))) 3.946 * [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)))))) 3.948 * [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)))))) 3.948 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.949 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.951 * [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 3.951 * [backup-simplify]: Simplify (- 0) into 0 3.951 * [backup-simplify]: Simplify (+ 0 0) into 0 3.952 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 3.953 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.953 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 3.955 * [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 3.955 * [taylor]: Taking taylor expansion of 0 in k 3.955 * [backup-simplify]: Simplify 0 into 0 3.955 * [backup-simplify]: Simplify 0 into 0 3.955 * [backup-simplify]: Simplify 0 into 0 3.955 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.957 * [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 3.958 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 3.958 * [backup-simplify]: Simplify (+ 0 0) into 0 3.959 * [backup-simplify]: Simplify (- 0) into 0 3.959 * [backup-simplify]: Simplify (+ 0 0) into 0 3.960 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 3.961 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 3.964 * [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))))) 3.967 * [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))))) 3.972 * [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)))))) 3.973 * [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)))) 3.973 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 3.973 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 3.973 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.973 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.973 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 3.973 * [taylor]: Taking taylor expansion of 0.25 in k 3.973 * [backup-simplify]: Simplify 0.25 into 0.25 3.973 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.973 * [taylor]: Taking taylor expansion of 1.0 in k 3.973 * [backup-simplify]: Simplify 1.0 into 1.0 3.973 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.973 * [taylor]: Taking taylor expansion of k in k 3.973 * [backup-simplify]: Simplify 0 into 0 3.973 * [backup-simplify]: Simplify 1 into 1 3.973 * [backup-simplify]: Simplify (/ 1 1) into 1 3.973 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.973 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.973 * [taylor]: Taking taylor expansion of 2.0 in k 3.973 * [backup-simplify]: Simplify 2.0 into 2.0 3.973 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.974 * [taylor]: Taking taylor expansion of PI in k 3.974 * [backup-simplify]: Simplify PI into PI 3.974 * [taylor]: Taking taylor expansion of n in k 3.974 * [backup-simplify]: Simplify n into n 3.974 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.974 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 3.974 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 3.974 * [backup-simplify]: Simplify (- 1) into -1 3.974 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.974 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 3.975 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 3.975 * [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))))) 3.975 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 3.975 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.975 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.975 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 3.975 * [taylor]: Taking taylor expansion of 0.25 in n 3.975 * [backup-simplify]: Simplify 0.25 into 0.25 3.975 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.975 * [taylor]: Taking taylor expansion of 1.0 in n 3.975 * [backup-simplify]: Simplify 1.0 into 1.0 3.975 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.975 * [taylor]: Taking taylor expansion of k in n 3.975 * [backup-simplify]: Simplify k into k 3.975 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.975 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.975 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.975 * [taylor]: Taking taylor expansion of 2.0 in n 3.975 * [backup-simplify]: Simplify 2.0 into 2.0 3.975 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.975 * [taylor]: Taking taylor expansion of PI in n 3.975 * [backup-simplify]: Simplify PI into PI 3.975 * [taylor]: Taking taylor expansion of n in n 3.975 * [backup-simplify]: Simplify 0 into 0 3.975 * [backup-simplify]: Simplify 1 into 1 3.975 * [backup-simplify]: Simplify (/ PI 1) into PI 3.976 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.976 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.976 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.976 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.976 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 3.977 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.978 * [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)))) 3.979 * [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))))) 3.979 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 3.979 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.979 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.979 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 3.979 * [taylor]: Taking taylor expansion of 0.25 in n 3.979 * [backup-simplify]: Simplify 0.25 into 0.25 3.979 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.979 * [taylor]: Taking taylor expansion of 1.0 in n 3.979 * [backup-simplify]: Simplify 1.0 into 1.0 3.979 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.979 * [taylor]: Taking taylor expansion of k in n 3.979 * [backup-simplify]: Simplify k into k 3.979 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.979 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.979 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.979 * [taylor]: Taking taylor expansion of 2.0 in n 3.979 * [backup-simplify]: Simplify 2.0 into 2.0 3.979 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.979 * [taylor]: Taking taylor expansion of PI in n 3.979 * [backup-simplify]: Simplify PI into PI 3.979 * [taylor]: Taking taylor expansion of n in n 3.979 * [backup-simplify]: Simplify 0 into 0 3.979 * [backup-simplify]: Simplify 1 into 1 3.979 * [backup-simplify]: Simplify (/ PI 1) into PI 3.980 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.981 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.981 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.981 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.981 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 3.982 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.982 * [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)))) 3.990 * [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))))) 3.990 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 3.990 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 3.990 * [taylor]: Taking taylor expansion of 0.25 in k 3.990 * [backup-simplify]: Simplify 0.25 into 0.25 3.990 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 3.990 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 3.990 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.990 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.990 * [taylor]: Taking taylor expansion of 2.0 in k 3.990 * [backup-simplify]: Simplify 2.0 into 2.0 3.990 * [taylor]: Taking taylor expansion of PI in k 3.990 * [backup-simplify]: Simplify PI into PI 3.991 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.991 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.991 * [taylor]: Taking taylor expansion of (log n) in k 3.991 * [taylor]: Taking taylor expansion of n in k 3.991 * [backup-simplify]: Simplify n into n 3.991 * [backup-simplify]: Simplify (log n) into (log n) 3.991 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.991 * [taylor]: Taking taylor expansion of 1.0 in k 3.991 * [backup-simplify]: Simplify 1.0 into 1.0 3.991 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.991 * [taylor]: Taking taylor expansion of k in k 3.992 * [backup-simplify]: Simplify 0 into 0 3.992 * [backup-simplify]: Simplify 1 into 1 3.992 * [backup-simplify]: Simplify (/ 1 1) into 1 3.992 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 3.993 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 3.993 * [backup-simplify]: Simplify (- 1) into -1 3.993 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.994 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 3.994 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 3.995 * [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))))) 3.996 * [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))))) 3.996 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.997 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.998 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.998 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.998 * [backup-simplify]: Simplify (- 0) into 0 3.998 * [backup-simplify]: Simplify (+ 0 0) into 0 3.999 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 3.999 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.000 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 4.001 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.001 * [taylor]: Taking taylor expansion of 0 in k 4.001 * [backup-simplify]: Simplify 0 into 0 4.001 * [backup-simplify]: Simplify 0 into 0 4.001 * [backup-simplify]: Simplify 0 into 0 4.002 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.002 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.004 * [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 4.004 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.005 * [backup-simplify]: Simplify (- 0) into 0 4.005 * [backup-simplify]: Simplify (+ 0 0) into 0 4.005 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 4.006 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.007 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 4.008 * [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 4.008 * [taylor]: Taking taylor expansion of 0 in k 4.008 * [backup-simplify]: Simplify 0 into 0 4.008 * [backup-simplify]: Simplify 0 into 0 4.008 * [backup-simplify]: Simplify 0 into 0 4.008 * [backup-simplify]: Simplify 0 into 0 4.009 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.010 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.012 * [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 4.013 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.013 * [backup-simplify]: Simplify (- 0) into 0 4.013 * [backup-simplify]: Simplify (+ 0 0) into 0 4.014 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 4.015 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.016 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 4.018 * [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 4.018 * [taylor]: Taking taylor expansion of 0 in k 4.018 * [backup-simplify]: Simplify 0 into 0 4.018 * [backup-simplify]: Simplify 0 into 0 4.018 * [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)))) 4.019 * [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))) 4.019 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 4.019 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 4.019 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.019 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.019 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 4.019 * [taylor]: Taking taylor expansion of 0.25 in k 4.019 * [backup-simplify]: Simplify 0.25 into 0.25 4.019 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.019 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.019 * [taylor]: Taking taylor expansion of k in k 4.019 * [backup-simplify]: Simplify 0 into 0 4.019 * [backup-simplify]: Simplify 1 into 1 4.019 * [backup-simplify]: Simplify (/ 1 1) into 1 4.019 * [taylor]: Taking taylor expansion of 1.0 in k 4.019 * [backup-simplify]: Simplify 1.0 into 1.0 4.019 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.020 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.020 * [taylor]: Taking taylor expansion of -2.0 in k 4.020 * [backup-simplify]: Simplify -2.0 into -2.0 4.020 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.020 * [taylor]: Taking taylor expansion of PI in k 4.020 * [backup-simplify]: Simplify PI into PI 4.020 * [taylor]: Taking taylor expansion of n in k 4.020 * [backup-simplify]: Simplify n into n 4.020 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.020 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.020 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.020 * [backup-simplify]: Simplify (+ 1 0) into 1 4.020 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 4.020 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 4.020 * [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)))))) 4.021 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 4.021 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.021 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.021 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 4.021 * [taylor]: Taking taylor expansion of 0.25 in n 4.021 * [backup-simplify]: Simplify 0.25 into 0.25 4.021 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.021 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.021 * [taylor]: Taking taylor expansion of k in n 4.021 * [backup-simplify]: Simplify k into k 4.021 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.021 * [taylor]: Taking taylor expansion of 1.0 in n 4.021 * [backup-simplify]: Simplify 1.0 into 1.0 4.021 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.021 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.021 * [taylor]: Taking taylor expansion of -2.0 in n 4.021 * [backup-simplify]: Simplify -2.0 into -2.0 4.021 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.021 * [taylor]: Taking taylor expansion of PI in n 4.021 * [backup-simplify]: Simplify PI into PI 4.021 * [taylor]: Taking taylor expansion of n in n 4.021 * [backup-simplify]: Simplify 0 into 0 4.021 * [backup-simplify]: Simplify 1 into 1 4.021 * [backup-simplify]: Simplify (/ PI 1) into PI 4.021 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.022 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.022 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.022 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 4.023 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.024 * [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)))) 4.024 * [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))))) 4.025 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 4.025 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.025 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.025 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 4.025 * [taylor]: Taking taylor expansion of 0.25 in n 4.025 * [backup-simplify]: Simplify 0.25 into 0.25 4.025 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.025 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.025 * [taylor]: Taking taylor expansion of k in n 4.025 * [backup-simplify]: Simplify k into k 4.025 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.025 * [taylor]: Taking taylor expansion of 1.0 in n 4.025 * [backup-simplify]: Simplify 1.0 into 1.0 4.025 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.025 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.025 * [taylor]: Taking taylor expansion of -2.0 in n 4.025 * [backup-simplify]: Simplify -2.0 into -2.0 4.025 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.025 * [taylor]: Taking taylor expansion of PI in n 4.025 * [backup-simplify]: Simplify PI into PI 4.025 * [taylor]: Taking taylor expansion of n in n 4.025 * [backup-simplify]: Simplify 0 into 0 4.025 * [backup-simplify]: Simplify 1 into 1 4.025 * [backup-simplify]: Simplify (/ PI 1) into PI 4.025 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.026 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.026 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.026 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 4.027 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.028 * [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)))) 4.028 * [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))))) 4.029 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.029 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.029 * [taylor]: Taking taylor expansion of 0.25 in k 4.029 * [backup-simplify]: Simplify 0.25 into 0.25 4.029 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.029 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.029 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.029 * [taylor]: Taking taylor expansion of k in k 4.029 * [backup-simplify]: Simplify 0 into 0 4.029 * [backup-simplify]: Simplify 1 into 1 4.029 * [backup-simplify]: Simplify (/ 1 1) into 1 4.029 * [taylor]: Taking taylor expansion of 1.0 in k 4.029 * [backup-simplify]: Simplify 1.0 into 1.0 4.029 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.029 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.029 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.029 * [taylor]: Taking taylor expansion of -2.0 in k 4.029 * [backup-simplify]: Simplify -2.0 into -2.0 4.029 * [taylor]: Taking taylor expansion of PI in k 4.029 * [backup-simplify]: Simplify PI into PI 4.029 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.030 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.030 * [taylor]: Taking taylor expansion of (log n) in k 4.030 * [taylor]: Taking taylor expansion of n in k 4.030 * [backup-simplify]: Simplify n into n 4.030 * [backup-simplify]: Simplify (log n) into (log n) 4.030 * [backup-simplify]: Simplify (+ 1 0) into 1 4.030 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.031 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 4.032 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 4.032 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 4.033 * [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))))) 4.034 * [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))))) 4.034 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.035 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.036 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.036 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.036 * [backup-simplify]: Simplify (+ 0 0) into 0 4.036 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 4.037 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.038 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.039 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.039 * [taylor]: Taking taylor expansion of 0 in k 4.039 * [backup-simplify]: Simplify 0 into 0 4.039 * [backup-simplify]: Simplify 0 into 0 4.039 * [backup-simplify]: Simplify 0 into 0 4.040 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.040 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.042 * [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 4.042 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.042 * [backup-simplify]: Simplify (+ 0 0) into 0 4.043 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 4.044 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.045 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 4.046 * [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 4.046 * [taylor]: Taking taylor expansion of 0 in k 4.046 * [backup-simplify]: Simplify 0 into 0 4.046 * [backup-simplify]: Simplify 0 into 0 4.046 * [backup-simplify]: Simplify 0 into 0 4.046 * [backup-simplify]: Simplify 0 into 0 4.047 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.047 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.050 * [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 4.050 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.051 * [backup-simplify]: Simplify (+ 0 0) into 0 4.051 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 4.052 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.053 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 4.055 * [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 4.055 * [taylor]: Taking taylor expansion of 0 in k 4.055 * [backup-simplify]: Simplify 0 into 0 4.055 * [backup-simplify]: Simplify 0 into 0 4.056 * [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)))))) 4.056 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2 2) 4.056 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) into (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) 4.056 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in (n k) around 0 4.056 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in k 4.056 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.056 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.056 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in k 4.056 * [taylor]: Taking taylor expansion of 0.125 in k 4.056 * [backup-simplify]: Simplify 0.125 into 0.125 4.056 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.056 * [taylor]: Taking taylor expansion of 1.0 in k 4.056 * [backup-simplify]: Simplify 1.0 into 1.0 4.056 * [taylor]: Taking taylor expansion of k in k 4.056 * [backup-simplify]: Simplify 0 into 0 4.056 * [backup-simplify]: Simplify 1 into 1 4.056 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.056 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.056 * [taylor]: Taking taylor expansion of 2.0 in k 4.056 * [backup-simplify]: Simplify 2.0 into 2.0 4.056 * [taylor]: Taking taylor expansion of (* n PI) in k 4.056 * [taylor]: Taking taylor expansion of n in k 4.056 * [backup-simplify]: Simplify n into n 4.056 * [taylor]: Taking taylor expansion of PI in k 4.056 * [backup-simplify]: Simplify PI into PI 4.056 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.057 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.057 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.057 * [backup-simplify]: Simplify (- 0) into 0 4.057 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.057 * [backup-simplify]: Simplify (* 0.125 1.0) into 0.125 4.057 * [backup-simplify]: Simplify (* 0.125 (log (* 2.0 (* n PI)))) into (* 0.125 (log (* 2.0 (* n PI)))) 4.057 * [backup-simplify]: Simplify (exp (* 0.125 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.125) 4.057 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in n 4.058 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.058 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.058 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in n 4.058 * [taylor]: Taking taylor expansion of 0.125 in n 4.058 * [backup-simplify]: Simplify 0.125 into 0.125 4.058 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.058 * [taylor]: Taking taylor expansion of 1.0 in n 4.058 * [backup-simplify]: Simplify 1.0 into 1.0 4.058 * [taylor]: Taking taylor expansion of k in n 4.058 * [backup-simplify]: Simplify k into k 4.058 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.058 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.058 * [taylor]: Taking taylor expansion of 2.0 in n 4.058 * [backup-simplify]: Simplify 2.0 into 2.0 4.058 * [taylor]: Taking taylor expansion of (* n PI) in n 4.058 * [taylor]: Taking taylor expansion of n in n 4.058 * [backup-simplify]: Simplify 0 into 0 4.058 * [backup-simplify]: Simplify 1 into 1 4.058 * [taylor]: Taking taylor expansion of PI in n 4.058 * [backup-simplify]: Simplify PI into PI 4.058 * [backup-simplify]: Simplify (* 0 PI) into 0 4.058 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.059 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.060 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.061 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.061 * [backup-simplify]: Simplify (- k) into (- k) 4.061 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.061 * [backup-simplify]: Simplify (* 0.125 (- 1.0 k)) into (* 0.125 (- 1.0 k)) 4.062 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.062 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.063 * [backup-simplify]: Simplify (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.063 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in n 4.063 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.063 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.063 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in n 4.063 * [taylor]: Taking taylor expansion of 0.125 in n 4.063 * [backup-simplify]: Simplify 0.125 into 0.125 4.063 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.063 * [taylor]: Taking taylor expansion of 1.0 in n 4.063 * [backup-simplify]: Simplify 1.0 into 1.0 4.063 * [taylor]: Taking taylor expansion of k in n 4.063 * [backup-simplify]: Simplify k into k 4.063 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.063 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.063 * [taylor]: Taking taylor expansion of 2.0 in n 4.063 * [backup-simplify]: Simplify 2.0 into 2.0 4.063 * [taylor]: Taking taylor expansion of (* n PI) in n 4.063 * [taylor]: Taking taylor expansion of n in n 4.063 * [backup-simplify]: Simplify 0 into 0 4.063 * [backup-simplify]: Simplify 1 into 1 4.063 * [taylor]: Taking taylor expansion of PI in n 4.063 * [backup-simplify]: Simplify PI into PI 4.064 * [backup-simplify]: Simplify (* 0 PI) into 0 4.064 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.065 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.066 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.066 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.066 * [backup-simplify]: Simplify (- k) into (- k) 4.066 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.066 * [backup-simplify]: Simplify (* 0.125 (- 1.0 k)) into (* 0.125 (- 1.0 k)) 4.067 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.068 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.068 * [backup-simplify]: Simplify (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.069 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.069 * [taylor]: Taking taylor expansion of (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.069 * [taylor]: Taking taylor expansion of 0.125 in k 4.069 * [backup-simplify]: Simplify 0.125 into 0.125 4.069 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.069 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.069 * [taylor]: Taking taylor expansion of 1.0 in k 4.069 * [backup-simplify]: Simplify 1.0 into 1.0 4.069 * [taylor]: Taking taylor expansion of k in k 4.069 * [backup-simplify]: Simplify 0 into 0 4.069 * [backup-simplify]: Simplify 1 into 1 4.069 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.069 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.069 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.069 * [taylor]: Taking taylor expansion of 2.0 in k 4.069 * [backup-simplify]: Simplify 2.0 into 2.0 4.069 * [taylor]: Taking taylor expansion of PI in k 4.069 * [backup-simplify]: Simplify PI into PI 4.069 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.070 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.070 * [taylor]: Taking taylor expansion of (log n) in k 4.070 * [taylor]: Taking taylor expansion of n in k 4.070 * [backup-simplify]: Simplify n into n 4.070 * [backup-simplify]: Simplify (log n) into (log n) 4.070 * [backup-simplify]: Simplify (- 0) into 0 4.070 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.071 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 4.072 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 4.072 * [backup-simplify]: Simplify (* 0.125 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.125 (+ (log (* 2.0 PI)) (log n))) 4.073 * [backup-simplify]: Simplify (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 4.074 * [backup-simplify]: Simplify (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 4.074 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.075 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.076 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.076 * [backup-simplify]: Simplify (- 0) into 0 4.076 * [backup-simplify]: Simplify (+ 0 0) into 0 4.076 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (- 1.0 k))) into 0 4.077 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.078 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 4.079 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.079 * [taylor]: Taking taylor expansion of 0 in k 4.079 * [backup-simplify]: Simplify 0 into 0 4.079 * [backup-simplify]: Simplify 0 into 0 4.085 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.087 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.087 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.087 * [backup-simplify]: Simplify (+ 0 0) into 0 4.088 * [backup-simplify]: Simplify (- 1) into -1 4.088 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.089 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 4.090 * [backup-simplify]: Simplify (+ (* 0.125 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 4.092 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 1) 1)))) into (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) 4.094 * [backup-simplify]: Simplify (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) into (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) 4.094 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.095 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.097 * [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 4.097 * [backup-simplify]: Simplify (- 0) into 0 4.097 * [backup-simplify]: Simplify (+ 0 0) into 0 4.098 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 4.099 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.099 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.101 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.101 * [taylor]: Taking taylor expansion of 0 in k 4.101 * [backup-simplify]: Simplify 0 into 0 4.101 * [backup-simplify]: Simplify 0 into 0 4.101 * [backup-simplify]: Simplify 0 into 0 4.101 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.103 * [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 4.104 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.104 * [backup-simplify]: Simplify (+ 0 0) into 0 4.105 * [backup-simplify]: Simplify (- 0) into 0 4.105 * [backup-simplify]: Simplify (+ 0 0) into 0 4.106 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.107 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 4.110 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) 4.113 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) 4.118 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) (* k 1)) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.0078125 (* (pow k 2) (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (* 0.015625 (* (pow k 2) (* (log (* 2.0 PI)) (* (log n) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n))))))))))) (+ (* 0.125 (* k (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (* 0.125 (* k (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (log (* 2.0 PI))))))) 4.119 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (/ (- 1.0 (/ 1 k)) 2.0) 2) 2)) into (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) 4.119 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in (n k) around 0 4.119 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in k 4.119 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.119 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.119 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in k 4.119 * [taylor]: Taking taylor expansion of 0.125 in k 4.119 * [backup-simplify]: Simplify 0.125 into 0.125 4.119 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.119 * [taylor]: Taking taylor expansion of 1.0 in k 4.119 * [backup-simplify]: Simplify 1.0 into 1.0 4.119 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.119 * [taylor]: Taking taylor expansion of k in k 4.119 * [backup-simplify]: Simplify 0 into 0 4.119 * [backup-simplify]: Simplify 1 into 1 4.119 * [backup-simplify]: Simplify (/ 1 1) into 1 4.119 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.119 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.120 * [taylor]: Taking taylor expansion of 2.0 in k 4.120 * [backup-simplify]: Simplify 2.0 into 2.0 4.120 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.120 * [taylor]: Taking taylor expansion of PI in k 4.120 * [backup-simplify]: Simplify PI into PI 4.120 * [taylor]: Taking taylor expansion of n in k 4.120 * [backup-simplify]: Simplify n into n 4.120 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.120 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.120 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.120 * [backup-simplify]: Simplify (- 1) into -1 4.120 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.121 * [backup-simplify]: Simplify (* 0.125 -1) into -0.125 4.121 * [backup-simplify]: Simplify (* -0.125 (log (* 2.0 (/ PI n)))) into (* -0.125 (log (* 2.0 (/ PI n)))) 4.121 * [backup-simplify]: Simplify (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.125 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 4.121 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in n 4.121 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.121 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.121 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in n 4.121 * [taylor]: Taking taylor expansion of 0.125 in n 4.121 * [backup-simplify]: Simplify 0.125 into 0.125 4.121 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.121 * [taylor]: Taking taylor expansion of 1.0 in n 4.121 * [backup-simplify]: Simplify 1.0 into 1.0 4.121 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.121 * [taylor]: Taking taylor expansion of k in n 4.121 * [backup-simplify]: Simplify k into k 4.121 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.121 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.121 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.121 * [taylor]: Taking taylor expansion of 2.0 in n 4.121 * [backup-simplify]: Simplify 2.0 into 2.0 4.121 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.121 * [taylor]: Taking taylor expansion of PI in n 4.121 * [backup-simplify]: Simplify PI into PI 4.121 * [taylor]: Taking taylor expansion of n in n 4.122 * [backup-simplify]: Simplify 0 into 0 4.122 * [backup-simplify]: Simplify 1 into 1 4.122 * [backup-simplify]: Simplify (/ PI 1) into PI 4.122 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.123 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.123 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.123 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.123 * [backup-simplify]: Simplify (* 0.125 (- 1.0 (/ 1 k))) into (* 0.125 (- 1.0 (/ 1 k))) 4.124 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.124 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.125 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.125 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in n 4.125 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.125 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.125 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in n 4.125 * [taylor]: Taking taylor expansion of 0.125 in n 4.125 * [backup-simplify]: Simplify 0.125 into 0.125 4.125 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.125 * [taylor]: Taking taylor expansion of 1.0 in n 4.125 * [backup-simplify]: Simplify 1.0 into 1.0 4.125 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.125 * [taylor]: Taking taylor expansion of k in n 4.125 * [backup-simplify]: Simplify k into k 4.125 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.125 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.125 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.125 * [taylor]: Taking taylor expansion of 2.0 in n 4.125 * [backup-simplify]: Simplify 2.0 into 2.0 4.125 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.125 * [taylor]: Taking taylor expansion of PI in n 4.125 * [backup-simplify]: Simplify PI into PI 4.126 * [taylor]: Taking taylor expansion of n in n 4.126 * [backup-simplify]: Simplify 0 into 0 4.126 * [backup-simplify]: Simplify 1 into 1 4.126 * [backup-simplify]: Simplify (/ PI 1) into PI 4.126 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.127 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.127 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.127 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.127 * [backup-simplify]: Simplify (* 0.125 (- 1.0 (/ 1 k))) into (* 0.125 (- 1.0 (/ 1 k))) 4.128 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.128 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.129 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.129 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.129 * [taylor]: Taking taylor expansion of (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.129 * [taylor]: Taking taylor expansion of 0.125 in k 4.129 * [backup-simplify]: Simplify 0.125 into 0.125 4.129 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.129 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.129 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.129 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.129 * [taylor]: Taking taylor expansion of 2.0 in k 4.129 * [backup-simplify]: Simplify 2.0 into 2.0 4.129 * [taylor]: Taking taylor expansion of PI in k 4.129 * [backup-simplify]: Simplify PI into PI 4.130 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.130 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.130 * [taylor]: Taking taylor expansion of (log n) in k 4.130 * [taylor]: Taking taylor expansion of n in k 4.130 * [backup-simplify]: Simplify n into n 4.130 * [backup-simplify]: Simplify (log n) into (log n) 4.130 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.130 * [taylor]: Taking taylor expansion of 1.0 in k 4.130 * [backup-simplify]: Simplify 1.0 into 1.0 4.130 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.130 * [taylor]: Taking taylor expansion of k in k 4.130 * [backup-simplify]: Simplify 0 into 0 4.130 * [backup-simplify]: Simplify 1 into 1 4.131 * [backup-simplify]: Simplify (/ 1 1) into 1 4.131 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.131 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 4.132 * [backup-simplify]: Simplify (- 1) into -1 4.132 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.132 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 4.133 * [backup-simplify]: Simplify (* 0.125 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.125 (- (log (* 2.0 PI)) (log n))) 4.134 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.135 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.135 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.135 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.136 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.136 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.137 * [backup-simplify]: Simplify (- 0) into 0 4.137 * [backup-simplify]: Simplify (+ 0 0) into 0 4.137 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.138 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.139 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 4.140 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.140 * [taylor]: Taking taylor expansion of 0 in k 4.140 * [backup-simplify]: Simplify 0 into 0 4.140 * [backup-simplify]: Simplify 0 into 0 4.140 * [backup-simplify]: Simplify 0 into 0 4.141 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.141 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.143 * [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 4.143 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.143 * [backup-simplify]: Simplify (- 0) into 0 4.144 * [backup-simplify]: Simplify (+ 0 0) into 0 4.144 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 4.145 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.146 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 4.147 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.147 * [taylor]: Taking taylor expansion of 0 in k 4.147 * [backup-simplify]: Simplify 0 into 0 4.147 * [backup-simplify]: Simplify 0 into 0 4.147 * [backup-simplify]: Simplify 0 into 0 4.147 * [backup-simplify]: Simplify 0 into 0 4.148 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.148 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.151 * [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 4.152 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.152 * [backup-simplify]: Simplify (- 0) into 0 4.152 * [backup-simplify]: Simplify (+ 0 0) into 0 4.153 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 4.153 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.155 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 4.156 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (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 4.156 * [taylor]: Taking taylor expansion of 0 in k 4.156 * [backup-simplify]: Simplify 0 into 0 4.156 * [backup-simplify]: Simplify 0 into 0 4.157 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 4.157 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2) 2)) into (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) 4.157 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in (n k) around 0 4.157 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in k 4.157 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.157 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.157 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in k 4.158 * [taylor]: Taking taylor expansion of 0.125 in k 4.158 * [backup-simplify]: Simplify 0.125 into 0.125 4.158 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.158 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.158 * [taylor]: Taking taylor expansion of k in k 4.158 * [backup-simplify]: Simplify 0 into 0 4.158 * [backup-simplify]: Simplify 1 into 1 4.158 * [backup-simplify]: Simplify (/ 1 1) into 1 4.158 * [taylor]: Taking taylor expansion of 1.0 in k 4.158 * [backup-simplify]: Simplify 1.0 into 1.0 4.158 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.158 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.158 * [taylor]: Taking taylor expansion of -2.0 in k 4.158 * [backup-simplify]: Simplify -2.0 into -2.0 4.158 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.158 * [taylor]: Taking taylor expansion of PI in k 4.158 * [backup-simplify]: Simplify PI into PI 4.158 * [taylor]: Taking taylor expansion of n in k 4.158 * [backup-simplify]: Simplify n into n 4.158 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.158 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.158 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.158 * [backup-simplify]: Simplify (+ 1 0) into 1 4.159 * [backup-simplify]: Simplify (* 0.125 1) into 0.125 4.159 * [backup-simplify]: Simplify (* 0.125 (log (* -2.0 (/ PI n)))) into (* 0.125 (log (* -2.0 (/ PI n)))) 4.159 * [backup-simplify]: Simplify (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 4.159 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in n 4.159 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.159 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.159 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in n 4.159 * [taylor]: Taking taylor expansion of 0.125 in n 4.159 * [backup-simplify]: Simplify 0.125 into 0.125 4.159 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.159 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.159 * [taylor]: Taking taylor expansion of k in n 4.159 * [backup-simplify]: Simplify k into k 4.159 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.159 * [taylor]: Taking taylor expansion of 1.0 in n 4.159 * [backup-simplify]: Simplify 1.0 into 1.0 4.159 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.159 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.159 * [taylor]: Taking taylor expansion of -2.0 in n 4.159 * [backup-simplify]: Simplify -2.0 into -2.0 4.159 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.159 * [taylor]: Taking taylor expansion of PI in n 4.159 * [backup-simplify]: Simplify PI into PI 4.159 * [taylor]: Taking taylor expansion of n in n 4.159 * [backup-simplify]: Simplify 0 into 0 4.159 * [backup-simplify]: Simplify 1 into 1 4.160 * [backup-simplify]: Simplify (/ PI 1) into PI 4.160 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.160 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.161 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.161 * [backup-simplify]: Simplify (* 0.125 (+ (/ 1 k) 1.0)) into (* 0.125 (+ (/ 1 k) 1.0)) 4.161 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.162 * [backup-simplify]: Simplify (* (* 0.125 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.163 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.163 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in n 4.163 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.163 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.163 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in n 4.163 * [taylor]: Taking taylor expansion of 0.125 in n 4.163 * [backup-simplify]: Simplify 0.125 into 0.125 4.163 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.163 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.163 * [taylor]: Taking taylor expansion of k in n 4.163 * [backup-simplify]: Simplify k into k 4.163 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.163 * [taylor]: Taking taylor expansion of 1.0 in n 4.163 * [backup-simplify]: Simplify 1.0 into 1.0 4.163 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.163 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.163 * [taylor]: Taking taylor expansion of -2.0 in n 4.163 * [backup-simplify]: Simplify -2.0 into -2.0 4.163 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.163 * [taylor]: Taking taylor expansion of PI in n 4.163 * [backup-simplify]: Simplify PI into PI 4.163 * [taylor]: Taking taylor expansion of n in n 4.163 * [backup-simplify]: Simplify 0 into 0 4.163 * [backup-simplify]: Simplify 1 into 1 4.164 * [backup-simplify]: Simplify (/ PI 1) into PI 4.164 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.164 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.165 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.165 * [backup-simplify]: Simplify (* 0.125 (+ (/ 1 k) 1.0)) into (* 0.125 (+ (/ 1 k) 1.0)) 4.165 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.166 * [backup-simplify]: Simplify (* (* 0.125 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.167 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.167 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.167 * [taylor]: Taking taylor expansion of (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.167 * [taylor]: Taking taylor expansion of 0.125 in k 4.167 * [backup-simplify]: Simplify 0.125 into 0.125 4.167 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.167 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.167 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.167 * [taylor]: Taking taylor expansion of k in k 4.167 * [backup-simplify]: Simplify 0 into 0 4.167 * [backup-simplify]: Simplify 1 into 1 4.167 * [backup-simplify]: Simplify (/ 1 1) into 1 4.167 * [taylor]: Taking taylor expansion of 1.0 in k 4.167 * [backup-simplify]: Simplify 1.0 into 1.0 4.167 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.167 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.167 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.167 * [taylor]: Taking taylor expansion of -2.0 in k 4.167 * [backup-simplify]: Simplify -2.0 into -2.0 4.167 * [taylor]: Taking taylor expansion of PI in k 4.167 * [backup-simplify]: Simplify PI into PI 4.168 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.168 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.168 * [taylor]: Taking taylor expansion of (log n) in k 4.168 * [taylor]: Taking taylor expansion of n in k 4.168 * [backup-simplify]: Simplify n into n 4.168 * [backup-simplify]: Simplify (log n) into (log n) 4.169 * [backup-simplify]: Simplify (+ 1 0) into 1 4.169 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.169 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 4.170 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 4.171 * [backup-simplify]: Simplify (* 0.125 (- (log (* -2.0 PI)) (log n))) into (* 0.125 (- (log (* -2.0 PI)) (log n))) 4.171 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.172 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.173 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.173 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.174 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.174 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.180 * [backup-simplify]: Simplify (+ 0 0) into 0 4.181 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (+ (/ 1 k) 1.0))) into 0 4.182 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.183 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.184 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.184 * [taylor]: Taking taylor expansion of 0 in k 4.184 * [backup-simplify]: Simplify 0 into 0 4.184 * [backup-simplify]: Simplify 0 into 0 4.184 * [backup-simplify]: Simplify 0 into 0 4.184 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.185 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.187 * [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 4.187 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.187 * [backup-simplify]: Simplify (+ 0 0) into 0 4.188 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 4.189 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.190 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 4.191 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.191 * [taylor]: Taking taylor expansion of 0 in k 4.191 * [backup-simplify]: Simplify 0 into 0 4.191 * [backup-simplify]: Simplify 0 into 0 4.191 * [backup-simplify]: Simplify 0 into 0 4.191 * [backup-simplify]: Simplify 0 into 0 4.192 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.192 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.195 * [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 4.196 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.196 * [backup-simplify]: Simplify (+ 0 0) into 0 4.197 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 4.197 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.199 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 4.200 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 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 4.200 * [taylor]: Taking taylor expansion of 0 in k 4.200 * [backup-simplify]: Simplify 0 into 0 4.200 * [backup-simplify]: Simplify 0 into 0 4.201 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.125 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 4.201 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 2 1) 4.201 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) into (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) 4.201 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in (n k) around 0 4.201 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in k 4.202 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.202 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.202 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in k 4.202 * [taylor]: Taking taylor expansion of 0.125 in k 4.202 * [backup-simplify]: Simplify 0.125 into 0.125 4.202 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.202 * [taylor]: Taking taylor expansion of 1.0 in k 4.202 * [backup-simplify]: Simplify 1.0 into 1.0 4.202 * [taylor]: Taking taylor expansion of k in k 4.202 * [backup-simplify]: Simplify 0 into 0 4.202 * [backup-simplify]: Simplify 1 into 1 4.202 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.202 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.202 * [taylor]: Taking taylor expansion of 2.0 in k 4.202 * [backup-simplify]: Simplify 2.0 into 2.0 4.202 * [taylor]: Taking taylor expansion of (* n PI) in k 4.202 * [taylor]: Taking taylor expansion of n in k 4.202 * [backup-simplify]: Simplify n into n 4.202 * [taylor]: Taking taylor expansion of PI in k 4.202 * [backup-simplify]: Simplify PI into PI 4.202 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.202 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.202 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.202 * [backup-simplify]: Simplify (- 0) into 0 4.202 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.203 * [backup-simplify]: Simplify (* 0.125 1.0) into 0.125 4.203 * [backup-simplify]: Simplify (* 0.125 (log (* 2.0 (* n PI)))) into (* 0.125 (log (* 2.0 (* n PI)))) 4.203 * [backup-simplify]: Simplify (exp (* 0.125 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.125) 4.203 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in n 4.203 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.203 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.203 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in n 4.203 * [taylor]: Taking taylor expansion of 0.125 in n 4.203 * [backup-simplify]: Simplify 0.125 into 0.125 4.203 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.203 * [taylor]: Taking taylor expansion of 1.0 in n 4.203 * [backup-simplify]: Simplify 1.0 into 1.0 4.203 * [taylor]: Taking taylor expansion of k in n 4.203 * [backup-simplify]: Simplify k into k 4.203 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.203 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.203 * [taylor]: Taking taylor expansion of 2.0 in n 4.203 * [backup-simplify]: Simplify 2.0 into 2.0 4.203 * [taylor]: Taking taylor expansion of (* n PI) in n 4.203 * [taylor]: Taking taylor expansion of n in n 4.203 * [backup-simplify]: Simplify 0 into 0 4.203 * [backup-simplify]: Simplify 1 into 1 4.203 * [taylor]: Taking taylor expansion of PI in n 4.203 * [backup-simplify]: Simplify PI into PI 4.203 * [backup-simplify]: Simplify (* 0 PI) into 0 4.204 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.205 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.205 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.206 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.206 * [backup-simplify]: Simplify (- k) into (- k) 4.206 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.206 * [backup-simplify]: Simplify (* 0.125 (- 1.0 k)) into (* 0.125 (- 1.0 k)) 4.207 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.208 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.208 * [backup-simplify]: Simplify (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.208 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in n 4.208 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.208 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.208 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in n 4.208 * [taylor]: Taking taylor expansion of 0.125 in n 4.208 * [backup-simplify]: Simplify 0.125 into 0.125 4.208 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.208 * [taylor]: Taking taylor expansion of 1.0 in n 4.208 * [backup-simplify]: Simplify 1.0 into 1.0 4.209 * [taylor]: Taking taylor expansion of k in n 4.209 * [backup-simplify]: Simplify k into k 4.209 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.209 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.209 * [taylor]: Taking taylor expansion of 2.0 in n 4.209 * [backup-simplify]: Simplify 2.0 into 2.0 4.209 * [taylor]: Taking taylor expansion of (* n PI) in n 4.209 * [taylor]: Taking taylor expansion of n in n 4.209 * [backup-simplify]: Simplify 0 into 0 4.209 * [backup-simplify]: Simplify 1 into 1 4.209 * [taylor]: Taking taylor expansion of PI in n 4.209 * [backup-simplify]: Simplify PI into PI 4.209 * [backup-simplify]: Simplify (* 0 PI) into 0 4.209 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.210 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.211 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.211 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.212 * [backup-simplify]: Simplify (- k) into (- k) 4.212 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.212 * [backup-simplify]: Simplify (* 0.125 (- 1.0 k)) into (* 0.125 (- 1.0 k)) 4.212 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.213 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.214 * [backup-simplify]: Simplify (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.214 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.214 * [taylor]: Taking taylor expansion of (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.214 * [taylor]: Taking taylor expansion of 0.125 in k 4.214 * [backup-simplify]: Simplify 0.125 into 0.125 4.214 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.214 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.214 * [taylor]: Taking taylor expansion of 1.0 in k 4.214 * [backup-simplify]: Simplify 1.0 into 1.0 4.214 * [taylor]: Taking taylor expansion of k in k 4.214 * [backup-simplify]: Simplify 0 into 0 4.214 * [backup-simplify]: Simplify 1 into 1 4.214 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.214 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.214 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.214 * [taylor]: Taking taylor expansion of 2.0 in k 4.214 * [backup-simplify]: Simplify 2.0 into 2.0 4.214 * [taylor]: Taking taylor expansion of PI in k 4.214 * [backup-simplify]: Simplify PI into PI 4.214 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.215 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.215 * [taylor]: Taking taylor expansion of (log n) in k 4.215 * [taylor]: Taking taylor expansion of n in k 4.215 * [backup-simplify]: Simplify n into n 4.215 * [backup-simplify]: Simplify (log n) into (log n) 4.215 * [backup-simplify]: Simplify (- 0) into 0 4.216 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.216 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 4.217 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 4.218 * [backup-simplify]: Simplify (* 0.125 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.125 (+ (log (* 2.0 PI)) (log n))) 4.218 * [backup-simplify]: Simplify (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 4.219 * [backup-simplify]: Simplify (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 4.219 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.220 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.221 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.221 * [backup-simplify]: Simplify (- 0) into 0 4.221 * [backup-simplify]: Simplify (+ 0 0) into 0 4.222 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (- 1.0 k))) into 0 4.222 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.223 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 4.224 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.224 * [taylor]: Taking taylor expansion of 0 in k 4.224 * [backup-simplify]: Simplify 0 into 0 4.224 * [backup-simplify]: Simplify 0 into 0 4.225 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.226 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.226 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.226 * [backup-simplify]: Simplify (+ 0 0) into 0 4.227 * [backup-simplify]: Simplify (- 1) into -1 4.227 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.228 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 4.229 * [backup-simplify]: Simplify (+ (* 0.125 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 4.231 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 1) 1)))) into (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) 4.233 * [backup-simplify]: Simplify (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) into (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) 4.233 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.234 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.236 * [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 4.236 * [backup-simplify]: Simplify (- 0) into 0 4.236 * [backup-simplify]: Simplify (+ 0 0) into 0 4.236 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 4.237 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.238 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.239 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.240 * [taylor]: Taking taylor expansion of 0 in k 4.240 * [backup-simplify]: Simplify 0 into 0 4.240 * [backup-simplify]: Simplify 0 into 0 4.240 * [backup-simplify]: Simplify 0 into 0 4.240 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.242 * [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 4.243 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.243 * [backup-simplify]: Simplify (+ 0 0) into 0 4.243 * [backup-simplify]: Simplify (- 0) into 0 4.244 * [backup-simplify]: Simplify (+ 0 0) into 0 4.245 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.246 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 4.248 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) 4.251 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) 4.257 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) (* k 1)) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.0078125 (* (pow k 2) (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (* 0.015625 (* (pow k 2) (* (log (* 2.0 PI)) (* (log n) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n))))))))))) (+ (* 0.125 (* k (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (* 0.125 (* k (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (log (* 2.0 PI))))))) 4.258 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (/ (- 1.0 (/ 1 k)) 2.0) 2) 2)) into (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) 4.258 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in (n k) around 0 4.258 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in k 4.258 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.258 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.258 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in k 4.258 * [taylor]: Taking taylor expansion of 0.125 in k 4.258 * [backup-simplify]: Simplify 0.125 into 0.125 4.258 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.258 * [taylor]: Taking taylor expansion of 1.0 in k 4.258 * [backup-simplify]: Simplify 1.0 into 1.0 4.258 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.258 * [taylor]: Taking taylor expansion of k in k 4.258 * [backup-simplify]: Simplify 0 into 0 4.258 * [backup-simplify]: Simplify 1 into 1 4.258 * [backup-simplify]: Simplify (/ 1 1) into 1 4.258 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.258 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.258 * [taylor]: Taking taylor expansion of 2.0 in k 4.258 * [backup-simplify]: Simplify 2.0 into 2.0 4.258 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.258 * [taylor]: Taking taylor expansion of PI in k 4.258 * [backup-simplify]: Simplify PI into PI 4.258 * [taylor]: Taking taylor expansion of n in k 4.258 * [backup-simplify]: Simplify n into n 4.258 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.258 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.258 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.259 * [backup-simplify]: Simplify (- 1) into -1 4.259 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.259 * [backup-simplify]: Simplify (* 0.125 -1) into -0.125 4.259 * [backup-simplify]: Simplify (* -0.125 (log (* 2.0 (/ PI n)))) into (* -0.125 (log (* 2.0 (/ PI n)))) 4.259 * [backup-simplify]: Simplify (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.125 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 4.259 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in n 4.259 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.259 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.259 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in n 4.259 * [taylor]: Taking taylor expansion of 0.125 in n 4.259 * [backup-simplify]: Simplify 0.125 into 0.125 4.259 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.260 * [taylor]: Taking taylor expansion of 1.0 in n 4.260 * [backup-simplify]: Simplify 1.0 into 1.0 4.260 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.260 * [taylor]: Taking taylor expansion of k in n 4.260 * [backup-simplify]: Simplify k into k 4.260 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.260 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.260 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.260 * [taylor]: Taking taylor expansion of 2.0 in n 4.260 * [backup-simplify]: Simplify 2.0 into 2.0 4.260 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.260 * [taylor]: Taking taylor expansion of PI in n 4.260 * [backup-simplify]: Simplify PI into PI 4.260 * [taylor]: Taking taylor expansion of n in n 4.260 * [backup-simplify]: Simplify 0 into 0 4.260 * [backup-simplify]: Simplify 1 into 1 4.260 * [backup-simplify]: Simplify (/ PI 1) into PI 4.260 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.261 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.261 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.261 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.261 * [backup-simplify]: Simplify (* 0.125 (- 1.0 (/ 1 k))) into (* 0.125 (- 1.0 (/ 1 k))) 4.262 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.263 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.263 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.263 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in n 4.263 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.263 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.263 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in n 4.263 * [taylor]: Taking taylor expansion of 0.125 in n 4.263 * [backup-simplify]: Simplify 0.125 into 0.125 4.263 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.263 * [taylor]: Taking taylor expansion of 1.0 in n 4.264 * [backup-simplify]: Simplify 1.0 into 1.0 4.264 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.264 * [taylor]: Taking taylor expansion of k in n 4.264 * [backup-simplify]: Simplify k into k 4.264 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.264 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.264 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.264 * [taylor]: Taking taylor expansion of 2.0 in n 4.264 * [backup-simplify]: Simplify 2.0 into 2.0 4.264 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.264 * [taylor]: Taking taylor expansion of PI in n 4.264 * [backup-simplify]: Simplify PI into PI 4.264 * [taylor]: Taking taylor expansion of n in n 4.264 * [backup-simplify]: Simplify 0 into 0 4.264 * [backup-simplify]: Simplify 1 into 1 4.264 * [backup-simplify]: Simplify (/ PI 1) into PI 4.264 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.265 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.265 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.265 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.265 * [backup-simplify]: Simplify (* 0.125 (- 1.0 (/ 1 k))) into (* 0.125 (- 1.0 (/ 1 k))) 4.266 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.267 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.267 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.267 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.267 * [taylor]: Taking taylor expansion of (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.267 * [taylor]: Taking taylor expansion of 0.125 in k 4.267 * [backup-simplify]: Simplify 0.125 into 0.125 4.267 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.267 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.267 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.267 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.268 * [taylor]: Taking taylor expansion of 2.0 in k 4.268 * [backup-simplify]: Simplify 2.0 into 2.0 4.268 * [taylor]: Taking taylor expansion of PI in k 4.268 * [backup-simplify]: Simplify PI into PI 4.268 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.268 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.268 * [taylor]: Taking taylor expansion of (log n) in k 4.269 * [taylor]: Taking taylor expansion of n in k 4.269 * [backup-simplify]: Simplify n into n 4.269 * [backup-simplify]: Simplify (log n) into (log n) 4.269 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.269 * [taylor]: Taking taylor expansion of 1.0 in k 4.269 * [backup-simplify]: Simplify 1.0 into 1.0 4.269 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.269 * [taylor]: Taking taylor expansion of k in k 4.269 * [backup-simplify]: Simplify 0 into 0 4.269 * [backup-simplify]: Simplify 1 into 1 4.269 * [backup-simplify]: Simplify (/ 1 1) into 1 4.269 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.276 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 4.276 * [backup-simplify]: Simplify (- 1) into -1 4.276 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.277 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 4.278 * [backup-simplify]: Simplify (* 0.125 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.125 (- (log (* 2.0 PI)) (log n))) 4.278 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.279 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.280 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.280 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.281 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.281 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.281 * [backup-simplify]: Simplify (- 0) into 0 4.282 * [backup-simplify]: Simplify (+ 0 0) into 0 4.282 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.283 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.283 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 4.285 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.285 * [taylor]: Taking taylor expansion of 0 in k 4.285 * [backup-simplify]: Simplify 0 into 0 4.285 * [backup-simplify]: Simplify 0 into 0 4.285 * [backup-simplify]: Simplify 0 into 0 4.285 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.286 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.287 * [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 4.288 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.288 * [backup-simplify]: Simplify (- 0) into 0 4.288 * [backup-simplify]: Simplify (+ 0 0) into 0 4.289 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 4.289 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.290 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 4.292 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.292 * [taylor]: Taking taylor expansion of 0 in k 4.292 * [backup-simplify]: Simplify 0 into 0 4.292 * [backup-simplify]: Simplify 0 into 0 4.292 * [backup-simplify]: Simplify 0 into 0 4.292 * [backup-simplify]: Simplify 0 into 0 4.292 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.293 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.296 * [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 4.296 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.296 * [backup-simplify]: Simplify (- 0) into 0 4.297 * [backup-simplify]: Simplify (+ 0 0) into 0 4.297 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 4.298 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.299 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 4.301 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (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 4.301 * [taylor]: Taking taylor expansion of 0 in k 4.301 * [backup-simplify]: Simplify 0 into 0 4.301 * [backup-simplify]: Simplify 0 into 0 4.301 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 4.302 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2) 2)) into (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) 4.302 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in (n k) around 0 4.302 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in k 4.302 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.302 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.302 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in k 4.302 * [taylor]: Taking taylor expansion of 0.125 in k 4.302 * [backup-simplify]: Simplify 0.125 into 0.125 4.302 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.302 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.302 * [taylor]: Taking taylor expansion of k in k 4.302 * [backup-simplify]: Simplify 0 into 0 4.302 * [backup-simplify]: Simplify 1 into 1 4.302 * [backup-simplify]: Simplify (/ 1 1) into 1 4.302 * [taylor]: Taking taylor expansion of 1.0 in k 4.302 * [backup-simplify]: Simplify 1.0 into 1.0 4.302 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.302 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.303 * [taylor]: Taking taylor expansion of -2.0 in k 4.303 * [backup-simplify]: Simplify -2.0 into -2.0 4.303 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.303 * [taylor]: Taking taylor expansion of PI in k 4.303 * [backup-simplify]: Simplify PI into PI 4.303 * [taylor]: Taking taylor expansion of n in k 4.303 * [backup-simplify]: Simplify n into n 4.303 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.303 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.303 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.303 * [backup-simplify]: Simplify (+ 1 0) into 1 4.303 * [backup-simplify]: Simplify (* 0.125 1) into 0.125 4.303 * [backup-simplify]: Simplify (* 0.125 (log (* -2.0 (/ PI n)))) into (* 0.125 (log (* -2.0 (/ PI n)))) 4.303 * [backup-simplify]: Simplify (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 4.304 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in n 4.304 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.304 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.304 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in n 4.304 * [taylor]: Taking taylor expansion of 0.125 in n 4.304 * [backup-simplify]: Simplify 0.125 into 0.125 4.304 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.304 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.304 * [taylor]: Taking taylor expansion of k in n 4.304 * [backup-simplify]: Simplify k into k 4.304 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.304 * [taylor]: Taking taylor expansion of 1.0 in n 4.304 * [backup-simplify]: Simplify 1.0 into 1.0 4.304 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.304 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.304 * [taylor]: Taking taylor expansion of -2.0 in n 4.304 * [backup-simplify]: Simplify -2.0 into -2.0 4.304 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.304 * [taylor]: Taking taylor expansion of PI in n 4.304 * [backup-simplify]: Simplify PI into PI 4.304 * [taylor]: Taking taylor expansion of n in n 4.304 * [backup-simplify]: Simplify 0 into 0 4.304 * [backup-simplify]: Simplify 1 into 1 4.304 * [backup-simplify]: Simplify (/ PI 1) into PI 4.304 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.305 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.305 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.305 * [backup-simplify]: Simplify (* 0.125 (+ (/ 1 k) 1.0)) into (* 0.125 (+ (/ 1 k) 1.0)) 4.306 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.307 * [backup-simplify]: Simplify (* (* 0.125 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.307 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.307 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in n 4.307 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.307 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.308 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in n 4.308 * [taylor]: Taking taylor expansion of 0.125 in n 4.308 * [backup-simplify]: Simplify 0.125 into 0.125 4.308 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.308 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.308 * [taylor]: Taking taylor expansion of k in n 4.308 * [backup-simplify]: Simplify k into k 4.308 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.308 * [taylor]: Taking taylor expansion of 1.0 in n 4.308 * [backup-simplify]: Simplify 1.0 into 1.0 4.308 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.308 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.308 * [taylor]: Taking taylor expansion of -2.0 in n 4.308 * [backup-simplify]: Simplify -2.0 into -2.0 4.308 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.308 * [taylor]: Taking taylor expansion of PI in n 4.308 * [backup-simplify]: Simplify PI into PI 4.308 * [taylor]: Taking taylor expansion of n in n 4.308 * [backup-simplify]: Simplify 0 into 0 4.308 * [backup-simplify]: Simplify 1 into 1 4.308 * [backup-simplify]: Simplify (/ PI 1) into PI 4.308 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.309 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.309 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.309 * [backup-simplify]: Simplify (* 0.125 (+ (/ 1 k) 1.0)) into (* 0.125 (+ (/ 1 k) 1.0)) 4.310 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.311 * [backup-simplify]: Simplify (* (* 0.125 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.311 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.311 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.312 * [taylor]: Taking taylor expansion of (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.312 * [taylor]: Taking taylor expansion of 0.125 in k 4.312 * [backup-simplify]: Simplify 0.125 into 0.125 4.312 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.312 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.312 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.312 * [taylor]: Taking taylor expansion of k in k 4.312 * [backup-simplify]: Simplify 0 into 0 4.312 * [backup-simplify]: Simplify 1 into 1 4.312 * [backup-simplify]: Simplify (/ 1 1) into 1 4.312 * [taylor]: Taking taylor expansion of 1.0 in k 4.312 * [backup-simplify]: Simplify 1.0 into 1.0 4.312 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.312 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.312 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.312 * [taylor]: Taking taylor expansion of -2.0 in k 4.312 * [backup-simplify]: Simplify -2.0 into -2.0 4.312 * [taylor]: Taking taylor expansion of PI in k 4.312 * [backup-simplify]: Simplify PI 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 * [taylor]: Taking taylor expansion of (log n) in k 4.313 * [taylor]: Taking taylor expansion of n in k 4.313 * [backup-simplify]: Simplify n into n 4.313 * [backup-simplify]: Simplify (log n) into (log n) 4.313 * [backup-simplify]: Simplify (+ 1 0) into 1 4.313 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.314 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 4.315 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 4.315 * [backup-simplify]: Simplify (* 0.125 (- (log (* -2.0 PI)) (log n))) into (* 0.125 (- (log (* -2.0 PI)) (log n))) 4.316 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.317 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.317 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.318 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.319 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.319 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.319 * [backup-simplify]: Simplify (+ 0 0) into 0 4.319 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (+ (/ 1 k) 1.0))) into 0 4.320 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.321 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.322 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.322 * [taylor]: Taking taylor expansion of 0 in k 4.322 * [backup-simplify]: Simplify 0 into 0 4.322 * [backup-simplify]: Simplify 0 into 0 4.322 * [backup-simplify]: Simplify 0 into 0 4.322 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.323 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.325 * [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 4.325 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.325 * [backup-simplify]: Simplify (+ 0 0) into 0 4.325 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 4.326 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.327 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 4.329 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.329 * [taylor]: Taking taylor expansion of 0 in k 4.329 * [backup-simplify]: Simplify 0 into 0 4.329 * [backup-simplify]: Simplify 0 into 0 4.329 * [backup-simplify]: Simplify 0 into 0 4.329 * [backup-simplify]: Simplify 0 into 0 4.329 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.330 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.333 * [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 4.333 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.333 * [backup-simplify]: Simplify (+ 0 0) into 0 4.334 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 4.335 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.336 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 4.337 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 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 4.337 * [taylor]: Taking taylor expansion of 0 in k 4.337 * [backup-simplify]: Simplify 0 into 0 4.337 * [backup-simplify]: Simplify 0 into 0 4.338 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.125 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 4.338 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 4.338 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 4.338 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 4.338 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.338 * [taylor]: Taking taylor expansion of 1.0 in k 4.338 * [backup-simplify]: Simplify 1.0 into 1.0 4.338 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.338 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.338 * [taylor]: Taking taylor expansion of k in k 4.338 * [backup-simplify]: Simplify 0 into 0 4.338 * [backup-simplify]: Simplify 1 into 1 4.339 * [backup-simplify]: Simplify (/ 1 1) into 1 4.339 * [backup-simplify]: Simplify (sqrt 0) into 0 4.340 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.340 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.340 * [taylor]: Taking taylor expansion of 1.0 in k 4.340 * [backup-simplify]: Simplify 1.0 into 1.0 4.340 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.340 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.340 * [taylor]: Taking taylor expansion of k in k 4.340 * [backup-simplify]: Simplify 0 into 0 4.340 * [backup-simplify]: Simplify 1 into 1 4.340 * [backup-simplify]: Simplify (/ 1 1) into 1 4.340 * [backup-simplify]: Simplify (sqrt 0) into 0 4.341 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.341 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.341 * [backup-simplify]: Simplify 0 into 0 4.342 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.342 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.343 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 4.345 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.346 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.346 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.346 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.348 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.350 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.350 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.351 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 4.351 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 4.351 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 4.351 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.351 * [taylor]: Taking taylor expansion of 1.0 in k 4.351 * [backup-simplify]: Simplify 1.0 into 1.0 4.351 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.351 * [taylor]: Taking taylor expansion of k in k 4.351 * [backup-simplify]: Simplify 0 into 0 4.351 * [backup-simplify]: Simplify 1 into 1 4.351 * [backup-simplify]: Simplify (sqrt 0) into 0 4.352 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.352 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.352 * [taylor]: Taking taylor expansion of 1.0 in k 4.352 * [backup-simplify]: Simplify 1.0 into 1.0 4.352 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.352 * [taylor]: Taking taylor expansion of k in k 4.352 * [backup-simplify]: Simplify 0 into 0 4.352 * [backup-simplify]: Simplify 1 into 1 4.352 * [backup-simplify]: Simplify (sqrt 0) into 0 4.353 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.353 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.353 * [backup-simplify]: Simplify 0 into 0 4.354 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.354 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.356 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.357 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.357 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.360 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.361 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.361 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.362 * [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)))))))) 4.363 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 4.363 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 4.363 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.363 * [taylor]: Taking taylor expansion of 1.0 in k 4.363 * [backup-simplify]: Simplify 1.0 into 1.0 4.363 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.363 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.363 * [taylor]: Taking taylor expansion of -1 in k 4.363 * [backup-simplify]: Simplify -1 into -1 4.363 * [taylor]: Taking taylor expansion of k in k 4.363 * [backup-simplify]: Simplify 0 into 0 4.363 * [backup-simplify]: Simplify 1 into 1 4.369 * [backup-simplify]: Simplify (/ -1 1) into -1 4.369 * [backup-simplify]: Simplify (sqrt 0) into 0 4.370 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.370 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.370 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.370 * [taylor]: Taking taylor expansion of 1.0 in k 4.370 * [backup-simplify]: Simplify 1.0 into 1.0 4.370 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.370 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.370 * [taylor]: Taking taylor expansion of -1 in k 4.370 * [backup-simplify]: Simplify -1 into -1 4.371 * [taylor]: Taking taylor expansion of k in k 4.371 * [backup-simplify]: Simplify 0 into 0 4.371 * [backup-simplify]: Simplify 1 into 1 4.371 * [backup-simplify]: Simplify (/ -1 1) into -1 4.371 * [backup-simplify]: Simplify (sqrt 0) into 0 4.372 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.372 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.372 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.373 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.374 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.376 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 4.376 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.377 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.379 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.381 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 4.381 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.382 * [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))))) 4.382 * * * [progress]: simplifying candidates 4.391 * [simplify]: Simplifying: (* (+ (+ (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)) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (* 1 (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (* 1 (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (* 1 (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ 1.0 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ k 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (cbrt (/ (/ (/ (- 1.0 k) 2.0) 2) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (/ (- 1.0 k) 2.0) 2) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 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(log (* h0 h1)) 2) (exp (* h9 (+ (log (* h0 h1)) (log h2))))))) (+ (* h10 (* (pow h4 2) (* (exp (* h9 (+ (log (* h0 h1)) (log h2)))) (pow (log h2) 2)))) (* h11 (* (pow h4 2) (* (log (* h0 h1)) (* (log h2) (exp (* h9 (+ (log (* h0 h1)) (log h2))))))))))) (+ (* h9 (* h4 (* (exp (* h9 (+ (log (* h0 h1)) (log h2)))) (log h2)))) (* h9 (* h4 (* (exp (* h9 (+ (log (* h0 h1)) (log h2)))) (log (* h0 h1))))))) (exp (* h9 (* (- (log (* h0 h1)) (log (/ 1 h2))) (- h3 h4)))) (exp (* h9 (* (- h3 h4) (- (log (* h8 h1)) (log (/ -1 h2)))))) (- (+ (exp (* h9 (+ (log (* h0 h1)) (log h2)))) (+ (* h10 (* (pow h4 2) (* (pow (log (* h0 h1)) 2) (exp (* h9 (+ (log (* h0 h1)) (log h2))))))) (+ (* h10 (* (pow h4 2) (* (exp (* h9 (+ (log (* h0 h1)) (log h2)))) (pow (log h2) 2)))) (* h11 (* (pow h4 2) (* (log (* h0 h1)) (* (log h2) (exp (* h9 (+ (log (* h0 h1)) (log h2))))))))))) (+ (* h9 (* h4 (* (exp (* h9 (+ (log (* h0 h1)) (log h2)))) (log h2)))) (* h9 (* h4 (* (exp (* h9 (+ (log (* h0 h1)) (log h2)))) (log (* h0 h1))))))) (exp (* h9 (* (- (log (* h0 h1)) (log (/ 1 h2))) (- h3 h4)))) (exp (* h9 (* (- h3 h4) (- (log (* h8 h1)) (log (/ -1 h2)))))) (- (+ (* h12 h4) (- (+ (* h12 (pow h4 2)) (- h12))))) (- (+ (* h12 (/ 1 (pow h4 2))) (- (+ (* h12 (/ 1 h4)) (- (* h12 (/ 1 (pow h4 3)))))))) (- (+ (* h12 (/ 1 (pow h4 2))) (- (+ (* h12 (/ 1 h4)) (- h12))))) 4.414 * * [simplify]: iteration 0 : 1941 enodes (cost 5499 ) 4.435 * * [simplify]: iteration 1 : 5002 enodes (cost 5298 ) 4.457 * * * [progress]: adding candidates to table 6.689 * [progress]: [Phase 3 of 3] Extracting. 6.689 * * [regime]: Finding splitpoints for: (# # # # # # # #) 6.692 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 6.692 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # # #) 6.731 * * * * [regimes]: Trying to branch on n from (# # # # # # # #) 6.769 * * * * [regimes]: Trying to branch on k from (# # # # # # # #) 6.806 * * * [regime]: Found split indices: #